A general formulation based on frame re-expansions of Gaussian beam fields in the course of Gaussian beam shooting algorithms will be outlined, and closed form expressions used for frame decomposition of incident beam fields and frame change will be given. The algorithm will be tested on a specific 3d problem chosen with a view toward ground-based Radar application in semi-urban environments. The range of validity of closed form expressions for frame re-expansion coefficients will be discussed, and the accuracy of Gaussian beam summations after such re-expansions will be compared to reference solutions in cases involving diffraction