Robust Cubature Kalman Filter for Moving-Target Tracking with Missing Measurements

Abstract

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.

Adaptive Multi-Sensor Joint Tracking Algorithm with Unknown Noise Characteristics

“…In tracking applications, the use of the Cartesian coordinate system for the modeling process and the fact that the measurements are usually in a polar or spherical coordinate system, as well as the motion model of the space target, all lead to the issue that the target tracking process is essentially a nonlinear filtering problem [ 11 ]. Nonlinear filtering algorithms, such as the extended Kalman filter, unscented Kalman filter, and particle filter, can perform well in their respective applicable scenarios to improve measurement accuracy [ 12 , 13 , 14 , 15 ]. There are also many current studies that have used various types of improved filtering methods for radar measurements or sensor measurements of a target’s motion trajectory.…”