A tetrahedron based multilateration method for high precision equipment alignment

Abstract During the construction phase of a high-intensity proton accelerator, alignment measurement is required for key equipment, such as the bunch compressor kicking cavity, with a stringent alignment accuracy requirement of better than 0.05 mm. Conventionally, a laser tracker is used to measure the three-dimensional coordinates of the control network points and equipment target points for equipment alignment. However, limited by the angular measurement error of the instrument itself, the 3D coordinate measurement accuracy of a single point cannot satisfy the precision demand of 0.05 mm. This study proposes a multilateration method based on the tetrahedral principle. The 3D coordinates of the target points of the equipment were obtained using a single laser tracker placed at three or more stations. Compared with the single-point 3D coordinate measurement method, the proposed method improves the measurement accuracy, realizes high-precision measurement under the condition of occlusion of equipment target points, and has no strict requirements for the instrument layout. The fundamental principle of the tetrahedron-based multilateration alignment method was elaborated, and a simulation analysis was performed on the relative layout between the instrument and the measured equipment. Further experimental verification is performed. The experimental results demonstrate that the proposed method exhibits higher accuracy in calibrated bar length measurements than the single-point 3D coordinate method. For target point measurement on the experimental frame, the single axis measurement uncertainty of the target points is approximately 0.02 mm, satisfying the 0.05 mm specification for accelerator alignment.