A long term fix with GPS and
GARtrip
By Heinrich Pfeifer
Abstract
The position of a fixed point was
recorded for a whole week, in 30 seconds
intervals. This should show the properties of
the position error by GPS. The records are shown
as scatter plots, histograms and with a list of
characteristics.
This test was made three times:
firstly when the intentional degradation
("Selective Availability", SA) was effective.
Secondly when the SA was gone.And thirdly with
the EGNOS correction (this is the European
version of WAAS). In addition, the effect of a
partly shielded sky was compared with a full sky
reception.
To conclude the most important
results: the removal of SA was a very big
improvement of precision, about a factor of
10.But the addition of EGNOS has no significant
effect at all. It seems that the present "test
state" of EGNOS means that the differential
correction is not yet effective. I will have to
repeat this test when this test mode is
finished.Do not rely on the "accuracy"
indication of your receiver. An accuracy
indication as low as 2 meters means only that
the receiver believes it is so accurate. It
does not mean that the position is really
within 2 meters!
Contents
1. How I made the records
2. The reference point
3. Scatter plots of the records
4. Histograms of the records (with EGNOS)
5. List of characteristics
6. Averaging to improve precision
1. How I
made the records
This document shows the results
of a long term GPS measurement of a fixed
position, in order to check the precision or, at
least, the reproducibility of a GPS measurement.
For this purpose, the position of a fixed point
was recorded for a whole week, in 30 seconds
intervals. This experiment shall show the
precision of long-term measurements with
averaging and the statistical distribution of
error under different conditions.
This check was made the first
time was when the intentional degradation
("Selective Availability", SA) was effective, in
fact this was in March and April 1999.
Measurements on this condition are marked in
black within this document.
The position of a fixed point was
recorded by a Garmin GPS12XL (Firmware 3.02)
with external antenna GA27. The antenna was
fixed directly below a roof window, 30° slanted
eastwards. Besides the roof itself there was
nothing obstructing the satellite reception. The
track log memory of the Garmin receiver is not
big enough, so it was substituted by the
function "Actual position" within GARtrip.
A deeper review was published by
David L. Wilson; further references may be found
at Joe and Jack.
On 2-MAY-2000 the SA was
cancelled. Then I repeated the whole
investigation without SA, using the same
equipment, in May 2000. The results without SA
are in red colour. You will notice a very
big improvement
A further improvement in GPS
precision should be due to WAAS, or EGNOS here
in Europe. EGNOS is active since April 2003. So
I made one more record, comparing the precision
with/without EGNOS, end of April 2003. The
results with EGNOS are shown in blue colour.
This test was made with a Garmin Etrex Vista
(Firmware 3.10). Unfortunately, the EGNOS
satellite was not received at the antenna
position of the previous tests but it was
received well at another west side roof window.
So I repeated the non-EGNOS test with the Vista
receiver at this window first, to prove that the
result is comparable to the previous result with
the 12XL. This was compared with the EGNOS test
then. You won't notice any significant
improvement here. It appears that the present
test mode of EGNOS means that it's useless at
present, although the "D" indication of the
satellite bars was there, and the "accuracy"
indication of the receiver goes down to 2
meters at some times. But please see yourself.
To investigate in the effect of
signal quality, two more records were made at
the same position. This time the antenna was
mounted 60 centimeters below the window (50 x 80
centimeters). The roof itself is coated by
aluminium. This worsens the reception of
satellite signals gradually, to simulate a
critical condition. Some times the receiver
showed "poor coverage". The record was started
after the receiver showed "3D" the first time.
In this record there are big errors (757 meters
maximum), which may persist for some minutes.
This additional "bad signal" tests were made for
the black and red condition (with SA and without
SA) but not for the blue one (with EGNOS).
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2. The
reference point
After recording, a new waypoint
was created by averaging the whole track log,
using the suitable GARtrip function. Now this
new waypoint should be compared with an exact
reference point, but such was not available.
Therefore the absolute precision cannot be
checked, but the reproducibility can. For this
purpose the record was repeated at another
position, displaced by 7 meters. In this case,
the average of the record showed 8 meters
distance from the original position. The error
of one meter can be disregarded as GARtrip
rounds all distances to the nearest meter.
It shall be noted that the second measurement
was made on another roof window, 30° slanted
westwards. It seems that the signal blocking at
an elevation of 30° has no effect. Actually,
this "other window" was the same I used later
for the EGNOS test.
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3. Scatter
plots of the records
Following scatter plots show the
GARtrip charts of both records, both with same
scale. The black center point marks the
calculated average position.
Black record: with SA, red record: without SA.
Left chart: good signal; right chart: bad
signal.
For the EGNOS record, no scatter plot is shown
because it would not look different; see the
histograms below.
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4.
Histograms of the records
The following histograms show the
probability that the GPS error is below a given
value. For example, the black condition (with
SA) is in 95 % of all measurements within 65
meters (good signal) or within 180 meters (bad
signal). This compares to 57 meters by David L.
Wilson.
Left line: good signal (Record
#1); right line: bad signal (Record #5).
And here the same without SA;
please note the different scale.
Left line: good signal (Record
#2); right line: bad signal (Record #6). The
difference to the black chart is tremendous!
And now the comparison
with/without EGNOS. Since the equipment was
different than before (Vista receiver instead of
12XL, and other antenna location), a comparison
record was made without EGNOS (Record #3). This
line is shown in red. It should be equal to the
left line of the histogram above, and in fact it
is nearly the same, except for the result at 1
meter.
The blue line shows the histogram
with EGNOS active and, in fact, the difference
seems negligible (Record #4).
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5. List of
characteristics
Other differences are shown on
the following table. Readers who wish to do
their own calculations based on these records
may ask the Author for the original records.
Record 1: with SA
Record 2: without SA
Record 3: like record 2, with Vista receiver
instead of 12XL
Record 4: with EGNOS
Record 5: like record 1, with partly shaded sky
("bad signal")
Record 6: like record 2, with partly shaded sky
("bad signal")
Record #
|
1
|
2
|
3
|
4
|
5
|
6
|
Number of recorded
points
|
20402
|
20127
|
22084
|
19973
|
1735 9
|
1920 5
|
Date
|
22-03 -99
to
29-03 -99
|
11-05 -00
to
18-05 -00
|
24-04 -03
to
03-05 -03
|
16-04 -03
to
24-04 -03
|
05-04 -99
to
12-04 -99
|
22-05 -00
to
29-05 -00
|
Interruptions (Pauses)
due to "Poor Coverage"
|
0
|
0
|
0
|
0
|
169 (15% of the time)
|
79 (5 % of the time)
|
Average speed of error
wandering
|
1.0 km/h
|
0.2 km/h
|
0.3 km/h
|
0.3 km/h
|
2.7 km/h
|
0.4 km/h
|
Total distance of error
wandering
|
175 km
|
35.6 km
|
46.9 km
|
47.5 km
|
390 km
|
62 km
|
Maximum Error
|
203 m
|
22 m
|
21 m
|
80 m
|
757 m
|
280 m
|
99% of samples within
|
92 m
|
11 m
|
13 m
|
18 m
|
301 m
|
52 m
|
95% of samples within
|
63 m
|
8 m
|
9 m
|
9 m
|
182 m
|
22 m
|
50% of samples within
|
25 m
|
3.5 m
|
3.5 m
|
3 m
|
56 m
|
5 m
|
It appears that EGNOS improves
the best possible precision a bit, but the worst
case went worse with EGNOS. Of course the 80 m
error could have happened by chance, and it
would be better to make records #3 and #4
simultaneously, but I have only one set of
receiver equipment. But I can say that errors
bigger than 40 m happened at three different
days during the record period. Officially, EGNOS
will get operative middle of 2004. The present
data transmitted by EGNOS are reported not to be
consistent; only test data are sent. So it is
recommended not to use it.
Back to contents
6.
Averaging to improve precision
Related to this investigation, it
is interesting to see how the precision may be
improved by averaging. Allen Oliver did such a calculation, based on
the same sets of data. He averaged the positions
for 5 minutes, up to 36 hours. The following
diagrams show the improvements for "good signal"
and "bad signal" conditions.
Good signal, without SA
|
|
Bad signal, without SA
|
|
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|