Sequentially best estimators for linear systems with non-linear noise-free sensors†
Hidenori Kimura · International Journal of Control · 1973
The problem considered is to estimate sequentially the state variables of a linear system given noise-free measurements on non-linear combinations of the state variables. Maximum likelihood is taken as the criterion for estimate. The first half of the paper is devoted to the analysis of linear cases. A simple sequential estimation scheme is obtained which generalizes the classical result of Kalman (960). Some new results are given which throw a light on the fundamental structure of the estimator. These results are applied to the derivation of the sequentially best estimator, the sequential estimator which is preferable to any other sequential estimator, for cases of general non-linear sensors. Two numerical examples are indicated in order to show the feasibility of the sequentially best estimator.