estimating error in my GPS position.

Hello all,


I have a time series of GPS positions, longitude and latitude, from a
drifter at the top of the ocean, and I am trying to estimate the
velocity of surface drift.

What I am doing is taking the difference between my first and last
longitude coordinate and convert them to meters. This gives me my
"delta x", and dividing by the time over which this occurred "delta t"
at the surface, I obtain an estimate of surface velocity U (positive
east)

I do the same for latitude,find the difference in latitudes, convert
to meters then divide by "delta t", to obtain my velocity V (positive
north).


But I need some kind of estimate of the error in these velocities, U
and V. I know the appropriate error formulas for propagating error but
I am unsure what number to use for my estimate in the error of my
longitude and latitude data respectively.

The manual says the GPS is good to within 30m but this is for the
radius around a point (lon,lat). What I require is an estimate of the
error in the longitude, and a separate estimate of the error in the
latitude. Or should I use 30m each for both? or perhaps half that for
each ?

Is there any way to figure this out?


Any help you can provide me on this would be greatly appreciated!

cheers,

- C

Oooh - you have all these data points, and you are only using the
first and the last? It seems to me you might hope to get better
results by using all the points and doing some smoothing of that
data, possibly even something as simple minded as a linear regression
of x and y coordinates with respect to time.


Note that much of the error will be due to variable atmospheric
conditions, which change slowly, meaning that the errors at different
times are not independent. This implies that your velocity estimates
may well be quite a bit more accurate than you would otherwise
assume. Or perhaps not; ocean currents are slow, so maybe your
measurement timescales are too long for this correlation to help.


I think you can get more detailed information of the nature of the
error if you know the geometry of the satellites at the time. This
data is of course available, but my uneducated guess is that you don't
get a very big improvement that way.

Did you log altitude also? That may seem silly for an ocean drifter,
but since you know the real altitude to be zero, any departure from
that should give you some indication of the quality of your data. It
could perhaps even be used to get an improved estimate on position.

Okay, so no very specific advice from me, but maybe some food for
thought?

--
- It is undesirable to believe a proposition
when there is no ground whatsoever for supposing it is true.
-- Bertrand Russell

Charlie wrote:

The estimated errors in the position are just that, estimates only. So
you can only assume some sort of error distribution in both lat and lon,
and compute an error based on that. If the errors followed a normal
distribution, you could assume the lat and lon errors each contributed
about 1/sqrt(2) to the total, ie around 20 m each. Real world GPS
positions suffer from all sorts of non-random errors, so doing the usual
RMS error analysis is unlikely to help much.

A further suggestion:
Many GPS units will output a velocity measurement which is independent
of the position, done by using Doppler shift on the signals themselves.
This value is often available to within 0.1 m/sec or better, depending
on the receiver, and might be better for measuring short term drift
velocity. At least its an independent measurement you could use as a
cross-check. Check your specific GPS unit specs. I know for instance
that some Garmin GPS engines will give velocity measurements to within
around 5 mm/sec resolution, if not accuracy.



--
Regards,

Adrian Jansen adrianjansen at internode dot on dot net
Design Engineer J & K Micro Systems
Microcomputer solutions for industrial control
Note reply address is invalid, convert address above to machine form.

Adrian Jansen wrote:

I have read this assertion many times, and I have no reason to doubt it.
Except that of course the Doppler shift will be largely caused by the motion
of the satellite, there will be at least four different ones because four
satellites are needed for a good fix, and they just add up to result in an
instantaneous varying voltage at the antenna. So what is needed is a very
accurate freequency analysis of at least four varying carriers, of
sufficient precision to subtract the satellite speed (component along the
line joining satellite and receiver) to leave the receiver speed. I find
this very impressive!

Mike.
--
If reply address = connectfee, add an r because it is free not fee.

The calculations will also have to account for the directions of travel of
the satellites and of the GPS receiver in 3 dimensions. It is my belief that
most receivers use distance travelled and time interval, possibly using more
that one time step, to calculate velocity.