Optimal mean velocity estimation for Doppler weather radars

Optimal Doppler velocity estimation is explored for a standard Gaussian signal measurement model and thematic maximum-likelihood (ML) and Bayes estimation. Because the model considered depends on a vector parameter [velocity, spectrum width (SW), and signal-to-noise ratio (SNR)], the exact formulation of an ML or Bayes solution involves a system of coupled equations that cannot be made explicit for any of the parameters. Simple computational forms are shown to exist when SW and SNR are assumed known. An information-theoretic concept is used to extend these equations to the general case of SW and SNR unknown. A Monte Carlo simulation experiment is used to verify that the method can work, with no a priori information for either SW or SNR and a very small (20 pulse) sample size. The improved performance of this new Doppler velocity estimator is documented by comparison with derived optimal bounds and with the performance of the pulse pair (PP) method. Bayes estimator results are used to provide true performance bounds for comparison. Cramer-Rao bounds are also derived and shown to be inferior to the Bayes bounds in the small sample case considered