Widely-linear Gaussian sum filter

Motivated by application of widely-linear signal processing techniques in recursive Bayesian estimation, the paper proposes a novel widely-linear Gaussian sum filter (WL/GSF) for non-linear state estimation problems. Although the literature on non-linear state estimation using Gaussian sum filters is rich, its widely-linear counterpart which incorporates the full second-order statistics of the system and can potentially cope with non-Gaussian/non-circular measurements, have not yet been investigated in the literature. The paper addresses this gap. The WL/GSF resolves the computational burden of the Gaussian sum approach by incorporating a collapsing step. The number of components in the WL/GSF is controlled adaptively at each step utilizing a Bayesian learning technique to collapse, in an intelligent way, the resulting non-Gaussian sum mixture to an equivalent Gaussian term. Simulation results provided as proof of concepts and show that the proposed WL/GSF algorithm outperforms its counterparts in non-linear filtering problems with non-circular and non-Gaussian observations.