Well, there is not much to do if you don't have the camera, or at least the model of it. As you may know a usual camera model is pin-hole, this basically consist in the 3D world coordinates are transformed (mapped) to the camera image plane 2D coordinates.
Camera Resectioning
If you don't have access to the camera or at least two chessboard images, you can't estimate the focal, principal point, and distortion coefficients. At least not in a traditional way, if you have more images than the one that you showed or a video from that camera you could try auto or self calibration.
Camera auto-calibration
Another auto-calibration
yet another
Opencv auto-calibration