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.