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Data filtering-based parameter and state estimation algorithms for state-space systems disturbed by coloured noises. (English) Zbl 1483.93621

Summary: In this paper, the combined parameter and state estimation issues of state-space systems are considered, and the process noises and observation noises are supposed to be coloured noises. By utilising the data filtering technique, we transform the original state-space system into the filtered system for eliminating the interference of the coloured noise in the state equation, and then we derive a filtering-based extended stochastic gradient (F-ESG) algorithm to estimate the system parameters. For estimating the unmeasurable states, we derive a new state estimator by using the preceding parameter estimates to take the place of the unknown system parameters in the Kalman filter. Furthermore, we propose a filtering-based multi-innovation extended stochastic gradient (F-MI-ESG) algorithm to achieve the higher parameter estimation accuracy. Finally, we provide two simulation examples to test and compare the performance of the proposed algorithms. The simulation results indicate that the F-ESG algorithm and the F-MI-ESG algorithm are effective for parameter estimation, and that the F-MI-ESG algorithm is able to achieve more accurate parameter estimates than the F-ESG algorithm.

MSC:

93E10 Estimation and detection in stochastic control theory
93E11 Filtering in stochastic control theory
93E12 Identification in stochastic control theory
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