Analyses of a Drop in GPS Satellite Numbers
Sam Wormley
http://sidt.gpsworld.com/gpssidt/content/printContentPopup.jsp?id=605171
Jun 22, 2009
Professor Richard Langley of the University of New Brunswick (also GPS World’s Innovation
editor) has done several analyses to see how the use of GLONASS satellites could help
compensate for a potential reduction in the number of available GPS satellites. These
studies came in response to a warning from the U.S. Government Accountability Office about
the potential drop in the number of healthy satellites in the GPS constellation as a
result of delays in both the Block IIF and Block III modernization programs.
An analysis posted on May 21 to the Canadian Space Geodesy Forum (CANSPACE) looked at the
effect that a reduced number of available GPS satellites would have on conventional 3D
positioning using pseudoranges as a typical handheld receiver would do over a period of 24
hours.
Assumptions:
1) Location: Fredericton, a typical mid-latitude site (results will be different for
different locations)
2) Sky visibility: Perfect down to an elevation angle of 5 degrees; no blockages
3) Pseudorange measurement and modelling accuracy: 3 metres (so minimal multipath for
example)
4) Simulation done for today's date for a full 24 hours at 300-second epochs using current
almanac
5) Started with the current 30 healthy satellites and then reduced the number one by one
using the satellites on the U.S. Air Force's watch list going from plane to plane and slot
to slot. The particular order in which specific satellites are dropped would affect the
outcome somewhat.
6) Predicted 95 percent 3D position errors computed as 2 x 3.0 m x PDOP. Horizontal
positioning errors (latitude and longitude) would be about 2/3 smaller than the 3D errors.
Results of the May 21 analysis are available online (see below).
Langley states “There is more or less a gradual increase in average error as we lose
satellites. But even when there are only 21 satellites available, we don't drop below 5
visible satellites at any time during the day and the average position error is only 13.1
m, about 3 m worse than when we have 30 satellites. I think this is so because the
satellites on the watch list are spread over the 6 GPS planes. If they were all in one or
two planes, things would be different. Nevertheless, the maximum error does increase from
14.4 m to 38.3 m as we go from 30 to 21 satellites.
“This isn't a definitive study. We'd have to look at a number of sample locations around
the globe to get a truly representative idea of what might happen if the number of
available satellites was to drop significantly.
“Also, the situation will be markedly different when there are sky obstructions. I might
repeat the study using a higher elevation angle cutoff, say 20 degrees.”
Later that same day, he redid the analysis using a 20 degree elevation angle cutoff such
as might be the case in small towns where low buildings and trees could block
low-elevation-angle signals. “For fewer than 25 satellites, there are times in the day
when the number of available satellites drops below 4 so that 3D GPS standalone
positioning is not possible.” The new results were added to the 5-degree results and a PDF
file was posted.
In the most recent study (May 29), Langley used an approach with both 5-degree and
20-degree elevation angle cutoffs but with these differences:
1) A full constellation of 24 GLONASS satellites based on the current constellation of 20
satellites plus four more to fill in the gaps. Even though three satellites in the current
constellation are set unhealthy at the moment, some of these will likely return to service
and six more GLONASS satellites are expected to be launched this year and so we can expect
a full 24-satellite constellation in 2010.
2) Took into account the fact that GLONASS satellite orbit and clock data contained in the
navigation messages are not as accurate as GPS. In computing DOPS and position accuracies,
GLONASS"measurements" were downweighted by a factor of 2 (sigma-GLONASS = 2 x sigma-GPS).
3) Started the simulations with 54 satellites (30 GPS plus 24 GLONASS) and then reduced
the number of GPS satellites one by one in the same order as before: 27, 25,30, 3, 6, 24,
10, 32, 26.
The results of the May 29 simulations can be found here.
"Even for the 20-degree elevation-angle-cutoff scenario," said Langley, "we never drop
below 7 satellites and so there are no positioning outages. The worse case scenario with
just 21 GPS satellites and 24 GLONASS satellites has an average 95 percent 3D positioning
error of about 21 meters."