Multi-dimensional belief fusion of multi-Gaussian structures

Abstract This paper describes the mathematical formulation of belief fusion of multi-Gaussian probability distribution functions (PDFs) in N-D, as well as the construction of some useful non-Gaussian structures. An emphasis of this work is the development of concise algorithms for constructing and efficiently fusing these non-Gaussian structures in N-space. In order to address decision-making using multi-Gaussian PDFs, an efficient probabilistic decision-making scheme is introduced and validated here. We investigate the trade-off between precision and efficiency in comparison with spatially discretizing fusion methods, concluding that the proposed techniques offer an improvement in both accuracy and efficiency for many contexts requiring non-Gaussian representation of belief. The proposed framework can be implemented in a diverse range of scenarios, potentially with real-time capability, and often without substantial sacrifice in accuracy.

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