Maximum entropy power spectrum estimation with uncertainty in correlation measurements

The purpose of this paper is to present a multidimensional MEM algorithm, valid for nonuniformly sampled arrays, which satisfies a "correlation-approximating" constraint. To this end, the correlation matching equality constraints of the usual MEM are replaced by a single inequality constraint whose form is based on a measure of the noise in the given autocovariance function (ACF). In this way, one can incorporate into the model knowledge of the noisy nature of the "given" ACF, since the "given" ACF is usually estimated from the samples of the wavefield. Specifically, the covariance matrix of the correlation estimates is used in a quadratic form that weights the difference between the "given" ACF and the one matched by the power spectrum. The maximization of entropy under this inequality constraint leads, ultimately, to a steepest-descent algorithm. The algorithm has been tested with 1-D synthetic data representing multiple sinusoids buried in additive white noise. The performance of this modified MEM algorithm is compared to a traditional MEM algorithm for extendible ACF's and for different SNR's. Examples of the MEM spectrum are given for the case of nonextendible ACF's.