Mathematics Clinic Probabilistic Position-Fixing

摘要

This is the final report of the 1985-86 Claremont Graduate School and Claremont Mckenna College Mathematics Clinic concerning a problem proposed by the Intelligence Analysis Group at the Jet Propulsion Laboratory. The problem is to determine confidence regions for the location of objects or emitters on which bearings are taken from two or more sensors whose positions are known. This clinic studied the classical approach to determining such regions which involved the assumption that an error of observation of the line of bearing displaces the line parallel to itself. By dropping this assumption, they found that the classical probability regions, which are ellipses, contained only 50% to 80% of the probability claimed. One goal of this year's clinic was to determine the reason for this very large discrepancy. As it turned out, the reason was neither the dropping of the parallel displacement assumption, nor computational errors in the clinic's work, but two equations in the original publication describing the classical approach were printed incorrectly. These errors are probably transcription errors, but no corrections or references to them were found in a search of the relevant literature.