Design of adaptive robust square-root cubature Kalman filter with noise statistic estimator

To solve the problem that when the model uncertainties exists or the prior noise statistics are unknown, the accuracy of the cubature Kalman filter (CKF) will decline or diverge, an adaptive robust square-root CKF (ARSCKF) algorithm with the noise statistic estimator is proposed. Firstly, the square-root version of the CKF (SCKF) algorithm is given when the means of process and measurement Gaussian noise sequences are nonzero. Secondly, based on strong tracking filter principle, the robust SCKF is designed to accommodate modeling uncertainties. Thirdly, the suboptimal unbiased constant noise statistic estimator based on the principle of maximum a posterior (MAP) is derived; on this basis, the recursive formula of the time variant noise statistic estimator using exponential weighted method is provided and then the implementation process of the ARSCKF algorithm is constructed. Finally, the efficacy of the ARSCKF is demonstrated by the numerical experiments of a high-dimensional target tracking system.