Satellite Position Computation, User Position Calculation (Least Squares Method), Navigation Message Decoding, and Coordinate Transformation

This article presents MATLAB-based implementations for satellite position computation, user position calculation (using the least squares method), navigation message decoding, and coordinate transformation. The process utilizes satellite antenna positions and clock bias information along with receiver time and pseudorange measurements. The least squares algorithm is employed to compute receiver positions by minimizing the residual errors between observed and calculated pseudoranges. Key MATLAB functions involved include matrix operations for solving the linearized observation equations and iterative refinement for position accuracy. These computed positions are then used for navigation message extraction and coordinate system conversions (such as ECEF to geodetic coordinates), providing enhanced precision for satellite-based navigation and related applications. The implementation demonstrates practical approaches for handling ephemeris data processing, error correction, and coordinate transformations in satellite navigation systems.