A simplified αβ based Gaussian sum filter

State estimation is a major problem in many fields, such as target tracking. For a linear Gaussian dynamic system, the KF provides the optimal state estimate, in the minimum mean square error sense. In general, however, real-world systems are governed by the presence of non-Gaussian noise and/or nonlinear systems. In this paper, the problem of state estimation in the case of a linear system affected by a non-Gaussian measurement noise is addressed. Based on the theoretical framework of the Gaussian sum filters (GSF), we propose a novel static version of this filter that uses the well known αβ filter. The simulation results show that the proposed filter has acceptable performances in terms of RMSE and a reduced computational load, compared to the classical GSF.

► For a linear Gaussian dynamic system, the KF provides the optimal state estimate.
► Real-world systems are governed by the presence of non-Gaussian noise.
► We estimate the state of a linear system with a non-Gaussian measurement noise.
► The well known αβ tracker is used within the GSF to form the new αβ-GSF.