Image to ECEF Transformation Matrix from Roll,Yaw,Pitch and GPS+Altitude

Question

I am trying to estimate initial camera pose with respect to ECEF system using EXIF metadata. I have the a DJI Drone's gimbal Roll, Pitch and Yaw readings along with the Latitude, Longitude and Altitude. Assuming these values are fairly accurate, I am hoping to obtain the transformation matrix from Image to ECEF to find all the objects (out of a collection of objects whose location and altitude is known) that lie in a particular image along with their pixel coordinates, and then imporve the pose estimation at a later stage. I have tried the Pix4d way by converting roll, yaw and pitch to omega, phi and kappa, and then find a rotation matrix from PATB coordinate system to ECEF coordinates. I am not even sure if the values of Omega,Phi and Kappa obtained are correct, but assuming they are, the rotation matrix that I obtain from them is orthonormal, so I cannot directly use it for constructing the 4x4 transformation matrix, I probably need a scale factor for that.

Here is the link for Pix4D article - https://support.pix4d.com/hc/en-us/articles/205678146-How-to-convert-Yaw-Pitch-Roll-to-Omega-Phi-Kappa-

Please help me, I have been scouring through websites and papers for a week now to find a solution, but to no avail.

Answer 1

If you work in Python or Matlab, I recommend using the excellent nvector library for these problems - I use it every day exactly for these things.