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In this work we propose an approximate Minimum Mean-Square Error (MMSE)filter for linear dynamic systems with Gaussian Mixture noise. The proposedestimator tracks each component of the Gaussian Mixture (GM) posterior with anindividual filter and minimizes the trace of the covariance matrix of the bankof filters, as opposed to minimizing the MSE of individual filters in thecommonly used Gaussian sum filter (GSF). Hence, the spread of means in theproposed method is smaller than that of GSF which makes it more robust toremoving components. Consequently, lower complexity reduction schemes can beused with the proposed filter without losing estimation accuracy and precision.This is supported through simulations on synthetic data as well as experimentaldata related to an indoor localization system. Additionally, we show that intwo limit cases the state estimation provided by our proposed method convergesto that of GSF, and we provide simulation results supporting this in othercases.

Approximate MMSE Estimator for Linear Dynamic Systems with Gaussian Mixture Noise