The fundamental nature of the map-matching problem is examined and theoretical justification for using various comparison metrics is investigated. Since the problem is one of statistical decision theory, the optimum solution is to compute the likelihood ratio for each comparison and choose the match point at a place where the likelihood ratio is maximum. That requires a knowledge of N-dimensional joint probability distributions; hence, we resort to approximations that maximize or minimize several functions called "metrics." By considering two-picture-element scenes, the features of various metrics are explained and compared with the likelihood ratio. In this way heuristic arguments are developed that support the use of the Product algorithm (a sum of products that is related to classical correlation) when S/N is low, and the MAD algorithm (mean absolute difference) when S/N is high.
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