There are many solutions to this, some already listed. For best effect apply all of them together: Rate limiting api requests and movement, hysteresis on distance, randomness on distance, snap to grid, increasing randomness the more you seem to be trilaterating, etc.

Some of thrm will also solve the problem of just discovering a user, starting a chat and then instantly loosing them, even though you were both siting still, as you were on the border.