Research Information System
28th International Conference on Information Fusion, FUSION 2025, Rio de Janeiro, Brazil, 7 - 11 July 2025, (Full Text)
We present analytical expressions for predicting the mean square error (MSE) performance of the Kalman filter (KF) and Kalman smoother (KS) when applied to fixed, non-random state trajectories. Unlike the standard Bayesian setting, where the state is modeled as a random process, some practical applications-such as benchmark evaluations in target tracking-rely on deterministic state trajectories. In such cases, the KF and KS become biased and inconsistent (in a non-random/frequentist sense), and their standard covariance estimates no longer reflect actual estimation errors. To address this issue, we derive batch and horizon-recursive MSE expressions for KF and KS to predict their performance without relying on Monte Carlo simulations. Our approach also accounts for measurement model mismatch, allowing performance evaluation under model misspecification. Simulation results validate the accuracy of the proposed analytical expressions, demonstrating their agreement with empirical MSE values.