Chapter 4. Linear Optimal Filters and Predictors

  1. Mohinder S. Grewal PhD, PE1 and
  2. Angus P. Andrews PhD2

Published Online: 28 MAY 2002

DOI: 10.1002/0471266388.ch4

Kalman Filtering: Theory and Practice Using MATLAB ®, Second Edition

Kalman Filtering: Theory and Practice Using MATLAB ®, Second Edition

How to Cite

Grewal, M. S. and Andrews, A. P. (2002) Linear Optimal Filters and Predictors, in Kalman Filtering: Theory and Practice Using MATLAB ®, Second Edition, John Wiley & Sons, Inc., New York, USA. doi: 10.1002/0471266388.ch4

Author Information

  1. 1

    California State University at Fullerton

  2. 2

    Rockwell Science Center, Thousand Oaks, California

Publication History

  1. Published Online: 28 MAY 2002
  2. Published Print: 2 JAN 2002

ISBN Information

Print ISBN: 9780471392545

Online ISBN: 9780471266389

SEARCH

Keywords:

  • linear optimal filters;
  • Kalman filter;
  • Kalman-Buey filter;
  • optimal linear predictors;
  • noise sources;
  • Wiener filter;
  • quadratic loss functions;
  • Riccati equations;
  • discrete time;
  • state variables;
  • smoothers

Summary

This chapter is prepared to derive the mathematical forms of optimal linear estimators for the states of linear stochastic systems defined in the previous chapters. This is called the linear quandratic Gaussian (LQG) estimation problem. The dynamic systems are linear, the performance cost functions are quadratic, and the random processes are Gaussian.