Constrained Abridged Gaussian Sum Extended Kalman Filter: Constrained Nonlinear Systems with Non-Gaussian Noises and Uncertainties
Mahshad Valipour, Luis Ricardez‐Sandoval
Abstract
This work presents a constrained abridged Gaussian sum extended Kalman filter (constrained AGS–EKF) that employs Gaussian mixture models to improve the estimation of extended Kalman filter (EKF) for constrained nonlinear applications involving non-zero mean non-Gaussian process uncertainties and measurement noises. The posterior estimation step in EKF is modified to adopt non-Gaussian measurement noises. An intermediate step is considered to approximate the non-Gaussian prior distribution of the constrained states at each sampling interval. This modified EKF also considers the modified prior estimation step proposed in AGS–EKF (to capture the non-Gaussian process uncertainties). Constrained AGS–EKF performs one (modified) EKF based on the mean value and covariance matrix of the overall Gaussian mixture model, thus avoiding additional computational costs and biased estimations observed in conventional Gaussian sum filters. Computational experiments were performed and showed that the proposed constrained AGS–EKF scheme is computationally efficient and provides appropriate estimates for applications involving active constraints on states, non-Gaussian process uncertainties, and measurement noises.