# [Taxacom] Estimation in GPS positioning

Bob Mesibov mesibov at southcom.com.au
Sat Dec 4 18:41:34 CST 2010

```Thank you for your contribution; it's good these issues are being carefully looked at.

Curtis Clark wrote:

"I was 100% with you until this. The estimates are different. if the population is 698473 +/- 1000 people, then 699470 is within the estimate. If it is instead 698000 +/- 1000, 699470 is outside the estimate."

You could be even more exact and say that the estimates are different because the range of the first is 697473-699473, and the second range is 697000-699000. I'm aware of that arithmetical difference. However, the two ranges are not comparable. 697473 is a number known to 6 significant figures, while 697000 is a number known to 3 significant places. You are putting the number 699470 first into a box where it fits with all its digits, and second into a box where it should be rounded off to 699000. Not fair.

""+/- 1000" is a statement of error around an estimated mean. Rounding to significant figures is also, indirectly, a statement of error around an estimated mean."

"+/- 1000" is not a statement of error around a mean. It is an uncertainty, plain and simple. The Alaska population number comes from Wikipedia and, ultimately, from the Census. It is not a mean, it is a head count. The +/- 1000 figure I added is my guess, for purposes of argument, at how reliable that number is. You can attach an uncertainty to any estimate, whether a mean or not.

"Dusty was writing about points, but every spatial coordinate is an ellipse which includes its error. We can specify the ellipse by rounding, or by some other indicator of error, but we probably shouldn't use both."

That's a very good argument, but it doesn't quite work for spatial data, for a reason mentioned (I think) by Rich Pyle. If I round a lat/long to the nearest second, that rounding implies a certain number of metres' uncertainty. For latitude, it's +/- 15 m; for longitude, it's roughly that number at the Equator and decreases towards the Poles. It is a coincidence that +/- 15 m is the RMS 'accuracy' for some GPS units. The real uncertainty could be larger and should be stated if it is. Again, I use +/- 25 m for single-point sampling because by going out to 25 m I am more likely to be including the true position than with 15 m (which, remember, is not a magical circle, but a 2/3 - 1/3 split in likelihood.) It's entirely appropriate for me to use nearest-second and +/- 25 m; it's the +/- 25 m figure that counts, not the +/- 15 m or less implied by the rounding.

"But they *are* points in a sampling distribution. If I were to take a few dozen measurements from the same spot over a period of an hour, that would give me a better estimate of error *at that time and place* than the published precision of the device. (Unfortunately it would be error in precision, rather than accuracy.)"

Absolutely correct. But what Rusty was trying to do was compare the estimate points with the true position (i.e., assess accuracy), which is unknown in the field. I thought I made that clear when I wrote 'It is just as likely that a rounded-off position will be closer to the true position than the non-rounded-off position, as for the rounded-off position to be further away. We have no idea what is happening within the estimate.'
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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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