GPS reported accuracy, error function

Question

Most GPS systems report "accuracy" in units of meters, with the figure varying over orders of magnitude. What does this figure mean? How can it be translated to an error function for estimation, i.e. the probability of an actual position given the GPS reading and its reported accuracy?

According to the Wikipedia article on GPS accuracy, a reading down to 3 meters can be achieved by precisely timing the radio signals arriving at the receiver. This seems to correspond with the tightest error margin reported by e.g. an iPhone. But that wouldn't account for external signal distortion.

It sounds like an error function should have two domains, with a gentle linear slope out to the reported accuracy and then a polynomial or exponential increase further out.

Is there a better approach than to tinker with it? Do different GPS chipset vendors conform to any kind of standard meaning, or do they all provide only some kind of number for the sake of feature parity?

Answer 1

The number reported is usually called HEPE, Horizontal Estimated Position Error. In theory, 67% of the time the measurement should be within HEPE of the true position, and 33% of the time the measurement should be in horizontal error by more than the HEPE.

In practice, no one checks HEPE's very carefully, and in my experience, HEPE's reported for 3 or 4 satellite fixes are much larger than they need to be. That is, in my experience 3 satellite fixes are accurate to within a HEPE distance much more than 67% of the time.

The "assumed" error distribution is circular gaussian. So in principle you could find the right ratios for a circular gaussian and derive the 95% probability radius and so on. But to have these numbers be meaningful, you would need to do extensive statistical testing to verify that indeed you are getting around 95%.

The above are my impressions from working in the less accuracy sensitive parts of GPS over the years. Concievably, people who work on using GPS for aircraft landing may have a better sense of how to predict errors and error rates, but the techniques and methods they use are likely not available in consumer GPS devices.