A ‘constrained third-order mean’-type estimator to calculate the parameters of exponentially damped sinusoids using third-order statistics

Abstract

The extraction of parameters of exponentially damped sinusoids using the extension of the minimum-norm principal eigenvectors method (also called Kumaresan-Tufts method) to the third-order statistic domain is considered. We present a modification of the approach introduced by Papadopoulos and Nikias (1990) and compare our method with theirs. This new method is designed as an adaptation of the ‘constrained third-order mean (CTOM) method’ for bispectrum estimation via AR modelling, to apply it to bispectral estimation of the poles of exponentially damped sinusoids. The method therefore constructs the basic third-order correlation matrix using a CTOM-type (unwindowed) estimator instead of the previously proposed TOR-type (two-windowed) one. By mean-simulation results, it is shown that the proposed method provides a much more accurate estimation of the poles than the TOR-type method when the number of available data is small and the SNR values are not excessively low. The case of exponentially damped signals with poles closely spaced in frequency and few data is also studied, with the CTOM-type estimator proving to have a much higher capacity for resolving them than the TOR-type one.