The feasibility of data whitening to improve performance of weather radar

The problem of efficient processing of correlated weather radar echoes off precipitation is considered. An approach based on signal whitening was rece ntly proposed that has the potential to significantly improve power estimat ion at a fixed pulse repetition rate/scan rate, or to allow higher scan rat es at a given level of accuracy. However, the previous work has been mostly theoretical and subject to the following restrictions: 1) the autocorrelat ion function (ACF) of the process must be known precisely and 2) infinite s ignal-to-noise ratio is assumed. Here a computational feasibility study of the whitening algorithm when the ACF is estimated and in the presence of no ise is discussed. In the course of this investigation numerical instability to the ACF behavi or at large lags (tails) was encountered. In particular, the commonly made assumption of the Gaussian power spectrum and, therefore, Gaussian ACF yiel ds numerically ill-conditioned covariance matrices. The origin of this diff iculty, rooted in the violation of the requirement of positive Fourier tran sform of the CF, is discussed. It is found that small departures from the G aussian form of the covariance matrix result in greatly reduced ill conditi oning of the matrices and robustness with respect to noise. The performance of the whitening technique for various meteorologically reasonable scenari os is then examined. The effects of additive noise are also investigated. T he approach, which uses time series to estimate the ACF from which the whit ener is constructed, shows up to an order of magnitude improvement in the m ean-squared error of the estimated power for a range of parameter values co rresponding to typical meteorological situations.