Gaussian Sum Filtering for Wiener State-Space Models with a Class of Non-Monotonic Piecewise Nonlinearities

State estimation of nonlinear dynamical systems has gained significant attention due to its countless applications in control, signal processing, fault diagnosis, and power networks. The complexity posed by challenging nonlinearities like dead-zones, saturations, and linear rectification requires advanced state estimation. This paper presents a novel filtering technique designed for state-space Wiener systems encompassing these specific nonlinear behaviors. The filtering approach developed in this work introduces an explicit model for the probability function of the nonlinear output conditioned to the system state, which is derived from a Gaussian quadrature-based approximation. A Gaussian sum filtering algorithm is then used to obtain the filtering distributions and state estimates of systems with the aforementioned nonlinearities. Extensive numerical simulations are conducted to assess the accuracy of the proposed method compared to conventional techniques.