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

Abstract

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.

Multilateration with Self-Calibration: Uncertainty Assessment, Experimental Measurements and Monte-Carlo Simulations

“…In these works, the results from the multilateration technique with self-calibration have been compared to reference positions provided by a coordinate measuring machine, a calibrated Zerodur ® hole plate standard, or a commercial laser tracker. For target without movements, the observed deviations between the measured positions and the reference ones were below 5 µm in [6] for a measurement volume of less than 1 m 3 , and submicrometric in [7] for a measurement volume of 5 m × 4 m × 2 m. The deviations, expressed as standard deviation, were equal to about 18 µm for a measurement volume of 1 m 3 in [8] and to about 40 µm for a measurement volume of 10 m × 5 m × 2.5 m in [9].…”

“…Our objective is to assess with a consistent metrological approach the uncertainties of the target positions obtained with such a coordinate measurement system. The study of this paper is applicable to any multilateration system such as those presented in [6,7] and based on laser tracking interferometers, the one presented in [8] and based on laser tracking absolute distance meters (repeatability of about 3.4 µm) or the one presented in [9] and based on absolute distance meters using the Frequency Scanning Interferometry technique (uncertainty of 5 ppm including air refractive index). In these works, the results from the multilateration technique with self-calibration have been compared to reference positions provided by a coordinate measuring machine, a calibrated Zerodur ® hole plate standard, or a commercial laser tracker.…”

Phase Unwrapping and Frequency Points Subdivision of the Frequency Sweeping Interferometry Based Absolute Ranging System

“…With the dominance of no ranging blind area, non-cooperative target, and high signal to noise ratio, the FSI is coming into prominence in the field of engineering application, such as optical coherence tomography [1], the measurement of three-dimensional coordinate [2] and parameters of rotors [3], important equipment manufacturing [4] and satellite formation [5]. FSI is based on the Michelson interferometer, and the distance is calculated by the beat frequency caused by the sweeping frequency and phase difference [6,7].…”