A Prediction-Enhanced Polynomial Kalman Filter Using Higher-Order Predictive Representations for State Estimation

Abstract

The conventional Kalman filter operates primarily in the original first-order state-prediction space, which limits the explicit utilization of higher-order state-coupling and predictive statistical structures. To enlarge the candidate prediction space, this study proposes a Prediction-Enhanced Polynomial Kalman Filter (PEPKF). Through Kronecker augmentation, the original one-step prediction is extended to second-, third-, and higher-order polynomial representation spaces, introducing nonlinear internal predictive transformations while preserving the linear physical state-space model. The resulting higher-order quantities are formulated as equivalent predictive pseudo-observations and fused with the original prediction through weighted least squares to construct an enhanced prior, followed by the standard Kalman measurement update. Numerical simulation results show that PEPKF achieves better state-estimation performance than the conventional KF, thereby demonstrating the effectiveness of the proposed method.