Least Squares Estimation of Doppler and Polarimetric Parameters for Weather Targets

Doppler and polarimetric parameters have shown to be of great utility in weather radar applications. Different measurement schemes have been proposed and implemented to obtain Doppler and polarimetric information of the sensed weather target. To date, none of these methods is capable of providing all polarimetric and Doppler parameters of interest for the whole range of temporal correlation conditions. To obtain all parameters, some of the systems require to assume different hypotheses about the Doppler or polarimetric characteristics of the targets. Failure of the assumed hypotheses leads to unacceptable bias and loss of performance of the estimated parameters. Other methods reach a tradeoff, reducing either the number of polarimetric parameters to be estimated or the maximum measurable range of Doppler parameters. With respect to polarimetric parameter estimation, it has already been shown that alternate transmission of three different polarizations improves polarimetric parameter estimation through decoupling of temporal and polarimetric effects. In this paper, this measurement system is generalized by means of a new data processing algorithm and a least squares estimation to provide joint estimates of all Doppler and polarimetric parameters for all temporal correlation conditions. No hypotheses are required. In fact, this method provides minimum variance unbiased linear estimates of all elements of the polarimetric covariance matrix. It also allows Doppler parameter estimation within their corresponding maximum measurable ranges, which are determined by the radar base pulse repetition frequency. The performance of Doppler parameter estimates is comparable to that reached by nonpolarimetric systems. Implementation of the method requires transmitting three known polarizations. Moreover, phase shifts between them should be either known or measured.