Worst-Case Prediction Performance Analysis of the Kalman Filter

In this paper, we study the prediction performance of the Kalman filter (KF) in a worst case minimax setting as studied in online machine learning, information, and game theory. The aim is to predict the sequence of observations almost as well as the best reference predictor (comparator) sequence in a comparison class. We prove worst-case bounds on the cumulative squared prediction errors using a priori knowledge about the complexity of reference predictor sequence. In fact, the performance of the KF is derived as a function of the performance of the best reference predictor and the total amount of drift that occurs in the schedule of the best comparator.