The Fragility of Noise Estimation in Kalman Filter: Optimization Can Handle Model-Misspecification
This work addresses the robustness of Kalman Filters for practitioners in domains like control systems and signal processing, offering an incremental improvement over standard noise estimation methods.
The paper tackles the problem of Kalman Filter (KF) parameter estimation under model misspecification, showing that traditional noise estimation fails when assumptions are violated, and proposes a gradient-based optimization method that consistently improves state prediction errors across multiple domains, making KF competitive with LSTM models even in nonlinear problems.
The Kalman Filter (KF) parameters are traditionally determined by noise estimation, since under the KF assumptions, the state prediction errors are minimized when the parameters correspond to the noise covariance. However, noise estimation remains the gold-standard regardless of the assumptions - even when it is not equivalent to errors minimization. We demonstrate that even seemingly simple problems may include multiple assumptions violations - which are sometimes hard to even notice. We show theoretically and empirically that even a minor violation may largely shift the optimal parameters. We propose a gradient-based method along with the Cholesky parameterization to explicitly optimize the state prediction errors. We show consistent improvement over noise estimation in tens of experiments in 3 different domains. Finally, we demonstrate that optimization makes the KF competitive with an LSTM model - even in non linear problems.