Variance bounds on the estimation of reflectivity and polarization parameters in radar meteorology

Cramer-Rao lower bounds are presented on the estimation accuracy of any unbiased estimator of power and polarization parameters of echoes received by a meteorological radar. The analysis is carried out by using a widely accepted model for radar meteorology-the multivariate Gaussian model (Rayleigh fading)-along with the assumptions that the time series of horizontally and vertically polarized echoes are acquired simultaneously, that the autocorrelation function of the process is known, and that the signal-to-noise ratio (SNR) is high. Two significant results of this analysis are that the lower bounds are independent of the known autocorrelation function, and that the effective number of independent samples is always equal to the total number of samples. An explicit construction of maximum-likelihood estimators is also provided.