Abstract
A Rigorous Proof for the Invariant Study of the Problem in Section VI in Matched Subspace Detectors
Highlights
The invariance principle in dealing with hypothesis testing problem was described in several nice texts[1,2,3]
A necessary and sufficient condition for AAT = BBT is that there exists another quasi-orthogonal matrix Xm×n, which means XXT = Im×m, such that AX = B
We proved rigorously the conclusion in[5] that the detection problem is invariant to set of rotation in < PS⊥x >⊥ and scaling γ>0
Summary
The invariance principle in dealing with hypothesis testing problem (or signal detecting problem) was described in several nice texts[1,2,3]. Invariance study is a way impose constraints on detectors so that outputs are not dependent on convention choices such as units, coordinate systems and secondly so that the impact of nuisance parameters is minimized. The second is helpful for systematically obtaining potential properties such as constant false alarm rate. Application of invariance principle to signal detection problem can be traced back as early as 1971[4], or even earlier. About fourteen years ago an important paper[5] appeared in IEEE Transaction on signal processing. The main contribution of the research is to use invariance principle to study the Generalized Likelihood Ratio Tests (GLRT) for four kinds signal detection problem. While the conclusion is all correct, the geometrical method used in this study is questionable as detailed in the two paragraphs
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
