基于稀疏迭代協(xié)方差估計的缺失數(shù)據(jù)譜分析及時域重建方法
doi: 10.11999/JEIT151008
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2.
(北京理工大學(xué)電子與信息學(xué)院 北京 100081) ②(中國人民解放軍軍械工程學(xué)院電子與光學(xué)工程系 石家莊 050003)
基金項目:
國家自然科學(xué)基金(61401024)
Sparse Iterative Covariance Estimation-based Approach for Spectral Analysis and Reconstruction of Missing Data
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2.
(School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China)
Funds:
The National Natural Science Foundation of China (61401024)
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摘要: 應(yīng)用于缺失數(shù)據(jù)恢復(fù)的迭代自適應(yīng)方法(IAA)被證實可利用20%的有效數(shù)據(jù)估計信號參數(shù)，并能高精度恢復(fù)缺失數(shù)據(jù)，優(yōu)于經(jīng)典GAPES方法，但當(dāng)缺失數(shù)據(jù)超過80%時其數(shù)據(jù)恢復(fù)性能迅速下降。該文基于稀疏迭代協(xié)方差估計提出一種新的缺失數(shù)據(jù)譜分析方法(M-SPICE)及針對該方法的缺失數(shù)據(jù)修正時域重建方法。該方法將加權(quán)缺失數(shù)據(jù)協(xié)方差擬合代價函數(shù)轉(zhuǎn)換為凸優(yōu)化問題，構(gòu)造循環(huán)最小化器保證缺失數(shù)據(jù)參數(shù)估計的全局收斂特性，通過對缺失數(shù)據(jù)估計算子的更新實現(xiàn)了時域重建方法的修正，使其在有效數(shù)據(jù)功率譜欠估計的情況下獲得更高的數(shù)據(jù)重建精度。仿真實驗表明無論是數(shù)據(jù)塊缺失還是任意缺失，該方法均能夠利用更少的有效數(shù)據(jù)進(jìn)行譜分析，并重建大比例缺失數(shù)據(jù)。
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關(guān)鍵詞:
- 缺失數(shù)據(jù)重建 /
- 譜估計 /
- 迭代自適應(yīng) /
- 稀疏協(xié)方差估計
Abstract: 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. -
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