gps world - april 2010

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GPS NUMBERSBY TH

E

RICHARDLANGLEY’S

200thINNOVATIONCOLUMN

VOL 21 | NO 4

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www.gpsworld.com April 2010 | GPS World 3

April 2010VOL. 21, NUMBER 4gpsworld.com

INNOVATION

GPS by the Numbers 42A Sideways Look at Howthe Global Positioning System WorksIn his 200th Innovation column, Contributing Editor Richard Langley takes a look at GPS by the numbers,getting a sense of how GPS works by examining thekey numbers that govern its remarkable capabilities, from zero to pi and beyond.By Richard Langley

»COVER STORY

OPINIONS &DEPARTMENTS

Out in Front 6What’s in a Number?By Alan Cameron

EXPERT ADVICE

Jamming: A Clear and Present Danger 8By Sally Basker

Letters 10The Other Shoe, the Spy, the Other Spy

THE SYSTEM 19Vistas from the Summit; GLONASS Back in Black; IGS Questions

THE BUSINESS 22Mobile World Congress 2010:Planet of the Apps; and more

ProductShowcase 27

ON THE EDGE

Lost Graves, Trail of Tears 50Application Challenge Winner

A team effort of RTK DGPS, GIS, and GPR — ground-penetrating radar.By Steven M. Di Naso, Vincent P. Gutowski, Harvey Henson, and Ryan Leonard

GNSS DESIGN & TEST

Galileo Test User Receiver 36Status, Key Results, PerformanceA fully stand-alone, multi-frequency, multi-constellation receiver unit, the TUR-N can autonomously generate measurements, determine its position, and compute the Galileo safety-of-life integrity.By Axel van den Berg, Tom Willems, Graham Pye, Wim de Wilde, Richard Morgan-Owen, Juan de Mateo, Simone Scarafia, and Martin Hollreiser

SURVEY

Low-Frequency Vibrations 28Detection with High-Rate Data and FilteringMultipath makes it difficult to detect low-frequency structural vibrations, important in characterizing dynamic loads and determining safe structural lifetimes for bridges and tall buildings. The authors have developed a phase-residual method for use with very high-frequency data to distinguish receiver noise, multipath, and periodic displacements. By Ana P. C. Larocca, Ricardo E. Schaal, and Augusto C. B. Barbosa

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GPS World | April 2010 www.gpsworld.com4

ONLINE RESOURCES

Stakes High for European GNSS IndustryExcerpt from the Professional OEM NewsletterGo to www.gpsworld.com/stakes for more

By Rob Lorimer, Professional OEM Editor

I am writing this month’s column after spending two weeks im-mersed in the European GNSS scene, first at the Galileo Application Days in Brussels then the Munich Navigation Summit. With the full operational capability of EGNOS im-minent and purchase orders for the first 14 Galileo satellites placed, there was a sense of revitalization and renewed enthusiasm in the European GNSS industry at both events. The game is afoot and the stakes are high, according to one presentation by the European GNSS Supervisory Authority (GSA); 6–7% of the EU economy already has some dependence on GNSS so they are keen to ensure that European companies are getting their “fair share” of the cake....the European Commission (EC), GSA, and others have been quietly seeding and nurturing a European applica-tions development capability.

Hottest Pages @ GPSWorld.comFebruary 14 – March 17, 2010

1 GPS OCX Contract Awarded: Some Observations

2Google or Nokia: Which Company Will Win the LBS War?(LBS Insider newsletter)

3 Raytheon Awarded Next-Generation Control Segment Contract

4GPS AEP 5.5C, the Rest of the Story: We Went to the Source (GNSS Design & Test newsletter)

5 GPS Snow Goggles to Hit the Slopes this Fall

6 Chilean Geodetic Observatory Faces Post-Quake Difficulties

7Northrop Grumman, Raytheon Discuss Pending OCX Contract(GNSS Design & Test newsletter)

8 Innovation: Mobile-Phone GPS Antennas

9 The Best and Final Look at the GPS 24+3 Configuration (Survey Scene newsletter)

10 Wide Awake Blog: The Spy Who Loved Me

» APRIL WEBINAR

GPS, GLONASS and SBAS Constellation UpdatesApril 22, 2010 10 a.m. Pacific / 1 p.m. Eastern / 6 p.m. GMT

Speaker: Survey/GIS Editor Eric Gakstatter

2010 is an exciting year of change for GNSS. GPS is undergoing the most significant constellation change since its inception. Russia will launch a record number of GLONASS satellites this year. The FAA will commission a new WAAS satellite. All of these changes will affect high-precision GNSS receivers as well as high-performance mapping GNSS receivers. Eric will discuss these changes and how the performance of GNSS receivers will be affected, both with multi-frequency high-precision RTK receivers as well as high-performance submeter single-frequency receivers.

Sign up for our webinars at www.gpsworld.com/webinar

Frank van Diggelen BroadcomPanel moderator frames the discussion.

Greg Turetzky SiRF/CSR

Moore’s and the mass market.

Neil Gerein NovAtelIn the high-precision professional OEM market.

Charles Abraham BroadcomRelationship to correlator-count receivers.

Moore’s Law on GNSS ChipsPresentations from the Munich Summit Watch at www.gpsworld.com/video

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Published monthly

www.gpsworld.com

Computers killed a trusty companion of my teenage years. That is, after those

proto-computers known as pocket calculators knocked him out and left him unconscious on the cooling floor.

But I come to praise my slide rule, not to bury him.

I marveled at the way he worked. You had a tactile relationship with numbers on a slide rule. You could see — and feel — how a small adjustment here effected a big change over there. With computers, it’s just numbers in, numbers out.

Maybe that high-tech approach led both the GPS Wing and the Government Accountability Office into trouble with constellation gaps. GPS satellites have proven themselves very hardy in space, outlasting their

predicted lifetimes. The GPS Wing has grown to lean on those longer lives a bit, and what with Congress and the Administration booting budgets a year or two to the right with addictive regularity, the Air Force has saved money by replenishing upon need. And need has been not all that great, so replenishment, and the contract awards and manufacturing that feed the replenishing line, have been allowed to relax.

But not the mathematical models

that someone has held to more conservative standards. Those models use the shorter predicted satellite lifetimes. When those models were projected against the real-world timelines for IIF and Block III — whoa GAO! Some black gaps suddenly yawned.

Now we learn that GAO and the Wing will re-undertake this exercise, factoring instead the longer lifetimes that the satellites have proved capable of. Tinker a small adjustment here, see a big change out there.

Speaking of numbers, I’ve grown fond of 20, and lately enamored of 200. The former being the number of years we have published this magazine, the latter the new world record for GNSS technical articles, attained by one Richard B. Langley.

With characteristic Canadian unbravura, Langley fidgets and frets that we have made too much of him on this magazine’s cover and page 42. It looks too braggy for him and he feels uncomfortable with it. But I have prevailed upon him to swallow his humility, to take one for the team. We bask in his reflected glory.

Quick, what’s the difference between 160 and 144.5? Not in absolute terms, but in tactical advantage. If I add a metric, east longitude, geosynchronous orbit, does that help? I’m puzzling out why Compass would move its G1 satellite from one location to another after only ten days in space. Better ground control might be the answer. But more mystifying, why China’s spokespersons at the Munich Summit would proffer the first location, when they must know very well — in fact, they so admitted when I confronted them with it — that the second is actually the case.

Numbers don’t obfuscate. People do.

Letters to Editor invited: email to [email protected].

What’s in a Number?

OUT IN FRONT

Trusty companion of my teendom.

EDITORIAL

Editor in Chief Alan Cameron | [email protected] Editor Tracy Cozzens | [email protected] Director Charles Park | [email protected]

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In 2010, we are celebrating

of innovation and making versatile GNSS OEM receivers for demanding applications.

Please come celebrate with us, and visit WWW.SEPTENTRIO.COM regularly!

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EXPERT ADVICE


Apacked audience attended the National Physical Laboratory in the United Kingdom for

a February 23 meeting titled, “GPS Jamming and Interference: A Clear and Present Danger,” organized by the Digital Systems Knowledge Transfer Network.

In his keynote address, David Last described a dark, silent and dangerous world without GPS. He regaled attendees with tales from his experience as a GPS forensic expert, assisting the police who beat a path to his door bearing interesting boxes that turned out to be all sorts of jammers: of GNSS, of mobile phones, and of other radio systems. Last pointed to the near future when he believes that spoofers will undoubtedly make an appearance. The defences are limited: detection, prosecution, and the use of alternative sources of positioning, navigation, and timing information,

perhaps eLoran.His final insight was this: “Navigation

is no longer about how to measure where you are accurately. That’s easy. Now it’s how to do so reliably, safely, robustly.”

Jim Doherty, from the U.S. Institute of Defense Analyses, discussed the use of existing resources for time and frequency backup. Drawing on his experience, Doherty delivered three overarching thoughts: � use all available means; � re-use existing systems where

possible; and� produce integrated time and

navigation. He advised the audience to be

conservative with their designs and not to go too close to the boundary conditions. He also noted that there is an important trade-off between independence and cost when considering complementary systems. Finally, he identified a potential need for eLoran to support synchronisation in aviation’s multi-lateration systems.

Moving on, Alan Grant of the UK General Lighthouse Authorities (GLA) described recent GPS jamming trials. He demonstrated that GPS jamming has wildly different effects, ranging from total denial to hazardously misleading i n for m at ion ( H M I ) . H M I wa s particularly problematic: it caused the ship’s GPS receivers to report a realistic course and speed well away from the truth that was provided by the GLA’s eLoran system. He noted that the impact depends on the ship’s bridge design.

Professor and consultant Martyn Thomas spoke on an ongoing Royal Academy of Engineering study on GPS vulnerability, which brings together experts from across the UK and will report in early June.

T h i s w a s f o l l o w e d b y t h r e e presentations on coverage prediction by Robert Watson of Bath University, on interference detection using the U.S. National Geospatial Intelligence Agency’s

GPS Jammer Location (JLOC) system by Alison Brown of NavSys Corporation, and on the GNSS Availability, Accuracy, Reliability anD Integrity Assessment for Timing and Navigation (GAARDIAN) interference detection system by Charles Curry of Chronos Technology.

The conference audience learned that any system can be jammed, that JLOC detects thousands of jammers on a da i ly ba s i s — nea rly a l l of them unintentional — and that the GAARDIAN system has integrated GPS, eLoran, and clocks for interference detection and mitigation.

Tom Willems from Septentrio and Peter McIlroy from Raytheon gave a good overview of what can be done with receivers and antennas. Willems focused on pulse blanking and adaptive notch filtering. He saw a clear trend towards hybridization, and conf irmed that manufacturers recognise that GNSS is not a golden bullet — they can mitigate some interference but not all.

Peter McIlroy told listeners to “defeat interference and jamming before you detect it.” This included hybridization with inertial systems, putting some form of barrier between the antenna and the jammer, and the use of controlled pattern-reception antennas. He suggested that controlled pattern-reception antennas might become available for civil use.

Fina l ly, Pau l Groves f rom the University College London gave a very useful overview on positioning without GNSS. He addressed radio and non-radio systems and presented a fascinating chart that related the various radio systems in terms of range and lifecycle (FIGURE 1). The message was very timely given the need for complementary systems expressed by all speakers.

I then chaired a lively panel discussion with David Last, Martyn Thomas, Charles Curry, Jim Doherty, and Tom Willems. I led off by focusing the discussion on resilient PNT, referring to the UK Center for the Protection

Jamming: A Clear and Present Danger

Cheap — and vulnerable —

GNSS receivers will inevitably

find their way to the heart of our

critical infrastructure. Very few

policymakers understand how a

loss of GPS impacts critical national

infrastructure.

By Sally Basker

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EXPERT ADVICE


of National Infrastructure’s definition for resi l ience : the equipment and architecture used are inherently reliable, secured against obvious external threats, and capable of withstanding some degree of damage.

The panel agreed on the need for hybrid solutions with multiple technologies. It expressed concerns that cheap GPS receivers are components in many systems, and it is too easy to overlook them. Martyn Thomas brought insight from the computing world and noted that we need to avoid single points of failure and to demonstrate independence.

Do our governments understand and should they do more? The panel thought that different governments are at different points on a journey, and that very few policymakers understand how a loss of GPS impacts critical national infrastructure. It was suggested that the European Union lags behind, due to the focus on Galileo.

This led to an interesting discussion about economics and funding. Martyn Thomas said that GPS vulnerabilities have grown, and that GPS competitors have disappeared for economic reasons, leaving us dependent on GPS. He pointed out that there are limited mechanisms for sharing funding and questioned whether there are many (any) organisations that

are prepared to take the risk.If you have limited funding, should it

be used for detection or mitigation? The panel agreed that both were needed, but the prevailing view was that mitigation is more important, and that this needs to be supported by human factors activity.

In Summary. GNSS interference is a real and present danger. It is probably more widespread than generally assumed, and it is here to stay. We can harden our GNSS systems with improved receiver and antenna design, but this wil l mitigate only some interference, not all. The problem is cost. Cheap — and vulnerable — GNSS receivers will inevitably find their way, unseen, to the heart of our critical infrastructure. We need resilient positioning, navigation, and timing based on independent and complementary systems and sensors. Demonstrating independence is vital but not necessarily straightforward, and true independence costs money. The greatest cha l lenge is helping policymakers understand the risks of relying on vulnerable systems and the need for resilience.

Finally, I return to Jim Doherty’s overarching thoughts: use all available means; re-use existing systems where possible; and produce integrated time and navigation.

eLoran, anyone? �SALLY BASKER is director of research and radionavigation for the General Lighthouse Authorities of the United Kingdom and Ireland.

ANA PAULA C. LAROCCA received the GPS Award Brazil from the U.S. Federal Aviation Administration (FAA) and the SDTP Foundation at a March ceremony in Washington D.C., for her work on the use of GPS in civil engineering as a tool for monitoring structural oscillations of bridges, recent aspects of which are described in the Survey article in this issue.

EDITORIAL ADVISORY BOARD

Vidal Ashkenazi Nottingham Scientific Ltd., United Kingdom

Sally Basker General Lighthouse Authorities, United Kingdom & Ireland

Alison K. Brown NAVSYS Corporation, United States

Pascal Campagne France Developpement Conseil, France

Ismael Colomina Institut de Geomàtica, Spain

Jordi Corbera Spanish Institute of Navigation, Spain

Paul A. Cross University College London, United Kingdom

Nicolas de Chezelles Ministry of Defense, France

Clem Driscoll C.J. Driscoll & Associates, United States

Børje Forssell Norwegian University of Science and Technology, Norway

Alain Geiger Institute of Geodesy and Photogrammetry, Switzerland

Art Gower Lockheed Martin, United States

Sergio Greco Alcatel Alenia Spazio, Italy

Jörg Hahn European Space Agency, The Netherlands

Michael Healy Astrium Limited, United Kingdom

Günter Hein University of the Federal Armed Forces, Germany

Larry D. Hothem U.S. Geological Survey, United States

Len Jacobson Global Systems & Marketing, United States

William J. Klepczynski Institute for Defense Analyses, United States

Gérard Lachapelle The University of Calgary, Canada

Wolfgang Lechner Telematica, Germany

Jingnan Liu National Research Center for Satellite Systems, China

Pietro Lo Galbo European Space Agency, The Netherlands Keith D. McDonald NavtechGPS, United States

Terence J. McGurn Consultant, United States

Jules G. McNeff Overlook Systems Technologies, United States

James Miller NASA, United States

Terry Moore University of Nottingham, United Kingdom

Ruth Neilan Jet Propulsion Laboratory, United States

Bradford W. Parkinson Stanford University, United States

Ivan G. Petrovski iP Solutions, Japan

Mario Proietti TechnoCom Corporation, United States

Jayanta Ray Accord Software and Systems, India

Martin U. Ripple European Aeronautics Defense and Space, Germany

Michael E. Shaw Lockheed Martin Space Systems, United States

Giorgio Solari Galileo Supervisory Authority, Belgium

Jac Spaans European Group of Institutes of Navigation, Netherlands

Thomas Stansell Jr. Stansell Consulting, United States

F. Michael Swiek U.S. GPS Industry Council, United States

David Turner Department of State, United States

A.J. Van Dierendonck AJ Systems, United States

Frantisek Vejrazka Czech Technical University, Czech Republic

Akio Yasuda Tokyo University of Marine Science & Technology, Japan

Å FIGURE 1 Range and lifecycles of current radio systems (courtesy Paul Groves).

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LETTERS TO THE EDITOR


I read Don Jewell’s column in the March Defense PNT newsletter (see www.gpsworld.com/othershoe),

on the troubling concern about GPS dependency, with considerable interest. I thought he made some excellent points, and, in my capacity as a member of GPS World’s Editorial Advisory Board, I would like to present some further thoughts for consideration.

I thought Don was pretty fair with General Schwartz’ comments, including the thinly veiled reference to underlying

Air Force (AF) motives toward a smaller GPS constellation. However, in addition to focusing on the comments of one senior individual, you might also give some thought to the actions and motives of many in both the civil and military communities who have not only failed to embrace but have also resisted the advancement of a National Positioning, Navigation and Timing (PNT) Architecture and the holistic management framework necessary to implement it.

After 2-plus years of work by 30-plus government agencies (military and civil), an enterprise-level view of the PNT Architecture was presented to the public at the ION conference in Savannah in 2008. Since that time, discussions regarding its implementation have proceeded very slowly within the government. The Architecture contains all the elements you identify as contributing to the “Perfect Handheld GPS,” though, at the enterprise level, many have not technologically matured to the necessary system-of-systems level that

would permit acquisition decisions under government rules. As you know, that will take focused technical analysis and trade studies, as well as further development in some cases to bring promising technologies along. Commercial industry does it faster, but its solutions are in most cases unique and proprietary, and not necessarily applicable for use by government agencies, particularly the military.

You also advocate for more tightly integrated GPS capability, “resulting in impregnable GPS for all users.”

That thought pervades the enterprise PNT Architecture, beginning with its foundational recommendation (that GPS remain the cornerstone) and extending through many of the 18 other recommendations which follow. In the Architecture, however, we put a slightly different twist on the objective of GPS integration.

We recognize that, while GPS service can be improved by increases in signal power, possible additional signal frequencies, and a larger constellation, GPS itself can never become “impregnable.” Rather, by integrating GPS with augmentations and complements of several different types, our objective is to create continuously available PNT of high precision and fidelity from a variety of sources without regard to which particular source(s) is/are contributing to the solution at any particular point. I like to refer to that as “cloud PNT” with a bow to the recent advancements in “cloud computing.”

Finally, with regard to eLoran, the PNT

Architecture envisioned a place in 2025 for an evolved eLoran-type capability, recognizing the possible value of frequency diversity, higher power, signal penetration, carrying 2D position and precise time, all in a relatively low-cost government-provided LF/MF service. Of course, it would have had to compete with other technology alternatives, but that potential course now seems foreclosed. You make the point that the basis for eLoran is, of course, the Loran-C system whose operation was recently terminated by the Obama Administration.

The most troubling aspect of that termination was the statement in the Federal Register announcement that the DHS would continue an assessment to determine if a single, domestic system is needed as a GPS backup for critical infrastructure applications at the same time it determined that the continued operation of the viable backup represented by Loran was not necessary.

Go figure.— Jules McNeff

Editorial Advisory Board (since 1990)GPS World

The SpyA prescient reader wrote a comment on the webpage of a recent story about the demise of Loran. See www.gpsworld.com/rtcm and scroll all the way down. It begins:

Tso had just installed the last of a series of innocuous-looking boxes in a field some miles to the west of New York City. . . . It, and the other 299 units like it, had a single purpose. It was so simple, and it had been handed like a gift to him by the U.S. government itself. . . . .

The Other SpyI loved your blog, “The Spy Who Loved Me” (see www.gpsworld.com/wideawake).Please make sure to keep us updated if there is any follow-up from him!

— Brett Buyan Santa Barbara, California �

The Other Shoe

While GPS can be improved by increases in signal power, added frequencies,

and a larger constellation, GPS itself can never become “impregnable.”

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Policy and system news and developments | GPS | Galileo | GLONASS

SYSTEMTHE


“This is an event where one gets one’s goals for the next year.” Paul Verhoef, program director for satellite navigation programs of the European Commission, may have exaggerated for effect, and for the benefit of his audience and hosts at the Munich Satellite Navigation Summit in March. But not by much.

The conference, now in its eighth year, has assumed increasing importance on the international circuit of GNSS policymakers and communicators. Although with a decidely European bent, it draws representatives from most if not all systems to mingle and present. A 16-member delegation from China’s Compass system furnished one of the liveliest topics of conversation — and speculation.

“When we started in 2003, there were many technical conferences on the one side, and we saw a niche for the institutional and political side of satellite navigation,” said Berned Eissfeller of the Institute of Geodesy and Navigation, German Federal Armed Forces University, conference

director and host. For video clips of Eissfeller and other speakers, see www.gpsworld.com/video.

GNSS came in for a check-up, a sort of self-examination this time. The 2009 conference was titled “The GNSS Race,” but this year it was “GNSS — Quo Vadis?” The Latin phrase means “Where are you going?” Following program updates, sessions focused on safety-of-life, compatibility, legal/intellectual property, and privacy issues.

Galileo. Paul Verhoef continued his remarks that open this story. “I have been given [my goal]: Galileo must succeed.

“You know the world today is not what it was a year ago. It means obviously the financial crisis has had an impact on our economies, on public finance, and therefore I would not be surprised it may leave its mark on satellite navigation. The reason is simple: the systems that are either operating or being deployed are being publicly financed. Galileo is the only system that is financed from a purely civilian budget. All the systems need

more than ever to demonstrate their public utility.

“I put it to you that this is an opportunity. As we’ve already heard, there is much to be gained in this market. After the PC, mobile communications, and Internet, satellite navigation is the next breakthrough technology. There are enormous revenues foreseen and already present in this market. There are many jobs possible for those who want to get it, and we think from the European side we have an enormous chance of capitalizing on this among other things by investing in this technology. Therefore, Galileo- and EGNOS-based innovation is certainly politically of interest.

“Obviously, it is not a path of roses. There will no doubt be many more critical questions during these days. However, from our side, we have set our goals. I think they are modest, but they are firm. We want to be the second system of choice. At least in the first instance, we will see where we will go after that. Obviously, this is

Three GLONASS-M satel-lites launched on March 1 are expected to enter serv-ice on March 22 and March 30, according to deputy general director Grigoriy Stupak’s statement in Mu-nich. This would bring the constellation, according to

his calculations, to 23 opera-tional satellites, though two of those are held in reserve.

With 21 satellites broad-casting signals, the system claim 98.5 percent global availability. Block 42 (three more satellites) has an Au-gust 2010 launch date, and Block 43 one for November 2010. By December, Stupak predicted 24 active satellites on orbit, for 99.5 percent global availability.

The GLONASS-M satellites have a stated seven-year lifetime. CDMA signals will begin with next-generation GLONASS-K satellites, while FDMA signals continue in parallel. The Russians plan to “reach 5-meter accuracy by 2017, almost equal to accuracy of other GNSS,” and are “paying more attention to differential corrections for integrity monitoring.”

Vistas from the Summit

See VISTAS, next page

GLONASS Back in Black

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THE SYSTEM

going to cost a bit of time. I shall invite you, if you get impatient, if the public gets impatient, to look at the history of the other systems. Developing and deploying these other systems is costing time.

“We think that Galileo will meet its deadlines. I think one of the important messages this year, and you have seen it, we are putting things in place. There are contracts in place, there are satellites on order, there are launches on order, there are installations being built — Oberpfaffenhoffen, Fucino, there are others around the world — EGNOS is operational, we’re going to declare the safety-of-life of EGNOS later this year. So we are really moving forward at good speed at the moment.

“We need to win the hearts of the users, the application providers, and the service providers. At the downstream market is the real challenge for these systems. We need to help do that. We are addressing this among other things by providing a more and more reliable schedule for availability of Galileo and EGNOS services.”

Galileo ICD Soon. “We are about to publish in the next couple of weeks the so-called signal-in-space Open Service interface control document, which I know a number of you have waited for a long time.

“We need also to move forward at a political level. In this case, no GNSS system can be credible if it is not backed by a long-term political commitment particularly by its owner. So after the decision of the Parliament and the Council to deploy the system, these two institutions are now clearly called upon to provide us such political long-term commitment that is credible in the eyes of the users.”

GPS. Anthony Russo, director of the U.S. National Space-Based PNT Coordination Office, said “Keeping cards close to the chest in a competitive situation can well

become a liability, creating a future need for a re-work or undoing if you paint yourself into a technological corner.” This appeared to refer to China and its Compass system; information has been singularly difficult to obtain on almost every aspect of this budding constellation.

Regarding the April 2009 U.S. General Accountability Office report that forecast gaps in constellation availability, Russo stated, “The GAO will revise its report somewhat. They were using a model that was a little too cautious, one used by the [GPS] Wing. But satellites on orbit have been performing past estimated life. Further, we can turn off secondary payloads to conserve energy onboard satellites [and thus extend life] if needed.”

The next morning, Lt. Col. Liz Roper, Air Force Space Command, gave a status and modernization briefing; the most eagerly awaited development is the launch of the first Block II-F satellite, scheduled for some time in May. She alluded to “a few setbacks” from the August 2009 launch of SVN49 with its well-documented signal problems, but emphasized the episode’s “positive aspects: the relationships we’ve been able to build in seeking solutions to

that situation.”GLONASS. Grigoriy Stupak, deputy

general director and general designer on GLONASS systems, briefed the audience in fluent Russian. For a recent launch update, see page 19.

Compass. Two of the Chinese delegates spoke in the opening session. Jiao Wenhai from China Satellite Navigation Office did elaborate the basic principles of the Beidou (Compass) system: � openness (“China will widely and

thoroughly communicate with other countries on satellite navigation issues.”)

� independence� compatibility (“China will pursue

solutions to realize compatibility and interoperability with other satellite navigation systems.”)

� gradualness.He promised an English-language

version of the governmental website www.beidou.gov.cn or www.compass.gov.cn “soon.” Wenhai recapped:� the frequencies Compass will use:

1561.098, 1207.14, and 1268.52 Mhz in Phase II until 2012; and 1575.42, 1191.795, and 1268.52 in Phase III by 2020.

� the general development plan: five geosynchronous, five inclined geosynchronous, and four mid-

Vistas, continued

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Earth orbit satellites providing a Chinese regional service using mainly Compass Phase II signals; then development of a global service broadcasting mainly Compass Phase III signals from five GEO, three IGSO, and 27 MEO satellites.The Chinese speakers displayed

a certain disingenuousness in giving verbally and in their slides the location of the January launch, Beidou G1 geostationary satellite, as 160 degrees East, somewhere over the open Pacific. When GPS World pointed out that NORAD satellite tracking shows G1 has been repositioned to a slot at 144.5 degrees East longitude, they huddled for several minutes before stating that yes, it had moved to that position and was

undergoing in-orbit testing. That spot was previously occupied by Beidou 1D, apparently decommisioned about a year ago due to power problems. 1D currently orbits in graveyard above geostationary altitude.

A personage civilly associated with

the U.S. Air Force confirmed the actual G1 location to the magazine, and could only speculate that it was more advantageous to Chinese ground control for monitoring and testing. As to why spokespersons misstated the location, that remains inscrutable. �

The International Committee on GNSS (ICG) Working Group on Compatibility and Interoperability invites GPS industry members to fill out a questionnaire, provided online in two formats: as a downloadable MS Word document or a PDF.

The Industry and User Community Questionnaire is designed to ob-tain worldwide input from industry, academic institutions, and other representatives of the GNSS user community with technical expertise regarding GNSS signals and other system characteristics that aid or hinder the combined use of the sig-nals in applications, equipment, or services. For instance, respondents are asked to grade certain signal char-acteristics as to their importance in overall interoperability considerations for a particular type of application.

Respondents are asked to e-mail completed questionnaires to the ICG by May 28.

To download instructions and the form, go to www.gpsworld.com/icg.

ICG Questions

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Industry news and developments | GPS | Galileo | GLONASS


By Moni Malek

It’s that time of year, around Valentine’s Day, when most of the who’s who in the mobile phone industry meet at the Mobile World Congress. I have been at-

tending this event for nearly 15 years, and have seen the location change from Cannes to Barcelona, and the name change from GSM World Congress to 3GSM World Con-gress to Mobile World Congress.

At the same time, the number of mobile phone users shot up from the millions to the billions. A new feature this year was the App Planet hall. The attendance of 47,000 was only marginally down from the 49,000 visitors in 2009, making it still a very busy a event, with no sign of the recession compared to other shows I’ve seen. It’s still the best place to meet companies in the mobile space — I met 25 in three days, as well as running into ex-colleagues and contacts who, like me, have been attending for years.

Smartphone Entry. The trend of the last year or so has been the burst entry of smartphones. First started by Apple iPhone for consumers and to some extent Black-berry for professionals (the so-called fruit phones), oper-ating systems (OS) have evolved to include Android from Google, Palm Pre’s webOS, Nokia and Intel merging their top-end smartphone operating systems, and Symbian going open source. Microsoft has people excited with Windows Phone 7, with the first handsets running on it scheduled to hit the markets around the holiday season.

Most of the smartphones are GPS-enabled, and as these phones increase the market penetration of GPS, GPS use will increase, leading to more use of location-based applications.

Deep Pockets. For those of you who think GPS personal navigation device market pricing is tough, the mobile phone market is cut throat. Volumes are out of this world, and in lots of countries around the globe, the volumes are more than the population! These volumes require deep pockets to keep up the investment to make money on decreasing margins.

There has been a trend toward consolidation in the GPS chip industry. Less than a year or two ago in Barcelona booths represented eRide (acquired by Furuno), Global Locate (acquired by Broadcom), GloNav (acquired by NXP, then wound up in ST Ericsson), Nemerix (which seems to have disappeared, though it’s rumored some assets went to another chip company),

and finally SiRF (now part of CSR-SiRF). CSR-SiRF’s booth was more like a fortress, but at least I got to talk to the SiRF founder.

It will be interesting to see what a Bluetooth-GPS company with a lot of cash in the bank plans as a next move. As for survivors, u-blox still had a booth (they weren’t acquired; they did an Initial Public Offering), and CellGuide had a small section of the Israel booth.

App Planet. Since I first attended this show, global mobile-phone technology has gone from GSM voice to GPRS data to 3G voice/data to HSPA. Now comes LTE (Long Term Evolution), which is really a packet data network that can use VoIP. Together, 3G and smartphones give us an environment which lets apps become a new business model worth billions. The Apps Planet hall showcased a lot of these models. The hall didn’t exist last year, but this year had 100 exhibitors. It easy to predict this number will grow.

There are so many applications, they will need to differentiate to stand out from the crowd and gain mass. I think location-based apps need to get better, and I see that happening at the show. deCarta allows searches for places based on real walking distances or near the route you are traveling. Aloqa has clients for every smartphone with channels that you can choose for your interest. Mireo impressed me with not only natural text

» LOCATION-BASED SERVICES, WIRELESS

Mobile World Congress 2010: Planet of the Apps

p APP PLANET featured 100 exhibitors and a lounge for old-fashioned social networking.

See CONGRESS, next page

BUSINESSTHE

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Rosum Corporation has launched the Alloy chip for indoor and urban environments. The Alloy chip, devel-oped in partnership with Siano, uses broadcast TV signals to provide pre-cise frequency, timing, and location information.

According to Rosum, the chip opens up commercial opportunities by enabling femtocell synchronization and location, tracking of people and assets, and localized advertising over mobile TV devices in deep indoor

guidance (“turn left after the Apple store”) but its super-fast routing in less that 2 seconds, as opposed to 30-seconds-plus on other devices. It features algorithms with pre-stored routes to major junctions, so only the rest is routed. In any case, the net effect is you are routed before you have to think which way to drive

or walk. I always say mobile phone users have short attention spans and expect instant gratification, and fast routing certainly helps.

Finally, an Audi A5 Cabriolet displayed a solution for the European Commission’s

eCall emergency call initiative, a car which automatically sends your position after an accident to a Public Safety Answering Point. eCall should be implemented in Europe by 2014, but Qualcomm is looking to put the system into the Audi A8 this year.

MONI MALEK is CEO of ML-C MobileLocation-Company GmbH, a new company integrating location and communication in a system platform.

Congress, continued

Rosum, Siano Chip Uses TV Signals for Indoor Positioning» WIRELESS

locations such as shopping malls, ho-tels, campuses, and factories.

The Alloy client combines the Alloy chip with an assisted GPS chip into a hybrid TV-GPS solution.

Broadcast TV signals have a 100,000x power margin advantage over GPS, and this extends location and syn-chronization capabilities deep into buildings and urban environments.

p MOTOROLA’S Christian Kurzke discusses Android with developers.

ARE YOU HEADING IN THE RIGHT DIRECTION?

Trimble GNSS OEM Systems: Performance You Can Rely One GNSS OEmble GT

www.trimble.com/GNSS-Inertial

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THE BUSINESS

The Central and Southern Andes GPS Project (CAP) team led by Mike Bevis at Ohio State University has com-puted the coseismic displacement field associated with the recent M 8.8 Maule earthquake in south-cen-tral Chile. Peak measured displace-ment is 3.04 meters near the city of Concepción, Chile.

While the CAP results were ob-tained from processing days worth of observations from before and after the earthquake, another procedure was used at the University of New Brunswick to estimate the shift in po-sition of a GPS station near Concep-ción. Precise point positioning was used to determine the position of the station every 30 seconds during the hour of the earthquake (06:00-07:00

UTC). Results show that most of the approximately 3-meter displacement occurred within about 60 seconds of the onset of the earthquake. A pre-cise trajectory of the station during the earthquake will be determined

once the high-rate (1 Hz) data cur-rently stored at the station is made available when normal communica-tions with the station are restored. For more, visit http://researchnews.osu.edu/archive/chilequakemap.htm.

» SURVEY, EMERGENCY RESPONSE

Personal navigation device (PND) maker Mio has se-lected u-blox’ AMY-5M GPS module to power the Moov V780, a high-end PND and multimedia player. The PND, introduced at CeBIT 2010 in March, earned an International Forum Design 2010 (iF) award for outstanding quality of design.

The slim 14-millimeter device with 7-inch touchscreen combines personal navigation with multime-dia features including web brows-ing, high-definition TV, photo and music management, and e-mail. The device depends on the low-profile small-footprint AMY-5M for fast, precise, and low-power posi-tioning, u-blox said.

“With u-blox’ cutting-edge AMY GPS receiver module at the heart of the Moov V780, we have designed

a sleek, high-performance PND with market-leading features,” said Justine Liu, global marcom director of Mio Technology. “The Moov V780 delivers a rich and powerful mix of navigation, entertainment, informa-tion, and fun.”

“AMY’s combination of leading GPS performance, low-power con-sumption and extremely small pro-file contribute to the compact size and high performance of the Moov V780,” said Ming Chiang, Country Manager, u-blox Taiwan.

Map of Chilean Earthquake Displacement Derived from GPS Data

Chilean Geodetic Observatory StrugglesHayo Hase, head of the Geodetic Observatory TIGO in Concepción, Chile, sent out a plea for help via the International GNSS Service and the CANSPACE listserv, describing in detail the difficulties he and his team face in the aftermath of the February 27 earthquake. The devastating magnitude 8.8 quake is one of the strongest ever recorded. The Geodetic Observatory TIGO has been operating since 2002, but has faced funding difficulties. Hase concludes with a plea for help. “Please be aware that the scientific community has a unique opportunity to get a complete picture of pre- and post-megathrust-event data, if the operation of TIGO can be financially assured for at least the next eight years...Shutting the observatory off right now would mean shutting it off just in the moment when humanity could get the most benefit out of it.”

Mio’s Moov V780 PND Based on u-blox AMY Module» CONSUMER OEM

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» PROFESSIONAL OEM

Trimble has introduced the BD982, a real-time kinematic (RTK) GNSS receiver for guidance and control applications. Capable of receiving a wide range of commercially available satellite signals, the BD982 receiver is designed to allow original equipment manufacturers (OEMs) and system integrators to easily add centimeter-level positioning and heading to spe-cialized or custom hardware solutions.

The Trimble BD982 delivers dual-an-tenna GNSS technology in an easy-to-integrate form factor for demand-ing applications such as unmanned vehicles and port automation, according to Dale Hermann of Trimble.

The Trimble BD982 GNSS receiver module is a single-board solution for precise position and heading in a compact form factor. The receiver is based on a pair of Trimble’s 220 channel Maxwell 6 chips, which allow dual-antenna inputs and the cal-culation of multiple GNSS RTK base-lines. This eliminates the traditional GNSS problem of determining vehicle heading in static or low-dynamic envi-ronments.

It supports a wide range of satellite signals, including GPS L1/L2/L5 and GLONASS L1/L2. Trimble says it is committed to providing Galileo-com-patible products in advance of Galileo availability, so the Trimble BD982 GNSS receiver is capable of tracking the experimental Galileo GIOVE-A and GIOVE-B test satellites for signal evaluation and test purposes. The Trimble BD982 also offers the option

Trimble’s BD982 Dual-Antenna Receiver Designed for Specialized Apps

MORE ONLINE

In-Depth CoverageFind more details on the news stories in this section at gpsworld.com.

For the latest GPS news, sign up for GPS World Alerts and our weekly Navigate! newsletter.

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Flexible connectivity options — Eth-ernet, RS232, USB or CAN — allow fast data transfer and configuration via

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» CONSUMER OEM

Intermap Technologies announced it has signed an agreement with Garmin Ltd. Under the terms of the three-year agreement, Intermap will furnish accurate 3D elevation data for the United States and Western Europe derived from its NEXTMap country-wide digital map database. Initial Garmin products using NEXTMap data are expected to reach the consumer market in the first half of 2010.

The data will be used to upgrade Garmin maps in the company’s outdoor GPS products, automotive portable navigation devices, and marine product lines, according to Brian Bullock, Intermap’s president and CEO. Garmin will be able to enhance its outdoor product line through terrain rendering and the creation of shaded raster imagery. Additionally, with accurate and seamless three-dimensional data across multiple countries, Garmin can create elevation-sensitive content and applications across the range of its product line.

Garmin Licenses Intermap’s 3D Terrain Models

DigitalGlobe announced that the el-evation data gathered from its latest high-resolution satellite, WorldView-2, has been verified as accurate within 30 centimeters by PhotoSat, based on data collected by MWH Geo-Surveys.

PhotoSat is a provider of high defi-nition elevation mapping from stereo satellite photos, while DigitalGlobe provides commercial high-resolution earth imagery products and services sourced from its own satellite con-stellation, including the WorldView-2.

According to the announcement, to conduct the test, PhotoSat con-structed an elevation grid using automatic geophysical processing of 50-centimeter ground resolution stereo satellite images taken by DigitalGlobe’s WorldView-2 satel-lite. The resulting elevations were then referenced against more than 20,000 gravity survey stations which had previously been established as being accurate to better than two centimeters.

DigitalGlobe Sat Data Verified to 30 Centimeters

IEEE/ION PLANS 2010May 4-6, 2010, Palm Springs, Californiawww.plansconference.org

The Position Location and Navigation System (PLANS) Conference provides a forum to share the lat-est advances in navigation technology.

SX-NSR Software Receiver WorkshopMay 5, 9:30 a.m., Palm Springs, Californiawww.ifen.com

This workshop during IEEE/ION PLANS focuses on multi-sensor, multi-frequency GNSS signal analysis with the SX-Navigation software receiver by IFEN GmbH.

UPINLBS 2010October 14–15, 2010, Helsinki, Finlandwww.fgi.fi/upinlbs

The international Ubiquitous Positioning, Indoor Navigation, and Location Based Service conference, sponsored by the Finnish Geodetic Institute, includes sessions on multi-constellation GNSS issues, wireless network and sensor fusion, pedestrian and indoor navi-gation, and 3D modeling/apping for indoor navigation applications.

Keynote speakers are Günter Hein, Gérard Lachapelle, Jari Syrjärinne, and Dorota Grejner-Brzezinska. Abstracts are due June 30.

» EVENTS

More events online: www.gpsworld.com/events

» SURVEY

Ashtech Introduces MobileMapper SoftwareAshtech has released MobileMapper Field and MobileMapper Office, a GIS and mapping software suite with advanced data-collection and pro-cessing features. The suite will first be introduced on the MobileMap-per 6 professional GPS/GIS handheld receiver, but over time it will be rolled out to the entire line of Ashtech Mo-bileMapper GPS/GIS receivers. The software suite replaces the previ-ously available Mobile Mapping and MobileMapper 6 Office applications.

According to the announcement, the new software suite provides a new graphical interface, common to Field and Office, and it includes all the features and options previously available in Mobile Mapping and Mo-bileMapper 6 Office software. In ad-dition, MobileMapper Field enables collection of multiple features at the same time, the ability to label col-lected features, configuration of an-tenna height, and support of the DXF, MIF or CSV formats. It also offers a direct interface to Laser Technology Inc.’s (LTI) range finders. The direct interface enables automatic input of distance and bearing to a distant ob-ject to easily collect offsets.

» SURVEY

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PRODUCT SHOWCASE

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LOCATION-BASED SERVICES

GPS-Enabled USB DeviceThe USBConnect Velocity from Option is the first GPS-enabled LaptopConnect device from AT&T. Option offers a free software application, the Option GPS Control Panel, that leverages location-enabled sites such as Yahoo! Maps and Bing for directions and local points of interest. Option GPS Control Panel is available for download on the Option support web page. Through TeleNav Track LITE and Xora GPS Locator from AT&T, enterprise customers can add tracking and location awareness. The device features an integrated micro SD-card slot. AT&T, www.att.com

CONSUMER OEM

Ultra-Mobile NotebookFujitsu has integrated u-blox’ GPS receiver into the LifeBook UH900 mini-notebook. The notebook has a 5.6-inch multi-touch screen display. It comes pre-loaded with Garmin Mobile PC navigation software and has a built-in u-blox’ NEO-5Q GPS module. The palm-sized device weighs a little over one pound and includes an integrated webcam, Bluetooth, and 62-gigabyte solid-state hard-drive. Fujitsu, www.fujitsu.com

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SURVEY | Built Structures


Ana P. C. Larocca, Ricardo E. Schaal, and Augusto C. B. Barbosa, University of São Paulo

Low-Frequency VibrationsDetection with High-Rate Data and Filtering

Civil engineers continuously seek reliable methods and tools to improve the quality and lifetime of large structures. Most studies in this fi eld have been

based on static loading. Nowadays, dynamic loading has be-come a particular concern, and GPS off ers direct measures of dynamic displacements of large structures induced by traffi c, wind, and earthquakes.

Precisely characterizing the vibrations that are a common behavior of large structures such as bridges, tall buildings, and towers undergoing dynamic loads facilitates structural analysis studies. It is feasible to detect structural vibrations using a computational model and GPS sensors. The critical vibration frequencies of bridges detectable with different GPS positioning techniques (real-time kinematic, static, quasi-static) range from 0 to 0.3 Hz

However, the unavoidable presence of multipath signals in the same frequency range makes it difficult to detect very low-frequency vibrations, mostly ranging from 0.05 up to 1 Hz, for short- to medium-span bridges.

Our preliminary results show that the structural vibra-tion measurements, mixed with random amplitude and fre-quency signals generated by electronics and the ionosphere, together with slowly varying signals generated by multipath, can be better detected with an oversampled GPS data set. Th is hypothesis relies on fact that the structure oscillation is

reasonably stable during the data-collecting period. Th e analyses of GPS time series used were done by math-

ematical addition of well-known sine waves in the raw phase of a 100-Hz data set collected from a short baseline. Th is strategy simulates the antenna vibrating vertically on a struc-ture, for example at the deck’s midpoint of a bridge.

MethodologyThe methodology used to collect and analyze GPS data was developed for providing low-cost high-accuracy monitoring with single-frequency GPS receivers. The technique is the in-terferometry method based on the analysis of the L1 double-difference phase residuals of regular static observations. In this data-processing, one satellite is considered as a reference, and its selection is according to the direction of the vibration to be measured. The satellite not taken as a reference — located in the same direction as the vibration movement — has the residual values that contain information about bridge deck vibrations (phase changes). In 2001, we named this the phase-residual method (PRM); see “Millimeters in Mo-tion” in GPS World, January 2005, at www.gpsworld.com/phaseresidual.

Th e residuals incorporate all phase deviations from the adjusted double-diff erence position during the observa-tion. Th ese phase deviations are due to electronic receiver

Å FIGURE 2 Residuals from L1 double-difference phase residual.Å FIGURE 1 Raw L1 double-difference phase residuals from a time series at a 100-Hz data rate.

Multipath makes it difficult to detect very low-frequency structural vibrations, ranging from 0.05 to 1 Hz, important in characterizing dynamic loads and determining safe structural lifetimes. The authors have developed a phase-residual method for use with very high-frequency data to distinguish receiver noise, multipath, and the periodic displacements that are most structurally significant. The methodology can apply to bridges, tall buildings, and towers.

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Built Structures | SURVEYs

noise, multipath, small dynamic antenna movements, and other error sources. Converting the residuals to the frequen-cy domain by the fast Fourier transform (FFT) associated with a continuous wavelet transform (CWT), it is possible to see the diff erent behaviors of the receiver phase noise, multipath, and periodic vibration, enabling the distinction between them. Th e periodic displacement presents a peak due to the fundamental vibration mode, while the receiver noise presents a white-noise spectrum, and the multipath presents a broad spectrum close to zero frequency. Th e last feature is very dependent on how the antennas “see” their vicinity. As PRM does not need well-known coordinates ep-och-by-epoch to determine the amplitude and the frequency values of the oscillations, it is possible to get reliability.

Th e spectrum analyses were done by FFT, which provides a design of the vibration’s peak amplitude values; the CWT was used to detect the variation of the frequency value dur-ing the timespan of observations, and for validating the results.

Simulation and Filtering The preliminary investigation was done by the mathemati-cal addition of sine waves on satellite signals close to zenith, which are the most affected by a vertical amplitude vibration in a real situation. The double-difference phase was calcu-lated, taking as reference the lowest satellite.

Th e mathematically generated sine wave had peak-to-peak amplitude of 1 millimeter and frequency values ranging from 0.06 Hz up to 1 Hz. Th e analyses for sine-wave detec-tion were done by applying the FFT and the CWT with the Morlet Wavelet, which deserves a short description.

Th e CWT was used because structural vibration signals with small peak-to-peak amplitudes in the low frequency re-gion are not well represented in time and frequency by the FFT methods. A particular wavelet, Morlet, was used and is defi ned as

(1)

where is dimensionless frequency and is dimensionless time. When using wavelets for feature extraction purposes, the Morlet wavelet is a good choice, because it provides a good balance between time and frequency localization.

Th e idea behind the CWT is to apply the wavelet as a band-pass fi lter to the time series. Th e CWT of a time series

with uniform time steps , is defi ned as the convolution of with the complex combination of the mother wavelet scaled and normalized, as:

(2)

where represents the similarity between wavelet func-tion and the analyzed time series ; that is, the higher the value of , the greater the similarity between the analyzed function and the mother wavelet function that modulates the analyzed signal. The CWT was implemented in MATLAB software.

100-Hz Phase DataRegarding the detection of low frequencies due to a small peak-to-peak amplitude vibration, it is important to show the L1 double-difference residuals of a 100-Hz data rate (FIGURE 1) and its spectrum before mathematically adding the sine-wave signal due to periodic vibrations. The fi gure shows the raw phase residuals of 20 seconds of data between two satellites, SV05 (lowest) and SV20 (highest).

FIGURE 2 presents a 1-second data span for better visual-ization of peak-to-peak amplitude of the raw double-diff er-ence phase residuals, which is lower than 3 millimeters.

FIGURE 3 was produced to verify the variability of 100-Hz residuals and the probability of errors in the signal that can contribute to degrading the identifi cation of the sine-wave vibration peaks. Th e resulting histogram is close to a bell curve of a Gaussian distribution, demonstrating the good quality of the 100-Hz data. FIGURE 4 shows the Mor-let CWT computed to identify the low-frequency bias term and a high-frequency noise term. Th e 5-percent signifi cance

Å FIGURE 3 The Gaussian distribution of 100-Hz data rate residuals.

Å FIGURE 4 Continuous Wavelet Transform of the residual time series. The 5-percent significance level of sine wave detection is shown as a thick contour.

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(95-percent confi dence) level of signifi cant signal-wave in-formation is delimited by a thick contour. Th e signal infor-mation of double-diff erence phase residuals was used as a reference for supporting a better distinction between noise and sine-wave signals.

Zero-Baseline TestA zero-baseline test was performed to determine the cor-rect operation of a GPS receiver, associated antennas, and cabling. The objective was to verify the precision of the receiver. A 1-minute data sample was collected. FIGURE 5 shows the residuals of L1 double-difference phase.

FIGURE 6 shows 5 seconds of the zero-baseline data; the peak-to-peak amplitude of residuals is very small, close to 2.0 millimeters. Th is information leads us to expect detec-tion of very low-frequency vibrations, ranging up to 0.3 Hz with a 1-millimeter amplitude displacement peak-to-peak.

FIGURE 7 shows the spectrum of the zero-baseline residu-als; it is possible to observe the region close to zero strongly aff ected by multipath. Th is makes the detection of very low frequencies diffi cult.

Th e CWT was applied to decomposing the zero-baseline double-diff erenced residuals into a low-frequency bias term and a low-frequency noise term. FIGURE 8 shows the behavior of the residuals of the 100-Hz phase data, where red regions

Å FIGURE 6 Residuals from a zero baseline with 100-Hz data.

Å FIGURE 7 Power spectrum of a zero-baseline residual.

Å FIGURE 9 Raw L1 residual time series with a sine wave of 1-Hz frequency and 1-millimeter amplitude.

Å FIGURE 8 Morlet CWT of zero-baseline residual time series. The 5-percent significance level of sine-wave detection is shown as a thick contour.

Å FIGURE 5 Zero baseline 100-Hz data rate residuals of L1 double-difference phase.

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represent the most suggestive energy level of the measure-ment noise term.

Preliminary Simulation ResultsFIGURE 9 illustrates the raw L1 double-difference phase re-siduals with a periodic sine wave of 1 millimeter peak-to-peak amplitude mathematically added to the time series. It is possible to observe the presence of the periodic signal.

FIGURE 10 shows that the stronger energy is close to 1 Hz due to the 1-Hz sine wave, as expected. Th e resulting well-defi ned peak is due to the high sampling rate provided by 100-Hz receivers. FIGURE 11 shows details of the peak due to the sine wave of 1 Hz added to the residuals.

We analyzed these data with the Morlet CWT to fi nd events to compared when other low frequencies had been simulated, helping separate noise from signal. FIGURE 12

Å FIGURE 10 Spectrum of L1 double-difference phase residuals with a sine wave of 1 Hz and 1 millimeter. Å FIGURE 11 Close-up of region with the most power at 1 Hz.

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presents the standardized time-series residuals, showing a region with highest power level. Th e continuous red region corresponds to a 1-Hz sine wave, and the spread-out red-or-ange regions may be due to electronic noise and multipath. Th e region outside the cone, delimited by the thick contour, indicates the detection of signifi cant signal information but without the 95-percent confi dence.

0.5-Hz Sine Wave. Th e second sine wave generated had the same peak-to-peak amplitude, 1 millimeter, and the frequency value of 0.5 Hz. FIGURE 13 illustrates the raw L1 double-diff erence phase residuals with a periodic 0.5-Hz sine wave mathematically added to the time series.

FIGURE 14 shows an energy peak at a frequency of approximately 0.5 Hz, also with a well defi ned peak. FIGURE 15 shows details of the peak.

Å FIGURE 16 Morlet CWT of time series of residuals with 0.5 Hz sine wave with 1 mm amplitude. The 5-percent significance level of sine wave detection is shown as a thick contour.

Å FIGURE 14 Spectrum of L1 double-difference phase residuals with a sine wave of 0.5 Hz.

Å FIGURE 15 Close-up of region with the most power at 0.5 Hz.

Å FIGURE 13 Raw L1 double-difference phase residuals with a sine wave of 0.5 Hz.

Å FIGURE 12 Morlet CWT of time series of residuals with 1-Hz sine wave with 1 millimeter amplitude. The 5-percent significance level of sine-wave detection is shown as a thick contour.

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Th e CWT in FIGURE 16 shows that the intensity energy level represented by the red continuous region and the spread-out red-orange regions are quite similar to those of the CWT of the 1-Hz sine wave (Figure 12). Note a de-crease in energy intensity (orange-yellow) that occurs due to decreased signal sampling of the 0.5-Hz signal (10 cycles) in 20 seconds of data, compared to 1 Hz (12 cycles) in the same 20 seconds.

0.1-Hz Sine Wave. The third sine wave mathematically generated had the same peak-to-peak amplitude, 1 millimeter, and a frequency of 0.1 Hz. FIGURE 17 illustrates the raw L1 double-diff erence phase residuals with the periodic 0.1-Hz sine wave mathematically added to the time series. FIGURE 18 shows

Å FIGURE 17 Raw L1 double-difference phase residuals with a sine wave of 0.10 Hz.

Å FIGURE 19 Morlet CWT of time series of residuals with 0.1-Hz sine wave with 1-millimeter amplitude; 5-percent significance level of sine wave detection shown as a thick contour.

Å FIGURE 18 Close-up of region with the most power at 0.10 Hz.

Built Structures | SURVEY

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the power at one frequency, approximately 0.10 Hz, still with a well-defi ned peak.

FIGURE 19 presents identifi cation of the 0.1-Hz sine wave by CWT with the 5-percent signifi cance level shown as a thick contour. A decrease of energy intensity (orange-yellow) occurs due to decreased signal sampling of 0.1 Hz (2.5 cycles) in 20 seconds of data compared to 0.5 Hz (ten cycles) in the same 20 seconds.

0.08-Hz Sine Wave. We simulated a sine wave of this frequency (FIGURE 20). FIGURE 21 presents identifi cation of the 0.08-Hz sine wave by CWT through the 5-percent signifi cance level shown as a thick contour. A decrease in energy intensity

(orange-yellow) occurs due to decreased signal sampling of 0.08 Hz (almost two cycles) in 20 seconds of data compared to 0.5 Hz (ten cycles) in the same 20 seconds.

0.06-Hz Sine Wave. Finally, a 0.06-Hz sine wave was simulated and added to the residuals, but the FFT spectral analysis did not present the power peak. This can be attributed due to the sine-wave period providing only 1.5 cycles during 20 seconds and did not generate enough power to be detected by FFT.

FIGURE 22 presents a close-up view of 0.06-Hz sine-wave power spectrum of the residuals not indicating a signifi cant peak close to the expected frequency region.

Th e investigation continued with a Morlet CWT. In FIGURE 23 it is possible to verify the presence of a faded red re-gion close to the period corresponding to 0.06 Hz — at the bottom of fi gure and under the cone’s thick contour — signalling that the wavelet was able to detect a very low frequency even with a small sampling. However, due to small signal sampling, the detection is not within a 95-percent confi dence. Other-wise, if the time series had lasted more than 20 seconds, certainly the sine wave would have been detected.

Th ese analyses suggest that longer time-series data would enable detection of very low frequencies with 95-percent confi dence.

Conclusions The lack of amplitude accuracy does not constitute a signifi cant restriction in large structure monitoring, as the exact-ness of its natural oscillating frequency, harmonics, and response to external dynamic forces are more important for identifi cation of a structural problem.

Using 100-Hz receivers to detect Å FIGURE 23 Morlet CWT of time series of residuals with 0.06 Hz sine wave with 1-millimeter amplitude.

Å FIGURE 22 Power spectrum of double-difference phase residuals with 0.06-Hz sine-wave signal.Å FIGURE 20 Close-up of region with most power at 0.08 Hz.

Å FIGURE 21 Morlet CWT of time series of residuals with 0.08 Hz sine wave with 1-millimeter amplitude; 5-percent level of sine-wave detection shown as a thick contour.

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very low-frequency vibrations, the combination of 100-Hz data with fi ltering techiniques enables detection of signal vi-brations of very low frequencies. Th e tests were conducted using a mathematical simulation of sine waves added to raw residuals of L1 double-diff erence phase.

Th e results of simulations and fi ltering techniques indi-cate that very low frequency vibrations can be detected when the sampling rate of GPS data and the sampling frequency of an embedded sine wave is large.

Additionally, zero baseline and static short baseline trials have been conducted to assess the noise of the receivers that is close to 2.5 millimeters — extremely low and contributing to detection of vibrations with low peak-to-peak amplitude.

Spectral analysis is a fundamental tool for engineering development. Despite such new analysis concepts as FFT and CWT used here, as well as higher-order spectra, basic frequency domain analysis will remain the practical analysis tool in the foreseeable future.

Future tests will be carried out collecting 100-Hz data, suffi cient for having oversampling of sine-wave frequencies due to structural vibrations, and using a new methodology with just one GPS receiver.

AcknowledgmentsThanks to the JAVAD GNSS Moscow Research and Devel-opment team for providing a Triumph receiver and 100-Hz data through Michael Glutting, whom we also thank. The researchers received a sponsorship from the National Counsel of Technological and Scientific Development Government (CNPq) of the Brazil Federal Government to purchase a pair of 100-Hz data-rate GPS receivers. �ManufacturersThe 20 seconds of data were kindly provided by JAVAD GNSS (www.javad.com) Moscow Research and Development team and were collected using Javad GNSS Triumph receiv-ers with JNS choke-ring antennas.

ANA P.C. LAROCCA is a lecturer in the Department of Transportation Engineering of the Polytechnic School at the University of São Paulo (USP) and holds a Ph.D from that same institution.

RICARDO E. SCHAAL is an associate professor with a Ph.D. from USP.

AUGUSTO C. B. BARBOSA is a Ph.D candidate at the Institute of Astronomy, Geophysics and Atmospheric Sciences, at USP.

phone 630.372.6800toll-free 800.323.9122website antenna.pctel.comemail [email protected]

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GNSS DESIGN & TEST | Galileo


Development of a reference Galileo Test User Receiver (TUR) for the verifi cation of

the Galileo in-orbit validation (IOV) constellation, and as a demonstrator for multi-constellation applications, has culminated in the availability of the fi rst units for experimentation and test-ing. The TUR-N covers a wide range of receiver configurations to demonstrate the future Galileo-only and GPS/Gali-leo combined services:

� Galileo single- and dual-frequency Open Services (OS)

� Galileo single- and dual-frequency safety-of-life services (SoL), including the full Galileo navigation warning algorithms

� Galileo Commercial Service (CS), including tracking and decoding of the encrypted E6BC signal

� GPS/SBAS/Galileo single- and dual- frequency multi-constellation positioning

� Galileo single- and dual-frequency differential positioning.

� Galileo triple-frequency RTK.In parallel, a similar test user receiver is

specifically developed to cover the Public Regulated service (TUR-P). Without the PRS components and firmware installed, the TUR-N is completely unclassified.

Main Receiver UnitThe TUR-N receiver is a fully stand-alone, multi-frequency, multi-constella-tion receiver unit. It can autonomously generate measurements, determine its position, and compute Galileo safety-of-life integrity, which is output in real time and/or stored internally in a com-pact proprietary binary data format.

The receiver configuration is fully flexible via a command line interface or using the dedicated graphical user interface (GUI) for monitoring and control. With the MCA GUI it is also possible to monitor the receiver operation (see FIGURE 2), to present various real-time visualizations of tracking, PVT and integrity performances, and off-line analysis and reprocessing functionalities. FIGURE 3 gives an example of the correlation peak plot for an E5 AltBOC signal.

A predefined set of configurations that map onto the different configurations as prescribed by the Test User Segment Requirements (TUSREQ) document is provided by the receiver.

The unit can be included within a local network to provide remote access for control, monitoring, and/or logging, and supports up to eight parallel TCP/IP connections; or, a direct connection can be made via one of the serial ports.

Receiver ArchitectureThe main receiver unit consists of three separate boards housed in a standard compact PCI 19-inch rack. See FIGURE 4 for a high-level architectural overview.

A dedicated analog front-end board has been developed to meet the stringent interference requirements. This board contains five RF chains for the L1, E6, E5a/L5, E5b, and E5 signals. Via a switch the E5 signal is either passed through separate filter paths for E5a and E5b or

A fully stand-alone, multi-frequency, multi-constellation receiver unit, the TUR-N can autonomously generate measurements, determine its position, and compute the Galileo safety-of-life integrity.

Axel van den Berg, Tom Willems, Graham Pye, and Wim de Wilde, Septentrio Satellite Navigation, Richard Morgan-Owen, Juan de Mateo, Simone Scarafia, and Martin Hollreiser, European Space Agency

Galileo Test User ReceiverStatus, Key Results, Performance

Å FIGURE 1 C/N0 plot with nine satellites and all five Galileo signal types: L1BC (green), E6BC (blue), E5a (red), E5b (yellow), and E5 Altboc (purple).

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Galileo | GNSS DESIGN & TESTs

via one wide-band filter for the full E5 signal. The front-end board supports two internal frequency references (OCXO or TCXO) for digital signal processing (DSP).

The DSP board hosts three tracker boards derived from a commercial dual-frequency product family. These boards contain two tracking cores, each with a dedicated fast-acquisition unit (FAU), 13 generic dual-code channels, and a 13-channel hardware Viterbi decoder. One tracking core interacts with an AES unit to decrypt the E6 Commercial Service carrier; it has a throughput of 149 Mbps.

Each FAU combines a matched filter with a fast Fourier transform (FFT) and can verify up to 8 million code-frequency hypotheses per second. Each of the six tracker cores can be connected

with one of the three or four incoming IF streams. To simplify operational use of the receiver, two channel-mapping files have been defined to configure the receiver either for a 5-frequency 13-channel Galileo receiver, or for a dual-frequency 26-channel Galileo/GPS/SBAS receiver. FIGURE 1 shows all five Galileo signal types being tracked for nine visible satellites at the same time.

The receiver is controlled using a COTS CPU board that also hosts the main positioning and integrity algorithms. The processing power and available memory of this CPU board is significantly higher than what is normally available in commercial receivers. Consequently there is no problem in supporting the large Nequick model used for single-frequency ionosphere correction, and achieving the 10-Hz update rate and low latency requirements when running the computationally intensive Galileo integrity algorithms. For commercial receivers that are normally optimized for size and power consumption, these might prove more challenging.

T h e T U R p r o j e c t i n c l u d e d development of three types of Galileo antennas:� a triple-band (L1, E6, E5) high-end

antenna for fixed base station appli-cations including a choke ring;

� a triple-band (L1, E6, E5) reference antenna for rover applications;

� a dual-band (L1, E5b) aeronautic antenna for SOL applicationsFIGURE 5 shows an overview of the

main interfaces and functional blocks of the receiver, together with its antenna and a host computer to run the MCA software either remotely or locally connected.

Receiver VerificationCurrently, the TUR-N is undergoing an extensive testing program. In order to fully qualify the receiver to act as a Å TABLE 1 Test user receiver data sheet.

Å FIGURE 2 TUR-N control screen.

Å FIGURE 3 E5 AltBOC correlation peak.

Å FIGURE 4 Receiver architecture.

TUR Data SheetRack type 19” 8HEDimensions 450 x 295 x 310 mmWeight 12 kgPhysical channels 78 dual code channelsLogical channel allocation

5 frequency 13 chan-nel GALILEO receiverDual frequency 26 channel GALILEO/GPS/SBAS receiver

Power consumption 80 WattEthernet ports 2 (supporting up to 8

remote connections in parallel)

Serial ports 2Input power 120/220 VAC

10 – 36 VDC

Å FIGURE 5 TUR-N with antenna and host computer.

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reference for the validation of the Gali-leo system, some challenges have to be overcome. The fi rst challenge that is encountered is that the performance verifi cation baseline is mainly defi ned in terms of global system performance. The translation of these global require-ments derived from the Galileo system requirements (such as global availabil-ity, accuracy, integrity and continuity, time-to-fi rst/precise-fi x) into testable parameters for a receiver (for example, signal acquisition time, C/N

0 versus el-

evation, and so on) is not trivial. Sys-tem performances must be fulfi lled in the worst user location (WUL), defi ned in terms of dynamics, interference, and multipath environment geometry, and SV-user geometry over the Galileo global service area.

A second challenge is the fact that in the absence of an operational Galileo constellation, all validation tests need to be done in a completely simulated environment. First, it is difficult to assess exactly the level of reality that is necessary for the various models of the navigation data quality, the satellite behaviour, the atmospheric propagation effects, and the local environmental effects. But the main challenge is that not only the receiver that is being verified, also the simulator and its configuration are an integral part of the verification. It is thus an early experience of two independent implementations of the Galileo signal-in-space ICD being tested together. At the beginning of the campaign, there was no previously demonstrated or accepted test reference.

Only the combined ef for ts of the various receiver developments benchmarked against the same simulators together with pre-launch compatibility tests with the actual satellite payload and finally IOV and FOC field test campaigns will ultimately validate the complete system, including the Galileo ground and space segments together with a limited set of predefined user segment configurations. (Previously some confidence was gained with GIOVE-A/B experimental satellites and a breadboard adapted version of TUR-N). The TUR-N was the first IOV-compatible receiver to

be tested successfully for RF compatibility with the Galileo engineering model satellite payload.

Key PerformancesReceiver requirements, including per-formance, are defi ned in the TUSREQ document.

Antenna and Interference. A key TUSREQ requirement focuses on receiver robustness against interference. It has proven quite a challenge to meet the prescribed interference mask for all user configurations and antenna types while keeping many other design parameters such as gain, noise figure, and physical size in balance. For properly testing against the out-of-band interference requirements, it also proved necessary to carefully filter out increased noise levels created by the interference signal generator.

TABLE 2 gives an overview of the measured values for the most relevant Antenna Front End (AFE) parameters for the three antenna types. Note: Asymmetry in the AFE is defined as the variation of the gain around the centre frequency in the passband. This specification is necessary to preserve the correlation peak shape, mainly of the PRS signals.

The gain for all antenna front ends and frequencies is around 32 dB. FIGURES 6 and 7 give an example of the measured E5 RHCP radiating element gain and axial ratio against theta (the angle of incidence with respect to zenith) for the high-end antenna-radiating element. Thus, elevation from horizontal is 90-theta.

UERE Performance. As part of the test campaign, TUR performance has been measured for user equivalent range error (UERE) components due to thermal noise and multipath.

TUSREQ specifies the error budget as a function of elevation, defined in tables at the following elevations: 5, 10, 15, 20, 30, 40, 50, 60, 90 degrees. The elevation dependence of tracking noise is immediately linked to the antenna gain pattern; the antenna-radiating element gain profiles were measured on the actual hardware and loaded to the Radio Frequency Constellation Simulator (RFCS), one file per frequency and

Å FIGURE 8 Reference antenna, power nominal-3 dB, C/N0 profile.

Å FIGURE 10 Reference antenna, power nominal-3 dB, thermal noise with multipath, single frequency.

Å FIGURE 6 High-end antenna E5 RHCP gain.

Å FIGURE 9 Reference antenna, power nominal-3 dB, thermal noise only, single frequency.

Å FIGURE 7 High-end antenna E5 axial ratio.

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per antenna scenario. The RFCS signal was passed through the real antenna RF front end to the TUR. As a result, through the configuration of RFCS, real environmental conditions (in terms of C/N

0) were emulated in factory.

The thermal noise component of the UERE budget was measured without multipath being applied, and interference was al lowed for by reducing the C/N

0 by 3 dB from nominal. Separately,

the multipath noise contribution was determined based on TUSREQ environments, using RFCS to simulate the multipath (the multipath model configuration was adapted to RFCS simulator multipath modeling capabilities in compliance with TUSREQ). To account for the fact that multipath is mostly experienced on the lower elevation satellites, results are provided with scaling factors applied for elevation (“weighted”), and without scaling factors (“unweighted”). In addition, following TUSREQ requirements, a carrier smoothing filter was applied with 10 seconds convergence time.

FIGURE 8 shows the C/N0 profile from

the reference antenna with nominal power reduced by 3 dB. FIGURE 9 shows single-carrier thermal noise performance without multipath, whereas FIGURE 10 shows thermal noise with multipath. Each of these figures includes performance for five different carriers: L1BC, E6BC, E5a, E5b, and E5 AltBOC, and the whole set is repeated for dual-frequency combinations (FIGURE 11 and FIGURE 12).

The plots show that the thermal noise component requirements are easily met, whereas there is some limited non-compliance on noise+multipath (with weighted multipath) at low elevations. The tracking noise UERE requirements on E6BC are lower than for E5a, due to assumption of larger bandwidth at E6BC (40MHz versus 20MHz). Figures 9 and 10 refer to UERE tables 2 and 9 of TUSREQ. The relevant UERE requirement for this article is TUSREQ table 2 (satellite-only configuration). TUSREQ table 9 is for a differential configuration that is not relevant here.

UERRE Performance. The complete single-frequency range-rate error budget as specified in TUSREQ was measured with the RFCS, using a model of the reference antenna. The result in FIGURE 13 shows compliance.

Position Accuracy. One of the objectives of the TUR-N is to demonstrate position accuracy. In FIGURE 14 an example horizontal scatter plot of a few minutes of data shows a clear distinction between the performances of two different single-frequency PVT solutions: GPS L1CA in purple and E5AltBOC in blue. The red marker is the true position, and the grid lines are separated at 0.5 meters. The picture clearly shows how the new E5AltBOC signal produces a much smoother position solution than the well-known GPS L1CA code. However, these early results are from constellation simulator tests without the full TUSREQ

worst-case conditions applied.T h e d e f i n e d T U S R E Q u s e r

environments, the basis for all relevant simulations and tests, are detailed in TABLE 3. In particular, the rural pedestrian multipath environment appears to be very stringent and a performance driver.

This was already identified at an early stage during simulations of the total expected UERE and position accuracy performance compliance with regard to TUSREQ, summarized in TABLE 4, and is now confirmed with the initial verification tests in Figure 10. UERE (simulated) total includes all other expected errors (ionosphere, troposphere, ODTS/BGD

Å TABLE 3 TUSREQ environments.

Environ-ment

Env. ID

Service Dynamics Multipath

Rural Pe-destrian

RP OS 10 m/s - Average delay 50 ns;- Linear decay slope 10 dB/µs;- Doppler bandwidth 4 Hz;- Line-of-sight multipath power

(relative to unobstructed line-of-sight path) -7.2 dB

Rural Vehicle

RV OS, CS,SOL

- velocity: 100 m/s (360 km/h) max;

- acceleration: 10 m/s² (1g) max;

- jerk: 20 m/s3 max.

- Average delay 50 ns;- Linear decay slope 10 dB/µs;- Doppler bandwidth 140 Hz;- Line-of-sight multipath power

(relative to unobstructed line-of-sight path) -7.2 dB

Aeronau-tical

AR OS, CS,SOL

- velocity:128.6 m/s (462.96 km/h) max;

- horizontal acceleration: 20 m/s² (2 g) max;

- vertical acceleration: 15 m/s² (1.5 g) max;

- jerk: 7.4 m/s3 (0.74g/s) max; - banking angle: 0° max.

ESA Aeronautical Multipath model

High-end AntennaFrequency L1 E5 E6Noise Figure (dB) 1.7 1.5 1.5Pass Band Ripple (dB) 1.5 1.9 1.6Asymmetry (dB) 0.35 0.2 0.65

Reference AntennaFrequency L1 E5 E6Noise Figure (dB) 2.5 2.8 2.3Pass Band Ripple (dB) 1.0 1.7 0.8Asymmetry (dB) 0.43 0.14 0.51

Aeronautical AntennaFrequency L1 E5bNoise Figure (dB) 4.8 5.8Pass Band Ripple (dB) 1.7 2.4Asymmetry (dB) 0.7 1.8

Å TABLE 2 Antenna measured parameters.

Å FIGURE 11 Reference antenna, power nominal-3 dB, thermal noise only, dual frequency.

Å FIGURE 12 Reference antenna, power nominal-3 dB, thermal noise with multipath, dual frequency.

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error, and so on) in addition to the thermal noise and multipath, whereas the previous UERE plots were only for selected UERE components. The PVT performance in the table is based on service volume (SV) simulations.

The non-compliances on position accuracy that were predicted by simulations are mainly in the rural pedestrian environment. According to the early simulations:� E5a and E5b were expected to have

43-meter vertical accuracy (instead of 35-meter required).

� L1/E5a and L1/E5b dual-frequency configurations were expected to have 5-meter horizontal, 12-meter vertical accuracy (4 and 8 required).These predictions appear pessimistic

related to the first position accuracy results shown in TABLE 5. On single frequency, the error is dominated by ionospheric delay uncertainty. These results are based on measurements using the RFCS and modeling the user environment; however, the simulation of a real receiver cannot be directly compared to service-volume simulation results, as a good balance

between realism and worst-case conditions needs to be found. Further optimization is needed on the RFCS scenarios and on position accuracy pass/fail criteria to account for DOP variations and the inability to simulate worst environmental conditions continuously.

Further confirmations on Galileo U E R E a n d p o s i t i o n a c c u r a c y performances are expected after the site verifications (with RFCS) are completed, and following IOV and FOC field-test campaigns.

Acquisition. FIGURE 15 gives an example of different signal-acquisition times that can be achieved with the TUR-N after the receiver boot process has been completed. Normally, E5 frequencies lock within 3 seconds, and four satellites are locked within 10 seconds for all frequencies. This is based on an unaided (or free) search using a FAU in single-frequency configurations, in initial development test without full TUSREQ constraints.

When a signal is only temporarily

lost due to masking, and the acquisition process is still aided (as opposed to free search), the re-acquisition time is about 1 second, depending on the signal strength and dynamics of the receiver. When the PVT solution is lost, the aiding process will time out and return to free search to be robust also for sudden user dynamics.

More complete and detailed time-to-first-fix (TTFF) and time-to-precise-fix (TTPF), following TUSREQ definitions, have also been measured.

In cold start the receiver has no prior knowledge of its position or the navigation data, whereas in warm start it already has a valid ephemeris in memory (more details on start conditions are available in TUSREQ). TABLE 6 shows that the acquisition performances measured are all compliant to TUSREQ except for warm start in E5a single frequency and in the integrity configurations. However, when the navigation/integrity message recovery time is taken off the measurement (as now agreed for updated TUSREQ due to

Å FIGURE 13 UERRE measurements.

Å FIGURE 14 L1 GPS CA versus E5 AltBOC position accuracy (early test result).

Å TABLE 4 Overall UERE and PVT compliance summary (SV simulation).

Confi guration Frequency Env.TUSREQ Accuracy [m] UERE

Table

Position Accuracy

ComplianceHorizontal Vertical Hor. Vert.

Single without Integrity

L1 RP 15 35 4 l l l

E5ARP 24 35

1 l l l

E5B 2 l l l

E5 (AltBoc) RP 24 35 26 l l l

Double without Integrity

E5B–L1RP

4 8

5 l l l

E5A–L1 7 l l l

E5 (AltBoc) –L1 27 l l l

E5B–L1RV

6 l l l

E5A–L1 8 l l l

E5 (AltBoc) –L1 28 l l l

Single with Integrity

E5BAR 35 85

22 l l l

L1 24 l l l

Dual with Integrity

E5B–L1 AR 4 8 9 l l l

Å TABLE 5 First position performance results (with RFCS).

Confi gurationExpected

Horizontal Accuracy (95%)

MeasuredHorizontal Accuracy

Expected Vertical

Accuracy (95%)

MeasuredVertical

AccuracyL1 15m 1.69m 35m 2.63mE5a+L1 4m 0.85m 8m 0.97mE5b+L1 4m 0.79m 8m 1.07mE5(Alt) +L1 4m 0.8m 8m 1.02mL1 w/INT 35m 0.65m 85m 2.42mE5b w/INT 35m 0.97m 85m 2.09mE5b+L1 w/INT 4m 0.58m 8m 2.61m

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message limitations), these performances also become compliant.

Specif ic examples of s tat i s t ics gathered are shown in FIGURES 16–21, these examples being for dual-frequency (E5b+L1) with integrity configuration. The outliers, being infrequent results with high acquisition times, are still compliant with the maximum TTFF/TTPF requirements, but are anyway under further investigation.

Integrity Algorithms. The Galileo SoL service is based on a fairly complex processing algorithm that determines not only the probability of hazardous misleading information (PHMI) based on the current set of satellites used in the PVT computation (HPCA), but also takes into consideration the PHMI that is achieved when one of the satellites used in the current epoch of the PVT computation is unexpectedly lost within the following 15 seconds. PHMI is computed according to alarm limits that are configurable for different application/service levels. These integrity algorithms have been closely integrated into the PVT processing routines, due to commonality between most processing steps.

Current test results of the navigation warning algorithm (NWA) indicate that less than 10 milliseconds of processing time is required for a full cycle of the integrity algorithms (HPCA+CSPA) on the TUR-N internal CPU board. Latency of the availability of the integrity alert information in the output of the receiver after it was transmitted by the satellite has been determined to be below 400 milliseconds. At a worst-case data output rate of 10 Hz this can only be measured

in multiples of 100 millisecond periods. The total includes 100 milliseconds of travel time of the signal in space and an estimated 250 milliseconds of internal latency for data-handling steps as demodulation, authentication, and internal communication to make the data available to the integrity processing.

ConclusionsThe TUR-N is a fully fl exible receiver that can verify many aspects of the Galileo system, or as a demonstrator for Galileo/GPS/SBAS combined op-eration. It has a similar user interface to commercial receivers and the fl ex-ibility to accommodate Galileo system requirements evolutions as foreseen in the FOC phase without major design changes.

The receiver performance is in general compliant with the requirements. For the important safety-of-life configura-tion, major performance requirements are satisfied in terms of acquisition time and position accuracy.

The receiver prototype is currently operational and undergoing its final verification and qualification, following early confirmations of compatibility with the RFCS and with the Galileo satellite payload.

ManufacturersTUR-N was developed by Septentrio Satellite Navigation (www.septentrio.com), with the participation of Orban Microwave Products (www.orbanmicrowave.com), Deimos Space (www.deimos-space.com), and QinetiQ (www.qinetiq.com). �

Å TABLE 6 Summary of measured acquisition performances.

Confi g. FrequencyWarm/cold

startFix type

TUS-REQ

Measured 95%

Compli-ant

Single without Integrity

E5ACold start TTFF 100s 79.8s l

Warm start TTFF 30s 32.6s l

E5 (AltBOC) Cold start TTFF 100s 60.05s l

Dual without Integrity

E5A–L1 Cold start TTFF 100s 61.14s l

E5 (AltBoc) –L1Cold start TTFF 100s 44.45s l

Warm start TTFF 30s 28.2s l

Cold start TTFF 200s 44.5 l

Single with Integrity L1

Cold start TTFF 100s 65.40s l

Warm start TTFF 30s 60s l

Dual with Integrity

E5B–L1Cold start TTFF 100s 53.71s l

Warm start TTFF 30s 50s l

Cold start TTFF 200s 68.6s l

Å FIGURE 21 TTFF warm-start distribution, dual frequency with integrity E5b+L1,

ÅFIGURE 20 TTFF warm-start performance, dual frequency with integrity E5b+L1.

Å FIGURE 19 TTPF cold-start distribution, dual frequency with integrity E5b+L1.

Å FIGURE 18 TTPF cold-start performance, dual frequency with integrity E5b+L1.

Å FIGURE 17 TTFF cold-start distribution, dual frequency with integrity E5b+L1.

Å FIGURE 15 Unaided acquisition performance.

Å FIGURE 16 TTFF cold-start performance, dual frequency with integrity E5b+L1.

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WELCOME TO INNOVATION COLUMN NUMBER 200. I have managed this col-umn continuously since the first issue of GPS World magazine, which appeared back in 1990. From the outset, we established that the column should deal with

issues that have broad application and interest and are presented in terms that are accessible to as wide a range of readers as possible. Since 1990, we have covered a wide range of topics, some of them at the leading edge of GPS development and some of them reviewing the basics of GPS operation in tutorial fashion. The column has appeared 199 times

and now we come to number 200.So clearly 200 is an important number for me and, I hope, for you. But the number

200 is interesting for other reasons, too. It is the smallest base 10 unprimeable number — you can’t turn it into a prime number by changing just one of its digits to any other digit. It’s how many dollars you get when you pass Go in Monopoly. And in 2012, it will be how many years have elapsed since The War of 1812 — the last time Canada and the United States had a serious quarrel (other than in hockey). But more to the point of this column, it is the designation of the basic refer-ence document that describes how GPS works: IS-GPS-200. Formerly known as an Interface Control Document or ICD, it has gone through several revisions since its first public release in July 1991. It is full of numbers. Numbers that tell us how the GPS signals are generated and how a receiver is to interpret the signals to provide a posi-tion fix.

If you are a regular reader of the Innovation column, then likely you have an inquisitive bent. You like to know how things work — GPS in particular. And you don’t have to be convinced about the importance of numbers and their role in understanding the world around us. As Sir William Thomson, a.k.a. Lord Kelvin, said in one of his lectures,

“I often say that when you can measure what you are speak-ing about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind.”

So in this column, the 200th, we’re going to look at GPS by the numbers, getting a sense of how GPS works by examining some of the key numbers that govern its remarkable capabilities, from the smallest to the largest. I’ll draw heavily on material from the past 199 columns.

Let’s get started.

A Sideways Look at How the Global Positioning System WorksGPS by the Numbers

Richard B. Langley

INNOVATION | Number 200

Innovation number 200

INNOVATION INSIGHTS with Richard Langley


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Numbers. We use them for count-ing and measuring, for labeling and ordering, and for codes and

calculations. The number of numbers is infinite. However, there are some spe-cial numbers that characterize how GPS works. Some of these are peculiar to GPS; others are more common, finding utility in other global navigation satellite systems or even in our everyday lives. In this article, we’ll take a look at some of these special numbers and their importance to GPS.

We’ll begin with the smallest non-negative number and work our way up to one of the largest GPS-relevant numbers, concluding with an imaginary but very important number.

0Zero. The smallest cardinal number and the smallest non-negative integer. While zero is a pure real number (a number on an infinitely long number line), it is also a purely imaginary number (see the last entry in this article) because it lies on both

the real and imaginary axes on the com-plex plane. It is used to indicate a null

amount. The English mathemati-cian, Alfred North Whitehead,

wrote in his 1911 book An Intro-duction to Mathematics, “The

point about zero is that we do not need to use it in the op-erations of daily life. No one goes out to buy zero fish. It is in a way the most civilized of all the cardinals, and its use is only forced on us by the needs of cultivated modes of

thought.” Perhaps it was not needed for daily operations in

1911 but it is indispensible in our modern world. For zero is also one of the two binary digits (the other is one, of course) used in the binary

or base-2 number system that is fundamental to how computers, digital electron-ics, and communications systems operate. For ex-ample, we represent the GPS pseudorandom noise (PRN)

ranging codes and the navigation message as sequences of zeros and ones and the zeros are just as important as the ones.

The C/A- and P(Y)-codes (see entries 1023 and 235,469,592,765,000), along with the navigation message, are modu-lated onto the signal carriers using binary phase-shift keying or BPSK. BPSK is a digital modulation scheme that conveys a signal by changing, or modulating, the phase of the carrier wave between two val-ues separated by 180°. The spectrum of a BPSK-modulated signal is a sinc func-tion, with most of the power concentrated around the carrier frequency. An alterna-tive modulation technique is binary offset carrier (BOC) modulation. BOC modu-lation uses a square-wave subcarrier to offset the spectral power from the carrier frequency and thus allows a BOC-modu-lated signal to share the same bandwidth as a BPSK signal. The new GPS M-code on L1 and L2 uses a BOC(10.23,5.115) — abbreviated as BOC(10,5) — modula-tion, which specifies a subcarrier frequency of 10�1.023 MHz and a spreading-code chipping rate of 5.115 megachips per sec-ond. The spreading code is a pseudoran-dom bit stream from a signal protection algorithm, having no apparent structure or period. The future L1C signal, the new civil signal to be implemented on L1 by Japan’s Quasi-Zenith Satellite System and the GPS III satellites, will also use BOC modulation. And Europe’s Galileo system, now in development, will also use this modulation technique, which has already been tested in space by the forerunner GIOVE test satellites.

0.00000000000001 (Or 1 � 10-14 in scientific notation). The approximate frequency stability of the rubidium atomic frequency standards in the GPS Block IIR satellites. These devices are used to control the frequency and tim-ing of all aspects of the navigation signals, including the generation of the carrier frequencies and the pseudorandom noise modulation codes. Given their role in con-trolling the timing of the signals, they are also referred to as clocks.

Each Block IIR satellite contains three

rubidium clocks, only one of which is ac-tive at any time. The others are spares and the GPS Control Segment carries out a “clock swap” when the performance of an active clock begins to deteriorate, cycling through the remaining units. Many of the Block IIR satellites are still on their first clock.

The Block IIF satellites will also contain three clocks, however, only two will be ru-bidium clocks. The third clock will be a cesium clock. This mixture of clock types is patterned after the arrangement used on the Block II and IIA satellites, which used two rubidium clocks and two cesiums.

0.77922077922… The rational number 60/77. A rational number is any number that can be ex-pressed as a fraction or quotient a/b of two integers, with the denominator b not equal to zero. The decimal expansion of a ratio-nal number always either terminates after a finite number of digits or begins to repeat the same sequence of digits over and over again. The digits 077922 of this particu-lar rational number repeat ad infinitum. And why should we be interested in this particular number? It is the ratio of the L2 and L1 carrier frequencies. This number and its inverse ( — the dot above the 3 indicates it repeats indefinitely) are used in various combinations of GPS measure-ments. For example, if we let � = 60/77, then the ionosphere-free pseudorange combination is

where P

1 is a pseudorange measurement

on L1 and P2 is the corresponding pseu-

dorange measurement on L2.

1The loneliest number according to the American rock band Three Dog Night and the Google calculator (try typing “loneliest number” into the Google search engine). It was also the space vehicle number (SVN) of the first Block I GPS satellite, which was launched on February 22, 1978. The satellite did not stay lonely for long. By

Number 200 | INNOVATION


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the end of the year, three more Block I satellites were launched. In total, 10 Block I satellites were successfully orbitted be-tween 1978 and 1985 to demonstrate the feasibility of GPS. SVN1 continued in operation until July 17, 1985.

The first satellite of the Block II op-erational constellation was launched in February 1989. The four-year hiatus in launches was due, in part, to the Space Shuttle Challenger disaster as it had been planned to launch the operational satellites using the Shuttle. Following the accident, it was decided to continue with expendable rockets for GPS launches but to switch to the newly designed Delta II rocket.

The pace of Block II launches was rapid, with five launches of the original Block II design in 1989 and four in 1990. A modi-fied version of the Block II satellite — the IIA — was developed, and between 1990 and 1997 19 Block IIAs were launched. The Block II and IIA satellites established the operational GPS constellation. Full operational capability was declared on April 27, 1995.

A new variant of the Block II satellite was developed for replenishing the constel-lation as the earlier satellites were retired. Following an initial launch failure, 12 of the Block IIR satellites were launched be-tween 1997 and 2004.

Under the GPS modernization pro-gram, the remaining eight Block IIR satellites were modernized with a new navigation payload that included the L2C and M-code signals as well as a new antenna panel (also included on the last four of the classic Block IIRs). The IIR-M satellites were launched between 2005 and 2009, bringing the total number of GPS satellites ever placed in orbit to 58.

One is also the PRN number of SVN49, the Block IIR-M satellite that was modified to transmit the first L5 GPS signals (see 1176.45).

2.4The approximate delay, in meters, expe-rienced by a GPS signal propagating verti-cally (from the zenith) through the neutral atmosphere to a receiver at mean sea level. Although the electrically neutral, or union-

ized, atmosphere extends from ground level up to 50 kilometers and more, the bulk of it is in the lowest most part we call the troposphere. Consequently, the neu-tral atmosphere delay is often termed the tropospheric delay. The delay varies with actual atmospheric conditions and the el-evation angle at which a GPS signal arrives at the receiver’s antenna. If unaccounted for, tropospheric delay would result in po-sition errors of several meters in the hori-zontal plane and two to three times these values in the vertical. Predictive or “blind” tropospheric models based on climatology attempt to significantly reduce the effect of the troposphere on GPS position fixes. One such model is UNB3m, developed at the University of New Brunswick. Using a look-up table of surface meteorological pa-rameter values from standard atmospheric models, it can compute the tropospheric delay for a given day of year, latitude, and station height. For example, the UNB3m zenith delay for a sea-level site at a latitude of 60° on day-of-year 201 is 2.435 meters. UNB3m is able to predict zenith delays with an average root-mean-square error of 4.9 centimeters. Better and more consis-tent performance has been obtained with a wide-area model developed specifically for North America, UNBw.na.

A version of an earlier UNB model be-came the basis of the RTCA Minimum Operational Performance Standards (MOPS) troposphere model that is in-cluded in the firmware of most GPS re-ceivers.

3.1415926….�Every nerd’s favorite number. It is the ratio of a circle’s circumference to its diameter in conventional or Euclidean space. We use it, for example, to convert angles measured in radians to degrees (�radians � 180 degrees). � is an irrational number, which means that its value can-not be expressed exactly as a fraction m/n, where m and n are integers. Consequently, its decimal representation never ends or repeats. But we sometimes use an easily remembered fraction, such as 22/7, to get an approximate value. In this case, 3.14. But, if we compute more digits with this

fraction, we get 3.1428571…, clearly an incorrect result. A better way to remember � to eight digits is to count the number of letters in each word of the mnemonic “May I have a large container of coffee?”

In computations related to GPS, how many digits of � should be used? It de-pends. If you are developing your own al-gorithms and software for modeling GPS observations or determining precise orbits for the satellites, you’ll likely need � to 16 digits for double-precision floating-point calculations. But it would be a mistake to use � to this precision in computing the position of a satellite from the broadcast ephemeris. The GPS interface specifica-tion document, IS-GPS-200, specifies a 14-digit value for � (3.1415926535898) in the satellite coordinate computation. Use fewer or more digits, and the result-ing satellite coordinates will not be as ac-curate.

4This is the minimum number of satellites that a receiver needs to track and generate a pseudorange measurement to produce a three-dimensional “instantaneous” posi-tion fix. The receiver solves a system of four nonlinear equations to obtain the three receiver coordinates and the offset of the receiver’s clock from GPS (System) Time. It is possible to use fewer than four satellites for positioning or navigation, but then additional information must come from elsewhere. For example, if we are navigating and we know our height accu-rately or can safely assume a value, say, so many meters above the sea surface, then only three pseudoranges would be needed to determine the horizontal coordinates. If the number of satellites drops to two, then another assumption must be made to con-tinue navigation (for example, holding the receiver clock offset constant or assuming a constant driving direction). If the clock offset is held constant, then position ac-curacy deteriorates quickly since the ac-tual receiver clock offset will diverge from the assumed value. On the other hand, if the direction of travel is held constant, the GPS receiver can at least compute the position along the assumed trajectory. In

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reality, the vehicle will likely not travel along a perfectly straight path and naviga-tion fails after the first turn.

For single-satellite navigation, three assumptions must be made concerning height, trajectory, and clock offset, but the navigation results are, at best, educated guesses.

If a receiver can acquire and track more than four satellites, it typically uses an op-timizing Kalman filter procedure to obtain its position.

10.23The frequency of a GPS satellite atomic frequency standard in megahertz and the fundamental frequency for signal genera-tion in the satellite. The carrier frequencies and the code chipping rates are harmoni-cally related to this frequency. The P-code chipping rate is identical to the fundamen-tal frequency, while the C/A-code rate is 1/10 of it.

12.5The length of the full navigation message in minutes. To convert the measured sig-nal delays or pseudoranges between the re-ceiver and the satellites, the receiver must know where the satellites are. To do this in real time requires that the satellites broad-cast this information. Accordingly, there is a message superimposed on both the L1 and L2 carriers along with the PRN codes. Each satellite broadcasts its own message, which consists of orbital information (the ephemeris) to be used in the position com-putation, the offset of its clock from GPS Time, and information on the health of the satellite and the expected accuracy of the range measurements.

The message also contains almanac data for all of the satellites in the GPS constella-tion, as well as their health status and other information. The almanac data, a crude description of the satellite orbits, is used by the receiver to determine the location of each satellite. The receiver uses this infor-mation to quickly acquire the signals from satellites that are above the horizon but are not yet being tracked. So, once one satel-lite is tracked and its message decoded, ac-quisition of the signal from other satellites

Modular ArithmeticGPS Time, like all time systems, is based on modular arithmetic. This arithmetic is a little different from conventional arithmetic in that numbers, typically restricted to integers, have a finite maximum value. Adding one to that number doesn’t get you a larger number — it gets you a smaller one, a much smaller one: zero.

Modular arithmetic is known to us all as clock arithmetic. Take the 24-hour time system as an example. If it’s currently 1800, then 8 hours later we say it’s 0200, not 2600. Similarly, if it’s currently 0400, then 6 hours earlier it was not �0200 but 2200. The idea here is that if two numbers differ by 24 or a multiple of 24, then they are “equal.” We could simply write 26�2 but this could be confusing. So we write 26 � 2 (mod 24), and �2 � 22 (mod 24), or in words, 26 is congruent (or somehow “equal”) to 2 (modulo 24) and �2 is congruent to 22 (modulo 24). In arithmetic modulo 24, any number larger than 24 is congruent to some number less than 24 because we can always subtract a multiple of 24 from the larger number to get the smaller one. Similarly, any negative number is congruent to some positive number less than 24, and 24 is congruent to 0. This means that in arithmetic modulo 24, we need deal only with integers from 0 to 23.

We can choose any positive integer for the modulus and carry out arithmetic operations accordingly. Using a modulus of 4, for example, we would have 2�2�0 in our loose notation — a disturbing result if interpreted as conventional arithmetic. But when written 2�2 � 0 (mod 4), the meaning is clear.

As another example of modular arithmetic, consider this question: If today is Monday, what day of the week is it 185 days from now? The mod-ulus here of course is 7, the number of days in the week. So, mathemati-cally stated: 1�185 � ? (mod 7). The answer: 4 or Thursday. The answer is obtained by dividing the sum on the left side of the congruency by 7, using “long division,” and noting the remainder. Or, alternatively, the sum is di-vided by 7, and the decimal part of the result is then multiplied by 7.

An interesting quirk of modular arithmetic is that a number and the sum of its digits are congruent, modulo 9. This property is the basis for a for-merly well-known procedure (before the days of calculators and computers) for checking the correctness of hand multiplication — the rule for casting out nines, which states that the product of two numbers and the product of the sums of their digits must have the same remainder on division by 9.

Many computer languages have a built-in modular arithmetic function or operator. Typically called MOD, it returns the remainder from an integer division operation. In BASIC, for example, if we enter 5 MOD 2, we get 1 because 5 divided by 2 is 2 with a remainder of 1. The same computation is coded 5 2 MOD in Forth, 5 % 2 in Python, and MOD (5,2) in FORTRAN.

The following line of FORTRAN code by Henry Fliegel of The Aerospace Corporation inherently uses modular arithmetic by way of integer division to determine the Julian day (JD) number from the year, month, and day of an AD Gregorian calendar date, incorporating all leap year rules:

JD�367*Y�7*(Y�(M�9)/12)/4�3*((Y�(M�9)/7)/100�1)/4�275* M/9�D�1721029

And just how can the GPS end-of-week rollover be described using modular arithmetic? Very simply: 1023�1 � 0 (mod 1024).

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is quite rapid. A receiver will store a copy of the almanac to speed up initial acquisi-tion of satellites when it is switched on.

The GPS navigation message is sent at a relatively slow rate of 50 bits per second, taking 12.5 minutes for all of the infor-mation to be transmitted. To minimize the time it takes for a receiver to obtain an initial position, the ephemeris and satel-lite clock offset data is repeated every 30 seconds.

24The number of satellites in the current GPS baseline constellation. The GPS constellation went through a number of design alternatives even after the first satel-lites were launched with different numbers of orbit planes, satellites per plane, and orbit inclinations. The current design has four satellites, irregularly spaced, in six orbit planes. The orbit planes, labeled A through F, are spaced at 60° intervals around the equator with a nominal incli-nation to the equator of 55°. However, we have typically had a surfeit of satellites with more than 24 in operation since the mid-1990s. In fact, during 2008, as many as 31 satellites were transmitting healthy signals at the same time. However, al-though a modern GPS receiver should be able to handle a 32-satellite active con-stellation, there are limits imposed by the GPS Control Segment and some legacy military equipment that currently imposes a 30-satellite active constellation limit.

Although the number of active satellites is well in excess of 24, the constellation has been operated as a 24-satellite constellation without optimizing the orbit locations of the “bonus” satellites. In fact, several pairs of satellites are bunched together minimiz-ing geometrical performance. This is in the process of being changed. The GPS Wing recently announced the transition to a 24�3 or “Expandable 24” baseline constellation. Taking about 24 months to complete, six on-orbit satellites are being rephased within their respective orbit planes to improve the overall geometry of the active constellation so that the number of GPS satellites in view from anywhere on Earth will increase, enhancing the pos-

sibility of getting a position fix in partially obscured environments, and potentially improving the accuracy of fixes.

Of course, 24 is also the number of hours in the day during which GPS is available at any point on the Earth’s sur-face with good sky visibility. It is also the title of a popular American TV series, whose protagonist, Jack Bauer, frequently makes use of imaginary GPS tracking ca-pabilities.

40.3The scaling factor, which together with the signal frequency and the total electron content, is used to compute the delay ex-perienced by a GPS signal as it propagates through the ionized part of the Earth’s at-mosphere. The total electron content is the integrated electron density along the sig-nal’s path. Basically, it is the total number of electrons in a tube with a cross-sectional area of one square meter centered on the signal path. To a very good approxima-tion, the delay, in meters, is computed as

where TEC is the total electron content in so-called TEC units or TECUs (1016

electrons per square meter) and f is the sig-nal carrier frequency in MHz. The scaling factor is a function of the electron’s charge and mass and a constant of electromagne-tism theory called the permittivity of free space also known as the electric constant. The scaling factor is actually 40.308193 but this much precision is not generally needed in GPS calculations.

While the code signals are delayed, making pseudoranges longer than they would be in the absence of the iono-sphere, the phases of the signal carriers are advanced, make carrier-phase measure-ments shorter — but by exactly the same magnitude as the code delays.

TEC is highly variable both temporally and spatially. The dominant variability is diurnal following the variation in incident solar radiation. Maximum ionization oc-curs at approximately 1400 local time. On the ionosphere’s nighttime side, in the absence of solar radiation, free electrons and ions tend to recombine, thereby re-

ducing the TEC. The protonosphere, or uppermost region of the ionosphere, may contribute up to 50 percent of the electron content during the nighttime hours. Typi-cal nighttime values of vertical TEC for mid-latitude sites are of the order of 10 TECU or less with corresponding daytime values of the order of 100 TECU. How-ever, such typical daytime values can be exceeded by a factor of two or more, espe-cially in near-equatorial regions. TEC also varies seasonally with higher values during equinoxes.

1023This is the number of chips in the C/A-code. The C/A-, or coarse/acquisition-, code is one of the two legacy PRN rang-ing codes that have been transmitted by all GPS satellites. These PRN codes consist of sequences of binary values (zeros and ones) that, at first sight, appear to have been randomly chosen. But a truly random se-quence can only arise from unpredictable causes over which, of course, we would have no control, and which we could not duplicate. However, using a mathemati-cal algorithm or special hardware devices called tapped feedback registers, we can generate sequences that do not repeat until after some chosen interval of time. Such sequences are termed pseudorandom. The apparent randomness of these sequences makes them indistinguishable from cer-tain kinds of noise such as the hiss heard when a conventional AM radio is tuned between stations.

The C/A-code is a sequence of 1,023 binary digits, or chips, which is repeated every millisecond. This means that the chips are generated at a rate of 1,023 mil-lion per second and that one chip has a duration of about 1 microsecond.

The C/A-code is generated by two 10-cell feedback registers referred to as G1 and G2. A delayed version of the G2 se-quence is obtained by binary adding the contents of a pair of tapped G2 cells and binary adding that result to the output of G1. That becomes the C/A-code. The various alternative pairs of G2 taps (de-lays) are used to generate the complete set of 36 unique PRN C/A-codes. There are

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actually 37 PRN C/A-codes, but two of them (34 and 37) are identical. The first 32 codes are assigned to satellites. Codes 33 through 37 are reserved for other uses such as for ground transmitters. This family of codes is a subset known as Gold codes, which have the property that any two have a very low cross correlation (are nearly orthogonal). The term for the codes comes from the inventor, Robert Gold, not from their lustrous properties.

The C/A-code is modulated only onto the L1 carrier, unlike the P(Y)-code (see 235,469,592,765,000) which appears on both L1 and L2. However, beginning with the first Block IIR-M or modernized Block IIR satellite, a new civil code, L2C or L2 Civil, has been transmitted on the L2 frequency. The future Block IIF satel-lites will also transmit L2C.

1023 is also the maximum value of the GPS week. This is the number of full weeks that have elapsed since the GPS Time zero point of midnight UTC be-ginning January 6, 1980 — but with a special counting procedure. GPS weeks are numbered consecutively with week zero starting on January 6 and ending on January 12, 1980. The GPS week, together with the Z-count (see 403199), specifies an epoch or event related to GPS signals or measurements. The current GPS week is included in subframe one of the navigation message, which — along with other subframes containing satellite clock, ephemeris data, and other user-required information — is transmitted every 30 seconds. Only 10 bits are used to represent the GPS week, and so the largest possible week number is 1023 (210�1). In other words, the GPS week number is modulo 1024 (see the “Modular Arithmetic” side-bar). At the end of week number 1023, the week number rolls over to zero. This first occurred on August 21/22, 1999, and caused difficulties for some GPS receivers as their manufacturers had failed to ac-count for the “end-of-week rollover” in receiver firmware. The next occurrence will be in April 2019. By that time, the new Civil Navigation (CNAV) message will be in use, in which the GPS week number is represented as a 13-bit value,

meaning it rolls over after 8192 weeks, or about every 157 years.

Although officially the GPS week num-ber is still modulo 1024, some agencies, such as the International GNSS Service, prefer to use a running count of the GPS week, ignoring the rollover. The number of the week beginning April 4, 2010, is then alternatively given as 1578 or 554. Or, mathematically speaking (see sidebar), 1578 � 554 (mod 1024).

1176.45The L5 carrier frequency in megahertz. The L5 carrier frequency is obtained by electronically multiplying the satellite 10.23 MHz standard frequency by 115. It is the lowest and the newest of the GPS frequencies and is used for the new civil-only GPS signal. The addition of the L5, or Link 5, civil signal to the suite of signals transmitted by the satellites is a key feature of GPS modernization. The introduction of such a signal on a differ-ent carrier frequency than that used by the legacy L1 GPS signal was proposed in the 1995 reports by the U.S. National Research Council and the National Acad-emy of Public Administration on the fu-ture of GPS. The reports argued that an unencrypted signal on a second frequency would offer civil users the benefit of iono-spheric delay correction, wide-lane car-rier-phase ambiguity resolution, improved interference rejection, and faster accuracy recovery in multipath environments. The frequency is in a protected aeronautical ra-dionavigtion services band and, unlike L2, means that L5 can be used for safety-of-life services. The L5 signal will be standard on all Block IIF and future satellites. An L5 demonstration payload was included on Block IIR-M satellite SVN49 to secure the L5 frequency under the rules of the Inter-national Telecommunication Union.

1227.60The L2 carrier frequency in megahertz. The L2, or Link 2, carrier is modulated with the P(Y)-code. Additionally, starting with the Block IIR-M satellites, a new civil ranging code, L2C, is being transmitted on L2 along with the new military M-

code. These new signals are also part of the GPS modernization effort. The L2 carrier frequency is obtained by electroni-cally multiplying the satellite 10.23 MHz standard frequency by 120.

1381.05The L3 carrier frequency in megahertz. This frequency is used in conjunction with the GPS satellites’ secondary pur-pose, which is to detect nuclear detona-tions. The L3 carrier frequency is obtained by electronically multiplying the satellite 10.23 MHz standard frequency by 135.

1575.42The L1 carrier frequency in megahertz. The L1, or Link 1, carrier is modulated with the C/A-code and the P(Y)-code. Starting with the Block IIR-M satellites, the new military M-code is also transmit-ted on L1. The L1 carrier frequency is ob-tained by electronically multiplying the satellite 10.23 MHz standard frequency by 154. If you’ve been counting, you’ll have noticed that we didn’t list an L4 fre-quency. L4 has never been implemented but it has been studied. For example, a fre-quency of 1841.40 MHz (10.23�180) was once considered for ionospheric cor-rection.

403199The maximum value of the GPS time of week count. The GPS satellites count and communicate GPS Time in a unique manner that is ultimately related to how they generate the PRN ranging codes. As described below, the P-code is generated by combining two shorter PRN codes, X1 and X2, which are clocked in phase at a chipping rate equal to the satellite’s 10.23-MHz oscillator frequency. X1 has a repeti-tion interval, or period, of 1.5 seconds — a fundamental GPS timing unit. The start of each 1.5-second interval identifies an epoch. The number of X1 epochs since the beginning of the week is called the time of week (TOW) count, which runs from zero to 403,199 at the end of week. The TOW count returns to zero coincident with the resetting of the PRN codes.

The TOW count can be represented as

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a 19-bit binary number, a truncated ver-sion (the 17 most significant bits) of which is part of the handover word (HOW) that a satellite transmits every six seconds. The HOW appears as the second word in each data subframe of the navigation message. These 17 bits correspond to the TOW count at the X1 epoch that occurs at the start of the immediately following subframe, and so effectively preannounces the arrival of a time marker, just like tele-phone “speaking clocks” and shortwave radio time and frequency stations.

The TOW count by itself cannot be used to unambiguously establish the date of an event. It can only time an event at modulo 604,800 seconds [(403199�1)�1.5] because it is reset every week. This time ambiguity is re-duced by noting the number of full weeks that have elapsed since January 6, 1980 modulo 1024 — the GPS week number (see 1023). The TOW count and the GPS week number combine to form the 29-bit Z count. The 19 least-significant bits are the TOW count and the 10 most-signifi-cant bits are the GPS week number.

299,792,458The speed of light in meters per second. This is the speed with which all electro-magnetic radiation propagates in a vac-uum. Until 1983, the speed of light was measured experimentally using adopted standards for the length of the second and the length of the meter. However, com-pared to the second, the definition of the meter had a large uncertainty. So in 1983, the 17th General Assembly of Weights and Measures defined the meter as the dis-tance travelled by light in a vacuum dur-ing 1/299,792,458 of a second, fixing the speed of light at 299,792,458 meters per second — exactly. This constant is used by a GPS receiver, for example, to convert the measured signal propagation time in seconds to a pseudorange in meters.

235,469,592,765,000(Or 2.35469592765000 � 1014 in scientific notation). This is the number of chips in the P-code if it were allowed to continue without being reset. The P-, or precision

code, is one of the two legacy PRN rang-ing codes that have been transmitted by all GPS satellites. The other is the C/A-code, already discussed.

The P-code is actually the product of two PRN codes, each of which is gener-ated with a pair of feedback registers. The X1 code has a length of 15,345,000 chips while the X2 code has a length of 15,345,037 or 37 chips longer. So the complete P-code has a length equal to the product of the lengths of the X1 and X2 codes, or 235,469,592,765,000. The codes are clocked at a rate of 10.23 MHz so that each chip has a length of about 0.097752 microseconds. This means the pattern of chips in the full P-code would not repeat for almost 266 days. Each satel-lite is assigned a unique one-week segment of the P-code, which is reset at Saturday/Sunday midnight each week. The indi-vidual P-codes have low cross-correla-tions with each other. In other words, no significant segments of the P-code of one satellite matches that of another.

Before transmission, a P-code chip sequence is encrypted to form a new se-quence called the Y-code. The combined sequence is usually referred to as P(Y). Although civil GPS receivers cannot use conventional correlation procedures to acquire and track the P(Y) code, they can use knowledge of the underlying P-code sequence and C/A-code tracking on L1 to produce pseudorange and carrier-phase measurements on both the L1 and L2 fre-quencies.

�-1The square root of -1. This is the unit of imaginary numbers. The concept of imaginary numbers, actually known to the ancient Greeks, was introduced in the effort to solve algebraic equations. Not all equations can be solved using real numbers. In particular, x2��1 has no real-valued solution. But we can say some solution exists and represent it by the sym-bol i. (Mathematicians and physicists use this symbol whereas electrical engineers prefer j, since i usually describes a varying electrical current.) Then i has the prop-erty — by definition — that its square is

�1. Of course, that equation would also permit the solution �i. An imaginary number — sometimes called pure imagi-nary — is any number of the form bi, where b is a non-zero, real number. A real number, a, and an imaginary number, bi, can be combined into a complex number, a�bi, or a�ib, the more usual notation. Using complex numbers and a set of rules governing their manipulations, any alge-braic equation can be solved.

It is useful to consider the real and imaginary parts of a complex number to be orthogonal so that we can represent a complex number geometrically on a plane — the complex plane — where the real component is plotted on the x-axis and the imaginary component on the y-axis. We can then represent a 2-di-mensional vector as a complex number, with one component considered real and the other imaginary. The magnitude or modulus of the vector, r, is the positive square root of the sum of the squares of the real and imaginary components with the vector making an angle, φ, with respect to the positive real axis.

It can be easily shown that.

This is Euler’s famous formula, which provides an enlightening connection be-tween plane geometry and algebra.

And, we may also write any complex number in the form

or even more compactly as .If the vector rotates counterclockwise

with angular speed ω, its projection onto the real axis generates a sine wave. The modulus of this vector is the amplitude of the oscillations, while its argument is the total phase, φ�ωt �θ, where t is time. The phase constant θ represents the angle that the vector forms with the real axis at t�0. This representation of a sine wave as a phase vector, or phasor, finds great util-ity in signal theory including descriptions of the propagation of radio waves such as those emitted by GPS satellites. �

Further ReadingFor references related to this article, go to gpsworld.com and click on Innovation under Resources in the left-hand navigation bar.

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During the winter of 1838–39, the great Native American Cherokee Nation trekked

across southern Illinois, in a forced removal by the U.S. government from their ancestral homeland in Tennessee. Harried, unequipped, and unsupported by their captors, thousands died on the Trail of Tears. Burial records were not kept, and burial locations remain lost to this day. Local history suggests that some Illinois settlers allowed the Cherokee to bury their dead on small plots of land adjacent to their own family cemeteries. One such plot, the Campground Presbyterian Church cemetery near Anna, Illinois, may contain unmarked Cherokee graves.

Researchers from Southern Illinois University and Eastern Illinois University used GPS to navigate and precisely map probes of a ground-penetrating radar (GPR) instrument in the cemetery. We monumented the geophysical survey grids using real-time kinematic (RTK) DGPS. Site topography was also mapped

using GPS, as were the individual cemetery headstones. Adding geographic information systems (GIS) software to our mix to map cemetery headstone distribution and record headstone attributes (dates of death, names), we could determine chronological gaps within the cemetery that coincide with the probable emigration of the Cherokee.

GPR and electromagnetic conductivity produced contour plots of high-resolution magnetic gradient data. Small dipolar anomalies detected are typically related to disruptions within near-surface soil horizons and may correspond to locations of shallow graves: the lost final resting places of many Cherokee.

By close examination of the geophysical survey data and the anomalies produced from them, we were able to present plausible if not possible locations of several gravesites. However, at this time, and for obvious reasons, the actual location must remain secure and cannot be published.

The top right figure shows a mosaic of amplitude depth slices at .30–.70 meter

intervals from processed interpolated 250-MHz GPR profile data. White rectangles denote known graves. Most marked graves were imaged, although some were represented as more subtle anomalies on this display. Some possible unmarked graves were interpreted at UTM coordinates xxxx, yyyy.

The cemetery is within working distance of CORS station ILCB at Southern Illinois University. Two RTK GPS units communicating with the station via CDMA cellular radio used real-time differential corrections along a variable baseline length of approximately 28.5 kilometers, enabling mapping of the site at centimeter-accuracy resolution.

Survey data were edited, mapped, and analyzed with a GIS. Family genealogy polygons were generated using last names, to produce family distribution plots throughout the cemetery.

ManufacturersThe study, supported by a National Park Service grant with Southern Illinois Uni-versity at Carbondale, used two Leica1250 RTK GPS units, a Leica TC802robotic total station, and ESRI ArcGIS ArcInfo. Equipment was provided by Kara Company of Countryside, Illinois. �

Lost Graves, Trail of TearsSteven M. Di Naso, Vincent P. Gutowski, Harvey Henson, and Ryan Leonard

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