Finding the Location of a Signal: A Bayesian Analysis

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Abstract
We study the problem of determining the location of an emergency transmitter in a downed aircraft. The observations are bearings read at fixed stations. A Bayesian approach, yielding a posterior map of probable locations, seems reasonable in this situation. We therefore develop conjugate prior distributions for the von Mises distribution, which we use to compute a posterior distribution of the location. An approximation to the posterior distribution yields accurate, rapidly computable answers. A common problem with this kind of data is the possibility that signals will reflect off orographic terrain features, resulting in wild bearings. Such bearings can affect the posterior distribution severely. We develop a sensitivity analysis, based on the idea of predictive distribution, to reject wild bearings. The method, which is based on an asymptotic argument, nonetheless performs well in a small simulation study. When the preceding approximation is used, the sensitivity analysis is practical in terms of computation time.

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