Performance metrics and bounds for Kalman filters with unknown or misspecified models

Date

2026-7-02

Author

Kurt, Batın

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This thesis proposes analytical and computationally efficient performance prediction methods for various Kalman filtering and smoothing algorithms under unknown or misspecified models. The considered setting is motivated by 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 true state trajectory is deterministic and available as reference data for performance evaluation, whereas Kalman filter and smoother-based estimators are derived under assumed stochastic state-space models. In addition, the true measurement model may differ from the model assumed by the estimators. This mismatched setting makes performance assessment nontrivial, while Monte Carlo evaluation can be computationally expensive. To address these problems, analytical mean square error (MSE) expressions are derived for the Kalman filter and smoother under deterministic state trajectories and measurement-model mismatch. Although the resulting batch and horizon-recursive formulations provide exact analytical performance predictions, their computational complexities grow cubically and quadratically, respectively, with the trajectory length. To overcome this limitation, an equivalent formulation of the Kalman smoother is considered, in which independent forward and backward recursions enable MSE computation with linear time complexity. The analysis is then extended to nonlinear systems by considering the iterated extended Kalman smoother under deterministic state trajectories and measurement-model misspecification. For this case, a lower bound on the MSE is derived using the misspecified Cramér-Rao lower bound. Simulation results validate the proposed methods and bounds, demonstrating their accuracy and computational efficiency for performance assessment.

Subject Keywords

Performance Prediction, Kalman Filter, Kalman Smoother, Model Misspecification, Fixed State Trajectories

URI

https://hdl.handle.net/11511/119934

Collections

Graduate School of Natural and Applied Sciences, Thesis