Accuracy of parameter extraction from sample-averaged sea-echo Doppler spectra

The mean, standard deviation, and confidence limits are obtained for quotients of random-variable sums. Such quotients are formed in the extraction of sea-state parameters from high-frequency (HF) radar Doppler spectra. An equivalent chi-squared process is shown to represent a spectral integration having a varying mean based on central-limit theorem arguments. The error of estimating the centroid of a spectral peak is derived and shown to depend only on the total length of the time series, not on how it is segmented into coherent spectra and incoherent averages. Finally, error in estimation of waveheight using a power-law relationship is analyzed and is seen to depend on how one does the averaging. When individual spectra contain varying path losses and/or system gains, averages of quotients for each spectrum remove such unknown factors; in this case spectra with greater frequency resolution lead to lower waveheight estimation errors.