<p>Identification of both position-independent geometric errors (PIGEs) and position-dependent geometric errors (PDGEs) of the rotary axis of five-axis machine tools is essential to ensure machining accuracy. However, conventional approaches do not identify such errors because of their reliance on the actual initial position, which is affected by the errors mentioned above, and installation errors of measuring artefacts. We therefore present a least-error estimation (LEE) method that uses the virtual initial positions of three precision balls that are not affected by such errors and installation errors of the artefacts when performing geometric analysis. The use of such positions enables more reliable identification of PIGEs and PDGEs. The PDGEs are geometrically minimized. This is not the case when actual initial positions. The geometric analysis consists of the following three steps: squareness errors are estimated by constructing three layered planes using the trajectories of the balls; offset errors are derived by determining the virtual initial positions of the balls; and the least PDGEs are then estimated. This yields the geometric errors of the rotary axis independently of the initial ball positions. Simulations show that the PIGEs and PDGEs estimated using this LEE method closely match actual values. In contrast, a conventional method that relies on the initial ball positions, resulted in deviations on the order of several tens of micrometers and microradians. The effectiveness of the LEE method was further validated experimentally by estimation of both PIGEs and PDGEs.</p>