Download - Surveying, GPS and GNSS Geomatics lectures
APG3016C
SURVEYING II
≈ 30 Lectures , 4 Assignments
Recommended Texts:
Surveying : H Kahmen & W Faig
GPS Theory & Practice : B Hofmann-Wellenhof, H Lichtenegger & J
Collins
+ many other texts
1
Monday to Friday: 10h00 to 10h45
Venue: GTL
Practical assignments: Wednesday afternoons,
see Vula calendar
Tests: see Vula calendar
Surveying 2 lecture times
Surveying 2 outline of modules
Module 1. History of surveying in southern Africa
Module 2. Advanced instrumentation
Module 3. GNSS basic principles and the Global
Positioning System (GPS)
Module 4. GNSS Differential data processing
techniques
Module 5. GNSS Carrier Phase data processing
techniques
Module 6: Other GNSS systems
3
1. Referencing Workshop
2. Essay: History of surveying / Walk up
Table Mountain
3. Assignment: Robotic Total Stations
4. Ntrip VRS RTK GPS
See Vula calendar
Assignments4
International: essays
National: readings on Vula
Module 1: History of Surveying5
Laser instrumentation
Robotic total stations
Inertial positioning systems and gyroscopy
Module 2: Advanced instrumentation6
Basic Concepts of GNSS ( GPS, Glonass,
other systems
Satellite Positioning
GPS space and control segments
GPS products and policy
GPS signals
Module 3: Principles of Global Navigation
Satellite Systems and GPS7
Mathematical principles
Biases and Errors
Differential Solutions (DGPS) Principles
Virtual reference stations
Data transmission media and formats
Space/satellite-Based Augmentation Systems (SBAS)
Ground-Based Augmentation Systems (GBAS)
Module 4: Differential Data Processing
Techniques8
Mathematical principles and differencing carrier phase
observation equations
Carrier phase data errors/biases and mitigation
Surveying methods:
integer ambiguity resolution
recovering L2
static GPS
kinematic positioning
network RTK/virtual reference stations
Practical aspects of GPS surveying
Module 5: Carrier Phase Data
Processing Techniques9
GLONASS
Galileo
Compass
Others proposed
Module 6: Other GNSS10
International: essays
National: readings on Vula
Module 1: History of Surveying11
La Caille and
Cassini de Thury
observing zenithal
stars for latitude
determination
National History of Surveying12
La Caille measuring
a baseline in France
National History of Surveying13
La Caille’sArc at the Cape
National History of Surveying14
Maclear
Triangulation end point at
Klypfontein
Cannon base station in
Golden Acre in Cape
Town
Teastern pyramid marker
of the Baseline
15
Baseline measurement16
17
National History of Surveying
H S Williams ( 1982), South African national report to the International Association of Geodesy
(IAG)
18
National History of Surveying
H S Williams ( 1982), South African national report to the International Association of Geodesy
(IAG)
19
National History of Surveying
H S Williams ( 1982), South African national report to the International Association of Geodesy
(IAG)
20
National History of Surveying
H S Williams ( 1982), South African national report to the International Association of Geodesy
(IAG)
21
Laser instrumentation
Robotic total stations• Including your seminars
Inertial positioning systems and gyroscopy
Module 2: Advanced instrumentation22
Laser Ranging: distance meters
Pulsed IR laser
Short range – up to 100m
Precision: 1mm to 3mm
Hand or tripod mounted
Some units have tilt sensors
Can be linked to GPS
Application in sectional title
surveys
from: www.leica-geosystems.com
23
Laser Ranging: EDM/electronic
tacheometers
Pulsed or Continuous Wave laser
Reflectorless or with prism
Medium range –
up to 1km reflectorless
up to 5km with prism(older CW models up to 25km)
Precision:
1mm to 3mm ± 1 to 2ppm
Integrated distance & angle measurement
Can be linked to GPS
from: www.agageo.com
24
Visible IR laser
Rotating beam, with tilt sensor
Can be set to specified gradient
Precision: 10" to 60"
Range: up to 200m
from: www.spectraprecision.com
Laser levelling
Construction sites:
Rotating laser beam 360 deg
inside/ outside constructions – transfer line of constant height
some can be tilted –transcribe a tilted plane
25
from: www.afgen.co.za
Laser alignment
Visible IR laser
Used to align drilling and boring machines
Range up to 1km, typically 200m
Spot size at 200m: 15mm
26
from: www.leica-geosystems.com
Laser alignment
Plumbing/centring of Theodolite
“vertical” laser beam
Position to middle of ground target
Relies on instrument to be correctly adjusted and axes and bubbles checked
27
Airborne laser mapping (LIDAR)
Read the excerpt in
the notes
Combination of
sensors
Integrated airborne
system
from: www.southernmapping.com
28
INS/IMU to get attitude (pitch, roll, yaw)
Differential GPS to get position
Can penetrate forest canopy
Can get multiple returns (e.g. powerline plus ground)
Applications:
DEMs
Corridor mapping (powerlines, railway lines, etc)
Forestry, coastal mapping
Airborne laser mapping (LIDAR)
Laser scanning
tS c + refraction and calibration corrections
2
Pulsed laser beam
Rotating mirror creates a swath along flight path
Return pulse(s) detected with photodiode
Distance:
Thousands of points per second
Swath width – up to 45° from vertical
Elevation accuracy: 10cm to 20cm
30
Robotic Total Stations
See Seminar Presentations!
Motorised with automatic target tracking only
Motorised with automatic target finding and tracking
Fully robotic total station
from: www.topcon-positioning.eu
31
IMU: inertial measurement unit : basic unit in:
IPS: Inertial Positioning Systems
ISS: Inertial Surveying Systems
INS: Inertial Navigation Systems
Inertial Positioning Systems
(IPS, ISS, INS, IMU)32
Consists of:
Three orthogonal accelerometers
Three orthogonal gyroscopes
Initially developed (and still used) for aircraft navigation
Vehicle-based units developed for military (passive)
Adapted for civilian use – low relative accuracy (±0.5m) surveying
Inertial Positioning Systems
(IPS, ISS, INS, IMU)33
Accelerometer
Double integration of acceleration over time yields distance travelled
Integration errors cause drift, and accumulation of error over time
Vertical accelerometer cannot distinguish acceleration from gravity – need to stop periodically to measure gravity - ZUPT
34
Gyroscope
MECHANICAL:
Spinning mass, maintains orientation with respect to inertial reference frame
Gimbal-mounted, senses change in orientation, servo-motors used to restore platform to null position
Local level system – V, N, E
Mechanically complicated, calculations simple
from: AD King: Inertial Navigation – Forty years of evolution
36
RING LASER:
Laser beam sent through glass tubes in opposite directions
Rotation of assembly causes small frequency difference between the two beams (Sagnaceffect)
Change of frequency is a measure of change of orientation
Strap-down system – fixed to vehicle
Mechanically simple, robust, but need high update rate and complex data processing
from: AD King: Inertial Navigation – Forty years of evolution
Gyroscope37
Applications in surveying
Inertial Surveying Systems (ISS, IPS) are no longer used (expensive, low accuracy)
INS/IMU used in conjunction with GPS for land navigation in areas of poor signal reception – IMU interpolates gaps in GPS coverage, GPS calibrates INS
GPS/IMU used for direct georeferencing of airborne sensors (e.g. cameras) – providing position and attitude
38
Basic Concepts of GNSS ( GPS, Glonass,
other systems
Satellite Positioning
GPS space and control segments
GPS products and policy
GPS signals
Module 3: Principles of Global Navigation
Satellite Systems and GPS39
Satellite positioning
Z
X
Y
Greenwich
M eridian
Point
Geocentre
Position
vector
M ean rotation
axis
Point Positioning
Relative Positioning
Z
X
Y
Greenwich
M eridian
Geocentre
M ean
rotation
axis
interstation
vector
Satellite positioning
Satellite Positioning
ri th
point
j th
satellite
geocentre
R i R j
i
j
Y
Z
X
Satellite positioning
Satellite observations
Directions:
Photograph satellite against a star background.
Interpolate direction to satellite from known co-ordinates (right ascension, declination) of stars. No longer used.
Ranges:
Pulsed laser (SLR), or time codes superimposed upon microwave radio carrier signals (GPS)
Range Rate:
Doppler shift in frequency of received radio signal can be integrated to obtain change in range –related to relative position of transmitter and receiver (DORIS, Argos, SARSAT)
Basic concepts of GPS
Originally developed for the US military
Joint Use Policy since 2004 (Defence,
Transportation)
Position, Navigation & Timing (http://pnt.gov)
Fully operational since 1995
44
Four GPS satellites
Four Ranges
3D Position & Time
Basic concepts of GPS45
from: www.punaridge.org/doc/factoids/GPS
Basic concepts of GPS46
Observation Equation:
2 2 2
i i P i P i P Pc t x x y y z z - c t
Four unknowns – solve for xP, yP, zP, tP
Basic concepts of GPS47
GPS time
GPS Week:
# of weeks since
6 January 1980
GPS Epoch:
# of seconds in
the week
(adapted from IERS graphic)
GPS Space segment – orbits revision
Geostationary orbits – fixed in relation to the earth
Geosynchronous – move within a defined range in relation to the earth
comms sats
37 000 km above the earth
Crowded orbits above the equator
Launch sites close to Equator
Orbital elements: e, a, i, W, w, Mo
(wikipaedia)
GPS Space segment - orbits
31 satellites in six orbital planes
55° orbit inclination
20 200km altitude
Period of 11h 58m
L1 and L2 carrier signalsC/A-code and P(Y)-code modulation
50
GPS Space segment – orbital
planes51
to receive and store information concerning their positions, health, and clock offsets and drifts
to maintain accurate time, within the GPS time system
to transmit time codes, ephemerides and other information to the users
GPS Space segment – satellite
functions52
GPS Control Segment:
Vandenberg
Colorado Springs
Cape Canaveral
Hawaii
AscensionDiego Garcia Kwajalein
Tahiti
New Zealand
Alaska
South Korea
South Africa Australia
USNO Wash, DC
England
Bahrain
Ecuador
Argentina
Master/Backup Control Station
Uplink Station
USAF Monitor Station
NGA Monitor Station
53
GPS Control Segment:
GPS
Monitor
station -
Pretoria
54
Tracking of all satellites by monitor stations
Processing at master control station to predict orbits (ephemerides) of all satellites at least 26 hours into the future
Uploading of ephemerides and satellite clock corrections twice daily
Improvement in prediction to achieve 1m accuracy in signal-in-space
GPS Control Segment:55
GPS Signal structure - old
GPS Signal structure -
modernized
L2C – currently only 8 Block IIRM satellites – allows civilian dual frequency code phase measurements, and better L2 carrier phase measurements
L5 – will be on new IIF satellites, with new civilian code
IIF satellites will have 3 carriers, with C/A code on L1, P(Y) code on L1 and L2, L2C on L2 and L5C on L5
New navigation message (CNAV) on L2C – more flexible, faster updates
Dual (and triple) frequencies provides greater redundancy and removal of ionospheric refraction effect
GPS Signal structure -
modernized
Amplitude Modulation
Frequency Modulation
Phase Modulation
GPS Signal modulation codes
C/A and L2C code: binary, chipping rate of 1.023MHz
P(Y) and L5C code: chipping rate of 10.23MHz
from: www.leicageosystems.com
GPS Signal modulation codes
generated code
received code
t
GPS Signal code correlation
Satellite clock time and satellite clock correction coefficients
Time offset between GPST and UTC
Satellite ephemeris (orbital parameters and their rates of change with respect to time)
Ionospheric refraction correction model coefficients
Almanac and health data for all the satellites
TLM and HOW – containing Z-count
GPS Signal navigation message
Standard Positioning Service (SPS):C/A-code observations on L1 only. Guaranteed accuracy of 3m horizontally (2σ level) and 5m vertically (2 σ); 40nanoseconds timing accuracy (2 σ). Globally, PDOP not to exceed 6
(actual horizontal accuracy (1 σ) better than 1m)
Precise Positioning service (PPS):C/A-code on L1, P(Y)-code observations on L1 and L2. Only available to US and NATO military. Accuracy specifications are cryptic – see www.gps.gove/technical/ps.
GPS Policy
Mathematical principles
Biases and Errors
Differential Solutions (DGPS) Principles
Virtual reference stations
Data transmission media and formats
Space/satellite-Based Augmentation Systems (SBAS)
Ground-Based Augmentation Systems (GBAS)
Module 4: Differential Data Processing
Techniques64
MATHEMATICS of pseudo-range
positioning
tc. - z - z y - y x- x d - d - c.dt - t.c2
ip2
ip2
iptropionii
or:i i i ion trop iR c. t - c.dt - d - d - c. t r
R i = r i
o +
x p o
- x i
r i
o . d x p +
y p o
- y i
r i
o . d y p +
z p o
- z i
r i
o . d z p - c . t
Linearised:
There are at least four such equations, and in matrix form:
A.x = ℓ
where:
A =
xp
o- x1
r 1
o
yp
o- y1
r 1
o
zp
o- z1
r 1
o- c
xp
o- x2
r 2
o
yp
o- y2
r 2
o
zp
o- z2
r 2
o- c
xp
o- x3
r 3
o
yp
o- y3
r 3
o
zp
o- z3
r 3
o- c
xp
o- x4
r 4
o
yp
o- y4
r 4
o
zp
o- z4
r 4
o- c
p
p
p
dx
dyx
dz
t
0
1 1
0
2 2
0
3 3
0
4 4
R
R
R
R
r
r
r r
MATHEMATICS of pseudo-range
positioning
Where there are more than four observations,
the least squares solution is:
1
T Tx A PA A P
MATHEMATICS of pseudo-range
positioning
Dilution of Precision (DOP)
Measures geometric strength of a single point position:
1
TGDOP Tr A PA
Also: PDOP, HDOP, VDOP, TDOP
Dilution of Precision (DOP) 69
Dilution of Precision (DOP)
Satellite visibility
Satellite sky plot
Satellite ground tracks
Cape Town 2014 10:00-16:00
Antarctica
Equator76
55 degrees latitude77
Satellite dependent:
Orbit bias
Clock bias
Propagation medium dependent:
Tropospheric refraction
Ionospheric refraction
Receiver dependent
Receiver resolution
Clock error
Multipath
Antenna phase centre error
BIASES AND ERRORS
Orbit Bias
ddB B.
r
r
For dr = 2m,
dB 0.1ppm of B
After application of the satellite clock correction (transmitted as part of the navigation message), the error in the clock is less than 5 nanoseconds. The effect on the pseudo-range is less than 2m
Satellite clock bias
3 2
trop
1255d 2.27 10 P 0.05 e tan sec
T
zenith
satellite
Reduced by:
Modelling (residual effect < 20cm)
Differencing (common errors eliminated)
Tropospheric refraction
zenith
satelliteion 2
40.3d TEC sec
f
16.2 sec
Reduced by:
Modelling (removes about 70%)
Differencing (common effect eliminated)
Eliminated by:
Use of dual-frequency receivers (frequency-dependent)
Ionospheric refraction
Sunspot
Activity
Sunspot activity
ion 2
40.3d TEC sec
f
Eliminated by use of dual-frequency receivers (frequency
dependent):
2
2ion 1 1 2 2 2
2 1
fd L L L .
f fr r r
2
2 1 1ion 1 1 2 1 22 2
2 1 2 2
f f fd L L L . N L N L .
f f f f
Modelling and reduction of
ionospheric refraction
Not an issue – better than 0.5% of effective wavelength:
1.5m for standard C/A-code handheld receivers10-20cm for C/A-code receivers using narrow correlators
1mm for carrier phase receivers
Receiver resolution
Determined as part of the solution for stand-alone pseudo-range positioning
Eliminated by differencing in differential positioning
Receiver clock error
Mitigation:
Siting
Antenna design
Narrow correlator
Choke ring
Averaging
Effect < 5cm
for carrier
phase
Multipath
Choke Ring Antennas
Variation in azimuth: use same type of antenna, oriented in same direction
Variation in zenith angle:
use same type of antenna
calibrate and use PCV correction tables
Carrier frequency:
use different phase centres for L1 and L2
Antenna phase centre
GoodPoor
Position accuracy ≈ UERE · PDOP (UERE approximately 1-2m)
Influence of satellite constellation
geometry
Error Source Stand-Alone GPS Differential GPS
Orbit < 2m < 0.1ppm
Satellite clock < 2m eliminated
Troposphere refraction < 20cm, after modelling < 1ppm
Ionospheric refraction 3-10m, after modelling < 1ppm
(dual frequency) eliminated eliminated
Receiver resolution 15cm - 1m 20cm - 2m
(carrier phase) 1mm 1-2mm
Receiver clock eliminated eliminated
Multipath < 10m < 10m
(carrier phase) < 5cm < 5cm
Antenna phase centre < 20cm < 10cm
(carrier phase) < 2cm < 1cm
Error and bias summary
Most errors are spatially correlated and can be reduced or removed by differencing:
DIFFERENTIAL GPS SOLUTIONS (DGPS)
222 )()()( i
R
i
R
i
R
i
R zzyyxx r
tcdddtctcR tropionii
i
R ...
i
R
i
R
i RR r
Ranges are computed at the reference station using the broadcast
ephemeris and the known reference station co-ordinates:
Measured ranges (corrected for receiver clock bias) at the reference
station:
Range corrections applied at rover unit, before computing
position:
Range corrections
With no multipath, single base:
2m - 3m (function of baseline length)
With multiple base stations:
sub-metre
(see also WAAS and VRS later)
DGPS accuracy95
Resolution: NOT reduced - limits the
solution
Satellite Orbits : Reduced to less than 0.1ppm(1cm on 100km)
Satellite Clocks : Eliminated
Ionosphere : Reduced to less than 1ppm
Troposphere : Reduced to less than 1ppm
Multipath : NOT reduced: 1-5m
DGPS effect on errors96
Range corrections are computed at reference station and transmitted to rover unit
reference
stationmobile
usercorrection signal
Realtime DGPS97
Virtual reference stations
DGPS corrections computed by a network of fixed
and continuously operating reference stations
Corrections interpolated to a point in the area of
work – point called the Virtual Reference Station
98
VRS concept99
VRS advantages
No user-operated base station is required
Reduced cost; increased productivity
More accurate corrections than owner-base station
More base station data is included
Sophisticated modelling of systematic errors sources can
be undertaken: refraction, orbits and multipath
100
VRS disadvantages
User may have to pay
Modernization of the GPS system may reduce the
advantages of DGPS in many cases
101
UHF/VHF
HF/MF
Satellite Communication links
Cell phones (GPRS)
Bluetooth
DGPS data transmission media
These are (more on the following slides):
RTCM SC-104 – Format for transmission of DGPS correction data from reference station to rover unit
RINEX – Format for GNSS data storage and processing
NMEA - Protocol/format for real-time communication of position from GPS to other devices
Realtime DGPS data transmission
formats
Radio Technical Commission Maritime, Special Commission 104
Message type 1: Differential GPS corrections
Message type 3: GPS reference station parameters
Also (version 3) capable of providing RTK data(code and carrier phase observations)
RTCM SC-104
Two main types:
Observation (file name: ssssdddf.yyo)
Navigation message (file name: ssssdddf.yyn)
(also compressed observation file: ssssdddf.yyd)
RINEX (Receiver Independent
Exchange) format
2.10 OBSERVATION DATA G (GPS) RINEX VERSION / TYPE
teqc 2007Feb5 20080702 00:35:07UTCPGM / RUN BY / DATE
HERM MARKER NAME
HERM MARKER NUMBER
CDSM CDSM TrigNet OBSERVER / AGENCY
Unknown TRIMBLE NETR5 Nav 3.50 / Boot 3 REC # / TYPE / VERS
0 RCV CLOCK OFFS APPL
ASH701941.B ANT # / TYPE
4973168.8045 1734085.3905 -3585434.1455 APPROX POSITION XYZ
0.0000 0.0000 0.0000 ANTENNA: DELTA H/E/N
1 1 WAVELENGTH FACT L1/2
9 C1 P1 P2 L1 L2 S1 S2 D1 D2# / TYPES OF OBSERV
30.0000 INTERVAL
MSXP|IAx86-PII|bcc32 5.0|MSWin95->XP|486/DX+ COMMENT
teqc 2007Feb5 20080702 00:34:02UTCCOMMENT
teqc edited: all GLONASS satellites excluded COMMENT
Forced Modulo Decimation to 30 seconds COMMENT
2008 7 1 0 0 0.0000000 GPS TIME OF FIRST OBS
2008 7 1 23 59 30.000000 GPS TIME OF LAST OBS
2.10 OBSERVATION DATA M (MIXED) COMMENT
teqc 2007Feb5 20080702 00:31:45UTCCOMMENT
GPSNet 2.51 2653 01-Jul-08 00:00:00 COMMENT
Cartesian values are base on the ITRF 2005 reference frame COMMENT
Station Position values are final COMMENT
END OF HEADER
RINEX sample
08 7 1 0 0 0.0000000 0 10G 5G30G22G14G16G12G31G32G29G20
24244117.102 24244115.152 -4907159.038 4 -3709921.24346
39.000 24.000
22318647.578 22318645.961 -14108663.616 7 -10866901.02347
48.000 36.000
23163277.086 23163274.066 -9810912.005 6 -7626200.02947
45.000 32.000
21058755.297 21058753.051 -21643392.083 7 -15891024.63547
49.000 41.000
23170436.898 23170434.449 -10175134.522 6 -7667313.47846
43.000 30.000
25266425.992 25266423.746 -601615.489 3 -449767.67745
37.000 20.000
20597668.336 20597665.492 -24949999.741 7 -19416354.05548
52.000 46.000
21413778.000 21413776.645 -18068659.996 6 -14038897.14847
47.000 38.000
24157775.781 24157775.074 -6390958.425 5 -4948960.63346
40.000 25.000
23966539.055 23966536.605 -7385208.568 6 -5419453.03446
43.000 25.000
08 7 1 0 0 30.0000000 0 9G 5G30G22G14G16G31G32G29G20
24261702.344 24261701.332 -4814742.678 5 -3637908.48546
40.000 24.000
RINEX sample
RS232 protocol, 4800bps, 8 data bits, no parity, one stop bit
Most common message: GGA:
$GPGGA,123519,4807.038,N,01131.000,E,1,08,0.9,545.4,M,46.9,M,,*47
NMEA (National Marine Electronics
Association)
Space-based (SBAS): Correction data are transmitted via geostationary satellites, using the L-band
Ground-based (GBAS): Correction data are transmitted via:
300MHz MF transmissions ("over-the-horizon") –Beacon DGPS (range of up to 500km)
Combination of internet and cellphone GPRS data transmission –NTRIP (restricted to cell network GPRS coverage)
SPACE/SATELLITE-BASED
AUGMENTATION SYSTEMS (SBAS)
Primary purpose is to provide GPS system integrity monitoring for safe aviation
Multiple reference stations (Ranging and integrity monitoring stations (RIMS)) over a region
Data processed at master station to produce satellite orbit and clock corrections, integrity data and ionospheric refraction correction grid
Data uploaded to geostationary satellites, which re-transmit data in the L-band
Accuracy improvement to around 1m, integrity warning latency of less than 6sec
SBAS key features
These are (pictures to follow):
WAAS: Wide Area Augmentation System, operated by the Federal Aviation Authority of the USA
Omnistar/FUGRO – private, paid, international
EGNOS: European Geostationary Overlay System, operated by the European Space Agency
QZSS: Japanese Quasi Zenith Satellite System
Starfix/NAVCOM
(also GAGAN and MSAS: Multifunction Satellite Augmentation
System, operated by the Japan Civil Aviation Bureau)
SBAS
from: http://gps.faa.gov
Wide Area Augmentation Systems (WAAS)
Commercial SBAS
Fugro Omnistar VBS (sub-metre):
EGNOS
from: http://www.egnos-pro.esa.int
Quasi Zenith Satellite System
Navcom Starfire
40 GNSS reference stations
JPL Real Time GYPSY (RTG)
Commercial SBAS
Beacon:
Network of single reference stations, with range corrections in RTCM-104 format
Distribution via MF (300KHz) marine radio navigation beacons, range of up to 500km
Generally provided as a free service by marine navigation authorities (coastguard, lighthouse service, harbour service)
GROUND-BASED AUGMENTATION
SYSTEMS (GBAS)
US NDGPS
from: www.navcen.uscg.gov
118
from: www.trignet.co.za
TRIGNET
Dual-frequency receivers with choke ring antennas
Network DGPS – sub-metre accuracy
Network RTK (VRS) – 2cm accuracy
Single base RTK – 5cm accuracy
Real time delivery in RTCM-104 format via NTRIP and GPRS (restricted to cell phone network data coverage)
Post-processed data available in RINEX format
TRIGNET
Network Transport of RTCM via Internet Protocol
Used for provision of RTCM-104 data via the internet(data are stored at an IP address for access by multiple users, over the internet or via GPRS)
NTRIP
accuracy of 3m –5m
from: Portnet brochure
PortNet DGPS
NGDGPS
NASA Global GPS Network (GGN) – JPL owned
70 reference stations
Internet or satellite comms
Mathematical principles and differencing carrier phase
observation equations
Carrier phase data errors/biases and mitigation
Surveying methods:
integer ambiguity resolution
recovering L2
static GPS
kinematic positioning
network RTK/virtual reference stations
Practical aspects of GPS surveying
Module 5: Carrier Phase Data
Processing Techniques125
Carrier phase GPS
With DGPS, best accuracy obtainable is 30-50cm
This is inadequate for surveying, geodesy, etc
Problem is mainly one of resolution – effective
“wavelength” of C/A-code is 300m. L1 carrier has
wavelength of 19cm
ij = i(T) - j(t)
signal transmitted
at time t
signal generated
at time T
Mathematical principles of carrier
phase GPS127
i
j
=f
c.r i
j
f.(dtj- t i) +
f
c.(-d ion + d trop)
2 2 2
j
i i j i j i jx x y y z zr
Mathematical principles of carrier
phase GPS128
integer cycle ambiguity
fractional phase
whole number of
cycles since lock-on
fractional phase
i
j
= m + N i
j
Mathematical principles of carrier
phase GPS
Integer Ambiguity
129
j j j
m i i trop ion i
f ff dt t d d N
c c r
j j j
m ion trop i i id d c dt t N r
Multiplying by the wavelength, and re-arranging:
Mathematical principles of carrier
phase GPS
1
r j
1r2
1
r j
2
1
2
j j j
21 ion trop 21 21 21d d c. t N r
Eliminates satellite clock error; effects of refraction and orbit bias
reduced
Mathematical principles of carrier
phase GPS
Differencing
between stations
131
Differencing carrier phase
observation equations
2
1
r1
ir2
i
i
21 21 21 21
i ion trop i id d c. dt N r
Eliminates receiver clock error
Differencing
between satellites
132
.21
21
+ 2
d ion - 2
d trop = r21
21
- .N21
21
2
1
r1
1r2
1
r1
2
r2
2
1
2
Eliminates clock errors; reduces orbit and refraction errors
Differencing carrier phase
observation equations
Double
differencing
133
134
i
1t
ri(t )2
ri(t )1
2t
Between epochs
differencing
.i
j
(t 2- t 1) + d ion - d t r op = r i
j
(t 2- t 1) + c.dtj(t 2- t 1) - c.t i(t 2- t 1)
Eliminates Integer Ambiguities
Differencing carrier phase
observation equations
135
Triple Differencing
Eliminates all nuisance unknowns
Differencing carrier phase
observation equations
.21
21
(t 2- t 1) + 3
d ion - 3
d t r op = r21
21
(t 2- t 1)
Satellite Orbits : 1-2m
Satellite Clocks : 1-2m
Ionosphere : 10-50m (model 2m)
Troposphere : 2-5m (model 20cm)
Multipath : < 5cm
Carrier phase data errors/biases and
mitigation136
Satellite Orbits : Reduced to less than 0.1ppm
(1cm on 100km)
Satellite Clocks : Eliminated
Ionosphere : Reduced to less than 1ppm
(eliminated using dual
frequency)
Troposphere : Reduced to less than 1ppm
Multipath : NOT reduced: < 5cm
Carrier phase data errors/biases and
mitigation137
A single double difference contains four unknowns:
three co-ordinates of the new point, one double-
differenced integer ambiguity
Adding another satellite just adds another integer
ambiguity
Need to observe several satellites over several
epochs, while maintaining lock (no fresh ambiguities)
Minimum configuration:
three satellites, three epochs
four satellites, two epochs
All differencing done with respect to a single reference
satellite
CARRIER PHASE GPS – receiver-
satellite configuration138
Minimum configuration of four satellites and
two epochs139
The double-differenced integer ambiguities in the
equation are resolved as real numbers ("floating
point") in the least squares solution
For greater accuracy they should be resolved as
integers, and the solution repeated, treating them as
known quantities.
The integer resolution ("initialization") makes use of
statistical testing:
Minimizing Sv2
Identifying integers within confidence intervals
Solving the integer ambiguity -
Initialization
If the observations are affected by errors ("noisy" data),
then it becomes difficult, if not impossible, to resolve the
correct integers.
More data helps - i.e. observing over a longer time span.
Residual ionospheric refraction makes the data appear
noisy – this effect can be eliminated by using dual-
frequency receivers:
Some form of iteration required, to solve for ionospheric
refraction correction and for integer ambiguities
2
2 1 1ion 1 1 2 1 22 2
2 1 2 2
f f fd L L L . N L N L .
f f f f
Solving the integer ambiguity -
Initialization
Want to use L2 as well as L1:
Calculate ionospheric correction and eliminate it
Better ambiguity resolution over longer baseline distances
BUT
L2 is encrypted by the Y-code (P-code)
Do not know this so cannot strip it off as in L1 code
Only newer satellites broadcast the L2C signal
which is available.
Using the L2 carrier for dual –
frequency GPS
Need to strip the code off the carrier before it can
be used. There is not a problem with the L1
carrier, as the C/A code is known and can be
removed.
For L2C-capable receivers the L2 carrier can be
recovered for the Block IIR-M-F satellites in a
similar fashion.
For the other satellites
and for older receivers the
technique of code-aided
cross-correlation must be
used to recover L2
Using the L2 carrier for dual–
frequency GPS
A number of different Surveying modes exist
–
Static GPS surveying
Kinematic GPS surveying
Initialisation
Continuous
Real time kinematic
Ambiguity resolution on the fly
GPS and GLONASS
Network RTK/VRS
Carrier Phase GPS Surveying Methods
Data collected over a time period of ten minutes
to several hours
Data stored, downloaded and post-processed
Single-frequency integer ambiguity resolution
possible, for baselines up to 20km in length
Dual-frequency integer ambiguity resolution
possible for baselines of 100's of km, using many
hours of data
(rule-of-thumb: 10min + 1min per kilometre)
Accuracy of 3mm + 0.5ppm
(with scientific software: 1mm + 0.01ppm)
Static GPS Surveying
Dual-frequency receivers – one at base station, the other
roving
Initialisation (resolution of integers) carried out over 1-2
minutes:
Rover at known point
"Antenna swapping" (obsolete)
Dual freq+wide laning (comb L1 and L2) +stat testing
Ambiguity resolution on the fly (AROF), with Kalman
filtering
Kinematic GPS Surveying
Need to maintain lock on at least four satellites, otherwise
re-initialisation required
Post-processed or Real Time
Cannot easily resolve integers over baselines longer than
20km
Accuracy of 1-2cm + 1ppm
Kinematic GPS Surveying
Continuous Kinematic
Rover moves in continuous trajectory – mounted
on vehicle or aircraft
Issues:
Initialisation carried out prior to vehicle/aircraft
moving
Range restricted: baseline lengths generally
under 100km
Synchronisation with other sensors
Orientation differences due to non-colocation
Loss of lock “in-flight”
Continuous Kinematic
Generally post-processed, with AROF (PPK)
Integrated with other sensors: ALS, INS, digital
camera
Accuracy of 5-10cm + 1ppm (multipath)
Real Time Kinematic (RTK) for
surveying
Required for searching and setting out; coords needed on
site
ALL data from base station transmitted to rover unit (code
and carrier phase observations)
Baseline data processing carried out at rover
Dual-frequency, with AROF, minimum of five satellites
Baselines restricted by communication link:
UHF/VHF need line of sight communication
NTRIP/GPRS needs cell phone link
On site statistical feedback
As in non-real time: 1-2cm + 1ppm
As in non-real time: Baselines < 20km
Start
ambiguities resolved
loss of lock
ambiguities resolved again
forward processing
backward
processing
backward
processing
forward processing
rover
Ambiguity resolution on the fly
No need to stop survey if re-
initialisation is required
rapid static approach
(combination of dual
frequency, wide-laning and
statistical testing) as well as
antenna trajectory are used
to resolve the integer
ambiguities
Ambiguities are back
substituted to obtain track
coordinates
Assists AROF by increasing constellation
Need at least 6 satellites as there is an additional unknown – the time offset between GPS and GLONASS (min 5 for non-AROF)
Recommended minimum is 6 satellites for GPS only and 7-8 for combined GPS/GLONASS for initialisation
Integer ambiguity resolution is faster with more satellites
Integer ambiguity resolution is more certain with more satellites – need FIXED solutions for cadastral work
Single frequency receiver performs better with GLONASS added (GNSS)
Number of satellites should be enough - NB in urban canyon, trees, obstructed sky view
GPS and GLONASS in surveying
All the time:
Data processed between multiple base stations (fixed
solution) yielding:
Local ionospheric errors
Local tropospheric errors
Orbit errors for
observed constellation
control centre
base station
Network RTK / VRS153
When client surveying:
Sends pseudo-range
solution to the control
centre
Requires two-way
communication –
cellphone link to web
site.
This position becomes
the Virtual Reference
Station
Error models for refraction
and satellite orbits are
interpolated to the position
approx. position
control centre
base station
Network RTK / VRS154
When client surveying:
Observation data from
the nearest reference
station is artificially
displaced to the VRS
position
artificial (virtual)
base station data
created (quasi-
carrier phase data)
like eccentric set-up
approx. position
virtual data
control centre
base station
Network RTK / VRS155
When client surveying:
Client surveys with
virtual base station data
baselines
determined are now
between the VRS
and the rover
Network RTK / VRS156
Advantages of network RTK/VRS
baseline lengths are shorter
higher accuracies are claimed
Initialization (ambiguity resolution) times reduced by as
much as 2/3rd’s
fixed-point solutions more easily achievable
position determined by the roving GPS receiver is
automatically integrated into the national control system as
defined by the Reference Stations included in the system.
temporal disturbances to the ionosphere are automatically
modeled in real time yielding better accuracy that those
predicted in the navigation message.
Network RTK / VRS157
TrigNet and VRS
from: www.trignet.co.za
3 VRS networks in SA
TrigNet and VRS
Provides a set of continuously operating reference
stations (CORS)
User only requires a single receiver to get position
Post-processing using downloaded RINEX data
RTK using single base stations and network RTK
(VRS)
(needs NTRIP/GPRS capable receiver)
Reference station heights are ellipsoidal,
not orthometric
Reference Frame:
Co-ordinates of all TrigNet stations are in the
ITRF2008 reference frame, updated to 2012.01
All real time results will be in this frame (DGPS,
RTK, VRS)
User can choose to use Hart94 co-ordinates for
TrigNet station, for post-processed static GPS
The official datum is Hartebeesthoek 1994
ITRF2008(2012.01) to Hart94 shifts are variable –
average of 19cm (y) and 41cm (x), but ranges from
4cm to 32cm (y) and from 28cm to 58cm (x)
TrigNet and VRS
PRACTICAL ASPECTS OF GPS
FOR SURVEYING
Reconnaissance and Design
Observations
Data processing
Datum transformation
Reconnaissance & Design
Select suitable sites – no multipath, no
electromagnetic interference, good overhead
visibility
Choose best time of day – most satellites, low
PDOP
Select independent baselines
( # baselines = # receivers – 1 )
Ensure redundancy – baselines form closed figures
– at least two, preferably three, connections to each
point
Ensure direct connections between close points –
20% rule
Connect to at least three higher order control points
Network Geometry
double polars
Contro l Network
163
Practical aspects of static observations
Select suitable observation period:
10 minutes plus 1minute per kilometre
Allow sufficient time to access points; plan
observation sequence; Ensure simultaneity
Check batteries
Double-check measurement of antenna heights
Static data processing
Data transfer – cable, memory card
Pre-processing, if required:
- download & import CORS (TrigNet) data
- download and convert precise ephemeris
Process independent baselines, solving for integer
ambiguities
(may require removal of satellites; editing of cutoff
elevation angle; use of precise ephemeris)
Combination of baselines in network adjustment:
- minimum constraint
- constrained to fixed points
- solve for datum transformation parameters
GPS for cadastral surveys:
RTK most common approach, often using TrigNet
Initialization is the process to determine (or re-
determining) integer ambiguities
Calibration is the process of tying (transforming) the
survey to the national datum (Hart94)
Checks are essential for cadastral surveys
Many (most) surveyors fail to take sufficient
redundant measurements to ensure that checks are
independent of calibration
Calibration for RTK
Calibration essential to
ensure transformation
from base station co-
ordinate frame (e.g.
ITRF2005) to official
datum (Hart94)
visit at least two
(preferably three) control
points after initialization
(on-board software
determines local
transformation parameters
and applies them to all
subsequent positions)
Checks for RTK
Poor design of checks
Single visit to surveyed
points
Although multiple base
stations
Poor occupation/incorrect
occupation of survey points
No checks on local control
Checks for RTK
Poor design of checks
One base station only
Double visitation of local
control and surveyed
points
If same points used for
datum transformation
no redundancy
errors absorbed into
transformation
parameters
Checks for RTK
Poor design of checks
One base, one rover
Invert rover
Only new integer ambiguity resolution
No check on correct occupation of base
station
No check on correct occupation of rover
station
No check on multipath or residual refraction,
satellite constellation errors
Checks for RTK
GOOD design of checks
Multiple base stations, one
or more rovers
Visit a local control point
after initialization
Visit all survey points
Visit a local control point
Repeat visits to survey
points
Visit a local control point
Datum transformations
Satellite coordinates are in WGS84
Using base station coordinates gives GPS derived
coordinates in base station system
TrigNet this is IRTF2008
Local base station – system of entered coordinates
If only once base used, shift only
To calculate swing and scale, use more than one control point
Datum transformations
To transform from base station system to Hart94
Use of published conversion packages use averages… not
accurate enough for cadastral work (up to 10m incorrect) …
local transformation is required
use a similarity/helmert transformation … min 3 points
For cadastral work, conversion of archival data in Cape Datum may
also be required prior to survey.
GPS for Engineering Surveys
Heights are needed, as well as positions - this can
be a problem
Topographic surveys: RTK or continuous kinematic
Problems with satellite visibility – buildings, cranes,
cliffs, etc:
use additional satellites (GLONASS)
use electronic tacheometer in conjunction with
GPS
use laser ranger, with tilt and orientation
sensors
Monitoring surveys need high accuracy, high data
rate and low multipath
GPS for GIS
DGPS systems are generally adequate (1-2m
accuracy)
Need not be real time, but need to record all code
measurements if not
Handheld unit must be able store attribute data, with
user-defined data dictionary
Results must be capable of conversion to standard
formats (e.g. DXF, Shape files)
GPS Heighting
GPS provides heights above the WGS84 ellipsoid.
Users need heights above MSL/geoid – orthometric
heights
In order to convert GPS-derived heights to orthometric
heights we need a good model of the geoid/ellipsoid
separation – the geoidal height N:
H
h
N
Terrain
Geoid
Ellipsoid
Geoid modelling
Small areas (a few km in extent) modelled by a tilted
plane
at least 3 points with known orthometric heights are
surveyed with GPS
this approach is often used in RTK
Larger areas
gravimetric model
model and the levelling network may have
systematic errors
A combination approach (hybrid geoid model) is best,
using GPS/levelling data to calibrate a gravimetric geoid
model
Hybrid Geoid Model
118 GPS/levelling
points
Accuracy of 7cm
International GNSS Service (IGS)
Consortium of agencies operating permanent
continuous tracking stations
Main product is post-computed precise ephemeris –
accuracy of 2 – 10cm
Also: precise satellite clock corrections; ionospheric
refraction correction model; raw data in RINEX
format
International GNSS Service
(IGS)
Precise Point Positioning (PPP)
Makes use of precise ephemeris and satellite clock
corrections to obtain precise stand-alone position.
Needs dual-frequency receiver to remove
ionospheric refraction; solves for tropospheric zenith
path delay.
Uses both carrier phase and code phase data.
Post-processing only, minimum of 1hour data
required (preferably 24hrs)
Accuracies of 1cm – 10cm
181
Internet-based GPS Processing
Involves collection of data, conversion to RINEX
format, uploading to web site, with results received
via e-mail (free processing)
Differential carrier phase post-processing using IGS
reference stations and precise ephemeris:
Relative accuracies of up to 1mm + 0.01ppm
Precise point positioning using IGS (or other)
precise ephemeris and satellite clock corrections:
Absolute accuracies of 1-2cm
182
GLONASS
Galileo
Compass
Others proposed
Module 6: Other GNSS183
GLONASS
USSR/Russia equivalent of GPS
24 satellites in three orbital planes
65° orbit inclination
19100km altitude
Period of 11h 15m
Two carrier signals, civil & military codes
184
GLONASS
Currently only 26 satellites available
Launch failure in December 2010, July 2013
Modernisation (2nd civil signal) GLONASS-M. First
launch in 2005
Not used as a stand-alone system. Supplements
GPS in urban canyon environment.
GLONASS-K launched in Feb 2011
185
GALILEO
Proposed ESA/EU civilian navigation system
Planned: 27 satellites, 56° inclination, 14 hour
orbits. First test satellite launched late 2005, 2nd in
April 2008. FOC in 2012 (or later?)
To be compatible with and interoperable with GPS -
common reference frame, broadcast of timing
offsets.
186
Open Access
Commercial
Safety of Life
Search and Rescue
Free to air; Mass market;
Simple positioning and
timing
Encrypted; High accuracy;
Guaranteed service
Open Service + Integrity and
Authentication of signal
Encrypted; Integrity;
Continuous availability
Near real-time; Precise;
Return link feasible
Public Regulated
Na
vig
ati
on
SA
R
GALILEO – proposed services
187
GALILEO Signal Structure
C/AOS/GPS III
L1
(1575.42 MHz)
E6
(1278.75 MHz)
L2
(1227.6 MHz)
L5
(1176.45
MHz)
M P(Y)PRS
L2C
M P(Y)PRS
CS
E5b
(1217.14
MHz)
L5 E5a E5bOS CS, SoL
188
COMPASS
Proposed Chinese satellite navigation system
Planned: 27 medium earth orbit satellites,
5 geostationary satellites, 3 inclined
geosynchronous satellites
Currently: three geostationary, one MEO
THE END