Two calculations needed by ionospheirc grid rectification for difference satellite for GPS

We have been under contract for certain improvements in positioning accuracy for difference satellite for GPS (global positioning system). One thing we did was to provide algorithms based on well-known theory of grid rectification^{[1, 2]} for calculating two quantities that are needed for better positioning: (1) vertical delay value; (2) false distance. Vertical delay value denotes the vertical delay of penetration point; we define carefully and in detail the penetration point as related to ionosphere and then explain in some detail the algorithm for calculating its vertical delay. We also explain in some detail the algorithm for calculating false distance. The two above-mentioned quantities, as accurately calculated by our two algorithms for a certain area in China, have already so improved the positioning accuracy for difference satellite for GPS as to satisfy fully the need of WAAS users in that area.