A method of implementing fast GNSS convergence by relative positioning is disclosed. A GNSS receiver which is coupled with a mobile machine is shut down. The GNSS receiver is in a converged state at shut down. A movement sensor is monitored to determine if net movement of a GNSS antenna coupled with the mobile machine exceeds a threshold net movement parameter while the GNSS receiver is shut down. Upon power up of the GNSS receiver, a shorter convergence algorithm is initiated in response to determining that the threshold net movement parameter has not been exceeded. The shorter convergence algorithm is also initiated upon power up of the GNSS receiver in response to determining that the threshold net movement parameter has been exceeded but information from the movement sensor has been used to update the location of the GNSS receiver since said shut down.