Equivalence between belief theories and naive bayesian fusion for systems with independent evidential data: part II, the example

Abstract

The process of fusing multiple independent sensor measurements. communication link data f.om other independent systems, and dynamic data base information is essential to support critical decisions in a timely way. Many real systems can be mapped to such a process. The independence of the input evidential data with an equal probable uniform prior probability distribution (i.e.. NaiLe Bayesian fusion) great& simplifies the mathematical techniques used to properly fuse the evidential data. Equivalence between Belief Fusion and NaiLe Bayesian is shown for this process. The equivalence comparison is done in probability space. The title of a 2001 colloquium, Data Fusion & Target ID: Dempster-Shafer & Probability Theories Hob War, depicts the state of mind of many researchers. The goal 01 this article is to show that large areas from both mathematical camps are equivalent This equivalence can be exploited by reducing the computational complexiry of thefusion process. Thefusion can be done in the linear probability set space rather than the exponential power-set representation of the belief space. For a system with IO possible hypotheses, The fusion of independent data in belief space would involve the fusion of as many as 1024 members of the power set, while exactly the same results can be obtained by fusion af 10 memkrs in probability space. This implies a non-trivial saving in computation complexiry for the implementation of many real systems, such as medical diagnostic systems, oil exploration systems, combat identzjkation, ballistic missile component discrimination, and homeland security automated systems.

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