An accurate perturbation analysis algorithm for music with Toeplitz covariance matrix

In this paper, a new perturbation analysis algorithm for the MUltiple SIgnal Classification (MUSIC) estimator applied to a Hermitian Toeplitz covariance matrix is presented. Inspired by the perspective that the MUSIC algorithm can be recognized as a structured matrix approximation, the perturbation of parameter estimates can be predicted more accurately by seeking the minimum of a Frobenius norm. The prediction results are analytically expressed through a weighted least squares method. The performance of the MUSIC estimators can also be predicted using our algorithm.

[1]  P. Vaidyanathan,et al.  Coprime sampling and the music algorithm , 2011, 2011 Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE).

[2]  Petre Stoica,et al.  Spectral Analysis of Signals , 2009 .

[3]  Philippe Forster,et al.  Operator approach to performance analysis of root-MUSIC and root-min-norm , 1992, IEEE Trans. Signal Process..

[4]  Jian Li,et al.  Computationally efficient maximum likelihood estimation of structured covariance matrices , 1999, IEEE Trans. Signal Process..

[5]  Xiaoli Ma,et al.  First-Order Perturbation Analysis of Singular Vectors in Singular Value Decomposition , 2007, 2007 IEEE/SP 14th Workshop on Statistical Signal Processing.

[6]  R. J. Marshall.  Autocorrelation estimation of time series with randomly missing observations , 1980 .

[7]  Yonina Rosen,et al.  Optimal ARMA parameter estimation based on the sample covariances for data with missing observations , 1989, IEEE Trans. Inf. Theory.

[8]  Petre Stoica,et al.  MUSIC, maximum likelihood and Cramer-Rao bound , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[9]  Zhengyuan Xu,et al.  Perturbation analysis for subspace decomposition with applications in subspace-based algorithms , 2002, IEEE Trans. Signal Process..

[10]  F. Li,et al.  Performance analysis for DOA estimation algorithms: unification, simplification, and observations , 1993 .

[11]  C. Eckart,et al.  The approximation of one matrix by another of lower rank , 1936 .

[12]  Yonina C. Eldar,et al.  Direction of Arrival Estimation Using Co-Prime Arrays: A Super Resolution Viewpoint , 2013, IEEE Transactions on Signal Processing.

[13]  Philippe Loubaton,et al.  Toeplitz rectification and DOA estimation with music , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[14]  Arye Nehorai,et al.  Coarrays, MUSIC, and the Cramér–Rao Bound , 2016, IEEE Transactions on Signal Processing.

[15]  R. O. Schmidt,et al.  Multiple emitter location and signal Parameter estimation , 1986 .

[16]  M. Viberg,et al.  Two decades of array signal processing research: the parametric approach , 1996, IEEE Signal Process. Mag..

[17]  P. P. Vaidyanathan,et al.  Remarks on the Spatial Smoothing Step in Coarray MUSIC , 2015, IEEE Signal Processing Letters.