Handling the challenge of missing measurements in nonlinear systems is a difficult problem in various scientific and engineering fields. Missing measurements, which can arise from technical faults during observation, diffusion channel shrinking, or the loss of specific metrics, can bring many challenges when estimating the state of nonlinear systems. To tackle this issue, this paper proposes a technique that utilizes a robust cubature Kalman filter (RCKF) by integrating Huber's M-estimation theory with the standard conventional cubature Kalman filter (CKF). Although a CKF is often used for solving nonlinear filtering problems, its effectiveness might be limited due to a lack of knowledge regarding the nonlinear model of the state and noise-related statistical information. In contrast, the RCKF demonstrates an ability to mitigate performance degradation and discretization issues related to track curves by leveraging covariance matrix predictions for state estimation and output control amidst dynamic disruption errors-even when noise statistics deviate from prior assumptions. The performance of extended Kalman filters (EKFs), unscented Kalman filters (UKFs), CKFs, and RCKFs was compared and evaluated using two numerical examples involving the Univariate Non-stationary Growth Model (UNGM) and bearing-only tracking (BOT). The numerical experiments demonstrated that the RCKF outperformed the EKF, EnKF, and CKF in effectively handling anomaly errors. Specifically, in the UNGM example, the RCKF achieved a significantly lower ARMSE (4.83) and ANCI (3.27)-similar outcomes were observed in the BOT example.
Keywords: cubature Kalman filter; missing data; robust cubature Kalman filter.