A two-stage Kalman estimator for state estimation in the presence of random bias and for tracking maneuvering targets

The authors provide the optimal solution of a two-stage estimation problem in the presence of random bias. Under an algebraic constraint, the optimal estimate of the system state can be obtained as a linear combination of the output of the first stage (a bias-free filter) and the second stage (a bias filter). The results presented provide a basis for assessing the suboptimality of a two-stage estimator when used for a specific system. By treating the bias vector as a target acceleration, the two-state Kalman estimator can be used for tracking maneuvering targets