POSIT with constraints

Hello,

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,