GPS error

Previously posted in a Facebook discussion. I thought I'd archive it here.

Article: Due to statistical bias, GPS distance estimates tend to always be about 10-20% higher than is correct.  (http://www.i-programmer.info/news/145-mapping-a-gis/9164-gps-always-over-estimates-distances.html)

My comments:  

This is surprising and counter-intuitive. I didn't follow the details of the explanation, so I did my own test: take points A and B, and place each in the center of a 3x3 grid. This grid represents possible error (each cell representing a place where the point might be measured), so there are 81 possible ways to measure the distance between A and B. The result: 27/81 (or 1/3) chance of under-measuring the distance; 9/81 (or 1/9) chance of measuring an equivalent distance; 45/81 (or 5/9) chance of over-measuring distance. How about that!
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As I worked through it, I could see the above falls out of the fact that at small angles, sin(θ) changes more quickly than cos(θ).
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I thought of a way to think about this for a continuous range of error. Say the true distance between A and B is D. B will be erroneously taken to be at a random point on a circle of radius R centered on B. Call this circle B-false.

Draw the circle of radius D centered at A. This divides B-false into 2 arcs. The smaller arc is where B can be falsely placed and result in a smaller measured distance between A and B. The larger arc, where B is more likely to be taken to be, results in a larger measured distance between A and B.