If your taking the time to read this, let me start by thanking you.
It should also be noted that the chances of me helping anyone with any math problem is very remote, not for lack of want, but skills (one semester tech math).
If this topic has been beat to death already, please let me know.
First question:
With two feedback devices, ones measures distance and the other measures the Yaw axis is it possible work out it's X,Y location?
This is possible yes but there are some accuracy issues to be aware of.
Note that when the angle is close to 90 degrees for one small change in angle A we get a sweeping distance (along the x axis) of some length xL1 but a much smaller distance along the y axis yL1, and when the angle is close to 0 degrees for that same small change in angle A we get a sweeping distance along the x axis of some small distance xL2 but a much larger distance along the y axis yL2. When the angle is close to 45 degrees on the other hand we get nearly the same distances in the direction of x and y for that same small change in angle. These differences mean that the accuracy in different areas for pointing out a given point (x,y) in the working field is going to vary sometimes quite a bit over the whole range of the device, and this accuracy has to be checked to make sure it works well enough with the application as needed.