On change detection in a Kalman filter based tracking problem

• Additive abrupt state change in a tracking process is considered.
• Effect of the additive change on the innovation process is expressed in closed form.
• Optimal detection method suggested depending on the available information.

ObjectiveThis work considers detecting an additive abrupt state change in a tracking process. It is assumed that the tracking is done by a Kalman filter and that the abrupt change takes place after the steady-state behavior of the filter is reached.ResultThe effect of the additive change on the innovation process is expressed in closed form, and we show that the optimal detection method depends on the available information, contained in the change vector.MethodWe take a Bayesian perspective and show that prior knowledge on the nature of the change can be used to significantly improve the detection performance.ResultSpecifically, we show that performance of such a detector coincides with that of a matched filter when the variance (uncertainty) of the change tends to zero, and it coincides with that of an energy detector when the variance tends to infinity.ConclusionFinally we conclude that utilizing the derived closed form improves the detection performance for abrupt changes for Kalman filter based tracking problems. In addition, it is concluded that incorporating prior knowledge can improve the detection performance only if the prior variance is less than a certain amount.