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Nonparametric methods of nonlinear filtering of stationary random sequences. (English. Russian original) Zbl 0539.93076
Autom. Remote Control 44, No. 6, 757-768 (1983); translation from Avtom. Telemekh. 1983, No. 6, 85-98 (1983).
A nonlinear method is proposed for filtering of strictly stationary ergodic random Markov sequence observed in noise. The state equation and the distribution of the signal is assumed to be unknown. The conditional probability density of observations is assumed to be of exponential type. The mean-square convergence of nonparametric estimates of a multivariate probability density and the convergence of the gradient in the uniform metric are proved.
Reviewer: M.Mokljacuk

93E10 Estimation and detection in stochastic control theory
60G35 Signal detection and filtering (aspects of stochastic processes)
62M20 Inference from stochastic processes and prediction
62G05 Nonparametric estimation