Wilsons Sandbox

After launching more discussion and disagreement than I had expected to regarding the precision of GPS measurements of distance (or speed), I decided to just go out and measure it. Accordingly, this morning I marked 11 waypoints in succession, with the GPS fixed in one spot. The time between marking each waypoint was about 3 seconds. The GPS was seeing 5 to 6 satellites during this time. I then plotted the 11 points and their geographic centroid, and set out to find the average deviation of the measured points. I did this two ways, the first way (method A) assuming that the 11 positions were randomly distributed, and the second (method B) assuming that the 11 positions followed a continuous trajectory. (Visual examination of the spatial distribution of points could support either assumption.) By method A, I computed the average deviation of the points from the centroid, and by method B I computed the average deviation between successive waypoints. With method B, to account for the fact that it took me about 3 seconds to acquire each waypoint, and because I want a measure of the variation to be expected in one second, I first divided each of the successive deviations by 3. The results were that method A yielded an error estimate for a single point (average deviation) of 6.65 feet, and method B yielded an error estimate of 1.55 feet. To measure the distance traveled (e.g., in one second), the distance between two successive points must be computed, and the error about the locations of the individual points must be propagated to yield an error estimate for the distance. Thus, method A yields an error estimate for a computed distance (any distance measured between two points) of 9.4 feet, and method B yields a corresponding error estimate of 2.2 feet. If the distance calculation is made using two points whose positions are measured one second apart, and the GPS (motorcycle) travels 85 feet in that second (or 58 mph), then the relative errors in the distance measurement are 11% and 2.6%, respectively. The GPS might actually do better than either of these by measuring positions more frequently, or might seem to do better (in the speed display) by presenting a running average of the last few measurements. And for a continuous record of distance traveled, all of those little measured distances (e.g., 85 foot segments) have to be added up, and their errors propagated. If you string together enough little distances and propagate the errors, the relative error will decrease; for example, if you string together 30,600 intervals, the relative error at the end is about 0.01%. Dreas