RFID for Distance Detection?

Hi there. I'm an undergraduate trying to help out a research lab with this problem:

PROBLEM:
I'm trying to put together a monitoring system that can continuously track the 3-D movement of a rat in order to quantify its physical activity. I'd like to detect the orientation of the rat (turned left, huddled down, standing up, etc.) as well. Also, whatever device is used on the rat preferably needs to be imperceptible (small, < 1g), but can be inserted and sealed in a ceramic headcap that the rat will have on. There will only be 1 rat per cage, and the total volume of the cage will be around 2 or 3 cubic feet, so less than 1m^3. However, distance accuracy needs to be around 1 cm.

CURRENT APPROACH:
A common way to approach this problem has been to use an overhead video camera to analyze frames based on object contour or even color densities when using colored tags or active light transmitters (like LEDs) on the rat. However, tracking in this manner requires calibration for each ambient light setting (including a dark setting) and is limited if the rat's body orientation partially blocks light transmission of the desired colors--in other words, it requires line-of-sight. In addition to all this, the algorithms for picking out color densities and determining vertical movement (in z direction) are complex and subject to inaccuracies.

NEW APPROACH (that will hopefully work):
Therefore, I came to radio communication hoping that it would simplify this task, and thought RFID tags would be small enough to get the job done. However, I've come to find out that RFID was not made for this application. This is exacerbated by the fact that transmitted RF will be bouncing around inside the cage, making it difficult to determine which incoming signal is the direct one. Although, to account for 6-deg-of-freedom movement (xyz + roll, pitch, & yaw), I could install 3 RFID readers to account for each xyz plane, and the euler angles could be accounted for by using two passive tags, or one active tag with the capability to detect that.

FINAL THOUGHTS:
Is this task possible with RFID? If not, are there other technologies that could solve it?

Thanks in advance for your help,
Alec