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**Optimal filtering.**
*(English)*
Zbl 0688.93058

Information and System Sciences Series. Englewood Cliffs, NJ: Prentice- Hall, Inc. x, 357 p. $ 85.00 (1979).

This book is concerned with discrete-time linear filtering. In the first chapters, the authors introduce the stochastic system which has to be studied, define the estimation problem and derive the Kalman filtering equations. This basic study is then completed by several relevant topics, including the stability of the filter, the innovations, computational aspects, linear smoothing, reduced-order filters. The authors also consider nonlinear discrete-time filtering and obtain suboptimal filters by approximating the conditional density by a Gaussian density (extended Kalman filter) or by a linear combination of Gaussian densities; they give applications to adaptive filtering (in case of an unknown slowly varying parameter) and to filtering with coloured noise.

This book also provides several problems included in the text, a list emphasizing the main points at the end of each section, and a list of references at the end of each chapter. All these features make it valuable for graduate students who are concerned with filtering theory.

This book also provides several problems included in the text, a list emphasizing the main points at the end of each section, and a list of references at the end of each chapter. All these features make it valuable for graduate students who are concerned with filtering theory.

Reviewer: J.Picard

### MSC:

93E11 | Filtering in stochastic control theory |

93E12 | Identification in stochastic control theory |

93-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory |

93E15 | Stochastic stability in control theory |

93E25 | Computational methods in stochastic control (MSC2010) |