On the estimation of spectral parameters using burst waveforms

This report addresses the problem of estimating the spectral parameters of an observed Doppler velocity spectrum using a burst radar waveform of arbitrary length. Maximum likelihood theory is applied and the exact M.L.E. algorithm for estimating the spectral mean is derived. This M.L.E. algorithm is shown to include, as a special case, the spectral mean estimator originally proposed by R. W. Miller for processing of burst waveforms. Also, when the burst waveform is a simple pulse pair, the M.L.E. algorithm reduces to the spectral mean estimator originally proposed by W.D. Rummler. The Cramer-Rao bound for estimating the spectral mean using burst waveforms is also derived. Simplifications to the exact maximum-likelihood algorithm are proposed and the performance of various estimators is compared to the Cramer-RAo lower bound. Some preliminary results of studies of spectral width estimators are also presented.