A Multi-step Selection Procedure for Estimating the Number of
Signals
ABSTRACT:
We consider a multi-step selection procedure to estimate the multiplicity of
the smallest eigenvalue of the covariance matrix. The unknown number of
signals present in a radar data can be formulated as the difference between
the total number of components in the observed multivariate data vector and
the multiplicity of the smallest eigenvalue. We propose a selection procedure
to estimate the multiplicity of the common smallest eigenvalue, which is
significantly smaller than the other eigenvalues. We derive the probability of
a correct estimation, P(CE), and the least favorable configuration (LFC) for
our procedures. Under the LFC, the P(CE) attains its minimum over the
parameter space of all eigenvalues. Therefore a minimum sample size can be
determined from the probability of CE under the LFC, P(CE|LFC), in order to
implement our new procedure with a guaranteed probability requirement.
Numerical examples are presented to illustrate our proposed procedure.
About the Speaker
Professor Chen did his undergraduate work at Cheng-Kung University
in Taiwan. He then moved to the United States where he obtained an M.Sc.
from the University of Miami and, in 1982, a Ph.D. from the University of
California at Santa Barbara. Immediately after obtaining his Ph.D., Dr.
Chen joined the Department of Mathematics at Syracuse University where he
has remained ever since rising to the status of full professor in 1994.
He is currently also the Director of the Interdisciplinary Statistics Program
of the College of Arts and Science at Syracuse University. His early
work was in the area of multivariate analysis and the multinomial
distribution. Over the past 10 years he has also become very interested in
signal detection and in particular the problems associated with radar.
Much of this work was carried out with the support of US Air Force grants.
References
References with background information will be posted here.
