GPS Dilution of Precision (DOP) Calculation Algorithm

This document presents a program for calculating Dilution of Precision (DOP) based on a satellite navigation system (GPS) receiver's Cartesian coordinates and the positions of four or more visible GPS satellites. The program serves as a validation tool for the DOP algorithm, incorporating reference positions with known DOP results to verify algorithmic accuracy. The core implementation involves matrix operations where the design matrix (H) is constructed from satellite-receiver geometry, followed by the computation of the covariance matrix (Q = (H^T H)^{-1}) to extract various DOP components (GDOP, PDOP, HDOP, VDOP, TDOP). Notably, the program focuses solely on DOP calculation without incorporating signal quality corrections. Therefore, practical applications require additional processing and analysis of the computed results for enhanced accuracy. The algorithm can be adapted for other satellite navigation systems like Galileo and BeiDou through modifications to coordinate systems and satellite parameters. Key functions would include coordinate transformations between ECEF and local tangent plane frames, and selective satellite weighting based on elevation masks.