Performance of the Kalman Filter and Smoother for Benchmark Studies

We propose analytical mean square error (MSE) expressions for the Kalman filter (KF) and the Kalman smoother (KS) for benchmark studies, where the true system dynamics are unknown or unavailable to the estimator. In such cases, as in benchmark evaluations for target tracking, the analysis relies on deterministic state trajectories. This setting introduces a model mismatch between the estimator and the true system, causing the covariance estimates to no longer reflect the actual estimation errors. To enable accurate performance prediction for deterministic state trajectories without relying on computationally intensive Monte Carlo simulations, we derive recursive MSE expressions with linear time complexity. The proposed framework also accounts for measurement model mismatch and provides an efficient tool for performance evaluation in benchmark studies involving long trajectories. Simulation results confirm the accuracy and computational efficiency of the proposed method.