6.2.3 Measurement Biases and Errors
The satellite ephemeris bias is the discrepancy between the true position
(and velocity) of a satellite and its known value. This discrepancy
can be parameterised in a number of ways, but a common way is via the three
orbit components: alongtrack, crosstrack
and radial (see Figure 1 below). In the case
of GPS satellites the alongtrack component is the one with the largest error.
Figure 1. Satellite ephemeris bias.
What is the effect of the satellite orbit bias on GPS positioning?
Expressed another way, if there was no other option but to assume that the
available ephemeris data is correct, what is the effect of a satellite orbit
error on GPS positioning? The following comments can be made:
- Height is a relatively weakly determined component, mainly because
there are no satellites below the horizon.
- The East-West (longitude) component is slightly weaker than the North-South
(latitude) component because of the motion of satellites (particularly
in equatorial regions.
- Effect on point positioning:
| Position error = PDOP . Orbit error |
| Example: |
|
|
If PDOP = 2 (section 1.4.9), orbit error
= 20m (or 1ppm)
Position error = 40m |
| Complicated further because orbit error varies on different satellites. |
- Effect on relative positioning, the following
"rule-of-thumb" can be used (BESER
& PARKINSON, 1982):
Baseline error =  . Orbit error |
|
d = baseline length in kms |
| Example: |
|
|
If d = 10km, orbit error = 20m (or 1ppm)
Baseline error = 1cm (or 1ppm) |
| Hence, the longer the baseline, the larger the effect of orbital error
(this is illustrated in Figure 2 below). Complicated further because
orbit error varies on different satellites. |
Figure 2. Approximate relationship between baseline length, accuracy and
GPS satellite orbit error.
There are two basic classes of satellite orbit information:
- Ephemerides that are predicted from past tracking
information, and are available to GPS users at the time of observation,
and
- Post-processed ephemerides, which are
orbit representations valid only for the time interval covered by the tracking
data. Obviously this information is not available real-time as there is
a delay between collection of the data, transmission of the data to the
computer centre, the orbit determination process and the subsequent distribution
to GPS users.
The former is available via the GPS Navigation Message (section
3.3.3). The ephemeris computation takes place at the Master Control
Station using tracking data acquired from the five monitor stations of the
GPS Control Segment (section 2.2.3). With
regards to the accuracy of the broadcast ephemerides,
there are (in principle) several distinct effects:
- There is the effect arising from the accuracy of the orbit computation
procedure itself. The data used is P code pseudo-ranges, and although the
tracking geometry is not strong (most of the tracking stations are in the
equatorial belt), accuracies better than 10 metres are achievable.
- There are errors resulting from unpredictable orbital motion during
the period since upload. These are essentially the prediction
errors. Their magnitude can vary from a few decimetres (close to the time
of Navigation Message update) to several tens of metres (for example, if
using ephemeris data several hours beyond the reference epoch).
- There is the effect due to Selective Availability, which involves
the deliberate degradation of the broadcast ephemeris parameters within
the Navigation Message. The resulting orbit error is highly variable (the
degradation algorithm is classified!), but it may be assumed that it could
be as high as 100 metres or more. (There is little evidence that such
orbit data degradation is in fact at present taking place.)
Evidence suggests that the accuracy of the broadcast ephemerides is below
10m for a single Navigation Message update per day, and better than 5m when
three daily updates are performed (HOFMANN-WELLENHOF
et al, 1998). Some GPS surveying systems can output files containing
the broadcast ephemerides in the RINEX format (see section 7.3 for a sample).
Post-processed ephemerides are, in general,
more accurate than predicted ephemerides, with demonstrated accuracies
well below the metre level. Over the last decade there has been considerable
activity in this area. The main requirement is a network of tracking stations
and an orbit processing facility. Since the mid 1980's there have been tracking
networks organised on regional, continental and global bases. There have
been scientific, private and/or government initiatives, as well as military
networks. Some networks have operated intermittently, for specific geodetic
applications, others were organised on a semi-permanent basis. Several of
these networks were the first examples of international civilian cooperation
in the field of GPS ground infrastructure. The following is a "potted
history" of independent tracking and orbit computation initiatives:
- The U.S. Defense Mapping Agency ( DMA ) has generated " precise
ephemerides " for mahy years, computed using tracking data from a
global network of 8 or so tracking stations ( comprising the monitor stations,
supplemented by several DMA sites ). These ephemerides are now mostly
used for internal DMA and Control Segment purposes.
- Private initiatives such as that by Aeroservices Inc. have pioneered
the non-military generation of GPS orbits. They originally established
a number of tracking stations in the continental U.S. to collect data for
satelite orbit computation. The orbits were then distributed to a small
group of MacrometerTM users. ( This network was then subsumed
into CIGNET. )
- The U.S. Geological Survey contracted the Center for Space Research,
the University of Texas at Austin, to generate post-computed ephemerides,
beginning in late 1986, based on data from continental U.S. tracking stations.
Gradually data was incorporated from all CIGNET stations.
- CIGNET ( Cooperative International GPS Network ) was a collection of
tracking stations spread throughout the world, that operated on a continuous
basis from the late 1980's until 1992 when the International GPS Services
for Geodynamics ( IGS ) was established (later changed simply to the "International
GPS Service"). The U.S. National Geodetic Survey ( NGS ) collected
and archived the tracking data, and generated ephemerides, that were then
made available to any user. This was the first global tracking network
initiative.
- During the 1980's and early 1990's several regional and continental
scale tracking networks were deployed in many parts of the world for national
ephemeris computation ( as well as GPS Integrity Monitoring -- section
4.4 ), as well as in support of high precision GPS crustal motion surveys.
These networks were generally not established on a permanent basis.
- In June 1992, a substantial " core " tracking network for
the IGS was established under the auspices of the International Association
of Geodesy. As well as organising the tracking network, the IGS has several
computing centres generating " products ", including
precise satelite ephemerides with decimetre level accuracies. A
number od test campaigns and pilot services have been organised ( see ZUMBERGE et al, 1995, for a
review ). The full service was launched in 1994 and nowadays is the
sole source of precise GPS ephemerides for the civilian user community.
At present the precise IGS orbits are available via Internet (see section 3.4.2), in the so-called SP3 ephemeris
format, a format first developed by NGS for the CIGNET products. The SP3 file format is explained in a document that can
be FTP'ed from the IGS Central Bureau.
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© Chris Rizos, SNAP-UNSW, 1999
IGNORE the problem, and
use the GPS Broadcast Ephemerides -- assume the available orbit data
are error-free.