Advancements in Differential Phase and Specific Differential Phase Estimation Using Linear Programming

Building upon the foundational work by Giangrande (2013), which introduced the application of linear programming (LP) to polarimetric radar differential phase processing, we present advancements in the estimation of differential phase (PHIDP) and specific differential phase (KDP).

Our approach leverages the improved performance of LP solvers on matrices with more columns and fewer rows. This has allowed us to transform the problem's matrix from a 3N-row by 2N-column configuration to a more computationally efficient 2N-row by 3N-column configuration, enabling real-time computation. Furthermore, we introduce an innovative modification to the monotonicity constraints, shifting from traditional self-consistency to a dependency on reflectivity and estimated PHIDP using the Vulpiani algorithm. This adjustment not only maintains the robustness of the estimation but also enables self-consistency calibration, further enhancing the reliability of radar measurements.

These advancements in matrix configuration and constraint formulation represent a meaningful step forward in polarimetric radar processing, offering improved accuracy, computational efficiency, and the potential for enhanced calibration techniques.