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JOURNALS // Problemy Peredachi Informatsii // Archive

Probl. Peredachi Inf., 1976 Volume 12, Issue 1, Pages 29–40 (Mi ppi1673)

Methods of Signal Processing

Spatial-Temporal Nonlinear Filtering for Poisson Random Fields

V. I. Fedoseev, F. V. Shirokov


Abstract: The article considers the problem of estimating a diffusion process $\mathbf x_t$ from results of observations of a Poisson random field $N(t,\xi)$ whose parameter (intensity function) depends on the process $\mathbf x_t$. On the basis of Grigelionis’ results [Lit. Mat. Sb., 1972, vol. 12, no. 4, pp. 37–51] the authors obtain a stochastic equation for the probability density of $\mathbf x_1$; expressions are derived in the Gaussian approximation for the estimate ${\mathbf x}^{\widehat{}}_t$ and covariation matrix $\mathbf D_t$; two examples are considered.

UDC: 621.391.1:519.27

Received: 11.03.1974
Revised: 28.03.1975


 English version:
Problems of Information Transmission, 1976, 12:1, 20–28

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