Optimal Deterministic State Estimation—A First Step

Abstract

Optimal deterministic observers are derived for all first order linear time invariant systems. The optimization process consists of minimizing an objective function which is quadratic in the observer gain and in the estimation error. The objective function was chosen such that the resulting observer gains would be independent of system initial-condition which would, in general, be unknown to the state estimator. The results of this optimization are sensible in the light of the stochastic estimation results of Kalman.