基于稀疏迭代协方差估计的缺失数据谱分析及时域重建方法

摘要

应用于缺失数据恢复的迭代自适应方法(IAA)被证实可利用20%的有效数据估计信号参数，并能高精度恢复缺失数据，优于经典 GAPES 方法，但当缺失数据超过80%时其数据恢复性能迅速下降。该文基于稀疏迭代协方差估计提出一种新的缺失数据谱分析方法(M-SPICE)及针对该方法的缺失数据修正时域重建方法。该方法将加权缺失数据协方差拟合代价函数转换为凸优化问题，构造循环最小化器保证缺失数据参数估计的全局收敛特性，通过对缺失数据估计算子的更新实现了时域重建方法的修正，使其在有效数据功率谱欠估计的情况下获得更高的数据重建精度。仿真实验表明无论是数据块缺失还是任意缺失，该方法均能够利用更少的有效数据进行谱分析，并重建大比例缺失数据。%Many researches confirmed the excellent performance of Iterative Adaptive Approach (IAA), when it is applied to spectrum analysis of missing data. Simulation results show that the IAA can use 20 percent of the data to recover the missing samples, which is superior to Gapped Amplitude and Phase EStimation (GAPES). But the reconstruction performance of IAA degrades rapidly when the missing data exceed 80%. This paper introduces a novel method of missing data spectrum analysis, and a relevant modified method of time-domain reconstruction is proposed, called Missing SParse Iterative Covariance-based Estimation(M-SPICE). This method converts the weighted missing data covariance fitting cost function to a convex optimization problem. The global convergence property is obtained by adopting cyclic minimizers. The time-domain reconstruction method is modified by renewing estimation operator, which increases the accuracy of the data reconstruction in the case of underestimation. The simulation indicates that the novel method can be used to estimate the missing data spectrum, and reconstruct missing data accurately, with even fewer valid samples, regardless of gapped or arbitrary missing patterns.