What's the equation to get 2d camera position from Aruco markers on the ceiling?

Let’s say I have a 2d map drawn with hardcoded positions of Aruco markers, but I want to update it and display the position of the camera on it. If I get the angles and distances of each marker in the camera frame what’s an equation to use this information to calculate the camera position on the map?

define a multi-marker “board” (need not be flat). seeing any one of many markers will be sufficient to get a pose for the whole board.

the result from pose estimation is the transformation expressing the marker/board pose in the camera frame, i.e. transforming points from marker/board-local to camera-local.

to get the camera pose in the marker/board frame, invert the transformation.

the transformation should be handled as a 4x4 matrix. don’t bother trying to work with bare rvec,tvec pairs. turn them into 4x4 matrices.

Since I’m only trying to get 2d x,y coordinates of the camera, after I do the perspective inversion I only need to use the translation variables to get the camera’s position relative to the marker right?

And the translation should not be affected by how much the camera is tilted around and unevenly placed on the ground?