Improved Self-Calibration of a Multilateration System Based on Absolute Distance Measurement

Multilateration tracking systems (MLTSs) are used in industrial three-dimensional (3D) coordinate measuring applications. For high-precision measurement, system parameters must be calibrated properly in advance. For an MLTS using absolute distance measurement (ADM), the conventional self-calibration method significantly reduces estimation efficiency because all system parameters are estimated simultaneously using a complicated residual function. This paper presents a novel self-calibration method that optimizes ADM to reduce the number of system parameters via highly precise and separate estimations of dead paths. Therefore, the residual function to estimate the tracking station locations can be simplified. By applying a suitable mathematical procedure and solving the initial guess problem without the aid of an external device, estimation accuracy of the system parameters is significantly improved. In three self-calibration experiments, with ADM repeatability of approximately 3.4 µm, the maximum deviation of the system parameters estimated by the proposed self-calibration method was 68.6 µm, while the maximum deviation estimated by the conventional self-calibration method was 711.9 µm. Validation of 3D coordinate measurements in a 1000 mm × 1000 mm × 1000 mm volume showed good agreement between the proposed ADM-based MLTS and a commercial laser tracker, where the maximum difference based on the standard deviation was 17.7 µm. Conversely, the maximum difference was 98.8 µm using the conventional self-calibration method. These results confirmed the efficiency and feasibility of the proposed self-calibration method.