Abstract: In order to overcome the problem that high-degree cubature Kalman filter decreases in accuracy with colored measurement noise, an improved high-degree cubature Kalman filter is presented in the paper. The first-order Markov model is used to whiten the colored measurement noise, then the nonlinear discrete stochastic system with colored measurement noise is transformed into a nonlinear time-delay system with normal white noise. The frame of Bayesian filter is derived in allusion to the whitened nonlinear time-delay system in Gaussian domain. High-degree cubature rule is applied in calculating the above frame to deduce the improved high-degree cubature Kalman filter with colored measurement noise. A maneuvering target tracking problem is used to test the performance of presented filter. The simulation results indicate that the improved high-degree cubature Kalman filter has the same accuracy as standard ones in the system with normal white Gaussian noise, has better accuracy and robustness when the measurement noise is colored.

Key words: nonlinear filtering, colored noise, high-degree cubature rule

摘要： 针对高阶容积卡尔曼滤波（HCKF）算法在有色量测噪声条件下滤波精度下降的问题，提出了有色量测噪声下的HCKF算法。通过一阶马尔科夫模型将有色量测噪声进行白化，将带有色量测噪声的非线性离散随机系统转化为白噪声下的非线性时滞系统，并给出高斯域内针对非线性时滞系统的贝叶斯滤波框架。利用高阶容积准则对该滤波框架进行近似计算，进而得到有色量测噪声下的HCKF算法。将所提算法应用到机动目标跟踪系统中，仿真实验结果表明，量测噪声为白噪声时，所提算法与标准HCKF算法具有相同的估计性能；在量测噪声为有色噪声时，所提算法相比于标准HCKF具有更优的估计精度和鲁棒性。

关键词: 非线性滤波, 有色噪声, 高阶容积准则