Multi-sensor signal processing on a PSD matrix manifold

We propose to use the power spectral density (PSD) matrices of the received signals of a multi-sensor system as the feature of processing. PSD matrices have structural constraints and they form a manifold in signal space. We introduce two new Riemannian distance (RD) measures on the PSD matrix manifold and developed algorithms to locate the means and medians of PSD matrices in terms of these RD. These concepts are then applied to the detection of narrow-band sonar signals in noise and the results are encouraging.

[1]  O. Strand Multichannel complex maximum entropy (autoregressive) spectral analysis , 1977 .

[2]  Marc Arnaudon,et al.  Riemannian Medians and Means With Applications to Radar Signal Processing , 2013, IEEE Journal of Selected Topics in Signal Processing.

[3]  A. Gualtierotti H. L. Van Trees, Detection, Estimation, and Modulation Theory, , 1976 .

[4]  J. Jost Riemannian geometry and geometric analysis , 1995 .

[5]  R. Fisher The Advanced Theory of Statistics , 1943, Nature.

[6]  Kon Max Wong,et al.  Riemannian Distances for Signal Classification by Power Spectral Density , 2013, IEEE Journal of Selected Topics in Signal Processing.

[7]  Lawrence M. Ostresh On the Convergence of a Class of Iterative Methods for Solving the Weber Location Problem , 1978, Oper. Res..

[8]  Paul Thomas,et al.  Editorial: Multi-sensor signal processing for defence: Detection, localisation & classification , 2012, IET Signal Process..

[9]  Suresh Venkatasubramanian,et al.  The geometric median on Riemannian manifolds with application to robust atlas estimation , 2009, NeuroImage.

[10]  James E. Barger,et al.  Underwater acoustic system analysis , 1985, Proceedings of the IEEE.

[11]  Jian-Kang Zhang,et al.  Detection of narrow-band sonar signal on a Riemannian manifold , 2015, 2015 IEEE 28th Canadian Conference on Electrical and Computer Engineering (CCECE).

[12]  Jimmie D. Lawson,et al.  Karcher means and Karcher equations of positive definite operators , 2014 .

[13]  Arthur L. Besse,et al.  Einstein Manifolds and Topology , 1987 .

[14]  Maher Moakher,et al.  A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices , 2005, SIAM J. Matrix Anal. Appl..

[15]  M. Melamed Detection , 2021, SETI: Astronomy as a Contact Sport.

[16]  Shuang Chen,et al.  Detection of narrow-band sonar signals using order statistical filters , 1987, IEEE Trans. Acoust. Speech Signal Process..

[17]  R. Bhatia Positive Definite Matrices , 2007 .