## TDOA synchronization and time-stamping problem

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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.

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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?

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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?

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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.

Navstar?

No RSTDISBL, no fun!

I don't really have the money to launch my own satellites into orbit, or even create my own nuclear clocks. Plus, as far as I am aware, neither GPS nor Galileo solve indoor problems.

Use 38khz audio transmitters and receivers?

Imagecraft compiler user

bobgardner wrote:
Use 38khz audio transmitters and receivers?

Unfortunately, I cannot constrain them to emit in any way, including ultrasound. I.e., I cannot add anything.

Even if I could, ultrasound would not work, as it would easily get blocked and would not be effective over longish distances unless I added many receivers. Plus you have directionality problems.

The lower RF frequencies that I expect to be transmitted will pass through just about anything within reason, which is why I am only interested ins olving the problem with passive sensoring components instead of making it more complex-- but far more feasible I admit!-- with active ones.

With your current description I don't see how it's going to be practically possible for you to have the different units so precisely sync'd in time, and then maintaining that time sync. Without that, your system falls apart.

You may really want to look again at some ability to modify what they do. For example, if your central server can periodically transmit a "query" signal that the modules all respond to, that would make things a lot easier.

Being able to have the modules transmit a modulated signal instead of just a simple carrier can also greatly improve the time-accuracy of detecting them. Google "gold codes".

Excluding GPS, indoor position tracking using TDOA is done by products such as those from Ekahau, WhereNet, Time Domain, and several others. The common time reference is needed, and it has to be accurate to a few nanoseconds. This is difficult. These companies have huge proprietary investments in very clever ways to do low-cost synchronization, either in real time on a pulse by pulse basis, or non-real time during time delayed processing. One company does accurate TDOA using 802.11 signals and a complex DSP scheme. Some use receivers that collaborate via a common wired back-end to time-synch.

My experience is that if your goal is tracking, say, a WiFi emitting device, and there are cheap RFID tag like WiFi tags, the best approach is "RF footprinting", where there is an system of WiFi access points permanently installed in the facility. More numerous than usual, so that any emitter is received, even weakly, by 3 or 4 APs. The signal strengths, compared in an elegant algorithm to a calibration database created once, yields 5m or so of accuracy, which yields room number. But to be successful, the Z axis (floor #) ambiguity has to be resolved, and this is more difficult that x and y. The RF signal strength gradient between floors is often larger, but simple wooden floors make it tough. The good commercial products deal with this via heuristics that take into account the history of movements: stairwells, elevators, to weigh the Z axis estimate. For example, 1 minute ago the emitter was on floor 1. It didn't appear to use a stairwell or elevator, so this new Z axis estimate must be accordingly weighted, perhaps by a Kallman filter device.

So TDOA is the hard way. And indoor, my experience is that the multipath in offices makes it just too inaccurate, even with a DSP grinding through the delay spread statistics trying to find the direct path signal though it is weaker than the multipath arrivals. Outdoors, with less short range multipath, TDOA is a good approach and Ekahau et al use it for things like child tracking in amusemement parks. And outdoors, RF footprinting works poorly due to the inverse square law whereas indoors there are walls/floors to create gradients to benefit the algorithms.

frankvh wrote:
You may really want to look again at some ability to modify what they do. For example, if your central server can periodically transmit a "query" signal that the modules all respond to, that would make things a lot easier.

Unfortunately, this is simply out of the question. If it were, it would take all the fun out of the project.

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Being able to have the modules transmit a modulated signal instead of just a simple carrier can also greatly improve the time-accuracy of detecting them. Google "gold codes".

So are you saying that it wouldn't work to use an antenna that feeds into a crystal oscillator (probably via an omp-amp) to synchronize clocks and stop clock drift?

The bit about Gold codes is really interesting. I guess what you mean is that the modules would transmit a gold code at a certain time, and could tell the TDOA by looking at the difference in phase between the reference (i.e. internally generated Gold code) and the externally received signal.

P.S. In case it wasn't clear, let me state that while I can't add anything to the mobile transmitters, I can make the receivers as complex as I want. They can have a syncing signal and on top of that communicate wirelessly on other frequencies in order to share all sorts of interesting information.