Extended adaptive Kalman filter with low noise observations

Abstract

The model of partially observed nonlinear system, called extended Kalman filter (EKF), and depending on some unknown parameters is considered. An approximation of the unobserved component is proposed. This approximation is realized in two steps. First a the method of moments estimator of unknown parameter is constructed and then this estimator is substituted in the equations of extended Kalman filter. The obtained equations describe the adaptive extended Kalman filter. The properties of estimator of the unknown parameter and of the unknown state are described in the asymptotic of small noise in observations.

Keywords

Partially observed nonlinear system / Hidden markov process / Parameter estimation / Method of moments estimators / On-line approximation / Adaptive extended Kalman filter

Acknowledgements

I would like to express my gratitude to Referees for helpful comments and suggestions. This research was financially supported by the Russian Science Foundation research project (Grant No. 24-11-00191).

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