# [Taxacom] Inappropriate accuracy of locality data

Bob Mesibov mesibov at southcom.com.au
Sat Dec 4 01:30:22 CST 2010

```Hi, Dusty.

It is mathematically impossible to round off to the nearest second and shift a position 37-38 m. A second of latitude is ca 30 m, so the most you can possibly shift a latitude by rounding off to the nearest second is 15 m. A second of longitude in Alaska is smaller than 30 m.  The biggest possible shift, near the Equator, is ca 20 m, with the latitude rounding going one way and the longitude rounding going the other, the worst possible case. Want to check your calculation?

You are still misunderstanding GPS error. From a single reading we simply do not know how far the GPS reading is from the true location of the GPS. No amount of experimenting with mailboxes in a town will tell you what the uncertainty is in a reading on a wet day in forest surrounded by hills, yet it is *that* uncertainty that we need to report. The conservative approach is to base the uncertainty on the manufacturer's estimate. Garmin goes for 15 m RMS, and I extend that to 25 m to get a higher probability inside my point-radius circle.

Now let's look at 41 52 38.84 N. If you don't explicitly include an uncertainty in your report (95-99% of published lat/longs?), then the implied uncertainty is 0.01s, or 30 cm. This is nonsense. Your GPS cannot determine a position to this accuracy. It can easily determine a position to the nearest second. The '.84' arises from a calculation within the GPS which has not been rounded off by the software to the correct number of significant figures. Most of '.84' is noise, not data. You should round off 38.84 to 39 because without an explicit uncertainty you should not report a result that is incompatible with the known error in the GPS measurement. 41 52 39 is compatible with the known error in the measurement.

On to reporting *with* uncertainty. The comparison is between 41 52 38.84 N 87 39 08.48 W +/- 25 m and 41 52 39 N 87 39 08 W +/- 25 m. For purposes of argument we will ignore the fact that these figures are *not real points*, they are both merely estimators. Treat them as points. How far apart are they? I won't bother to do the calculation, because I can see from the numbers that the distance between these two estimates is much less than the error in the estimation. There is no statistical way to show how far *either* is from the true location. They are not different, within the error of the measurement.

Rounding off to 41 52 39 N 87 39 08 W +/- 25 m is not throwing away good data, because what you are ignoring is noise. Keeping the '.84' and '.48' does not improve the accuracy of your position, and does not introduce some big new error into the GPS reading.
--
Dr Robert Mesibov
Honorary Research Associate
Queen Victoria Museum and Art Gallery, and
School of Zoology, University of Tasmania
Home contact: PO Box 101, Penguin, Tasmania, Australia 7316
Ph: (03) 64371195; 61 3 64371195
Webpage: http://www.qvmag.tas.gov.au/?articleID=570

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