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A multi‐tone central divided difference frequency tracker with adaptive process noise covariance tuning
International Journal of Adaptive Control and Signal Processing ( IF 3.1 ) Pub Date : 2020-04-13 , DOI: 10.1002/acs.3111
Alessandro Brumana 1 , Luigi Piroddi 1
Affiliation  

The problem of real‐time frequency estimation of nonstationary multi‐harmonic signals is important in many applications. In this paper, we propose a novel multi‐frequency tracker based on a state‐space representation of the signal with Cartesian filters and the second‐order central divided difference filter (CDDF), which improves the performance of the extended Kalman filter (EKF) by using Stirling's interpolation method to approximate the mean and covariance of the state vector. A crucial element of the method is the adaptive scaling of the process noise covariance matrix appearing in the filter equations, as a function of the innovation sequence, which tunes the accuracy‐reactivity trade‐off of the filter. The proposed solution is evaluated against two approaches from the literature, namely the factorized adaptive notch filter (FANF) and the extended Kalman filter frequency tracker (EKFFT). Several experiments emphasize the estimation accuracy of the proposed method as well as the improved robustness with respect to initial errors and input signal complexity. The presented method appears to be particularly efficient with rapidly varying frequencies, thanks to the update mechanism that adjusts the filter parameters based on the amplitude of the estimation error.

中文翻译:

具有自适应过程噪声协方差调整的多音中央分频跟踪器

非平稳多谐波信号的实时频率估计问题在许多应用中很重要。在本文中,我们提出了一种新颖的多频跟踪器,它基于信号的状态空间表示,具有笛卡尔滤波器和二阶中央分差滤波器(CDDF),从而提高了扩展卡尔曼滤波器(EKF)的性能通过使用斯特林插值法来近似状态向量的均值和协方差。该方法的关键要素是根据创新序列对滤波器方程中出现的过程噪声协方差矩阵进行自适应缩放,从而调整滤波器的精度-反应性权衡。根据文献中的两种方法对提出的解决方案进行了评估,即因式自适应陷波滤波器(FANF)和扩展卡尔曼滤波器频率跟踪器(EKFFT)。一些实验强调了该方法的估计精度以及相对于初始误差和输入信号复杂度的改进的鲁棒性。由于更新机制根据估计误差的幅度调整滤波器参数,因此提出的方法在快速变化的频率下显得特别有效。
更新日期:2020-04-13
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