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SVY 207: Lecture 12GPS Error Sources: Part 2

– Satellite: ephemeris, clock, S/A, and A/S

– Propagation: ionosphere, troposphere, multipath

– Receiver: antenna, clock, measurement error

– Earth: Earth surface kinematics

– Processing: cycle-slips, ambiguitystochastic (errors in the error

model)

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Tropospheric Delay• Lower atmosphere

– Very thin and local: most delay from last several km

• Two components: – Dry: mainly nitrogen and oxygen

– Wet: water vapour (very small effect from clouds and rain)

• “Dry Delay” affects radio + optical– Zenith delay 1.9 to 2.3 m

– Function of pressure and temperature profile

– Therefore, depends on height above sea-level

– Predictable and easily calibrated

• “Wet Delay” strongly affects radio– Zenith delay of 0 to 20 cm

– Function of humidity profile

– Therefore, depends on climate (e.g., tropical, desert, etc.)

– Unpredictable and difficult to calibrate

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Tropospheric Effects• Delay

– Total effect (dry + wet) at zenith: 1.9 - 2.5 m

– Total effect near horizon: 20 m

– Very little variation with azimuth

• Variation– Zenith delay typically varies only 1 cm in 1 hour

– Strongly correlated between stations < 30 km

• GPS Data Processing– Surface meteorological measurements inadequate

– Must account for difference in station height

» software can use standard atmospheric model

– Set elevation angle cutoff in software to 15 degrees

– For lines > 30 km estimate tropospheric delay

» software should estimate relative zenith delay(with geometric model for variation with zenith angle)

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Multipath

• Multiple paths between satellite and receiver

• Caused by reflection of signal from conducting surfaces in receiver environment– chain link fence, vehicles, wet ground, sea surface, etc.

– Beware of large, regularly-shaped surfaces nearby

• Secondary path is weaker, and error is often difficult to detect

• Tends to produce oscillating errors– tends to average down very quickly (few minutes)

– but oscillation is slower (and stronger) for closer objects

– measurements within < 1 minute are physically correlated

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Antenna• Phase Centre Offset

– Electrical centre doesn’t coincide with geometrical centre

– Each antenna has a phase centre offset

– Same type of antenna has approximately the same offset(especially if both are oriented North)

– Hence this approximately cancels for relative positions

– But offset values must be used if antennas are different

• Antenna structure also produces multipath– causes an apparent “phase centre variation”

– electrical centre moves depending on satellite direction

– can be at the 1 centimetre level

– but approximately cancels between similar antennas

– antennas can be calibrated as function of sky direction

– however, phase centre variation can also be a function of the local environment around the antenna (like multipath)

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Receiver Clock• Receiver clock is used to stamp the time

associated with each measurement– Effect on observation is cancelled by double differencing

• But it is also used as the epoch time to compute the geometrical range (in b vector)– which changes as the satellites move and Earth rotates

• If clock is synchronised to GPS time to s – satellite position error 10-6 s4 km/s mm

– Earth rotation error 10-6 s5 km/s mm

– computed range error 10-6 s1 km/s mm

• If not synchronised, then:– first use pseudorange point position method to estimate

receiver clock offset.

– then use carrier phase relative positioning, where double difference geometry is computed using corrected time

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Receiver Position• In double differencing, one receiver is held fixed,

while the other is estimated– Fixing one receiver to an incorrect coordinate, is equivalent to

moving the orbits in the opposite direction to the error (a functional model error)

– Sometimes fixed receiver coordinate is obtained from a poor point position

– Hence, we can estimate the effect of fixed receiver position error

• Rule of thumb– 10 meter error in fixed station coordinate can produce

» 1 cm relative position error over 20 km

» 5 cm relative position error over 100 km, or 10-6 L

– a 50 meter error can produce

» 5 cm relative position error over 20 km, or 5 x 10-6 L

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Measurement Error• Definition

– The difference between the actual measurement, andone that would be made using perfect instrumentation

• Systematic– Caused by physical effects which have a pattern that could be

predicted if we had sufficient data and a good enough model about the processes involved.

– Receiver firmware (code correlation, phase tracking loop)

– Electronic channel biases which vary with temperature

• Random– Caused by physical effects which have no predictable pattern, but

may be treated statistically

– Electronic noise (random atomic motion)

– Sampling error (finite bandwidth smooths out signal)

– Finite clock instability (random atomic motion)

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Earth Model• In static positioning, receiver is attached to

Earth’s surface.

• But Earth is constantly changes shape, rate of spin, and spin direction.– Precession, nutation, length of day, polar motion

– Solid Earth tides

– Distortion due to atmospheric pressure

– Distortion due to oceanic pressure

– Plate tectonics, seismic motion.

• If ignored, relative accuracy is limited L

• Most of this can be modelled to allow for relative position at the level L– Will be covered in SVY307: Geophysical Geodesy

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Cycle-Slips• Discontinuities in the integer ambiguity.

• If not accounted for– this consistutes a blunder

– Error estimates will be meaningless unless sufficient confidence can be place in removing cycle-slips.

• Cycle slips are more prone to happening:– obstructions (e.g., operator stands near antenna!)

– magnetic disturbance in ionosphere

– antenna undergoes significant acceleration

– receiver clock becomes unstable

– signal to noise is low (e.g., long antenna cable, low elevation satellite).

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Carrier Phase Ambiguity

• Formal error– If all ambiguities can be resolved (fully “fixed” solution)

» reduces number of least squares parameters

» improves redundancy (No. data No. parameters)

» therefore improved formal precision (covariance matrix)

– If not all ambiguities can be resolved (partially fixed solution)

» larger number of least squares parameters than above

» formal precision (covariance matrix) larger than above

• Blunders– If resolved to the wrong integer, this constitutes a blunder

– several centimetre error possible

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Stochastic Errors• Finally, it should be recognised that we will

introduce an error into our estimates if we have an error in our error model.

• Incorrect weight matrix for least-squares– software might ignore known mathematical correlations

(see lecture 10)

– incorrect data variances might be used

» low-elevation satellites usually more noisy (low S/N ratio)

» In a network solution, we might apply inappropriate weights to a particularly noisy receiver

– We might ignore physical correlations between measurements

» due to multipath

» due to varying atmospheric conditions, etc.

» these types of error can equivalently be considered as systematic errors in the functional model.