Valid Decoding in Gaussian Mixture Models

A novel recursive Bayesian inference method for state observation models with Gaussian mixture assumptions is presented. The proposed approach is located between marginal and maximum a posteriori (MAP) inference, both of which have been extensively explored over the last decades. A tight coupling is revealed between inferring the predicted and filtered marginal distributions and recursively decoding MAP predecessors. Based on these findings, an algorithm is presented to decode state sequences that are valid, i.e., consistent with underlying model assumptions. Since Gaussian mixtures can be used as universal approximators for density functions, an appropriate decoder holds considerable potential for various applications. Preliminary simulation results from ongoing research on object tracking, where observations are affected by multimodal noise, suggest that the proposed decoder may exhibit superior characteristics over traditional inference methods.