MATLAB Source Code for Comprehensive Geodetic Coordinate Transformation Functions

Geodetic coordinates play a crucial role in surveying, navigation, and aerospace applications. MATLAB, as a powerful scientific computing tool, efficiently handles transformations between these coordinate systems. This implementation covers four essential transformation requirements: mutual conversion between latitude-longitude coordinates and East-North-Up (ENU) coordinates, as well as their transformations with Earth-Centered Earth-Fixed (ECEF) coordinates.

### 1. Geographic Coordinates to ENU Coordinates The East-North-Up (ENU) coordinate system is commonly used for local area navigation and positioning. This transformation requires a reference point as the origin, converting geographic coordinates to relative coordinates in the east, north, and up directions. The conversion process involves calculating rotation matrices from the geodetic coordinate system to the local coordinate system, ensuring directional accuracy. MATLAB implementation typically uses matrix operations and trigonometric functions to compute the transformation matrix based on the reference point's latitude and longitude.

### 2. Geographic Coordinates to ECEF Coordinates The Earth-Centered Earth-Fixed (ECEF) coordinate system uses the Earth's center as the origin and is widely employed in satellite orbit calculations and global positioning systems. The transformation utilizes ellipsoid models (such as WGS84) to convert latitude, longitude, and altitude into X, Y, and Z coordinates. The MATLAB code implements the standard equations involving ellipsoidal parameters and requires careful handling of elevation components to maintain ECEF system precision.

### 3. ECEF Coordinates to ENU Coordinates This transformation is typically used to convert satellite or global positioning data into local navigation coordinate systems. It similarly requires a reference point and involves coordinate translation and rotation matrices to convert ECEF coordinates to ENU coordinates. The MATLAB implementation calculates the rotation matrix based on the reference point's geodetic coordinates and performs matrix multiplication with the translated ECEF coordinates.

### 4. ECEF Coordinates to Geographic Coordinates This is the reverse process of the previous function, converting X, Y, Z coordinates in the ECEF system to geographic latitude, longitude, and altitude. The computation involves iterative solutions using ellipsoid models to ensure latitude and longitude accuracy. MATLAB implementations typically employ iterative algorithms like Newton-Raphson method to solve the nonlinear equations, with convergence checks for numerical stability.

These transformations in MATLAB rely on matrix operations and geodetic formulas, ensuring computational efficiency and accuracy. Through flexible input-output design, users can easily integrate these functions into larger systems such as UAV navigation, satellite data processing, and other application scenarios. The code structure includes error handling, unit consistency checks, and support for multiple coordinate reference systems.