This nebulous system has to be defined a bit more in purpose and construction before you can get a meaningful answer. Anyone can specifiy a need for infinite precision, but very few people have any actual use for it. Even aerospace projects are rarely more precise than a tenth of a thousandth of an inch. In addition to the questions I asked previously, it would be a good idea to know how big this system is going to be in the first place. If it is supposed to have a work volume of a few cubic feet, then it is an entirely different scale of problem than one that must operate in a 50 cubic meter work volume, or one which is constrained only by the (adjustable) length of its arms.
The same goes for speed. Is this thing going to track bullets and carefully alter their trajectory enroute? Is it going to just pick up a box and put it on a shelf?
How about starting with the basics? Just what is this system? How is it designed? Is it a gantry, or a multijoint arm? How fast do you need the answer? Is the precise position during a trajectory needed, or just the endpoints? What is happening during travel?
What are the system requirements of accuracy and precision, and repeatability? In many cases, the extra expense of the extra decimal isn't worth it. If it costs an extra $10,000 to get the next decimal point, is it worth it? Remember, a toaster might be able to pop the toast up to within a thirty second of an inch each time, but all we really care about is that it is up and toasted. We could do with a tolerance of -0.5 +2 inches easily on that position. Making one more precise and accurate on position would be a waste. Instead of worrying about the precision you can obtain with the sensors, look at exactly what precision you need for your application.
It is possible to use optical measurements to detect the position of a gantry to within a few millionths of an inch if you really need to. That can be extended to 3 dimensions if you want. It is expensive, but it can be done.
Simple motor encoding and a good control board will get you a couple decimal places. Is that enough? Perhaps adding some models that define the stiffness of the device, masses, travel, etc will get you a little closer.