Huber-based high-degree cubature Kalman tracking algorithm

Abstract

In recent decades, nonlinear Kalman filtering based on Bayesian theory has been intensively studied to solve the problem of state estimation in nonlinear dynamical system. Under the Gaussian assumption, Bayesian filtering can provide a unified recursive solution to the estimation problem that is described as the calculation of Gaussian weighted integrals. However it is typically intractable to directly calculate these integrals. The numerical integration methods are required from a practical perspective. Therefore, nonlinear Kalman filters are generated by different numerical integrations. As a representative of nonlinear Kalman filter, cubature Kalman filter (CKF) utilizes a numerical rule based on the third-degree spherical-radial cubature rule to obtain better numerical stability, which is widely used in many fields, e.g., positioning, attitude estimation, and communication. Target tracking can be generalized as the estimations of the target position, the target velocity and other parameters. Hence, nonlinear Kalman filters can also be used to perform target tracking, effectively. Since the CKF based on the third-degree cubature rule has a limited accuracy of estimation, it is necessary to find a CKF based a cubature rule with higher accuracy in the case of target tracking system with a large uncertainty. High-degree cubature Kalman filter is therefore proposed to implement state estimation due to its higher numerical accuracy, which is preferred to solve the estimation problem existing in target tracking. To improve the filtering accuracy and robustness of high-degree cubature Kalman filter, in this paper we present a new filtering algorithm named Huber-based high-degree cubature Kalman filter (HHCKF) algorithm. After approximating nonlinear measurements by using the statistical linear regression model, the measurement update is implemented by the Huber M estimation. As a mixed estimation technique based on the minimum of l1-norm and l2-norm, the Huber estimator has high robustness and numerical accuracy under the assumption of Gaussian measurement noises. Therefore, the Huber-based high-degree cubature Kalman tracking algorithm is generated by combining the state prediction based on the fifth-degree spherical radial rule. In this paper, the influence of tuning parameter on the tracking performance is discussed by simulations. Simulations in the context of bearings only tracking and reentry vehicle tracking demonstrate that the new HHCKF can improve the tracking performance significantly.