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The Feasibility of Data Whitening to Improve Performance of Weather Radar

A. C. KoivunenDepartment of Physics, Michigan Technological University, Houghton, Michigan

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A. B. KostinskiDepartment of Physics, Michigan Technological University, Houghton, Michigan

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Abstract

The problem of efficient processing of correlated weather radar echoes off precipitation is considered. An approach based on signal whitening was recently proposed that has the potential to significantly improve power estimation at a fixed pulse repetition rate/scan rate, or to allow higher scan rates at a given level of accuracy. However, the previous work has been mostly theoretical and subject to the following restrictions: 1) the autocorrelation function (ACF) of the process must be known precisely and 2) infinite signal-to-noise ratio is assumed. Here a computational feasibility study of the whitening algorithm when the ACF is estimated and in the presence of noise is discussed.

In the course of this investigation numerical instability to the ACF behavior at large lags (tails) was encountered. In particular, the commonly made assumption of the Gaussian power spectrum and, therefore, Gaussian ACF yields numerically ill-conditioned covariance matrices. The origin of this difficulty, rooted in the violation of the requirement of positive Fourier transform of the ACF, is discussed. It is found that small departures from the Gaussian form of the covariance matrix result in greatly reduced ill conditioning of the matrices and robustness with respect to noise. The performance of the whitening technique for various meteorologically reasonable scenarios is then examined. The effects of additive noise are also investigated. The approach, which uses time series to estimate the ACF from which the whitener is constructed, shows up to an order of magnitude improvement in the mean-squared error of the estimated power for a range of parameter values corresponding to typical meteorological situations.

Corresponding author address: Prof. A. B. Kostinski, Dept. of Physics, Michigan Technological University, 1400 Townsend Dr., Houghton, MI 49931-1295.

kostinsk@phy.mtu.edu

Abstract

The problem of efficient processing of correlated weather radar echoes off precipitation is considered. An approach based on signal whitening was recently proposed that has the potential to significantly improve power estimation at a fixed pulse repetition rate/scan rate, or to allow higher scan rates at a given level of accuracy. However, the previous work has been mostly theoretical and subject to the following restrictions: 1) the autocorrelation function (ACF) of the process must be known precisely and 2) infinite signal-to-noise ratio is assumed. Here a computational feasibility study of the whitening algorithm when the ACF is estimated and in the presence of noise is discussed.

In the course of this investigation numerical instability to the ACF behavior at large lags (tails) was encountered. In particular, the commonly made assumption of the Gaussian power spectrum and, therefore, Gaussian ACF yields numerically ill-conditioned covariance matrices. The origin of this difficulty, rooted in the violation of the requirement of positive Fourier transform of the ACF, is discussed. It is found that small departures from the Gaussian form of the covariance matrix result in greatly reduced ill conditioning of the matrices and robustness with respect to noise. The performance of the whitening technique for various meteorologically reasonable scenarios is then examined. The effects of additive noise are also investigated. The approach, which uses time series to estimate the ACF from which the whitener is constructed, shows up to an order of magnitude improvement in the mean-squared error of the estimated power for a range of parameter values corresponding to typical meteorological situations.

Corresponding author address: Prof. A. B. Kostinski, Dept. of Physics, Michigan Technological University, 1400 Townsend Dr., Houghton, MI 49931-1295.

kostinsk@phy.mtu.edu

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