Receding-Horizon Nonlinear Kalman (RNK) Filter for State Estimation

Abstract

This technical note presents a new Receding-horizon Nonlinear Kalman (RNK) filter for state estimation in nonlinear systems with state constraints. Such problems appear in almost all engineering disciplines. Unlike the Moving Horizon Estimation (MHE) approach, the RNK Filter formulation follows the Kalman Filter (KF) predictor-corrector framework. The corrector step is solved as an optimization problem that handles constraints effectively. The performance improvement and robustness of the proposed estimator vis-a-vis the extended Kalman filter (EKF) are demonstrated through nonlinear examples. These examples also demonstrate the computational advantages of the proposed approach over the MHE formulation. The computational gain is due to the fact that the proposed RNK formulation avoids the repeated integration within an optimization loop that is required in an MHE formulation. Further, the proposed formulation results in a quadratic program (QP) problem for the corrector step when the measurement model is linear, irrespective of the state propagation model. In contrast, a nonlinear programming problem (NLP) needs to be solved when an MHE formulation is used for such problems. Also, the proposed filter for unconstrained linear systems results in a KF estimate for the current instant and smoothed estimates for the other instants of the receding horizon.