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Investigating GPS accuracy

I am a full subscriber to the school which warns amateur navigators against
imprudent reliance on GPS-based equipment.  In order to inform a course on
electronic navigation which I run at a local sailing school I set out to
collect data and display the performance of a cheap hand-held GPS receiver.

I have ended up with data and events recorded which are more perturbing
than I had anticipated.  The tables at the end of this note tell their own
story:  if only to warn me about the performance of my own GPS receiver!

I would be interested to hear from anyone who has done anything similar or
can point me in the direction of explaining the observations.  (I have
trawled the Web and Usenet, but may well have missed good material).

Anyway;  here's the story:

A few years ago I bought a Magellan 3000 hand-held GPS with NMEA interface.
In order to have a look at its performance I wrote a modest programme for
the PC which:
        - recorded each NMEA message
        - displayed the time and position
        - calculated the long term average position
        - recorded the frequency distribution of displacement from the
        long-term average position
        - calculated the RMS displacement
It plotted on the screen:
        - long-term average position
        - 1 minute moving average position
        - instantaneous position
and I set it running for many hours at a time.

In the days of Selective Availability I observed the anticipated dance of the
instantaneous position around the long-term average position;  routinely
observing displacements of 100-200 metres.  What I also recorded however
were major 'excursions' where the position readings would track in a fixed
direction away from the average position - steadily moving up to 2-3 NM away
- and then tracking steadily back along the same radial plot to the vicinity
of the average position.

These 'excursions' would take between 10 and 30 seconds to complete.
They occurred at random times, but typically there might be up to 2 or 3 per
hour.
They were directed randomly around the compass;  the long-term plot would
show them apparantly uniformly distributed.
Some days - when SA seemed to be particularly 'quiet' - there would be no
major excursion for many hours, but sooner or later they would restart.
The same phenomena were recorded in different locations with unobstructed
sky aspects.
On passage at sea I have observed similar spikes recorded on the track
display of the unit.

There were several plots of position readings posted on the web at that time.
Most were for commercial units.  Plots for cheaper GPS units rarely showed
data for the length of runs I was recording, but occasionally showed the odd
few readings which looked very much like what I was observing - but the plot
dimensions never were on a scale to record how far any excursions went.

So..... , when SA was discontinued in May I was eager to see what the same
set-up would record after the change.

What I found was, as expected, the instantaneous position now danced around
the long-term average routinely at less than 20 metres displacement.  But the
'excursions' still occurred in the same way:  steadily following a specific
azimuth out to a maximum and then tracking back along the same bearing.

Since May I have again tried the set-up out at different locations - again
observing similar results - and have again observed erratic spikes on the
set's track screen when at sea.
The frequency of excursions and their uniform distribution in direction
remain the same, but I have noted a reduction in the magnitude of the
maximum displacement.  (Statistics at the end of this note)

Has anyone observed similar phenomena?
        - plots of readings I have found now on the web show beautifully
        compact areas;  just as predicted!
Is there a well-understood explanation?
        - eg a faulty receiver?  I find it difficult to envisage how a faulty
        unit could generate the smoothness and consistency of azimuth of the
        observed excursions - and why I am now observing smaller scale
        excursions since May.
        - an artifact of receivers with limited channel capacity?


Proportion of position readings displaced from the long-term average position
by more than:

                        Prior to May 2000               After 1 May 2000

        2 NM                  0.05%                           0
        1.5 NM                0.08%                           0.08%
        1 NM                  0.19%                           0.09%
        0.5 NM                0.59%                           0.36%
        0.3 NM                1.08%                           0.77%
        0.2 NM                2.00%                           1.21%
        0.1 NM                6.22%                           2.65%

        RMS displacement       206m                            130m
        Number of readings   360072                           77909

(ie, 1 in 1100 readings is more than 1 NM in error)

With best regards

Geoff Butt

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 Geoff Butt at GTBT Network
 geoff@butt.demon.co.uk
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