I was thinking about a TDOA (Time Difference Of Arrival) multilateration application for indoor use. I would be trying to track multiple RF-emitting objects, with a required resolution of <1m. A quick calculation tells me that that means being able to distinguish between events 3ns apart.
The problem breaks down into two parts, the way I see it. First, there needs to be an absolute time reference between all modules, and, second, events need to be precisely time-stamped.
Problem #1: In order to precisely locate the objects in 3D space, I would need at least 4 receivers. These receivers would have to be precisely synchronized, probably down to an order of hundreds of pico seconds.
My thinking is to use a crystal resonator that receives an impulse from an antenna that is tuned to an RF-emitting master source. The antenna-driven oscillating signal would converge the crystal to the same frequency and phase (minus the transmission delay) as the master. Would this work?
In addition, if you know the distance between the master source and the receiver then you can calculate the transmission delay and be able to correct for absolute time.
However, supposing that we could not accurately measure the distance between the master source and the receiver, could you then use a higher-frequency PLL signal response sent from the receiver back to the master and then measure the time difference between zero-crossings in order to calculate the round-trip distance?
Problem #2: The tracked objects cannot be constrained to emit a signal of any kind. They might even go silent for extended periods of time. So passive TDOA is the only solution (that I can think of).
I think that the best solution is simply to sample and time-stamp the transmitter's frequency band at 1GHz and then perform cross-correlation between each receiver's signals in order to establish the relative distances. What kind of chip or circuit would be best for this?
I'm sorry, did I just say 3ns of resolution? And a 1GHz sampling rate??? Well, the devil is in the details.
Fortunately, refresh rate doesn't have to be that high. Maybe 1-10Hz, depending on accuracy. Plus we're going to suppose that the frequency band is reserved and that there is reasonable line-of-sight. And there are no critical systems, so if we get bad values nothing bad happens and no one gets hurt. At least we've got that going for us, because the rest of this is not easy!
Lastly, this is just for fun, so if it winds up being impossibly difficult-- either due to physics or my shoestring budget-- there are no hard feelings and no one becomes desperate not to lose his/her job.