Estimating the upper limit of the number of signals

  • Authors:

  • Pinyuen Chen

  • Affiliations:

  • Department of Mathematics, Syracuse University, 215 Carnegie Hall, Syracuse, NY

  • Venue:
  • Signal Processing - Special section: Security of data hiding technologies
  • Year:
  • 2003

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Abstract

This paper considers a multi-step selection procedure to estimate the upper limit of the number of signals. 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 lower limit for the multiplicity of the common smallest eigenvalue, which is significantly smaller than the other eigenvalues. As a consequence, an estimate for the upper limit of the number of signals can be obtained. With a guaranteed probability requirement, the proposed procedure selects a subset that contains the smallest eigenvalues. The size of the subset is random from sample to sample. The number of signals present is estimated as the difference of the number of components and the cardinality of the selected subset. Therefore, our estimate gives an upper bound for the number of signals present. Numerical examples are presented to illustrate our proposed procedure.