Filtering of Gaussian Systems

Book chapter (2021)

Authors

J.H. van Schuppen Mathematical Physics -

Research Group

Mathematical Physics () (TU Delft)

Kalman filter Filter algebraic Riccati equation

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Published Date

2021

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Mathematical Physics

Abstract

The filter problem is to derive an expression for the conditional distribution of the state of a stochastic system conditioned on the past outputs of the considered system and a recursion of the parameters of that conditional distribution. In this chapter the filter problem for a Gaussian stochastic system is solved. The Kalman filter is derived, including the time-varying, the time-invariant Kalman filter, and the conditional Kalman filter. The relation of the Kalman filter with stochastic realization is discussed. The Kalman filter is used in a very large number of research areas including signal processing, information theory, communication theory, weather prediction, hydrology, etc.