Robust square-root cubature Kalman filter based on Huber’s M-estimation methodology

In practical engineering applications, the performance of the standard cubature Kalman filter (CKF) and its square-root version can be severely degraded due to outliers in measurement or contaminated distribution. In order to address the problem, a robust version of CKF is presented using Huber’s M-estimation methodology and square-root filtering framework. By making use of the Huber technique to reformulate the measurement update of CKF in square-root filtering framework, the proposed filter can exhibit robustness and numerical stability against deviation from Gaussian distribution assumption. In simulation tests, four versions of CKF—the standard, the square-root, Huber-based, and the proposed are evaluated in terms of estimation accuracy, numerical stability, and robustness under Gaussian and non-Gaussian distribution. The results are concluded that the square-root version outperforms the others under Gaussian distribution, whereas the proposed filter has improved performance in maintaining the robustness and numerical stability under non-Gaussian distribution. The investigated robust framework can be extended to other Gaussian filtering algorithms and the study is expected to facilitate applications of CKF in practical engineering as well.