Compute camera position

I would like to use unity for projection and I need to calibrate the projector relative to the real world. In blender I use BLAM (BLAM - Geometry camera matching add-on - BlenderNation) to do this and it computes the position of the camera and helps me project on the 3d space.

Using unity can I achieve this?

To go in detail I have a unit cube and the world is relative to it. I could match the corners of the cube from the projector and would like to compute the position of the projector in unity using the co ordinates and recreate my scene in unity for projection.

Is there a better way to go about this or any tool which I can use?

I do this using augmented reality toolkits like Vuforia and others. Put some markers (in this case, on your cube) and calibrate them in real world.