How to calculate distance from Wifi router using Signal Strength?

I would like to calculate the exact location of a mobile device inside a building ( so no GPS access)

I want to do this using the signal strength(in dBm) of at least 3 fixed wifi signals(3 fixed routers of which I know the position)

Google already does that and I would like to know how they figure out the exact location based on the this data

Check this article for more details : http://www.codeproject.com/Articles/63747/Exploring-GoogleGears-Wi-Fi-Geo-Locator-Secrets

Solution 1:

FSPL depends on two parameters: First is the frequency of radio signals；Second is the wireless transmission distance. The following formula can reflect the relationship between them.

FSPL (dB) = 20log10(d) + 20log10(f) + K

d = distance
f = frequency
K= constant that depends on the units used for d and f
If d is measured in kilometers, f in MHz, the formula is:

FSPL (dB) = 20log10(d)+ 20log10(f) + 32.44

From the Fade Margin equation, Free Space Path Loss can be computed with the following equation.

Free Space Path Loss=Tx Power-Tx Cable Loss+Tx Antenna Gain+Rx Antenna Gain - Rx Cable Loss - Rx Sensitivity - Fade Margin

With the above two Free Space Path Loss equations, we can find out the Distance in km.

Distance (km) = 10(Free Space Path Loss – 32.44 – 20log10(f))/20

The Fresnel Zone is the area around the visual line-of-sight that radio waves spread out into after they leave the antenna. You want a clear line of sight to maintain strength, especially for 2.4GHz wireless systems. This is because 2.4GHz waves are absorbed by water, like the water found in trees. The rule of thumb is that 60% of Fresnel Zone must be clear of obstacles. Typically, 20% Fresnel Zone blockage introduces little signal loss to the link. Beyond 40% blockage the signal loss will become significant.

FSPLr=17.32*√(d/4f)

d = distance [km]
f = frequency [GHz]
r = radius [m]

Source : http://www.tp-link.com/en/support/calculator/

Solution 2:

To calculate the distance you need signal strength and frequency of the signal. Here is the java code:

public double calculateDistance(double signalLevelInDb, double freqInMHz) {
    double exp = (27.55 - (20 * Math.log10(freqInMHz)) + Math.abs(signalLevelInDb)) / 20.0;
    return Math.pow(10.0, exp);
}

The formula used is:

distance = 10 ^ ((27.55 - (20 * log10(frequency)) + signalLevel)/20)

Example: frequency = 2412MHz, signalLevel = -57dbm, result = 7.000397427391188m

This formula is transformed form of Free Space Path Loss(FSPL) formula. Here the distance is measured in meters and the frequency - in megahertz. For other measures you have to use different constant (27.55). Read for the constants here.

For more information read here.

Solution 3:

K = 32.44
FSPL = Ptx - CLtx + AGtx + AGrx - CLrx - Prx - FM
d = 10 ^ (( FSPL - K - 20 log10( f )) / 20 )

Here:

• K - constant (32.44, when f in MHz and d in km, change to -27.55 when f in MHz and d in m)
• FSPL - Free Space Path Loss
• Ptx - transmitter power, dBm ( up to 20 dBm (100mW) )
• CLtx, CLrx - cable loss at transmitter and receiver, dB ( 0, if no cables )
• AGtx, AGrx - antenna gain at transmitter and receiver, dBi
• Prx - receiver sensitivity, dBm ( down to -100 dBm (0.1pW) )
• FM - fade margin, dB ( more than 14 dB (normal) or more than 22 dB (good))
• f - signal frequency, MHz
• d - distance, m or km (depends on value of K)

Note: there is an error in formulas from TP-Link support site (mising ^).

Substitute Prx with received signal strength to get a distance from WiFi AP.

Example: Ptx = 16 dBm, AGtx = 2 dBi, AGrx = 0, Prx = -51 dBm (received signal strength), CLtx = 0, CLrx = 0, f = 2442 MHz (7'th 802.11bgn channel), FM = 22. Result: FSPL = 47 dB, d = 2.1865 m

Note: FM (fade margin) seems to be irrelevant here, but I'm leaving it because of the original formula.

You should take into acount walls, table http://www.liveport.com/wifi-signal-attenuation may help.

Example: (previous data) + one wooden wall ( 5 dB, from the table ). Result: FSPL = FSPL - 5 dB = 44 dB, d = 1.548 m

Also please note, that antena gain dosn't add power - it describes the shape of radiation pattern (donut in case of omnidirectional antena, zeppelin in case of directional antenna, etc).

None of this takes into account signal reflections (don't have an idea how to do this). Probably noise is also missing. So this math may be good only for rough distance estimation.

Solution 4:

the simple answer to your question would be Triangulation. Which is essentially the concept in all GPS devices, I would give this article a read to learn more about how Google goes about doing this: http://www.computerworld.com/s/article/9127462/FAQ_How_Google_Latitude_locates_you_?taxonomyId=15&pageNumber=2.

From my understanding, they use a service similar to Skyhook, which is a location software that determines your location based on your wifi/cellphone signals. In order to achieve their accuracy, these services have large servers of databases that store location information on these cell towers and wifi access points - they actually survey metropolitan areas to keep it up to date. In order for you to achieve something similar, I would assume you'd have to use a service like Skyhook - you can use their SDK ( http://www.skyhookwireless.com/location-technology/ ).

However, if you want to do something internal (like using your own routers' locations) - then you'd likely have to create an algorithm that mimics Triangulation. You'll have to find a way to get the signal_strength and mac_address of the device and use that information along with the locations of your routers to come up with the location. You can probably get the information about devices hooked up to your routers by doing something similar to this ( http://www.makeuseof.com/tag/check-stealing-wifi/ ).