Positioning system for work machine, work machine, and positioning method for work machine

A positioning system for a work machine using realtime kinematic positioning that uses a satellite positioning system, the positioning system comprising:

• a calculation unit that calculates a position of an antenna, of the satellite positioning system, disposed in the work machine based on a position of working equipment, of the work machine, aligned with a known reference point positioned at a work site;
• and
• an initialization control unit that outputs a control command that causes a receiver, of the satellite positioning system, that performs positioning calculation by the realtime kinematic positioning to execute initialization processing of the positioning calculation in which an integer value bias of each satellite and the position of the antenna of the satellite positioning system are unknown, by using the position of the antenna of the satellite positioning system that the calculation unit calculates, wherein
• the calculation unit calculates the position of the antenna of the satellite positioning system based on a position of the reference point and an angle representing a posture of the working equipment.