Data Driven Kalman Filter via Dynamic Mode Decomposition

Abstract

The Extended Kalman Filter (EKF) requires an analytical Jacobian of the system dynamics for uncertainty propagation, which is unavailable or expensive to compute in many practical settings. We propose a data-driven alternative in which the Jacobian is replaced by a local linear operator identified online from a sliding window of state observations using Dynamic Mode Decomposition (DMD). The nonlinear state prediction is retained in its original form via fourth-order Runge–Kutta integration, while the covariance matrix is propagated through the DMD operator, preserving the Gaussian structure of the uncertainty estimate. The proposed DMD KF algorithm is validated on the nonlinear inverted pendulum benchmark. Simulation results demonstrate that DMD KF achieves estimation accuracy comparable to the standard EKF without requiring any knowledge of the system Jacobian, and adapts online to changes in system dynamics.