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Neural networks for nonlinear state estimation. (English) Zbl 0814.93064

The paper deals with the problem of designing a state estimator for a linear stochastic dynamic system with a nonlinear noisy measurement channel. The authors propose non-recursive and recursive estimators, which are constrained to take the structure of multilayer neural networks. It is shown that the original optimization problem can be reduced to a nonlinear programming one. The approximation properties of neural estimators are investigated. For practical applications, the authors represent gradient techniques to design a recursive neural estimator. In comparison with classical methods, like the extended Kalman filter, the neural estimators require neither linearization nor strong a priori assumptions on the statistical properties of the random noise acting on both the dynamic system and the observation channel. The efficiency of the proposed methods is illustrated by some simulation results.

MSC:

93E10 Estimation and detection in stochastic control theory
93C10 Nonlinear systems in control theory
92B20 Neural networks for/in biological studies, artificial life and related topics
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