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Complex-Valued Gaussian Sum Filter for Nonlinear Filtering of Non-Gaussian/Non-Circular Noise

Motivated by application of Gaussian sum filters (GSF) and multiple model adaptive estimation (MMAE) approaches in scenarios where assumption of proper (circular) Gaussian signals is not valid, the letter proposes a novel complex-valued Gaussian sum filter (C/GSF) for non-linear filtering of non-Gaussian/non-circular measurement noise. Although the literature on recursive state estimation using GSF is rich, its complex-valued counterpart which incorporates the full second-order statistics of the system and can cope with non-Gaussian/non-circular measurements, has not yet been investigated in the literature. The paper addresses this gap. The C/GSF is a computationally attractive adaptive filter where the number of non-circular Gaussian components is controlled utilizing a modified Bayesian learning technique which is used to collapse the resulting non-Gaussian sum mixture into an equivalent complex-valued Gaussian term. Simulation results indicate that the C/GSF provides significant performance improvement over its traditional counterparts.