Estimation of a Random Feedback Control System With Unknown Input

A method to estimate/track the state of a high-speed target that can be modeled as a feedback control system in three-dimensional (3-D) space is presented in this paper. The target's lateral acceleration input is not known, but it is known that the target will probably reach a destination position at a future time. The trajectory may involve random maneuvers. If the parameters of the modeled control loop are observable, the proposed model reduces the prediction and estimation errors. If the target's destination is known, then the accuracy can be increased further. The model, based on proportional navigation (PN), is nonlinear and can be used in a multiple-model estimator if the target can also perform random maneuvers along its route to the final destination. It is applied to a 3-D maneuvering aerial target state estimation problem with a target capable of high-magnitude, random lateral accelerations under a PN control policy. It is shown that due to the observability of the feedback control parameters, the filter significantly reduces the error of estimated position/velocity and provides a flexible estimation model for laterally maneuvering point targets in a 3-D fluid.