Cubature Kalman Filters推荐.pdf

1254 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 54, NO. 6, JUNE 2009 Cubature Kalman Filters Ienkaran Arasaratnam and Simon Haykin, Life Fellow, IEEE Abstract— In this paper, we present a new nonlinear filter for • Time update, which involves computing the predictive high-dimensional state estimation, which we have named the cuba- density ture Kalman filter (CKF). The heart of the CKF is a spherical-ra- dial cubature rule, which makes it possible to numerically com- pute multivariate moment integrals encountered in the nonlinear Bayesian filter. Specifically, we derive a third-degree spherical-ra- dial cubature rule that provides a set of cubature points scaling lin- early with the state-vector dimension. The CKF may therefore pro- vide a systematic solution for high-dimensional nonlinear filtering (3) problems. The paper also includes the derivation of a square-root version of the CKF for improved numerical stability. The CKF is tested experimentally in two nonlinear state estimation prob- lems. In the first problem, the proposed cubature rule is used to where denotes the history of input- compute the second-order statistics of a nonlinearly transformed measurement pairs up to time ; is the Gaussian random variable. The second problem addresses the use old posterior density at time and the state transition of the CKF for tracking a maneuvering aircraft. The results of both density is obtained from (1). experiments demonstrate the improved