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7 May 2007 A unified Bayesian theory of measurements
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Abstract
Bayesian target detection, tracking, and identification is based on the recursive Bayes filter and its generalizations. This filter requires that measurements be transformed into likelihood values. Conventional likelihoods model the randomness of conventional measurements. Other measurement types involve not only randomness but also imprecision, vagueness, uncertainty, and contingency. Conventional measurements and target states are also mediated by precise, deterministic models. But in general these models can also involve imprecision, vagueness, or uncertainty. This paper describes three major types of generalized measurements and their associated generalized likelihood functions. If measurements are "UGA measurements" then fuzzy, Dempster-Shafer, and rule-based measurement fusion can be rigorously reformulated as special cases of Bayes' rule.
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Ronald Maher "A unified Bayesian theory of measurements", Proc. SPIE 6567, Signal Processing, Sensor Fusion, and Target Recognition XVI, 65670P (7 May 2007); https://doi.org/10.1117/12.721126
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