Global calibration of unleveled theodolite using angular distance constraints.

The theodolite is an important optical measurement instrument in application. Its global calibration, including position and orientation, is a prerequisite for measurement. Most global calibration methods require the theodolite to be leveled precisely, which is time-consuming and susceptible to error. We propose a global calibration method without leveling: it solves position results using the angular distance of control points by nonlinear optimization and then computes orientation parameters (rotation matrix) linearly based on position results. Furthermore, global calibration of multiple theodolites is also introduced. In addition, we introduced a method that can compute the dip direction and tilt angle by decomposing the rotation matrix. We evaluate the calibration algorithms on both computer simulation and real data experiments, demonstrating the effectiveness of the techniques.