[Taxacom] Estimation in GPS positioning

[Curtis Clark]

On 12/4/2010 1:50 PM, Bob Mesibov wrote:
> Here's a simple example: the estimated population of Alaska is 698473 +/- 1000 people. What I've just said is that the true population of Alaska is estimated to be between 697473 and 699473. I have *not* said that the population is 698473.
>
> The statement looks a little funny because the population is given to the nearest person, but there is a 1000-person uncertainty in the estimate. The standard practice in dealing with significant figures is for the estimate to agree with the uncertainty, so I'll round off: 698000 +/- 1000. I have *not* just said that the population is 698000.
>
> There is no difference between these two estimates. I have not moved the population of Alaska from 698473 to 698000. I have not created a new population figure.
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.

"+/- 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. If we express 698000 as 6.98 x 10^5, to be precise about 
significant figures, we've said that we estimate the correct value to be 
between 697500 and 698499. If we add in +/- 1000, we've added error to 
error.

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.

> You cannot, as you seem to have done in your last post, treat possible positions within the estimate as real, and compare them.
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.)

-- 
Curtis Clark                  http://www.csupomona.edu/~jcclark/
Director, I&IT Web Development                   +1 909 979 6371
University Web Coordinator, Cal Poly Pomona