Sparse Spatial Spectral Estimation: A Covariance Fitting Algorithm, Performance and Regularization
Sparse Spatial Spectral Estimation: A Covariance Fitting Algorithm, Performance and Regularization
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DOI：
10.1109/tsp.2013.2256903
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发表时间：
2013-06-01
影响因子：
5.4
通讯作者：
Kaveh, Mostafa
中科院分区：
文献类型：
--
作者：
Zheng, Jimeng;Kaveh, Mostafa
介绍了多源波达方向估计的稀疏谱拟合（SpSF）算法，研究了该算法在渐近和有限样本情况下的渐近一致性和有效正则化。通过对该方法最优性条件的分析，证明了稀疏空间谱模型下DOA和不相关源接收功率的SpSF估计在快拍数下的渐近相合性。沿着这个结果，得到了无限次快拍下SpSF估计的最佳正则化参数的显式表达式.然后，我们建立在这些结果调查的问题，选择一个适当的正则化参数的SpSF有限的快照。这样的正则化参数的自动选择器的基础上制定的上界正确的支持恢复的概率SpSF，这可以有效地通过Monte Carlo模拟评估。仿真结果说明了该选择器的有效性和性能，并讨论了SpSF在相关源测向中的应用。
In this paper, the sparse spectrum fitting (SpSF) algorithm for the estimation of directions-of-arrival (DOAs) of multiple sources is introduced, and its asymptotic consistency and effective regularization under both asymptotic and finite sample cases are studied. Specifically, through the analysis of the optimality conditions of the method, we prove the asymptotic, in the number of snapshots, consistency of SpSF estimators of the DOAs and the received powers of uncorrelated sources in a sparse spatial spectra model. Along with this result, an explicit formula of the best regularization parameter of SpSF estimator with infinitely many snapshots is obtained. We then build on these results to investigate the problem of selecting an appropriate regularization parameter for SpSF with finite snapshots. An automatic selector of such regularization parameter is presented based on the formulation of an upper bound on the probability of correct support recovery of SpSF, which can be efficiently evaluated by Monte Carlo simulations. Simulation results illustrating the effectiveness and performance of this selector are provided, and the application of SpSF to direction-finding for correlated sources is discussed.