A multi-step selection procedure for estimating the number of signal components

This paper considers a multi-step, selection procedure to estimate the multiplicity of the smallest eigenvalue of a covariance matrix. The unknown number of signals present in 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 R, to estimate the multiplicity of the smallest common eigenvalue, which is significantly smaller that the other eigenvalues. We derive the probability of correct estimation, P(CE|R), and the least favorable configuration (LFC) for our procedure. Under the LFC, the P(CE|R) attains its minimum value over the parameter space of all eigenvalues. Therefore, a minimum sample size can be determined from the probability of CE under LFC, P(CE|LFC), in order to implement our new procedure while meeting a guaranteed probability requirement. Numerical examples are presented in order to illustrate our proposed procedure.