基于高阶累积量ESPRIT算法的指数衰减正弦信号参数估计  

Parameter estimation of exponentially decayed sinusoidal signals based on high-order cumulant ESPRIT algorithm

作　　者：单泽彪[1,2] 徐恩达 张旭 刘小松 Shan Zebiao;Xu Enda;Zhang Xu;Liu Xiaosong(School of Electronic and Information Engineering,Changchun University of Science and Technology,Changchun 130022,China;Changchun Meteorological Instrument Research Institute,Changchun 130102,China)

机构地区：[1]长春理工大学电子信息工程学院,长春130022 [2]长春气象仪器研究所,长春130102

出　　处：《电子测量与仪器学报》2024年第1期187-194,共8页Journal of Electronic Measurement and Instrumentation

基　　金：吉林省自然科学基金项目(YDZJ202301ZYTS412);吉林省教育厅科学技术项目(JJKH20240938KJ);吉林省教育厅产业化培育项目(JJKH20240940CY)资助。

摘　　要：工程应用中环境噪声多表现为高斯有色噪声,而针对高斯白噪声进行处理的算法失效问题,提出了一种高斯色噪声环境中用于多分量衰减正弦信号频率和衰减因子估计的四阶累积量ESPRIT算法。首先,推导出四阶累积量与观测样本中的自相关矩阵和互相关矩阵之间的关系,求出其四阶累积量矩阵。其次,通过对四阶累积量进行广义特征值分解,根据广义特征值即可得到信号衰减因子和频率的估计值。最后对所提算法进行了仿真实验验证,在混合信噪比为0 dB时,所提算法针对多分量衰减正弦信号角频率和衰减因子的平均估计误差分别为0.002 0πrad和0.002 0。在高斯白噪声和高斯色噪声背景下与ESPRIT算法和Prony算法相比具有更强的噪声抑制能力和更高的估计精度。Aiming at the problem that the actual environmental noise in engineering applications is mainly manifested as Gaussian colored noise and the algorithms for processing Gaussian white noise fail,a fourth-order cumulant ESPRIT algorithm is proposed for the estimation of the frequency and attenuation factor of multicomponent attenuated sinusoidal signals in Gaussian colored noise environments.First,the relationship between the fourth-order cumulants and the autocorrelation and intercorrelation matrices in the observed samples is derived to find their fourth-order cumulant matrices.Second,the generalized eigenvalue decomposition of the fourth-order cumulants is performed,and the signal attenuation factor and frequency estimates can be obtained based on the generalized eigenvalues.Finally,the proposed algorithm is validated by simulation experiments.The average estimation errors of the proposed algorithm for the angular frequency and the attenuation factor of the multicomponent fading sinusoidal signal are 0.002 0π rad and 0.002 0 at the hybrid signal-to-noise ratio of 0 dB.Compared with ESPRIT and Prony algorithms,the proposed algorithm has stronger noise suppression ability and higher parameter estimation accuracy in Gaussian white noise and Gaussian colored noise backgrounds.

关 键 词：衰减正弦信号 高阶累积量 ESPRIT算法 衰减因子估计 频率估计 

分 类 号：TN911[电子电信—通信与信息系统] TH765[电子电信—信息与通信工程]