Abstract: In order to solve the nonlocal sampling problem inherent in CKF for high dimensional problems, a new methodology based on orthogonal matrix is proposed in this paper. The performance of the UT is analyzed based on the multi-dimensional Taylor series, to illustrate that even the problem of numerical instability of UKF can be solved by CKF, but the nonlocal sampling problem is introduced. Through the orthogonal matrix the new algorithm named ICKF is proposed in this paper. It is proved theoretically that ICKF has higher estimation accuracy than CKF in the high-dimentional and strongly nonlinearity situation, where local sampling problems is prominent. Simulation example verifies the effectiveness of the proposed algorithm.

Key words: nonlocal sampling problem, numerical integration formulas, orthogonal transformation, CKF algorithm

摘要： 针对传统CKF算法在解决高维问题时因非局部采样造成的滤波性能下降问题，基于设计的正交矩阵提出了一种改进的CKF算法。采用多元Taylor级数展开，揭示了CKF虽能解决UKF的数值不稳定性问题，但同时也引入了非局部采样问题这一事实；进一步设计出一种正交变换矩阵，用于对CKF算法中的采样点进行变换，并从理论上证明了提出的改进CKF算法相对于CKF在高维、强非线性等非局部采样问题突出的应用场合具有更高的估计精度。仿真结果验证了算法的有效性。

关键词: 非局部采样, 数值积分准则, 正交变换, CKF算法