A system includes a fixture having a known location in a surgical reference frame, a medical instrument, a position measuring device, and a computing system. The fixture includes a constraint structure having a known constraint structure pose in the surgical reference frame. The medical instrument includes a reference portion movably coupled to the fixture, an elongate flexible portion coupled to the reference portion, wherein the elongate flexible portion is sized to pass through the constraint structure, and a shape sensor. The position measuring device measures motion of the reference portion with respect to the fixture. The computing system is configured to receive shape information for the medical instrument, receive reference portion position information in the surgical reference frame, determine an estimated constraint structure pose from the reference portion position information and the shape information, determine a correction factor, and modify the shape information based upon the correction factor.