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Efficient Positivity Test Algorithms for Parametric and Nonparametric Sequences of Covariance Estimates

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1 Author(s)
Issa M. S. Panahi ; Dept. of Electr. Eng., Univ. of Texas at Dallas, Richardon, TX, USA

In statistical signal processing problems involving second-order information of data such as covariance estimation, spectral factorization, and optimal filtering, one often needs to test positivity of a real sequence obtained from the finite length of data as covariance estimates. In this correspondence, we present efficient time-domain algorithms for testing nonnegativity of real finite nonparametric and linearly parametric sequences as valid covariance estimates. For a parametric sequence, the algorithm searches entire parameter space to find a unique set of parameters for which the sequence is positive-definite. Examples show performance of the proposed algorithms versus direct use of DFT/FFT.

Published in:

IEEE Transactions on Signal Processing  (Volume:57 ,  Issue: 11 )