High-Fidelity Discrete-Time State-Dependent Riccati Equation Filters for Stochastic Nonlinear Systems with Gaussian/Non-Gaussian Noises

Two filtering techniques are proposed by using the discrete-time state-dependent Riccati equation (D-SDRE) methodology. Detailed derivation of the D-SDRE-based filter (D-SDREF) with the two-step procedure (measurement and update) is provided under the assumption of Gaussian noises. The input-to-state stability of the error signal between the measured and the estimated signals is proven under reasonable assumptions on system properties. For the non-Gaussian distributed noises, we propose a filter by combining the D-SDREF and the particle filter (PF), named the combined D-SDRE/PF. Algorithms of D-SDREF and combined D-SDRE/PF are provided. Performance of the latter techniques is compared with that of several other ones through the use of a challenging numerical example. Using the latter example, the reliability and the efficacy of the proposed D-SDREF and the combined D-SDRE/PF are demonstrated.

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