[Taxacom] Estimation in GPS positioning

Curtis Clark lists at curtisclark.org
Sun Dec 5 15:41:43 CST 2010

As I thought more about it, I realized that there is a kind of 
"precision" that doesn't involve repeatability.If I have a measuring 
stick gradated in meters, and I measure my height repeatedly (without 
interpolation), it will always be 2 m. There will be no statistical 
distribution. The precision of the measuring instrument is a fundamental 
limitation in its construction and use.

I imagine that GPS units have a similar fundamental precision: given a 
spherical Earth in a vacuum :-), the maximum theoretical number of 
satellites, and no electromagnetic interference, precision will be 
limited by the antenna length of the unit, and, given an antenna of 
infinite length, the wavelength of the radio signal and the accuracy of 
the clocks in the satellites.

No real-life situation ever comes close to this theoretical precision. 
Real-life situations are subject to measurement error, which can be 
treated as precision, but (if my pondering is correct) is not really the 
same thing. I'd like to believe that the published "accuracy" is the 
result of a sampling distribution under specified conditions, or, less 
optimally, a simulated sampling distribution.

And I wonder if it wouldn't be best, had we the data, to round to 
theoretical precision, and add error estimates, preferably as probabilities.

On 12/4/2010 5:54 PM, Bob Mesibov wrote:
> 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.
It means nothing, statistically. I'd like it to mean that the actual 
measurement has a 95% probability of being within 30 m of the reported 
measurement, but I doubt that's what it means.
> Not if the smaller uncertainty is contained within the larger uncertainty.
I might agree, but that's not what I thought you meant. Certainly your 
rounded example has a shifted ellipse relative to your unrounded, and 
that still seems an unnecessary discarding of data.
> 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?
Repeatability provides a framework for understanding single 
measurements. Repeatability is what tells us that the balance is truly 
unpredictable; otherwise it is just a surmise.

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

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