From: Michael B. Heflin
Date: 19 Feb 1996 12:21:26 
Subject: [SCIGN-0152] GPS Error Sources 

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SCIGN Electronic Mail    Mon Feb 19 12:21:26 PST 1996      Message Number 0152
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Author: Michael B. Heflin
Subject: GPS Error Sources

As the SCIGN community continues to debate the various pros and cons of GPS, I
thought it might be helpful to review some of the known error properties of
GPS estimates.  There is a session at the Spring AGU Meeting which should
address many of these issues and look very closely at time series derived to
date.

REVIEW OF GPS ERROR SOURCES

1.  Absolute position errors predicted from covariance analysis.

                            N        E        V
                           mm       mm       mm
Receiver Noise              2        2        4
Phase Ambiguities           2        6        4
Tropospheric Zenith Delay   0        2       12
Orbits                      4        4        8
Atmospheric Loading         0        0        3
Ocean Loading               0        0        1
Total                       5        8       16

Observed Global Mean        5        7       12
Observed in California      4        7       11

2.  Baseline errors scale with length because common errors such as those due
    to orbits cancel for short baselines.

Length:                     2 mm + 1.5 parts per billion

                            N        E        V
                           mm       mm       mm
California Baselines:       2        3        7
With Ambiguity Resolution:  2        2        5

3.  Monument Instability

Comparisons of GPS with other techniques agree at the level of 1-3 mm/yr,
placing an upper limit on monument instability for common sites.  The first
global plate motion model derived solely from GPS data was rigorously compared
to VLBI and NUVEL-1A in 1995 (Argus and Heflin, GRL).

                            N        E        V
                        mm/yr    mm/yr    mm/yr
GPS - NUVEL-1A              2        2
GPS - VLBI                  3        3        6
GPS - ITRF93                2        2        5

A recent paper by Langbein et al. (GRL, 1995) indicates instability of the
worst monuments at Parkfield to be on the order of 1-2 mm / sqrt(year) and
demonstrates clearly that more expensive deeply anchored monuments can help
to mitigate seasonal variations.

Some of the non-white noise in the time series has clearly been reduced as
orbits and analysis strategies have improved.

3.  Estimation of Antenna Changes

A span of data of length T yields velocity errors which are inversly
proportional to T.  If the span is broken by N evenly spaced position biases
and one velocity estimate is derived, the velocity error is inversly
proportional to SQRT(N+1)*T/(N+1).  Hence the degradation caused by N evenly
spaced breaks is SQRT(N+1)/(N+1) = SQRT(N+1).
One break  ==> SQRT(2)
Two breaks ==> SQRT(3)
...

4.  Elevation dependent phase center variations.

Baselines between receivers with different antennas are biased unless the
phase center variations of each antenna are removed.  The effect on velocities
is minimal as long as the antennas are unchanged.

5.  Multipath

A paper by Elosegui et al. (JGR, 1994) indicates that near-field multipath
makes vertical GPS estimates sensitive to the choice of elevation cutoff.
The impact on velocities is minimal if the elevation cutoff is constant.

6.  Software Bugs

GAMIT had a serious software bug related to the mapping of the troposphere that
was not fixed until the summer of 1995.  Orbits estimated before the software
was correct were noisier by as much as a factor of two relative to orbits
estimated with other software packages.  Results for short baselines were
affected minimally but global results were seriously degraded.  Results derived
after the software was fixed are greatly improved.


[Mailed From: mbh@cobra.jpl.nasa.gov]