Tikhonov regularization based algorithm for position measurement of laser tracer

The position measurement for heavy-duty machine tools by sequential multilateral method is modeled as a nonlinear redundant (overdetermined) problem, which is generally solved by ordinary least square (OLSQ) method. Due to the influences of repeatability error and distance detection error of laser tracer, the positions retrieved via OLSQ are associated with low stability due to noise and error in the laser tracers data. To reduce the influence of data uncertainties and find a stable solution, Tikhonov regularization is adopted in this paper to mathematically minimize the fluctuation in the calculation results. Simulation is conducted based on Monte Carlo method to prove the concept. The results show that the solution of the proposed method could be more accurate with lower average error and standard deviation compared with that from OLSQ method.