Analyses of a Drop in GPS Satellite Numbers

Analyses of a Drop in GPS Satellite Numbers
http://sidt.gpsworld.com/gpssidt/content/printContentPopup.jsp?id=3D60=
5171

Jun 22, 2009

Professor Richard Langley of the University of New Brunswick (also GPS Wo=
rld=E2=80=99s Innovation=20
editor) has done several analyses to see how the use of GLONASS satellite=
s could help=20
compensate for a potential reduction in the number of available GPS satel=
lites. These=20
studies came in response to a warning from the U.S. Government Accountabi=
lity Office about=20
the potential drop in the number of healthy satellites in the GPS constel=
lation as a=20
result of delays in both the Block IIF and Block III modernization progra=
ms.

An analysis posted on May 21 to the Canadian Space Geodesy Forum (CANSPAC=
E) looked at the=20
effect that a reduced number of available GPS satellites would have on co=
nventional 3D=20
positioning using pseudoranges as a typical handheld receiver would do ov=
er a period of 24=20
hours.

Assumptions:
1) Location: Fredericton, a typical mid-latitude site (results will be di=
fferent for=20
different locations)
2) Sky visibility: Perfect down to an elevation angle of 5 degrees; no bl=
ockages
3) Pseudorange measurement and modelling accuracy: 3 metres (so minimal m=
ultipath for=20
example)
4) Simulation done for today's date for a full 24 hours at 300-second epo=
chs using current=20
almanac
5) Started with the current 30 healthy satellites and then reduced the nu=
mber one by one=20
using the satellites on the U.S. Air Force's watch list going from plane =
to plane and slot=20
to slot. The particular order in which specific satellites are dropped wo=
uld affect the=20
outcome somewhat.
6) Predicted 95 percent 3D position errors computed as 2 x 3.0 m x PDOP. =
Horizontal=20
positioning errors (latitude and longitude) would be about 2/3 smaller th=
an the 3D errors.

Results of the May 21 analysis are available online (see below).

Langley states =E2=80=9CThere is more or less a gradual increase in avera=
ge error as we lose=20
satellites. But even when there are only 21 satellites available, we don'=
t drop below 5=20
visible satellites at any time during the day and the average position er=
ror is only 13.1=20
m, about 3 m worse than when we have 30 satellites. I think this is so be=
cause the=20
satellites on the watch list are spread over the 6 GPS planes. If they we=
re all in one or=20
two planes, things would be different. Nevertheless, the maximum error do=
es increase from=20
14.4 m to 38.3 m as we go from 30 to 21 satellites.

=E2=80=9CThis isn't a definitive study. We'd have to look at a number of =
sample locations around=20
the globe to get a truly representative idea of what might happen if the =
number of=20
available satellites was to drop significantly.

=E2=80=9CAlso, the situation will be markedly different when there are sk=
y obstructions. I might=20
repeat the study using a higher elevation angle cutoff, say 20 degrees.=E2=
=80=9D

Later that same day, he redid the analysis using a 20 degree elevation an=
gle cutoff such=20
as might be the case in small towns where low buildings and trees could b=
lock=20
low-elevation-angle signals. =E2=80=9CFor fewer than 25 satellites, there=
are times in the day=20
when the number of available satellites drops below 4 so that 3D GPS stan=
dalone=20
positioning is not possible.=E2=80=9D The new results were added to the 5=
-degree results and a PDF=20
file was posted.


In the most recent study (May 29), Langley used an approach with both 5-d=
egree and=20
20-degree elevation angle cutoffs but with these differences:

1) A full constellation of 24 GLONASS satellites based on the current con=
stellation of 20=20
satellites plus four more to fill in the gaps. Even though three satellit=
es in the current=20
constellation are set unhealthy at the moment, some of these will likely =
return to service=20
and six more GLONASS satellites are expected to be launched this year and=
so we can expect=20
a full 24-satellite constellation in 2010.

2) Took into account the fact that GLONASS satellite orbit and clock data=
contained in the=20
navigation messages are not as accurate as GPS. In computing DOPS and pos=
ition accuracies,=20
GLONASS"measurements" were downweighted by a factor of 2 (sigma-GLONASS =3D=
2 x sigma-GPS).

3) Started the simulations with 54 satellites (30 GPS plus 24 GLONASS) an=
d then reduced=20
the number of GPS satellites one by one in the same order as before: 27, =
25,30, 3, 6, 24,=20
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=20
below 7 satellites and so there are no positioning outages. The worse cas=
e scenario with=20
just 21 GPS satellites and 24 GLONASS satellites has an average 95 percen=
t 3D positioning=20
error of about 21 meters."