According to ChatGPT, this code will do it.
DISCLAIMER: I have no idea if this code is accurate. I don't know what ECEF or LLA coordinates are.
It provided the following commentary to the code:
"Below is an example MATLAB code that demonstrates how to convert a covariance matrix from ECEF to LLA coordinates using a simplified transformation for illustration purposes. Please note that this example assumes a flat Earth for simplicity, and you might need to use more accurate equations depending on your requirements.
Make sure to replace cov_xx, cov_xy, etc., x, y, z, and R with your actual values. Additionally, if your Kalman filter operates in a non-linear setting, you might need to linearize the transformation equations using methods like Taylor series expansion.
Keep in mind that this code is a basic example, and for more accurate results, especially when dealing with the Earth's curvature, you should consider using more sophisticated coordinate transformation equations."
Perhaps it will at least provide a code base for you to modify.
% Sample covariance matrix in ECEF
sigma_ecef = [cov_xx, cov_xy, cov_xz;
cov_xy, cov_yy, cov_yz;
cov_xz, cov_yz, cov_zz];
% Sample ECEF coordinates
x_ecef = [x; y; z];
% Transformation equations (simplified for illustration)
lat = asin(z / norm(x_ecef));
lon = atan2(y, x);
alt = norm(x_ecef) - R; % R is the Earth's radius
% Jacobian matrix
partial_lat_partial_x = z / norm(x_ecef);
partial_lat_partial_y = 0;
partial_lat_partial_z = x / norm(x_ecef);
partial_lon_partial_x = -y / (x^2 + y^2);
partial_lon_partial_y = x / (x^2 + y^2);
partial_lon_partial_z = 0;
partial_alt_partial_x = x / norm(x_ecef);
partial_alt_partial_y = y / norm(x_ecef);
partial_alt_partial_z = z / norm(x_ecef);
Jacobian = [partial_lat_partial_x, partial_lat_partial_y, partial_lat_partial_z;
partial_lon_partial_x, partial_lon_partial_y, partial_lon_partial_z;
partial_alt_partial_x, partial_alt_partial_y, partial_alt_partial_z];
% Transform covariance matrix
sigma_lla = Jacobian * sigma_ecef * Jacobian';
% Print the result
disp('Covariance Matrix in LLA:');
disp(sigma_lla);
