Cubic spline fit

LSQ is a practical phase unfolding approach. However, it creates a test condition to check for phase unfolding when at times the test may fail.

The cubic spline fit approach transforms the PhiDP between the 2 receive channels to the complex domain, creating an Angular PhiDP vector. This is a similar concept used when creating I,Q for signal processing. The advantage in using Angular PhiDP is that the data remains continuous in the complex domain, where as the traditional PhiDP moments in the real domain phase wraps with abrupt jumps. To compute the Angular PhiDP moment:

$ϑ ( r ) = e j ψ d p ( r )$ for STAR mode dual-polarization

$ϑ ( r ) = e j 2 ψ d p ( r )$ for alternating mode of dual-polarization

Where ϑ(r) is the Angular PhiDP at some range and ψ_dp is the total differential phase.

For information on conditioning and smoothing of Angular PhiDP, see Adaptive Kdp Moment Estimation.