Does accuracy depend on the location update rate?

Background

This article has sister articles about accuracy, location update rate and latency:
 
 
Check them first before going the new topics that are deeper covered in this article.

Does accuracy depend on the location update rate?

The question whether accuracy depends on the location update rate splits into several questions and answers. There are even seemingly contradictions. But, in fact, there are not contradictions – just different usage scenarios

Key topics to understand:

  • Positioning accuracy doesn’t depend on the location update rate
  • It is easy to achieve high location update rate, but difficult to get low latency
  • Tolerating higher latency it is possible to get better accuracy

Positioning accuracy doesn't depend on the location update rate

Let’s first consider NIA as an example. It is the easiest to understand architecture:

  • Modem commands via radio which mobile beacon to emit the ultrasound pulse
  • At the same time, all beacons – stationary and mobile – synchronize their clocks very precisely. They immediately know not only who will be emitting, on which ultrasound frequency, but also when exactly
  • Since there is only one mobile beacon emits in pure NIA system at a given timeslot (time reset). Thus, any received ultrasound pulse will be the signal from our mobile beacon (hedgehog). Of course, we need to filter out noise and other false signals, but that is a different task. Purely, from distinguishing “our” signal from “non-our” signal, it is very simple and very straightforward
  • Since the ultrasound pulse is very short (0.15-1.5ms), it is effectively a flash. The location measurements are kind of frozen at that particular moment. The mobile beacon emitted the pulse, the pulse is flying towards the stationary beacons and when all measurements and calculations are done, we will know the location very precisely

Thus, the biggest misconception of linking between location update rate and accuracy is the following:

“If you have 1Hz location update rate or 10Hz location update, will the accuracy be higher in the 10Hz, because the object is moving and while it is moving its location is changing. Therefore, if it is changing, we cannot measure it precisely, if our location update rate is slow, right?”

No, it is not a correct assumption, because:

  • The location measurement is a very short process – ~1ms or even less in some cases. During this time even the fastest indoor mobile objects can be considered as nearly static. But even they are not static, the impact on the accuracy of the measurement is not substantial
  • The misconception is in timing. Thus, there are questions like the one above
  • Yes, we will know the measured location very precisely. But what location? – not the location of the object, when we finally calculate the location, but the location of the object when location was sampled. That is the key. That is the source of misunderstanding
 
Location measurement is done at one time – the location sample – but the knowledge about that location comes with a latency. Where the object is at that moment, we don’t know and can’t know. We can predict using different models. And the object can predict. But it is a prediction – not a measurement. Sure! It can be very good and very useful in practice. But it is not a measurement per se.

It is easy to achieve high location update rate, but difficult to get low latency

Imaging that we don’t care about latency and care only about the location update rate. It is possible to gather several location updates, interpolate them, and populate with as many intermediate location measurement points, thus, effectively, to have as high location update rate as you wish.

For example, this is exactly what the Realtime Player in the Dashboard does:

  • Based on several location points before the time stamp and several location points after the time stamp, the system interpolates with a function the location in between those real measurements
  • The function is actually returning, though artificial (calculated – not purely measured), but even more accurate points than just measured points, because of embedded noise filtering the function
  • As a result, you can have as high update rate as you wish, but with high latency
 
Misconception between location update rate is latency is another source of confusion. Typically, people assume that if the system has 100Hz update rate, it would have 1/100Hz=10ms latency, which is not the true in the majority of cases. Even in the least latency-constrained systems, the latency is always larger than 1/update rate. But in many cases, latency and update rate are almost not linked at all.

It is difficult to reduce latency for ultrasound based systems, because of slow speed of ultrasound wave propagation. The very reason why ultrasound-based location systems are so precise is the core reason why it is very difficult to have low latency. Let’s calculate:

  • For example, we have a submap of 20m
  • The time of flight of ultrasound will be roughly 20m/340m/s and the upper limit of location update rate 340m/s/20m = 17Hz
  • That is a theoretical upper limit not counting required time for filtering, all possible calculations and the radio traffic overhead. In reality, depending on the architecture, the number of ultrasound frequencies, etc. the resulting update rate can easily be 5-12Hz or so instead of theoretical 17Hz
  • So, the real latency can be smaller than 1/location update rate, i.e. 80-200ms

Tolerating higher latency it is possible to get better accuracy

The statement that with higher latency is possible to get higher accuracy seemingly contradicts to the earlier given statement that the accuracy doesn’t depend on the location update rate. Both are correct.

We have a train of location updates. If we accumulate several of them, perform all sort of mathematical operations, we can get higher accuracy. It is very straightforward for static and slow-moving objects, but with not too complex logic can be shown for fast-moving objects as well.

For static and slow-moving objects: for N samples and N-time increase in latency, it is possible to achieve sqrt(N) time accuracy improvement just be averaging. Thus, of 16-time averaging, it is possible to reduce the noise of the location measurement by a factor of 4.

See below an example of the Realtime Player (RTP) affecting the resulting noise of the location measurement that drops significantly, when the RTP is activated. But for the expense of latency.

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