The Kalman filter: A robust estimator for some classes of linear quadratic problems
- 1 September 1976
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 22 (5) , 526-534
- https://doi.org/10.1109/tit.1976.1055611
Abstract
In this paper, theoretical justification is established for the common practice of applying the Kalman filter estimator to three classes of linear quadratic problems where the model statistics are not completely known, and hence specification of the filter gains is not optimum. The Kalman filter is shown to be a minimax estimator for one class of problems and to satisfy a saddlepoint condition in the other two classes of problems. Equations for the worst case covariance matrices are given which allow the specifications of the minimax Kalman filter gains and the worst case distributions for the respective classes of problems. Both time-varying and time-invariant systems are treated.Keywords
This publication has 5 references indexed in Scilit:
- On a Minimax Estimate for the Mean of a Normal Random Vector Under a Generalized Quadratic Loss FunctionThe Annals of Statistics, 1973
- On the minimax principle and zero sum stochastic differential gamesPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1972
- A Kalman filter as a minimax estimatorJournal of Optimization Theory and Applications, 1972
- Error bounds of continuous Kalman filters and the application to orbit determination problemsIEEE Transactions on Automatic Control, 1967
- A New Approach to Linear Filtering and Prediction ProblemsJournal of Basic Engineering, 1960