This article develops the modified extended Kalman filter based recursive estimation algorithms for Wiener nonlinear systems with process noise and measurement noise. The prior estimate of the linear block output is computed based on the auxiliary model, and the posterior estimate is updated by designing a modified extended Kalman filter. A multi-innovation gradient algorithm and a recursive least squares algorithm are derived to estimate the parameters of the linear subsystem, respectively. The simulation examples are provided to demonstrate the effectiveness of the proposed algorithms.
This paper develops a bias compensation-based parameter and state estimation algorithm for the observability canonical state-space system corrupted by colored noise. The state-space system is transformed into a linear regressive model by eliminating the state variables. Based on the determination of the noise variance and noise model, a bias correction term is added into the least squares estimate, and the system parameters and states are computed interactively. The proposed algorithm can generate the unbiased parameter estimate. Two illustrative examples are given to show the effectiveness of the proposed algorithm.
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