A multi-lag correlation estimator for polarimetric radar variables in the presence of noise

It has been recognized that the quality of polarimetric radar data degrades as the signal-to-noise ratio (SNR) reduces. This substantially limits the usage of observed polarimetric data in the low-SNR region. To improve radar performance and data quality, a multi-lag correlation estimator is introduced and examined in terms of moment estimation, where lag 0 is excluded to minimize noise effects. In this paper, we present the theory, simulation results, and experimental validation of the multi-lag estimation technique for radar reflectivity, differential reflectivity, copolar correlation coefficient, radial wind velocity, and spectrum width. The biases and standard deviations are calculated and compared with that of the conventional method. Theoretical analysis of the estimation errors are provided and verified by numerical simulations. It is found that the muti-lag estimator outperforms the conventional method at low SNR for certain spectrum width ranges.