An overdetermined approach to autocorrelation based spectral moment estimators for use in Doppler weather radar

Estimating the spectral moments of a process is commonly done through computation of the autocorrelation function from observed sample functions of the process. The common pulse-pair estimator uses estimates of the autocorrelation function at only two lag values to provide spectral mean and width estimates. The pulse-pair algorithm can be viewed as a closed system solution of a set of equations derived by a general series expansion of the complex autocorrelation function. This paper investigates the potential for reducing error in spectral moment estimators by considering computation of the autocorrelation function at additional (higher order) lags which also contain spectral information. The approach is to truncate the series expansion of the complex autocorrelation function as formulated by Passarelli (1983) to form an overdetermined system of equations and then use a least squares solution for the spectral moments of interest. The approach has been analyzed using simulated Doppler weather radar returns to represent a distributed target environment. Improvement in the error performance of spectral variance estimators is demonstrated through the application of additional autocorrelation lag estimates in an overdetermined system. The error performance is shown to be dependent upon process spectral width, the number of terms used in the series expansion, the number of samples used in the autocorrelation estimates, and the signal-to-noise ratio.