ISSN : 1796-2021
Volume : 2    Issue : 3    Date : May 2007

A Matrix Extension Built Under-Sampled Likelihood Ratio Test with Application to MUSIC
Breakdown Prediction and Cure
Ben A. Johnson and Yuri I. Abramovich
Page(s): 64-72
Full Text:
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Likelihood ratio tests are used in a range of detection-estimation problems, but normally cannot be
extended to cases where training data volume T is smaller than the dimension M of the
observations. We propose a non-degenerate normalized LR test that can be used for
detection-estimation in such under-sampled training conditions. The LR is formed based on
non-degenerate band extension of the original degenerate sample covariance matrix. This LR is
then applied within a generalized likelihood ratio test framework to an array processing problem
where the presence of closely spaced signal can be robustly detected, but their individual directions
of arrival cannot be fully resolved by subspace-based DOA techniques such as MUSIC. In that case,
MUSIC produces direction of arrival estimates for some sources with very large errors (outliers). We
use the under-sampled likelihood ratio to detect the presence of such MUSIC outliers and provide
corrected DOA estimates.

Index Terms
maximum likelihood estimation, direction of arrival estimation, array signal processing, parameter
estimation, signal resolution.