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When looking for an AirTag, the iPhone shows the angle and distance to where the AirTag is located.

The distance can be calculated from the signal strength. But how do they find out the angle in which the tag is located?

Screenshot taken from MKBHD's Youtube video

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It is possible to determine the angle because the AirTag has a carefully designed antenna emitting a signal in essentially all directions. When the signal arrives at the iPhone, which is responsible for the angle calculation, the pulse amplitude will vary according to the angle in which the signal arrives at the iPhone antennas. Carefully created software can then use the measured amplitude values to calculate the angle.

Note that this is by no means a simple task, as it concern handling input at high speeds from two or more antennas and correlating information to determine when the same emitted signal is received by the antennas at different times. As far as I know, the AirTag also transmits at two different UWB frequencies at the same time - presumably to alleviate inaccuracies due to multi-pathing.

Note that the software also has to keep track of the phone’s own movement under use. I.e. if you rotate the phone, the angle shown to the user should be compensated for that. This is quite simple, and it is not in any way necessary for the user to move the phone around in circles in order to do the localization.

As for distance measurements, that is actually not calculated based on the signal strength itself as you speculate, but rather it is done by measuring time of arrival (i.e. Time Of Flight based localization).

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    Is there any documentation on this?
    – nohillside ♦
    Commented May 3, 2021 at 9:24
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    Apple does not publish documentation describing precisely how their algorithms work. However, UWB (as in the U1) is used by lots of other actors for in-door localization and positioning, so you can read about the general ideas involved lots of places. You'll want to learn about ToF (time of flight) and AoA (angle of arrival). You can also read the patent applications for patents granted to Apple for this - they're publically available. For angle estimation, it is most commonly done by having two antennas and determining phase shifts. However, techniques also exist for done angle [...]
    – jksoegaard
    Commented May 3, 2021 at 9:34
  • [...] estimation with a single antenna - for example with a tag with dual-chip anchors.
    – jksoegaard
    Commented May 3, 2021 at 9:34
  • Is it patented? The details would then be in the patent.
    – Barmar
    Commented May 3, 2021 at 14:49
  • ... which is what I wrote in the comment just above yours 😉
    – jksoegaard
    Commented May 3, 2021 at 16:00

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