Estimations from irregular arrays

A general approach is presented for estimating statistics of a random process from a finite data set from an irregularly spaced array of measurement locations. Particular attention is focused upon estimation of the spectrum under circumstances where it is smooth (i.e., broadband). A procedure is proposed based upon the technique of optimal linear estimation or generalized least squares fits in order to estimate coefficients of spectral features of interest to the investigator. Selection of which features are appropriate for estimation from a given array and set of measurements is made within the formalism of Bayesian statistical inference. The converse problem is also addressed: given a set of spectral features and a fixed number of possible measurements, which configuration of measurement locations will yield the most information about the amplitudes of those features? Finally, an assessment is made of the efficiency (i.e., the bias and accuracy) of various previously proposed methods of spectral estimation from irregular arrays.