Download - GPS-Signal-Reference-Time and Codes
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• Position is usually given as geographic
coordinates, Latitude/Longitude
• Datums
–WGS84
– Many others usually available
• Projections
– UTM
– State Plane
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Latitude and Longitude
Defining a Location
units of measurement are Degrees
equator
Prime
Meridian
Degree is divided into 60 Minutes, Minute is divided into 60 Seconds
Authalic Sphere
•Cartographer realised that earth is not a
perfect Sphere and hence they visualised it
as a perfect sphere with Surface area same
as that of the real earth
•This authalic Sphere has a radius of 6371
km and hence circumference of 40,030.2
km.
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Earth As an Ellipsoid
•Newton (1670) proposed that the earth would be flattened
because of rotation. The polar flattening would be1/300 th of
the equatorial radius.
• Actual flattening is about 21.5km.
•The amount of the polar flattening as per (WGS [world geodetic
system] 84) is 1/ 298.257.
WGS 84 ellipsoida = 6,378,137m
b = 6,356,752.3m
equatorial diameter = 12,756.3km
polar diameter = 12,713.5km
equatorial circumference =
40,075.1km
surface area = 510,064,500km2
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Graticule
•The imaginary network of parallels and meridians on the earth
and their projection onto a flat map is called graticule.
•The properties of the graticule are used to compute distance,
direction and area.
•Assume the earth to be spherical.
Definition of Ellipse
Area of an Ellipse
πab
a < b
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Eccentricity of an Ellipse is a measure of how close it is to Circular Shape
? Eccentricity of a Circle 0
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Geoidal Earth
•Geoid (“earth like”): Sea level equi-potential surface.
•Gravity is everywhere equal to its strength at mean
sea level.
•The surface is irregular, with difference of -104m at
the southern tip of India to a Maximum of 75 m near
Guinea.
• The direction of gravity everywhere is not directed
towards the centre of the earth.
Geoid surface computed from the GEM-T3 gravity model by
the NASA/Goddard Space Flight Centre. (Cited in Robinson, et al., 2002)
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In the fields of chronology an epoch
means an instant in time chosen as the origin
of a particular era. The "epoch" then serves as
a reference point from which time is measured.
Time measurement units are counted from the
epoch so that the date and time of events can
be specified unambiguously.
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epoch date uses rationale for selectionJanuary 1, 0 MATLAB, Turbo DB and tdbengine
January 1, 1 Symbian, Microsoft .NET, REXX This epoch date is known as Rata Die
January 1, 1601 NTFS, COBOL, Win32/Win64
1601 was the first year of the 400-year
Gregorian calendar cycle at the time
Windows NT was made. [7]
December 31, 1840 MUMPS programming language
1841 was roughly the birthyear of the world's
oldest living person when the language was
designed.[8]
November 17, 1858VMS, United States Naval Observatory, other astronomy-
related computations
November 17, 1858 equals the Julian Day
2,400,000.[9]
December 30, 1899 Microsoft COM DATE
Technical internal value used by Microsoft
Excel; to simplify calculations by falsely
assuming 1900 to be a leap year.[10]
January 0, 1900 Microsoft Excel[10], Lotus 1-2-3
While logically January 0, 1900 is equivalent
to December 31, 1899, these systems do not
allow users to specify the latter date.
January 1, 1900 Network Time Protocol, IBM CICS, Mathematica, RISC OS
January 1, 1904Apple Inc.'s Mac OS through version 9, Palm OS, MP4,
Microsoft Excel (optionally)[10]
1904 is the first leap year of the twentieth
century.[11]
January 1, 1960 S-Plus, SAS
December 31, 1967 Pick OS
January 1, 1970
Unix time, used by UNIX, Linux, other UNIX-like systems, Mac
OS X, as well as Java, JavaScript, C and PHP Programming
languages
January 1, 1978 AmigaOS
January 1, 1980 MS DOS, OS/2, FAT16 and FAT32 filesystem
January 6, 1980 Qualcomm BREW, GPS
January 1, 1981 Acorn NetFS
January 1, 2001 Apple's Cocoa framework2001 is the year of the release of Mac OS X
10.0.
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? Time
• Time has been defined as the continuum in which events occur in
succession from the past to the present and on to the future.
•Time has been a major subject of religion, philosophy, and science, but
defining it in a non-controversial manner applicable to all fields of study has
consistently eluded the greatest scholars.
•Time is one of the seven fundamental physical quantities in the
International System of Units
Temporal measurement has occupied scientists and technologists, and
was a prime motivation in navigation and astronomy. Periodic events
and periodic motion have long served as standards for units of time.
Examples include the apparent motion of the sun across the sky, the
phases of the moon, the swing of a pendulum, and the beat of a heart.
Currently, the international unit of time, the second, is defined in terms of
radiation emitted by caesium atoms . Time is also of significant social
importance, having economic value ("time is money") as well as
personal value, due to an awareness of the limited time in each day and
in human life spans.
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The second is the duration of 9,192,631,770 periods of the radiation
corresponding to the transition between the two hyperfine levels of the ground
state of the caesium 133 atom.
At its 1997 meeting, the CIPM affirmed that this definition refers to a caesium
atom in its ground state at a temperature of 0 K.
Prior to 1967, the second was defined as:
the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12
hours ephemeris time.
The current definition of the second, coupled with the current definition of the
metre, is based on the special theory of relativity, which affirms our space-
time to be a Minkowski space.
International Atomic Time (TAI) is a statistical atomic time scale based on a
large number of clocks operating at standards laboratories around the world
that is maintained by the Bureau International des Poids et Mesures; its
unit interval is exactly one SI second at sea level. The origin of TAI is such that
UT1-TAI is approximately 0 (zero) on January 1, 1958. TAI is not adjusted for
leap seconds. It is recommended by the BIPM that systems which cannot
handle leapseconds use TAI instead.
Coordinated Universal Time (UTC) is defined by the CCIR (Consultative
Committee on International Committee) Recommendation 460-4 (1986). It
differs from TAI by the total number of leap seconds, so that UT1-UTC stays
smaller than 0.9s in absolute value. The decision to introduce a leap
second in UTC is the responsibility of the International Earth Rotation
Service (IERS). According to the CCIR Recommendation, first preference
is given to the opportunities at the end of December and June, and second
preference to those at the end of March and September. Since the system
was introduced in 1972, only dates in June and December have been
used. TAI is expressed in terms of UTC by the relation TAI = UTC + dAT,
where dAT is the total algebraic sum of leap seconds.
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The Global Positioning System (GPS) epoch is January 6, 1980 and is
synchronized to UTC. GPS Time is NOT adjusted for leap seconds.
BEFORE THE 2012 LEAP SECOND: GPS-UTC IS 15 (GPS IS AHEAD OF
UTC BY 15 SECONDS) AFTER THE 2012 LEAP SECOND: GPS-UTC WILL
BE 16 (GPS WILL BE AHEAD OF UTC BY 16 SECONDS)
As of 1 January 2008, and until the leap second of June 30 2012
TAI is ahead of UTC by 34 seconds.
TAI is ahead of GPS by 19 seconds.
GPS is ahead of UTC by 15 seconds.
After 30, June 2012,
TAI is ahead of UTC by 35 seconds.
TAI is ahead of GPS by 19 seconds.
GPS is ahead of UTC by 16 seconds.
•Definition:
• GPS time is synchronized with UTC (within ~1 microsecond), but does
not contain leap-seconds. GPS Time is currently ahead of UTC by ‘N’
seconds due to the leap-seconds that have been inserted into UTC. The
GPS epoch is identified as the number of seconds that have elapse since
the previous Saturday/Sunday midnight. GPS weeks start with week 0
on January 6, 1980.
• GPS satellites are equipped with atomic clocks and contribute to the
TAI* average. Parameters are uploaded to each GPS satellite to allow
the satellite to convert the reading of its atomic clock to GPS Time.
GPS Time
•TAI: International Atomic Time
( French Origin: Temps Atomique International )
UTC: Coordinated Universal Time ( CUT)
Temps Universel Coordonne ( TUC) French
Compromised as : UTC
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UT1: Time given by rotation of Earth. Noon is “mean” sun crossing meridian at Greenwich
UTC: UT Coordinated. Atomic time but with leap seconds to keep aligned with UT1
UT1-UTC must be measured
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� Definition:
� Terrestrial Time (TT) is a dynamic time scale based upon
the orbital motions of the Earth, Moon, and planets. It is
defined by clocks using SI seconds on the surface of the
Earth.
� Epoch is 00:00:00 January 1, 1977
� TT = TAI + 32.18 sec
(Note seconds in SI units is defined as the duration of 9,192,631,770 cycles of radiation of cesium 133)
Terrestrial Time (TT)
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-4
-2
0
2
4
6
8
1980 1985 1990 1995 2000 2005
Length-of-day (ms)
Year
Measured
Atmospheric Angular Momentum (converted to LOD)
-4
-2
0
2
4
6
8
1980 1985 1990 1995 2000 2005
Length-of-day (ms)
Year
Measured
Atmospheric Angular Momentum (converted to LOD)
LOD compared to Atmospheric Angular Momentum
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Integral of LOD is UT1 (or visa-versa)
If average LOD is 2 ms, then 1 second difference between UT1 and atomic time develops in 500 days
Leap second added to UTC at those times.
Jumps are leap seconds, last one before 2006 was 1999.
Historically had occurred at 12-18 month intervals
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1992.00 1994.00 1996.00 1998.00 2000.00 2002.00 2004.00 2006.00
UT1-UTC (s)
UT1-UTC (s)
Year
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1992.00 1994.00 1996.00 1998.00 2000.00 2002.00 2004.00 2006.00
UT1-UTC (s)
UT1-UTC (s)
Year
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Year Jun 30 Dec31
1972 +1 +1
1973 0 +1
1974 0 +1
1975 0 +1
1976 0 +1
1977 0 +1
1978 0 +1
1979 0 +1
1980 0 0
1981 +1 0
1982 +1 0
1983 +1 0
1984 0 0
1985 +1 0
1986 0 0
1987 0 +1
1988 0 0
1989 0 +1
1990 0 +1
1991 0 0
1992 +1 0
1993 +1 0
1994 +1 0
1995 0 +1
1996 0 0
1997 +1 0
1998 0 +1
1999 0 0
2000 0 0
2001 0 0
2002 0 0
2003 0 0
2004 0 0
2005 0 +1
2006 0 0
2007 0 0
2008 0 +1
2009 0 0
2010 0 0
2012 0 +1
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Overview of Satellite Transmissions
• All transmissions derive from a fundamental frequency of 10.23 Mhz
– L1 = 154 x 10.23 = 1575.42 Mhz
– L2 = 120 x 10.23 = 1227.60 Mhz
– L5 = 115 x 10.23 = 1176.45 MHz
• All codes initialized once per GPS week at midnight from Saturday to Sunday
– Chipping rate for C/A is 1.023 Mhz
– Chipping rate for P(Y) is 10.23 Mhz
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• L5 carrier (1176.45 MHz) =115x10.23(Safety Of Life Applications)
CARRIER WAVES
And C/A code
Schematic of GPS codes and carrier phase
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GPS Signal Characteristics
, L2
M-Code
• Satellites will transmit two distinct signals from two antennas: one for whole
Earth coverage, one in a spot beam.
• Modulation is binary offset carrier
• Occupies 24 MHz of bandwidth
• It uses a new MNAV navigational message, which is packetized instead of
framed, allowing for flexible data payloads
• There are four effective data channels; different data can be sent on each
frequency and on each antenna.
•I t can include FEC and error detection
• The spot beam is ~20 dB more powerful than the whole Earth coverage beam
• M-code signal at Earth's surface: –158 dBW for whole Earth antenna, –138 dBW
for spot beam antennas
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3rd civil signal on L5 (1176.45 MHz) =115x10.23Better accuracy under noisy and multipath conditions
Should improve real-time kinematic (RTK) surveys
Modulations
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Digital Modulation Methods
• Amplitude Modulation (AM) also known as amplitude-shift keying. This method requires changing the amplitude of the carrier phase between 0 and 1 to encode the digital signal.
• Frequency Modulation (FM) also known as frequency-shift keying. Must alter the frequency of the carrier to correspond to 0 or 1.
• Phase Modulation (PM) also known as phase-shift keying. At each phase shift, the bit is flipped from 0 to 1 or vice versa. This is the method used in GPS.
Modulation Schematics
AM
FM
PM
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? Code• Stream of binary digits known as bits or chips
– Sometimes called pseudorandom noise (PRN) codes
• C/A code on L1
• P code on L1 and L2
• Phase modulated
• NEW (2008-09)
• C/A code on L2 (L2C)
• M Code ( Military Use )
• L5 (GPS IIF, 27 May 2009 on SVN49)
C/A Code
• 1023 binary digits
• Repeats every millisecond
• Each satellite assigned a unique C/A-code
– Enables identification of satellite
• Available to all users
• Sometimes referred to as Standard Positioning
Service (SPS)
• Used to be degraded by Selective Availability (SA)
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P Code
• 10 times faster than C/A code
• Split into 38 segments
– 32 are assigned to GPS satellites
– Satellites often identified by which part of the message they are broadcasting
• PRN number
• Sometimes referred to as Precise Positioning Service (PPS)
• When encrypted, called Y code
– Known as antispoofing (AS)
Future Signal
• C/A code on L2 (L2C)
• 2 additional military codes on L1 and L2
• 3rd civil signal on L5 (1176.45 MHz)
– Better accuracy under noisy and multipath
conditions
– Should improve real-time kinematic (RTK) surveys
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GPS Calendar and Almanac Data Utility
http://www.ngs.noaa.gov/CORS/Gpscal.html
http://www.navcen.uscg.gov/GPS/almanacs.htm
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The L2C Initiative• 1996 – Presidential Decision Directive
– "encourage acceptance and integration of GPS into peaceful civil, commercial and scientific applications worldwide; and to encourage private sector investment in and use of U.S. GPS technologies and services."
– “committed the U.S. to discontinuing the use of SA by 2006 with an annual assessment”
• With S/A off, ionospheric error becomes significant
• 1998 – V.P. Gore announced L2 as 2nd civil signal• 1999 – V.P. Gore “for launch beginning in 2003”• 2001 – L2C was defined & presented to the public
– Two public meetings, ION paper, GPS World article,ICD-GPS-200 update, NAVCEN WEB posting
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user
position,
velocity, and time (PVT)
determination
The accuracy with which a user receiver can determine its position or velocity, or
synchronize to GPS system time, depends on a complicated interaction of various
factors. In general, GPS accuracy performance depends on the quality of the
pseudorange and carrier phase measurements as well as the broadcast navigation
data. In addition, the fidelity of the underlying physical model that relates these
parameters is relevant. For example, the accuracy to which the satellite clock offsets
relative to GPS system time are known to the user, or the accuracy to which satellite-
to-user propagation errors are compensated, are important. Relevant errors are
induced by the control, space, and user segments.
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What is the smallest possible unit of time?
Is time infinitely divisible, or is there a smallest possible unit of time measurement? Is space infinitely divisible, or is there a
smallest possible unit of spatial measurement? The following thought experiment suggests that neither space or time are
infinitely divisible.
Suppose I want to “demonstrate” the “value” of any very large number by counting down one number at a time to zero
and that I want to do this so that the count will not take longer than a typical working day, say 10 hours/600
minutes/36,000 seconds/3.6 x 104 seconds.
Lets start by taking a number that is around 3.6 x 1010. To count down from this number in the time set we need to count
106 numbers each second. This means that each number in the final column of our counting device needs to be displayed
for 10-6 second. During this period light will travel around 300m.
What if our number is a bit larger, say around 3.6 x 1020. To count down from this number in the time set we need to count
1016 numbers each second. This means that each number in the final column of our counting device needs to be displayed
for 10-16 second. During this period light will travel around 300nm. But 300nm is less than half the wavelength of visible
light – humans could never see that the number had changed from looking at the lowest digit.
Theoretically there is no limit to the size of number we could want to count down in our experiment. What if our number is
a bit larger, say around 3.6 x 1030. To count down from this number in the time set we need to count 1016 numbers each
second. This means that each number in the final column of our counting device needs to be displayed for 10-26 second.
During this period light will travel around 300 x 10-10nm. But 300 x 10-10nm is so small that it is probably not detectable by
anything a human could make. Just how small is the smallest measurable distance? Unfortunately when we get down to
the size of things like photons we are into quantum mechanics, with its consequential uncertainty of position and hence
size. The Proton Compton wavelength, however, is 10-6nm, so we are thinking here of something orders of magnitudes
smaller than a proton.
If we consider the Proton Compton wavelength (or any of the other Compton wavelengths, such as those for neutron and
the marginally smaller tau) as the smallest measurable thing there is, and compare this with the speed of light, 3 x 108m/s,
can we come up with a smallest possible measurable unit of time? There would seem to be no more than 3 x1023
measurable units within the space covered by light in a second. Doesn’t this imply that the shortest measurable time is 3 x
10-24s?