Understanding ibeacon distancing

Question

Trying to grasp a basic concept of how distancing with ibeacon (beacon/ Bluetooth-lowenergy/BLE) can work. Is there any true documentation on how far exactly an ibeacon can measure. Lets say I am 300 feet away...is it possible for an ibeacon to detect this?

Specifically for v4 &. v5 and with iOS but generally any BLE device.

How does Bluetooth frequency & throughput affect this? Can beacon devices enhance or restrict the distance / improve upon underlying BLE?

ie

               | Range       | Freq       | T/sec      | Topo       |      
               |–—–––––––––––|–—––––––––––|–—––––––––––|–—––––––––––|
Bluetooth v2.1 | Up to 100 m | < 2.481ghz | < 2.1mbit  | scatternet |
               |-------------|------------|------------|------------|
Bluetooth v4   |     ?       | < 2.481ghz | < 305kbit  | mesh       |
               |-------------|------------|------------|------------|
Bluetooth v5   |     ?       | < 2.481ghz | < 1306kbit | mesh       |

Jennifer

Answer 1

The distance estimate provided by iOS is based on the ratio of the beacon signal strength (rssi) over the calibrated transmitter power (txPower). The txPower is the known measured signal strength in rssi at 1 meter away. Each beacon must be calibrated with this txPower value to allow accurate distance estimates.

While the distance estimates are useful, they are not perfect, and require that you control for other variables. Be sure you read up on the complexities and limitations before misusing this.

When we were building the Android iBeacon library, we had to come up with our own independent algorithm because the iOS CoreLocation source code is not available. We measured a bunch of rssi measurements at known distances, then did a best fit curve to match our data points. The algorithm we came up with is shown below as Java code.

Note that the term "accuracy" here is iOS speak for distance in meters. This formula isn't perfect, but it roughly approximates what iOS does.

protected static double calculateAccuracy(int txPower, double rssi) {
  if (rssi == 0) {
    return -1.0; // if we cannot determine accuracy, return -1.
  }

  double ratio = rssi*1.0/txPower;
  if (ratio < 1.0) {
    return Math.pow(ratio,10);
  }
  else {
    double accuracy =  (0.89976)*Math.pow(ratio,7.7095) + 0.111;    
    return accuracy;
  }
}   

Note: The values 0.89976, 7.7095 and 0.111 are the three constants calculated when solving for a best fit curve to our measured data points. YMMV

Chayachayote

Great answer and code David. Where does the txPower value come from? Is it a calibration value done on the client (receiving) side? Or is it a metric you can get from a beacon? – Strobotron

yes, that is the calibration constant transmitted by the iBeacon. You calibrate an iBeacon by measuring the signal strength of its transmission at 1 meter away, then configure the iBeacon to transmit that constant. – Chayachayote

what are the 0.89976, 7.7095 and 0.111 values for? – Delanie

Those our the three constants calculated when solving for a best fit curve to our measured data points. – Chayachayote

With this equation I end up with 84457991114.574738 when the beacon is laying on 1/4 from my phone. – Fusspot

@jnewport, what are your txPower and rssi inputs to the function? – Chayachayote

That was the issue. Gimbal will only let you set the txPower to at most/least -23. So I had to override there is my code and use -67. – Fusspot

FYI - Tried your app, but it doesn't pick up Gimbal's when they are set to iBeacon mode. – Fusspot

@jnewport, I am happy to help. Can you post a new question on StackOverflow or contact us at [email protected]. this comment thread is way too long already! – Chayachayote

@Roberto, I agree that this is what the Apple documentation says, but I stand by my description of what the field actually represents. If you experiment with it, I think you will agree. I have long wondered about the description in the documentation and have concluded that it is most likely just poor wording. – Chayachayote

How can you convert that to meter? It is for a rough estimate. – Mandal

@davidgyoung: Can you say how many different measurements from different distances you did to get this formula? Thanks a lot. – Pradeep

I used about 10. More are better, but provide diminishing returns. – Chayachayote

@Chayachayote one of my beacon transmitting Tx Power Value as "F0". Exactly how much TxPower should I consider for calculating distance(or for calculateAccuracy method)? – Larianna

Thanks @Chayachayote I am able to get the distance for iBeacons . What if eddystone beacons? Can I apply same algorithm? – Salazar

Eddystone beacons work the same way, except their reference calibration constant is expressed as dBm at 0 meters instead of 1 meter (everybody likes to be different!). Since it is impractical to measure the signal strength at 0m, in practice you measure it at 1m, then subtract 41 dB. For the formula, you must also subtract 41 dB from the reference calibration constant transmitted by the Eddystone beacon. – Chayachayote

@Chayachayote There's one thing that's puzzling me. Why do you define the ratio as division (rssi/txPower)? Aren't we dealing with dBm (a logarithmic scale), in which case a division should have been defined as rssi-txPower? Also, why do you recommend to subtract 41 dBm when dealing with Eddystones. Is that the loss between 0 and 1 meters? – Galanti

Eddystone is a 0 m reference point, yrs. The division vs. Subtraction is because we are not using a logarithmic function in this case. Subtracting did not work for the curve fit we used. – Chayachayote

@Chayachayote can you please share best curve fit formula or anything through which we can find out these 3 values for our device? – Swish

this formula is usable for any device? – Professoriate

This formula was derived from a best fit curve of RSSI readings as measured by an iPhone 4S. Because each device has a different bluetooth antenna and different gain on the receiver, the curve will be slightly different for each one. Even adding a case to your phone will change the results! While there are variations between different iOS devices, they are minor. Android devices can have much larger differences so the Android Beacon Library project has attempted (with very limited success) to compile a database of best fit curve coefficients on a per-device basis. – Chayachayote

The explanation of this method can be found at this article drive.google.com/open?id=0B8l-9ZkakYqaV3JqWHlna2lyS1k – Amphetamine

Getting moving average of RSSI instead of single RSSI broadcasted by the device is a recommended practice? I keep getting 6.930024667870472E-77 but actually it takes round 69cm distance – Soidisant

Answer 2

I'm very thoroughly investigating the matter of accuracy/rssi/proximity with iBeacons and I really really think that all the resources in the Internet (blogs, posts in StackOverflow) get it wrong.

davidgyoung (accepted answer, > 100 upvotes) says:

Note that the term "accuracy" here is iOS speak for distance in meters.

Actually, most people say this but I have no idea why! Documentation makes it very very clear that CLBeacon.proximity:

Indicates the one sigma horizontal accuracy in meters. Use this property to differentiate between beacons with the same proximity value. Do not use it to identify a precise location for the beacon. Accuracy values may fluctuate due to RF interference.

Let me repeat: one sigma accuracy in meters. All 10 top pages in google on the subject has term "one sigma" only in quotation from docs, but none of them analyses the term, which is core to understand this.

Very important is to explain what is actually one sigma accuracy. Following URLs to start with: http://en.wikipedia.org/wiki/Standard_error, http://en.wikipedia.org/wiki/Uncertainty

In physical world, when you make some measurement, you always get different results (because of noise, distortion, etc) and very often results form Gaussian distribution. There are two main parameters describing Gaussian curve:

1. mean (which is easy to understand, it's value for which peak of the curve occurs).
2. standard deviation, which says how wide or narrow the curve is. The narrower curve, the better accuracy, because all results are close to each other. If curve is wide and not steep, then it means that measurements of the same phenomenon differ very much from each other, so measurement has a bad quality.

one sigma is another way to describe how narrow/wide is gaussian curve.
It simply says that if mean of measurement is X, and one sigma is σ, then 68% of all measurements will be between X - σ and X + σ.

Example. We measure distance and get a gaussian distribution as a result. The mean is 10m. If σ is 4m, then it means that 68% of measurements were between 6m and 14m.

When we measure distance with beacons, we get RSSI and 1-meter calibration value, which allow us to measure distance in meters. But every measurement gives different values, which form gaussian curve. And one sigma (and accuracy) is accuracy of the measurement, not distance!

It may be misleading, because when we move beacon further away, one sigma actually increases because signal is worse. But with different beacon power-levels we can get totally different accuracy values without actually changing distance. The higher power, the less error.

There is a blog post which thoroughly analyses the matter: http://blog.shinetech.com/2014/02/17/the-beacon-experiments-low-energy-bluetooth-devices-in-action/

Author has a hypothesis that accuracy is actually distance. He claims that beacons from Kontakt.io are faulty beacuse when he increased power to the max value, accuracy value was very small for 1, 5 and even 15 meters. Before increasing power, accuracy was quite close to the distance values. I personally think that it's correct, because the higher power level, the less impact of interference. And it's strange why Estimote beacons don't behave this way.

I'm not saying I'm 100% right, but apart from being iOS developer I have degree in wireless electronics and I think that we shouldn't ignore "one sigma" term from docs and I would like to start discussion about it.

It may be possible that Apple's algorithm for accuracy just collects recent measurements and analyses the gaussian distribution of them. And that's how it sets accuracy. I wouldn't exclude possibility that they use info form accelerometer to detect whether user is moving (and how fast) in order to reset the previous distribution distance values because they have certainly changed.

Poona

Excellent intro to "sigma" correlation. Also it would be odd for a geek (even an Apple geek) to use the variable name "accuracy" when they meant "distance". Every RSSI "distance" or "location" determination comes with a "margin of error" (e.g., you are here +/- this much). So it makes sense their library would have both a function for "distance" and a function for "accuracy". – Bellyache

@r00dY a brilliant explanation I must say. Now, just a question if you can help. I have a callibration data for beacon measured at 1m, 2m ... 15m,... 20m and so on. I have the average distance values for each distance. Now, from the location manager delegate when we get beacon data like beacon major, minor,rssi,etc is it advisable to use the distance obtained from the above calibration that I explained? Please suggest, any help would be appreciated. Thanks in Advance. – Mona

Apple's accuracy is a function of both rssi and tx power. It's not entirely impossible that Estimote decided to reverse engineer the accuracy function and began providing tx power values such that reading accuracy estimates the distance. This provides a simpler developer experience for estimating distance, but breaks Apple's definition of accuracy. Other brands might stay more true to Apple's definition of accuracy and actually provide a "1 meter estimate" rather than a reverse-engineered value that makes accuracy estimate distance. – Guadiana

Answer 3

The iBeacon output power is measured (calibrated) at a distance of 1 meter. Let's suppose that this is -59 dBm (just an example). The iBeacon will include this number as part of its LE advertisment.

The listening device (iPhone, etc), will measure the RSSI of the device. Let's suppose, for example, that this is, say, -72 dBm.

Since these numbers are in dBm, the ratio of the power is actually the difference in dB. So:

ratio_dB = txCalibratedPower - RSSI

To convert that into a linear ratio, we use the standard formula for dB:

ratio_linear = 10 ^ (ratio_dB / 10)

If we assume conservation of energy, then the signal strength must fall off as 1/r^2. So:

power = power_at_1_meter / r^2. Solving for r, we get:

r = sqrt(ratio_linear)

In Javascript, the code would look like this:

function getRange(txCalibratedPower, rssi) {
    var ratio_db = txCalibratedPower - rssi;
    var ratio_linear = Math.pow(10, ratio_db / 10);

    var r = Math.sqrt(ratio_linear);
    return r;
}

Note, that, if you're inside a steel building, then perhaps there will be internal reflections that make the signal decay slower than 1/r^2. If the signal passes through a human body (water) then the signal will be attenuated. It's very likely that the antenna doesn't have equal gain in all directions. Metal objects in the room may create strange interference patterns. Etc, etc... YMMV.

Alienism

out of curiosity: how does ratio_dB = txCalibratedPower - RSSI work out? Since both measures are in dBm, I would assume the outcome to be in dBm as well? – Moe

Yes @Moe I expect the result to be in dBm – Dilettante

Answer 4

iBeacon uses Bluetooth Low Energy(LE) to keep aware of locations, and the distance/range of Bluetooth LE is 160ft (http://en.wikipedia.org/wiki/Bluetooth_low_energy).

Junie

Answer 5

Distances to the source of iBeacon-formatted advertisement packets are estimated from the signal path attenuation calculated by comparing the measured received signal strength to the claimed transmit power which the transmitter is supposed to encode in the advertising data.

A path loss based scheme like this is only approximate and is subject to variation with things like antenna angles, intervening objects, and presumably a noisy RF environment. In comparison, systems really designed for distance measurement (GPS, Radar, etc) rely on precise measurements of propagation time, in same cases even examining the phase of the signal.

As Jiaru points out, 160 ft is probably beyond the intended range, but that doesn't necessarily mean that a packet will never get through, only that one shouldn't expect it to work at that distance.

Boutonniere

Answer 6

With multiple phones and beacons at the same location, it's going to be difficult to measure proximity with any high degree of accuracy. Try using the Android "b and l bluetooth le scanner" app, to visualize the signal strengths (distance) variations, for multiple beacons, and you'll quickly discover that complex, adaptive algorithms may be required to provide any form of consistent proximity measurement.

You're going to see lots of solutions simply instructing the user to "please hold your phone here", to reduce customer frustration.

Spoofery