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- estimating-error-in-my-GPS-position
- 01-19-2008
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On 19/01/2008, Charlie wrote in message <cb368800-5a05-4fc8-8ffd-
fda57dc06252@k2g2000hse.googlegroups.com>:
> 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 ?
> 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 ?
30m for both. In both dimensions. But before you proceed any further
it's vital to decide if you're measuring speed or velocity. If you're
measuring velocity then splitting up your measurement into x and y
components is absolutely the wrong thing to do.
------------------
But assuming it's the right thing to do, read on.
Suppose point 1 is at 10,100 and point 2 is at 20,200. You initial
estimate of the distance between the two points is 10 in the x direction
and 100 in the y direction. But you want to allow for the smallest
possible distance and the biggest possible distance.
The biggest possible distance in the x direction would be 10 + 30 + 30 =
70: purely by bad luck the two errors were both the maximum possible
amounts in the opposite directions.
The smallest possible distance in the x direction would be zero: the first
point might be 5 meters too low and the second point might be 5 meters too
high.
The biggest possible distance in the y direction would be 100 + 30 + 30 =
160. The smallest possible distance in the y direction would be 100 - 30 -
30 = 40.
Putting these two together into a velocity figure you get
A maximum of sqrt(160^2 + 40^2) = 165m
A minimum of sqrt(70^2 + 0^2) = 70m
------------------
On the other hand, if you're calculating based on velocity rather than
speeds in the x and y direction,
Suppose point 1 is at 10,100 and point 2 is at 20,200. You initial
estimate of the distance between the two points is sqrt(10^2 + 100^2) =
100.5.
The biggest possible distance would be 100.5 + 30 + 30 = 160.50m
The smallest possible distance would be 100.5 - 30 - 30 = 40.50m
As you can see from the above, where you do your splitting up your
movement into two different components -- the x and y components -- makes a
difference to your results.
Simon.
--
http://www.hearsay.demon.co.uk
> 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 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)
It strikes me that you have a lot of data from all the intermediate
positions that may be valuable but which the above approach is
ignoring. I'd be inclined to enter all of the data into a spreadsheet
such as Excel and plot a graph of how the position (lat. and long.)
varies with time. If it looks like a reasonably straight line (i.e.
uniform drift), then use a linear least-squares fit (a built in
function of Excel and similar tools) to find the average velocity as
well as the standard deviation in that velocity. Note that such an
average is likely to be more accurate than just taking the result from
the first and last measurements since it's based on multiple
measurements so the effect of random fluctuations of individual
measurements is reduced.
OTOH, looking at the plot might show behavior that's quite different
from a straight line. E.g. maybe there's periodic variation with the
tides or large variations due to storms or other disturbances. In
that case some further investigation would be called for rather than
just reporting the overall average velocity.
> [snip]
Peter the Dick head has spoken.
No one cares.
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