Source Code for Calculating GPS Satellite Elevation and Azimuth Angles

In satellite positioning systems, elevation angle and azimuth angle are two critical geometric parameters. Elevation Angle represents the satellite's angle above the observer's horizon, ranging from 0° (horizon) to 90° (zenith). Azimuth Angle indicates the satellite's horizontal direction relative to true north, measured clockwise from 0° to 360°. The calculation of these parameters requires the following inputs: - Receiver coordinates in Latitude, Longitude, and Altitude (LLA) system - Satellite position coordinates (typically in Earth-Centered, Earth-Fixed/ECEF coordinate system) The fundamental computation workflow consists of four key steps: 1. Coordinate Transformation: Convert receiver LLA coordinates to ECEF system using transformation algorithms (e.g., WGS84 ellipsoid model) to unify the reference frame with satellite coordinates 2. Relative Vector Calculation: Subtract receiver ECEF coordinates from satellite ECEF coordinates to obtain the line-of-sight vector from receiver to satellite 3. Local Coordinate System Conversion: Transform the relative vector to the receiver's East-North-Up (ENU) local coordinate system using rotation matrices based on receiver latitude and longitude 4. Geometric Resolution: Calculate azimuth and elevation angles using ENU components through mathematical operations In mathematical implementation, elevation angle is computed using the arctangent function applied to the ratio of Up component to horizontal distance (sqrt(East² + North²)). Azimuth angle requires quadrant determination, typically implemented using the four-quadrant arctangent function (atan2) to avoid directional ambiguity - specifically atan2(East, North) with quadrant adjustments. For beginners, it's essential to consider Earth's curvature and coordinate system rotation effects on results. Practical applications should incorporate atmospheric refraction corrections, though basic calculations already capture core geometric relationships. This algorithm can be extended to visibility analysis for other satellite systems (e.g., BeiDou, GLONASS) by adapting coordinate system parameters.