The Method Of Cubature Kalman Filter And Its Application Research

With the rapid development of control and computer technology, the filter precision demand is higher and higher. Due to the nonlinear filtering algorithm can obtain the higher filtering precision, and has become more and more widely used.in the signal processing, automatic control, computer vision, wireless communications, aerospace, and target tracking and recognition and other fields, related experts and scholars have also caused wide attention and research. Extended Kalman filtering(EKF) algorithm is simple and easy to implement has been widely applied. However, EKF has some shortcomings. For example, it needs to calculate Jacobin matrix. Meanwhile, in hardy nonlinear and non-gaussian filtering performance is poorer, can appear even filtering divergence, limits the application of EKF in engineering practice. Although Unscented Kalman Filtering(UKF) and Central Difference Kalman Filtering(CDKF) do not need to calculate Jacobian matrix, have to choose the appropriate parameter to ensure the convergence. Particle Filtering(PF), as the number of sampling particles increases, increasing the amount of calculation and have poor real-time performance. Cubature Kalman Filter(CKF) is a superior performance of nonlinear filtering algorithm, which is emerging in recent years. Its mathematical theory is rigorous, convenient parameter selection, convergence effect is good. Moreover, it overcomes some problems of nonlinear filtering algorithm and is gradually become the focus and the development direction of nonlinear filtering technology in the current and future. This article revolves around CKF algorithm to improve the optimization research. The main work is as follows:For the interactive multiple model algorithm at the expense of the filtering precision of the implementation model matching problem, this paper proposes a virtual sampling promotion strategy based on measurement of interactive multiple model Cubature Kalman filter(IMM-CKF-S) algorithm. The algorithm adopts the current moment measurement and measurement noise prior statistical information to build a virtual measurement. Improving the reliability of the system measurement information based on the virtual measuremen of sampling and fusion. At the same time, under the framework of the interactive multiple model Cubature Kalman filtering algorithm to apply the realization of the distributed weighting fusion structure. In the precondition of the filtering precision, greatly improve the switching speed between models.In view of the problem of the system noise statistics properties of the nonlinear state estimation problem in the unknown situations, the Expectation Maximization(EM) algorithm applied in a nonlinear state space model, so we proposed an algorithm based on the Cubature Rauch Tung Striebel Smoother(CRTSS). The algorithm makes use of the maximum likelihood criterion to construct the logarithm likelihood function containing noise statistical properties. In step E, logarithmic likelihood function noise estimation problem can be converted to mathematical expectation, and in the step M, using the gradient descent algorithm deduced the recursive equations of the noise statistical estimator. The algorithm not only effectively overcome the decline of the filtering precision of the system noise statistics feature under unknown situation, and also realizes the system online estimation of noise statistical properties.