Is Adaptive Pseudowhitening Compatible with New Radar-Variable Estimators?

Adaptive pseudowhitening has been implemented in real time on the National Weather Radar Testbed (NWRT) Phased Array Radar (PAR) and applied to time series data from the research KOUN Weather Surveillance Radar – 1988 Doppler (WSR-88D). It is a range oversampling processing technique that can reduce observation times without increasing the variance of estimates or that can decrease the variance of estimates using the same observation times. Range oversampling techniques consist of sampling the received signals at a rate faster than the inverse of the transmitted pulse, which produces complex voltages that are correlated in range. The range samples are then transformed with a linear transformation to decorrelate the signals leading to more precise estimates of the radar variables after averaging. Adaptive pseudowhitening applies a different transformation at each range gate that adjusts to the characteristics of the signals and attempts to minimize the variance of estimates.

The current implementation of adaptive pseudowhitening relies on explicit expressions for the variance of all the radar-variable estimators. Variance expressions are used along with estimates of the signal-to noise ratio and the normalized spectrum width (plus differential reflectivity and correlation coefficient for the polarimetric radar variables) to adaptively calculate a nearly-optimal linear transformation. Some recently introduced radar-variable estimators exhibit improved statistical properties compared to conventional estimators. However, they may not have an explicit expression for their variance, rendering them incompatible with the current implementation of adaptive pseudowhitening.

In this paper, we introduce a framework that utilizes optimization to produce look-up tables that can replace the explicit variance expressions for new radar-variable estimators that do not have one. The performance of adaptive pseudowhitening using the look-up tables is compared to the conventional approach using variance expressions to validate the framework. The new look-up table approach is then applied to a new correlation-coefficient estimator that lacks an explicit variance expression. It is demonstrated that by using the proposed framework, adaptive pseudowhitening is compatible with new radar-variable estimators.