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为了解决容积卡尔曼滤波(CKF)算法在处理高维问题时出现的非局部采样问题,提出基于采样点正交变换的改进CKF算法(TCKF).从数值积分近似角度导出无迹卡尔曼滤波(UKF)和CKF两种近似滤波算法,并指出CKF只是UKF的一个特例;基于多元Taylor级数展开分析,揭示CKF在克服UKF数值不稳定性问题的同时,引入非局部采样问题;对Cubature点集进行正交变换得到TCKF算法,并从理论上证明,在高维、强非线性等非局部采样问题突出的滤波模型中,TCKF具有比CKF更高的估计精度.仿真实例验证了所提出算法的有效性.
In order to solve the problem of non-local sampling when the volumetric Kalman filter (CKF) algorithm deals with high-dimensional problems, an improved CKF algorithm (TCKF) based on orthogonal transform of sampling points is proposed. From the numerical integration approximation, an unscented Kalman filter UKF) and CKF, and points out that CKF is only a special case of UKF. Based on the multiple Taylor series expansion analysis, it reveals that CKF overcomes the UKF numerical instability problem and introduces non-local sampling problem. The orthogonal transform is used to get the TCKF algorithm, and it is proved theoretically that TCKF has higher estimation accuracy than CKF in high-dimensional and strongly nonlinear non-local sampling problems. Simulation results show that the proposed algorithm Effectiveness.