Optimal multi-model detection with application to Gaussian problems

Detection with multiple distributions is considered. Rather than formulating the problem with multiple hypotheses, we formulate the problem in a binary hypothesis testing framework by a multiple model approach. Three classes of the Multi-Model Detection (MMD) problems are considered: simplex, compound, and mixture. Three concepts of optimality are given for these three problems, including Uniformly Most Powerful over Mixtures (UMPM) for the mixture case. The relationships between different optimality are analyzed. A method of designing a UMPM test based on Uniformly Most Powerful (UMP) test is proposed. Several examples of the UMPM test for MMD problems with Gaussian distributions are given. Simulation results are provided that verify the theoretical conclusions.

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