Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 597474, 13 pages
Research Article

Decomposition of the Time Reversal Operator for Target Detection

1MOE Key Laboratory of Mechanical Manufacture and Automation, Zhejiang University of Technology, Hangzhou 310014, China
2Zhejiang Key Laboratory of Signal Processing, Zhejiang University of Technology, Hangzhou 310014, China
3Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China

Received 8 September 2012; Revised 6 November 2012; Accepted 12 November 2012

Academic Editor: Fatih Yaman

Copyright © 2012 Chun-xiao Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A thorough theory of detection problem using active time reversal has been investigated in several recent papers. Although active time reversal method is theoretically superior to the others, its practical implementation for target detection is far more difficult. This paper investigates the detection problem using passive decomposition of the time reversal operator (DORT) method. Provided that the signal components can be modeled as a linear combination of basis vectors with an unknown signal subspace, the generalized likelihood ratio test (GLRT) is derived based on Neyman-Person lemma with the unknown signal subspace replaced by its maximum likelihood estimation. The test statistics is one of the dominant eigenvalues of the time reversal operator for a point-like scatterer. Finally, the performance of the DORT detector is investigated with acoustic data collected from a waveguide tank. The experimental results show that the DORT detector can provide, respectively, 1.4 dB, 1.1 dB, and 0.8 dB performance gains over the energy detector given false alarms rate of 0.0001, 0.001, and 0.01.