Asymptotically \(\epsilon\)-optimal nonparametric procedure for nonlinear filtering of stationary sequences with unknown statistical characteristics.

*(English. Russian original)*Zbl 0563.93064
Autom. Remote Control 45, 1569-1576 (1984); translation from Avtom. Telemekh. 1984, No. 12, 40-49 (1984).

A nonparametric procedure is given for the nonlinear filtering of Markov random sequences which are stationary in the narrow sense, whose state equations and family of finite-dimensional distributions are unknown. Such a procedure is based on a unique realization of the observed process with strong mixing under certain assumptions about the noise distribution in the observations. Asymptotically, i.e., for increasing length of the realization, the performance of this procedure differs by arbitrary \(\epsilon >0\) from optimal nonlinear filtering, which is based on completely known statistical characteristics of unobserved signals. Examples are considered and results of a model experiment are given.

##### MSC:

93E11 | Filtering in stochastic control theory |

60G10 | Stationary stochastic processes |

60G20 | Generalized stochastic processes |

60G35 | Signal detection and filtering (aspects of stochastic processes) |

62M20 | Inference from stochastic processes and prediction |