Performance of the Kalman Filter and Smoother for Benchmark Studies

TL;DR

This paper introduces analytical MSE expressions for the Kalman filter and smoother tailored for benchmark studies with unknown true system dynamics, enabling efficient performance evaluation without extensive simulations.

Contribution

It develops recursive MSE formulas that account for model mismatch and deterministic trajectories, improving performance prediction in benchmark scenarios.

Findings

Analytical MSE expressions match simulation results.

Method reduces computational complexity to linear time.

Framework effectively handles measurement model mismatch.

Abstract

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.