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Currently, I am thinking that since electromagnetic waves loose energy over distance, you might be able to figure out the relative distance to each of three radio "beacons" and use this information to triangulate the position of a Raspberry Pi robot with a radio sensor on-board.

What kind of radio receiver may I need to use, and what information about the radio signal could I use to calculate the distance to the beacon? Amplitude, perhaps? The entire system would be running indoors as an Indoor Positioning System.

In short, my question is what specific type of radio receiver would be adequate for using radio signal strength for triangulation. If amplitude contains the information of the strength of the signal, then I need a sensor that is sensitive enough to pick that up, and can provide amplitude readings in the first place.

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    $\begingroup$ Good question. maybe engineering SE can help further. Because, the answer depends more on radio wave physics and sensors than the application of that via raspberry. $\endgroup$ May 13 '18 at 11:45
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Unfortunately, There is too much interference for this to work probably, as Olin Lathrop said here on the Engineering SE:

While your concept is theoretically correct, it doesn't work well in practice except for rough locations.

The problem is interference. Radio waves get absorbed, reflected, diffracted, and in some cases even refracted. All those mean that there isn't just a single point source from the receiver's point of view. The various components of the signal bouncing around the environment can interfere constructively and destructively, making received amplitude only a very rough estimate of distance.

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I believe there has been some research done on robot localization based on Wifi signal strength. For example: http://robotics.usc.edu/~ahoward/projects_wifi.php and http://www.cs.cmu.edu/~mmv/papers/10icra-joydeep.pdf. But I believe accuracy is very rough (maybe meters of error).

For more precise radio localization (cm level), you can use ultrawideband (UWB) radios which can measure the time of flight between endpoints. Yes, there are multipath issues indoors, but there are ways to mitigate this. There are two main players here: https://www.decawave.com/ and http://bespoon.com/.

Also FYI, triangulation is when you know the angle to the fixed beacons, trilateration is when you know the range. See: https://en.wikipedia.org/wiki/Trilateration. Your proposed application would be trilateration.

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