Optimal tracking index relationship for random and deterministic target maneuvers
Leonardo F. Urbano, Paul R. Kalata, Moshe Kam · 2012
In the standard formulation of the Kalman filter, target maneuver (acceleration) is assumed to be a random process that can be modeled as zero-mean additive white noise in the filter plant model. In the optimal reduced state estimator (ORSE) recently introduced by Mookerjee and Reifler, target maneuver is assumed to be a deterministic parameter in the plant model, equal to the maximum target acceleration. In this paper we exploit the steady-state equivalency of the Kalman filter and ORSE to derive an exact analytic expression relating the random tracking index of the Kalman filter, ΛR, and the deterministic tracking index of the ORSE, ΛD. The relationship offers a solution to a central problem in target tracking theory, namely how should the white plant noise level for a Kalman filter be selected for minimum mean square error state estimates in the presence of maximum target acceleration? Using the new relationship, a Kalman filter can be constructed with identical steady-state performance to the ORSE but without the additional computational complexity of the ORSE.