New version of continuous-discrete cubature Kalman filtering for nonlinear continuous-discrete systems

For nonlinear continuous-discrete systems, this paper elaborates a new accurate implementation of continuous-discrete cubature Kalman filter (CD-CKF). As the main contribution of this work, the new Kalman prediction stage begins by integrating the nonlinear continuous model for all the cubature sample vectors; the prior estimate state and covariance prediction are based on the weighted statistics of these integrated cubature sample vectors and the Gauss-Legendre approximation scheme. The new square root form CD-CKF is also derived and accurately implemented by combining with the modified variable stepsize NIRK. As the advantages of proposed approach, the complicated and error-prone processes of solving covariance differential equation or calculating derivatives are avoided, while the positive semi-definiteness of prior error covariance are numerically guaranteed. Simulations of traffic control scenarios further confirm the new approach's superior filtering performance in both reliability and accuracy.