The Fragility of Noise Estimation in Kalman Filter: Optimization Can Handle Model-Misspecification

Understand

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.