Two ranging or TDOA or PDOA


I want to use 4 anchors, which are positioned on the corner of 1m x 1m square.
and localize a tag inside and outside the square.

Which approach could give better accuracy: Two ranging or TDOA or PDOA?

Many thanks

Hi Nori,

For better accuracy, my guess would be to use Two way ranging in this case as it will not depend on clock synchronization and thus will lead to the best accuracy you can reach for this use case.
TDOA would be the best fit, if you want to minimize power consumption because you’ll need to send only one message to localize the tag if the clock of the anchors are synchronized.
I think PDOA could be interestring if you want to reduce the number of anchors. Theoratically, with only one Anchor having 2 antennas, you can localize the tag.

Hope it helps,

Thank you Wassim.
Which method (Two way ranging or pdoa or tdoa) can give the best accuracy?
Is cm accuracy possible?

A TDoA system should in theory be most accurate.
To achieve the best possible accuracy all the anchors should be on a wired common clock with good synchronisation between them and calibrated antenna delays. You can manage without that wired clock but it drops the accuracy which seems to be what you care about. Also for a solution you need one more anchor than for TWR, there is one more unknown that needs to be solved, the tag transmit time.
TDoA is also better for movement since all measurements are made at the same time rather than one at a time so there is no opportunity to move between each measurement.

TWR will be a little less accurate but doesn’t require the clock synchronisation between the anchors making it a lot simpler to deploy.

There are also differences in things like where locations are calculated and the maximum number of tags supported but it sounds like you don’t care about those details so much.

PDoA can be added to either system type to give more information per anchor. This either allows you to decrease the number of anchors or increase the accuracy for a fixed number of anchors.

By far the best way to improve accuracy for either system is to add anchors. Even if you manage to dial out all the biases and offsets in the measurements there will be some random noise. The more anchors to average between the more the effects of this noise can be decreased. But more anchors means more complexity, especially for a TDoA system if you need to worry about clock synchronisation.

If things are fairly static then averaging over time will also decrease noise significantly. However this isn’t as good as adding anchors. All anchors will end up having a slight bias in their measurements, averaging won’t remove these but if you add more anchors then the influence of individual anchor biases will be reduced and there is more chance of the biases averaging out.

When you say 1 cm accuracy do you mean absolute or relative? Relative accuracy would be if you move 50 cm then the two locations are 50 cm apart but both outputs could offset from the correct positions… Absolute accuracy is that the real world location for any given point is also correct.

Getting good relative accuracy over short distances is relatively simple. Getting absolute accuracy or relative accuracy over larger distances can be a lot harder.

We run a TWR system and can achieve ~3 cm RMS absolute accuracy using 8 anchors, dropping closer to 2 cm if you use 12 anchors. But a lot of work has gone into maintaining that accuracy over large areas, initial tests had a pincushion effect, if you travelled in a line through the middle it was straight, if you travelled in a line down the side it was slightly curved.
I remember someone posting here that they had a TDoA system deployed that achieved sub-cm accuracy over a basketball court but that was using something like 50 anchors.

So to answer your question:
TDoA + PDoA is in theory going to give the best accuracy but is also more complex to implement. To achieve the best possible accuracy you will need to put a lot of work into tuning and calibrating the system. 1 cm accuracies are probably not possible with 4 anchors but you may come close if you can average over time. Adding more anchors will improve accuracy.

Hi AndyA,
thank you for your for the information. I would like to achieve the cm absolute accuracy in 2mx2m square area. The 4 anchors are inside this area and are located in the corner of 1mx1m square. As you mentioned TDOA with wired synchronization would be a good choice.
You talked about the bias. Could they be removed by simple calibration?

The bias I mentioned isn’t a single thing, I was talking about the total of all non-random error sources. This will be comprised of the antenna delay, signal level effects, temperature effects etc…
In theory most of these can be calibrated out but it gets tricky. Antenna delay will often vary slightly with orientation relative to the signal source, this is on top of signal level orientation effects. Signal level will depend on the orientation and elevation angles of the signal path at both the transmitting and the receiving antennas. Temperature also has an impact on the measurements, the exact impact of this is slightly different on each unit.

So yes they can be calibrated out and coming up with a first approximation of this calibration that removes a large proportion of the errors is fairly simple. However getting a perfect calibration that removes all of them to within the system resolution is non-trivial.

Are you familiar with the concept of Geometric Dilution of Precision or DoP? It’s a concept normally used for GPS, it allows you to calculate the impact that your anchor positions will have on your position output. If you know the accuracy of your individual tag to anchor range measurements and the locations of the anchors then you can calculate the theoretical position accuracy at any given point. Or given an accuracy requirement and a test area / geometry tell you how accurate you need to get the range measurements.

Either way, as soon as you go outside the box defined by the anchors the DoP starts to increase rapidly. You are only going 50cm outside so it should still work but your accuracy is going to be worse than if you could put the anchors on the corners of the 2m square.

My gut call is that you’re not going to get the accuracy you’re aiming at without either more anchors or integrating some other sensor source like an IMU into your solution.

You didn’t mention if this was a 2d or 3d system. If 3d then barometers in the tag and anchors can be used to give a significant improvement in the height accuracy, the DoP for height calculations is terrible for most UWB installations.

Thank you AndyA. That help me a lot. :smiley: