What are You Weighting For? Improved Weights for Gaussian Mixture Filtering
Dalton Durant, Andrey A. Popov, Renato Zanetti · 2024
Gaussian mixture-type filters have become indispensable tools for modeling intricate and nonlinear systems, offering a departure from traditional Gaussian-centric approaches. This work focuses on the critical aspect of accurate weight computation during the measurement incorporation phase of Gaussian mixture filters. The proposed novel approach computes weights by linearizing the measurement model about each component’s posterior estimate rather than the the prior, as traditionally done. This work proves equivalence with traditional methods in linear scenarios and empirically demonstrates improved performance in nonlinear cases. Two illustrative examples, the Avocado and Lorenz’ 63 models, serve to elucidate the advantages of the new weight computation technique by analyzing filter accuracy and efficiency through varying the number of Gaussian mixture components.