一种基于压缩感知的无需超参数的测向算法
A Hyperparameter-Free Direction-Finding Algorithm in the Compressive Sensing Framework
摘要: 全自动的稀疏参数估计算法不需要用户对于超参数的数值做出任何艰难的决定(可能是试错而来)，因而更加实用。本文给出了现有方法的统一阐释，包括协方差矩阵拟合(CMF)、基于稀疏迭代协方差的估计(SPICE)以及基于似然的稀疏参数估计(LIKES)，认为它们全部都是不同统计距离下的基于协方差矩阵拟合的方法。在此基础上，本文提出了一种新的协方差矩阵拟合方案，将两种非对称Itakura-Saito距离的其中一种最小化。计算机仿真表明，本文提出方法相比上述方法的性能具有优势。
Abstract: The fully automatic sparsity-parameter estimation algorithms do not require the user to make any hard decision (possibly via trial-and-error) on the values of the hyperparameters, making them more pragmatic in practice. This paper provides a unified interpretation of the existing approaches including covariance matrix fitting (CMF), sparse iterative covariance based estimation (SPICE) and likelihood-based estimation of sparse parameters (LIKES). The point of view taken is that they are all covariance-fitting-based algorithms under different statistical distances. Following this, we present a new covariance-fitting scheme trying to minimize one of the two asymmetrical Itakura-Saito distances. Simulations show that the proposed method appears to be preferable as it outperforms the aforementioned algorithms in general.
文章引用：马向东, 郭明, 吴向阳. 一种基于压缩感知的无需超参数的测向算法[J]. 无线通信, 2019, 9(1): 1-7. https://doi.org/10.12677/HJWC.2019.91001

参考文献

[1] ITU (2011) Spectrum Monitoring Handbook. ITU, Geneva.
[2] Capon, J. (1969) High-Resolution Frequency-Number Spectrum Analysis. Proceedings of the IEEE, 57, 1408-1418.
[Google Scholar] [CrossRef] 
[3] Schmidt, R.O. (1986) Multiple Emitter Location and Signal Parameter Estimation. IEEE Transactions on Antennas and Propagation, 34, 276-280.
[Google Scholar] [CrossRef] 
[4] Malioutov, D., ?etin, M. and Willsky, A. (2005) A Sparse Signal Reconstruction Perspective for Source Localization with Sensor Arrays. IEEE Transactions on Signal Processing, 53, 3010-3022.
[Google Scholar] [CrossRef] 
[5] Yardibi, T., Li, J., Stoica, P., et al. (2008) Sparsity Constrained Deconvolution Approaches for Acoustic Source Mapping. Journal of Acoustical Society of America, 123, 2631-2642.
[Google Scholar] [CrossRef] [PubMed]
[6] Stoica, P., Babu, P. and Li, J. (2011) SPICE: A Sparse Covariance-Based Estimation Method for Array Signal Processing. IEEE Transactions on Signal Processing, 59, 629-638.
[Google Scholar] [CrossRef] 
[7] Stoica, P. and Babu, P. (2012) SPICE and LIKES: Two Hyperparameter-Free Methods for Sparse-Parameter Estimation. Signal Processing, 92, 1580-1590.
[Google Scholar] [CrossRef] 
[8] Tibshirani, R. (1996) Regression Shrinkage and Selection via the Lasso. Journal of Royal Statistical Society: Series B (Statistical Methodology), 58, 267-288.
[Google Scholar] [CrossRef] 
[9] Gorodnitsky, I.F. and Rao, B.D. (1997) Sparse Signal Reconstruction from Limited Data Using FOCUSS: A Re-Weighted Minimum Norm Algorithm. IEEE Transactions on Signal Processing, 45, 600-616.
[Google Scholar] [CrossRef] 
[10] Cotter, S.F., Rao, B.D., Engan, K., et al. (2005) Sparse Solutions to Linear Inverse Problems with Multiple Measurement Vectors. IEEE Transactions on Signal Processing, 53, 2477-2488.
[Google Scholar] [CrossRef] 
[11] Xu, D.Y., Hu, N., Ye, Z.F., et al. (2012) The Estimate for DOAs of Signals Using Sparse Recovery Method. Proceedings of the 37th IEEE International Conference on Acoustics, Speech, and Signal Processing, Kyoto, 2573-2576.
[Google Scholar] [CrossRef] 
[12] Ottersten, B., Stoica, P. and Roy, R. (1998) Covariance Matching Estima-tion Techniques for Array Signal Processing Applications. Digital Signal Processing, 8, 185-210.
[Google Scholar] [CrossRef] 
[13] Kullback, S. (1997) Information Theory and Statistics. Dover Edition. Dover, New York.
[14] Bensaid, S. and Slock, D. (2012) Blind Audio Source Separation Exploiting Periodicity and Spectral Envelops. Pro-ceedings of International Workshop on Acoustic Signal Enhancement, Aachen.
[15] Vandenberghe, L., Boyd, S. and Wu, S.P. (1998) Determinant Maximization with Linear Matrix Inequality Constraints. SIAM Journal on Matrix Analysis and Applications, 19, 499-533.
[Google Scholar] [CrossRef] 
[16] Landi, L., De Maio, A., De Nicola, S., et al. (2008) Knowledge-Aided Covariance Matrix Estimation: A MAXDET Approach. IET Radar, Sonar & Navigation, 3, 341-356.
[Google Scholar] [CrossRef] 
[17] Li, J., Du, L. and Stoica, P. (2008) Fully Automatic Computation of Di-agonal Loading Levels for Robust Adaptive Beamforming. Proceedings of the 33rd IEEE International Conference on Acoustics, Speech, and Signal Processing, Las Vegas, 2325-2328.
[18] Wu, S.P., Vandenberghe, L. and Boyd, S. (1996) MAXDET: Software for Determinant Maximization Problems. Information Systems Laboratory, Stanford University, Stanford.
[19] Grant, M. and Boyd, S. (2012) CVX: MATLAB Software for Disciplined Convex Programming, Version 2.0 Beta. http://cvxr.com/cvx
[20] Bhattacharyya, A. (1943) On a Measure of Divergence between Two Statistical Populations Defined by Their Probability Distributions. Bulletin of the Calcutta Mathematical Society, 35, 99-109.
[21] Zolotarev, V.M. (1984) Probability Metrics. Theory of Probability and Its Applications, 28, 278-302.
[Google Scholar] [CrossRef]