Is is possible to perform 3D triangulation on two sets of 2D data without knowing camera parameters?

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Hi all,
I am tracking the movement of an object inside a cube using two cameras - one above and one side-on.
I need to recreate the 3D path of this object in world coordinates however I can't use checkerboards etc to calibrate the cameras because the tracking data is being processed by another piece of software which imposes its own origin on the data.
Is it possible to use something similar to Matlab's triangulate function but without access to camera matrices? perhaps using the corners of my cube instead somehow?
Thanks for any help,
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Right Grievous
Right Grievous el 11 de Mayo de 2015
Well we are measuring several features of the object (temp, electrical conductance etc) which are processed in a separate piece of hardware, which requires its own software.
To keep all of the data synchronized (we need micro second accuracy) we have to really use this software for tracking too.
Besides, I have other problems - the cameras we are using are great for tracking in IR but they don't capture very high quality images which makes camera calibration difficult. Furthermore, these cameras use a BNC connection, so to take stills with them I have to run the signal through a graphics adapter which also no doubt interferes with the images in such a way as to make my tracked coordinates no longer align with the captured stills... it's all a bit of a mess.
I do know where the corners of the cube are, and that the cube is a nice square cube, so I'm hoping to sort out the data using this as a reference.

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