Navigation Error

Okay, I’m fascinated by navigation problems . . . One interesting one is error in location calculations. Clearly there is really no way to get `perfect’ resolution of one’s current location. However, one might use some sort of average of multiple measures to come up with one better than all the others individually.

The fascinating part is how to accommodate all the information multiple measures of location provides. To the naive, each point is a single piece of information and sufficient in its own right. To the slightly more informed, it is half of a piece of information because it is an estimate and thus must be coupled with some concept of error in order to be properly appreciated.

So let’s say you have three GPS recievers which all provide different answers. Further, you`know’ the error is never more than 10 meters on any given reciever. Then the best estiamte isn’t the simple average of the three values, but a number drawn from the intersection of the error circles around the three points. Funny enough, under uniform error assumptions, that means any point int he intersection is equally valid and the average is simply one possible measure.

On the other hand, it is perhaps more reasonable to associate the 10 meter error bound as the 95th or 99th percentile of a chi-square distribution and from there derive the mean and variance for the associated normal distributions. Then one can perform maximum likelihood analysis on the problem to provide a `best’ estimate.

It makes me wonder how high quality navigation software does the math . . . probably not the sophisticated way.

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