POSIT with constraints

I'm building a robot (a car) that has a webcam mounted on it. I want to compute the position of the robot based on a model of the
environment around the robot: I find in the picture of the webcam some features that I map on the model, I then use POSIT to compute the position of the robot. I'd like to take advantage of the fact that the position of webcam has only 3 degree of freedom and not 6 (the altitude as well as 2 angles are fixed since the camera is fixed on the robot that evolves on a plan).
How should I modify the POSIT algorithm to take those constraints into account? (I'm starting from the implementation in OpenCV if that matters)
Thank you,
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