MATLAB Implementation of GPS Single Point Positioning

This article provides a comprehensive guide to implementing GPS single point positioning using MATLAB. The process begins with reading data from NMEA files (containing navigation data) and observation files (containing satellite measurements). Key implementation steps include parsing these files using MATLAB's textscan or fread functions to extract ephemeris data and pseudorange measurements. The positioning calculation involves solving the navigation equations using least squares estimation, where we implement algorithms like Bancroft's method or iterative least squares to compute receiver coordinates. This includes handling satellite clock corrections, ionospheric delays, and tropospheric corrections using established mathematical models. Coordinate transformation is implemented using MATLAB's mapping toolbox or custom functions to convert between ECEF (Earth-Centered Earth-Fixed) coordinates to geodetic coordinates (latitude, longitude, altitude) or local ENU (East-North-Up) frames. We'll demonstrate how to apply transformation matrices and rotation formulas for accurate coordinate conversions. Error analysis and correction techniques are implemented through variance-covariance matrix computation and residual analysis, allowing for accuracy assessment and outlier detection. The implementation includes weighted least squares approaches based on satellite elevation angles. Finally, we detail visualization techniques using MATLAB's plotting functions to display positioning results, error distributions, and satellite sky plots. The analysis covers practical applications of the positioning results and their accuracy implications for real-world GPS applications. This comprehensive implementation provides both theoretical understanding and practical MATLAB coding guidance for complete GPS single point positioning solutions, including all essential error handling and quality assessment components.