# [Taxacom] Estimation in GPS positioning

Bob Mesibov mesibov at southcom.com.au
Sat Dec 4 19:54:34 CST 2010

```Curtis Clark wrote:

"But we're estimating an integer. There exists an exact, correct value; it's not a measurement. If we knew that value, we'd never round it off (and see below)."

So the population example and my rounding off in that case isn't a good analogy with GPS measurement. OK, I agree, my bad. I used it to simplify the GPS story. I tried using a comparison of a balance and its sensitivity a few posts back, but that seemed to have fallen flat. Maybe you can come up with a better analogy. See if you can get it to cover Patrick Alexander's understanding that both the GPS manufacturer's accuracy claim and the GPS unit's accuracy declarations are maxima.

"If uncertainty is not error, it has no meaning statistically. It can't be used for inference, and no probability can be associated with it."

Fine. Now go to the Darwin Core's specification of position 'uncertainty', and tell me what (position) 43.1129 N 142.8837 E and (uncertainty) 30 m means, statistically.

"If you add an uncertainty value to a rounded number, you are broadening the ellipse. If either value alone is a good measure of uncertainty, combining them throws away actual precision."

Not if the smaller uncertainty is contained within the larger uncertainty. No 'precision' is thrown away. It sounds like you would prefer no. (2) of these 3:

(1) 41 52 38.84 N 87 39 08.48 W (+/- ca 15 cm implied)
(2) 41 52 38.84 N 87 39 08.48 W +/- 25 m
(3) 41 52 39 N 87 39 08 W +/- 25 m
(4) 41 52 39 N 87 39 08 W (+/- ca 15 m implied)

What appears in many published records today is (1), and that's why I started this thread. I like rounding off to a lat/long appropriate to the measurement, and (4) isn't right, so I prefer (3).

"But at its basis, precision is about repeatability, and that's something that can be dealt with statistically."

But repeatability doesn't come into the picture with one-off GPS measurements under field conditions with unknown measurement uncertainty. It's like measuring someone's weight just once on a balance with variable and unpredictable reliability. How does statistics help?
--
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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