School of Automation Science and Electrical Engineering, Beihang University, No. 37 Xueyuan Road, Haidian District, Beijing 100083, China.
Science and Technology on Aircraft Control Laboratory, Beihang University, No. 37 Xueyuan Road, Haidian District, Beijing 100083, China.
Sensors (Basel). 2019 Mar 19;19(6):1371. doi: 10.3390/s19061371.
The unscented Kalman filter (UKF) is widely used to address the nonlinear problems in target tracking. However, this standard UKF shows unstable performance whenever the noise covariance mismatches. Furthermore, in consideration of the deficiencies of the current adaptive UKF algorithm, this paper proposes a new adaptive UKF scheme for the time-varying noise covariance problems. First of all, the cross-correlation between the innovation and residual sequences is given and proven. On this basis, a linear matrix equation deduced from the innovation and residual sequences is applied to resolve the process noise covariance in real time. Using the redundant measurements, an improved measurement-based adaptive Kalman filtering algorithm is applied to estimate the measurement noise covariance, which is entirely immune to the state estimation. The results of the simulation indicate that under the condition of time-varying noise covariances, the proposed adaptive UKF outperforms the standard UKF and the current adaptive UKF algorithm, hence improving tracking accuracy and stability.
无迹卡尔曼滤波器（UKF）被广泛用于解决目标跟踪中的非线性问题。然而，当噪声协方差不匹配时，这种标准的 UKF 表现出不稳定的性能。此外，考虑到当前自适应 UKF 算法的缺陷，本文提出了一种新的自适应 UKF 方案，用于解决时变噪声协方差问题。首先，给出并证明了新息和残差序列之间的互相关。在此基础上，利用新息和残差序列推导出一个线性矩阵方程，实时求解过程噪声协方差。利用冗余测量值，应用改进的基于测量的自适应卡尔曼滤波算法来估计测量噪声协方差，该算法完全不受状态估计的影响。仿真结果表明，在时变噪声协方差条件下，所提出的自适应 UKF 优于标准 UKF 和当前的自适应 UKF 算法，从而提高了跟踪精度和稳定性。
