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Regarding 1., my phone reads strength and inclination of the field. I suppose that these two, coupled with a compass, could in theory give enough information to collapse the belief state to a single position. Moving a bit should give you enough data to further ensure precision.

Either that, or WiFi. :)

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(no expertise here)

How do you get 'inclination' of the field? Is it based on phone orientation? If so then you just opened up a lot more possibilities for position. Also, in this solution the phone doesn't know you're moving. It just sees: magnetic field is changing...

You must have to start it at a specific place, or tell it where you are when you start it (eliminating the 'where am I' use case).

I have some experience with indoor location tech, but not magnetic fields. If I had to guess (and I do) I'd suspect that the algorithm depends on consensus based on traffic/usage. The map's gonna change regularly, but if enough people use the technology you can take the algorithm's guesses for everyone and start to build a confidence weight for your prediction, weed out anomalies, and update your understanding of the magnetic fingerprint of the space over time. I'd also assume it uses GPS to get your bootstrapped whenever possible, ie: sort out what entrance you came through, use pathfinding over time to get some limit the possible locations you might be in currently.

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