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With enough data points you'd easily figure out that offset. Just overlay each data point with map data and decide whether the location makes sense.

(i.e. you're unlikely to most of the time be in the middle of a lake, farm field etc)

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Or if the person is traveling at highway speed, it would be pretty easy to fit that track to nearby highways.

Offset as function of user and location?

Where is this function stored?

As a random secret in the reporting device. The secret can then be used with a cryptographic hash to produce a deterministic but unpredictable offset, based on the current location.

Something like:

reported_position = true_position + hash(secret + true_position)

Hm that will essentially behave like random noise though, assuming that the position is sufficiently high resolution. So you'll need to round it in any case, and once you do that heavily enough, there is no need for this crypto magic.

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