Bayesian Identifying One or Two Close Sources by Gaussian Estimates of Planar Location under Double Emission

Abstract

Oleg I. Gerasimov

In case the separation for the parameters of interest appears below the resolution limit of the estimator, the ambiguity arises whether the two parameter estimates relate to one source emitted twice or to two close sources emitted once. The paper develops novel Bayes technique aimed to identify one/two closely spaced sources having a pair of Gaussian estimates of planar location as parameter. Prior probabilities of the one/two-sources hypotheses are available from the analysis of the physical characteristics of the emissions, assuming that they can be equally probable. The technique calculates minimal and maximal posterior probabilities of the hypotheses across all the positions at a given distance between them. When the minimal probability of one source is bigger than the maximal probability of two sources the decision is adopted in favor of one source and vice versa. Identification procedure is applied to distinguish two planar location estimates obtained for the users of basic station network by the time difference of arrival algorithm. The application gives an example of how the procedure revises the prior probabilities and can change thereby the initial preference with the distance between users.

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