MSE of Kalman Filter and Smoother for Fixed Non-Random State Trajectories

Date

2025-01-01

Author

Kurt, Batin
Orguner, Umut

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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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.

Subject Keywords

Kalman filter, Kalman smoother, model mismatch, model misspecification, performance evaluation

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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105015882563&origin=inward
https://hdl.handle.net/11511/115829

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Department of Electrical and Electronics Engineering, Conference / Seminar