Whitening of Signals in Range to Improve Estimates of Polarimetric Variables

Abstract

A method to reduce errors in estimates of polarimetric variables beyond those achievable with standard estimators is suggested. It consists of oversampling echo signals in range, applying linear transformations to decorrelate these samples, processing in time the sequences at fixed range locations to obtain various secondorder moments, averaging in range these moments, and, finally, combining them into polarimetric variables. The polarimetric variables considered are differential reflectivity, differential phase, and the copolar correlation coefficient between the horizontally and vertically polarized echoes. Simulations and analytical formulas confirm a reduction in variance proportional to the number of samples within the pulse compared to standard processing of signals behind a matched filter. This reduction is possible, however, if the signal-to-noise ratios (SNRs) are larger than a critical value. Plots of the critical SNRs for various estimates as functions of Doppler spectrum width and other parameters are provided.

Compressed sensing applied to weather radar

“…Consequently, Iowa XPOLs can be deployed at any location of interest and provide better near-ground observations than those basins that were previously covered by only 4 km × 4 km NEXRAD pixels. Secondly, because XPOL systems can acquire data at a programmable range oversampling which can be as low as 7.5 m, they provide more accurate polarimetric estimates without decreasing the scan rate (Torres and Zrnić 2003). Thirdly, unlike existing X-band networks, the Iowa XPOL network provides very high-resolution precipitation profiles of up to 15 m range resolution.…”

Bootstrap Dual-Polarimetric Spectral Density Estimator

“…In the following chapter, the statistical performance of the proposed Bootstrap DPSD estimator will be analyzed under different scenarios. A dual polarimetric version of the weather-like signal simulator (Zrnić 1975) is used, as presented in Torres and Zrnić (2003) and Yu et al (2012). Let V H (m) and V V (m) be the I/Q time-series signals of the H and V channels, respectively.…”

“…Let V H (m) and V V (m) be the I/Q time-series signals of the H and V channels, respectively. As shown in Torres and Zrnić (2003), and by following the procedure in Galati and Pavan (1995), these can be obtained as: …”

“…The N i independent realizations are performed to assess the statistical characteristics of the DPSD. The weather-like I/Q time-series signals are simulated using the procedure described in Zrnić (1975), extended to dual-polarized signals with the procedure described by Galati and Pavan (1995), as presented in Torres and Zrnić (2003). This procedure is the same for all the methods evaluated hereafter.…”

Oversampling and Whitening with the CASA Radar

“…The original work performed on range oversampling and whitening found in [1] and [2] defines the process and theoretically expected results on the improvements of the estimated radar moments. Confirmation for the spectral moments was produced in [3] with data analysis.…”