Optimal simultaneous detection and estimation under a false alarmconstraint
Baygun, B.; Hero, A.O., III
Information Theory, IEEE Transactions on
Volume 41, Issue 3, May 1995 Page(s):688 - 703
Digital Object Identifier 10.1109/18.382015
Summary:This paper addresses the problem of finite sample simultaneous
detection and estimation which arises when estimation of signal
parameters is desired but signal presence is uncertain. In general, a
joint detection and estimation algorithm cannot simultaneously achieve
optimal detection and optimal estimation performance. We develop a
multihypothesis testing framework for studying the tradeoffs between
detection and parameter estimation (classification) for a finite
discrete parameter set. Our multihypothesis testing problem is based on
the worst case detection and worst case classification error
probabilities of the class of joint detection and classification
algorithms which are subject to a false alarm constraint. This framework
leads to the evaluation of greatest lower bounds on the worst case
decision error probabilities and a construction of decision rules which
achieve these lower bounds. For illustration, we apply these methods to
signal detection, order selection, and signal classification for a
multicomponent signal in noise model. For two or fewer signals, an SNR
of 3 dB and signal space dimension of N=10 numerical results are
obtained which establish the existence of fundamental tradeoffs between
three performance criteria: probability of signal detection, probability
of correct order selection, and probability of correct classification.
Furthermore, based on numerical performance comparisons between our
optimal decision rule and other suboptimal penalty function methods, we
observe that Rissanen's (1978) order selection penalty method is nearly
min-max optimal in some nonasymptotic regimes
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