Practical algorithm for the estimation of Doppler velocity and differential phase from dual polarized radar measurements

There are an increasing number of coherent dual polarized radars that switch between horizonatal (H) and vertical (V) polarizations on a pulse to pulse basis which make it possible to measure copolar differential phase (Ψ_co) together with Doppler velocity (v). The general method for estimating Ψ_co and v is well known. This involves calculating the two first lag covariances of the copolar times serives, which we call R_a and R_b. It can be shown that the argument of these covariances are, arg{R_b } = v -Ψ_co. In contrast to coherent single polarization radars, these arguments contain velocity phase and differential phase which need to be separated. It appears that it should be trivial to separate Ψ_co and v once R_a and R_b are known, however, this is not the case. If one simply tries to use the formulas without considering the issues of phase wrapping and obtaining the maximum Nyquist velocity, the data can potentially contain many unnecessary phase discontinuities which makes it difficult to interpret the Ψ_co and v fields. This paper describes the potential problems when calculating Ψ_co and v and gives an algorithm that can be implemented on a signal processor so that the various phase wrappings can be eleiminated. Also, an iterative filtering technique is suggested for estimating specific differential phase (K_DP).