Chapter 13. Linear Estimation

  1. Fredrik Gustafsson

Published Online: 16 OCT 2001

DOI: 10.1002/0470841613.ch13

Adaptive Filtering and Change Detection

Adaptive Filtering and Change Detection

How to Cite

Gustafsson, F. (2001) Linear Estimation, in Adaptive Filtering and Change Detection, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/0470841613.ch13

Author Information

  1. Linkoping University, Linkoping, Sweden

Publication History

  1. Published Online: 16 OCT 2001

ISBN Information

Print ISBN: 9780471492870

Online ISBN: 9780470841617



  • data segmentation;
  • change detection;
  • jump Markov model;
  • piecewise linear regression model;
  • Matlab;
  • Matlab toolbox;
  • autotuning;
  • signal processing;
  • adaptive signal processing;
  • adaptive systems;
  • fault diagnosis;
  • monitoring;
  • surveillance;
  • signal detection;
  • decision making;
  • statistics;
  • stochastic processes;
  • modeling;
  • estimation;
  • identification;
  • parameter estimation;
  • state estimation;
  • observers;
  • stochastic systems;
  • time-varying systems;
  • discrete time systems;
  • sampled data systems;
  • filters;
  • communication systems;
  • adaptive control


Linear estimation using algebraic projections, conditional expectation and Wiener filter theory is described.

First, we outline how projections are computed in linear algebra for finite dimensional vectors. Functional analysis generalizes this procedure to some infinite-dimensional spaces (so-called Hilbert spaces), and finally, we point out that linear estimation is a special case of an infinite-dimensional space. As an example, we derive the Kalman filter. Then, we use arguments and results from mathematical statistics to derive the Kalman filter. Finally, the Wiener filter is derived.