An error similarity-based error-compensation method for measurement in the nonuniform temperature field

Measurement error compensation is a key issue for the application of laser trackers in an unsteady environment, especially in the nonuniform temperature field. Aimed at reducing induced measurement uncertainty, a measurement error compensation method with error similarity analysis is proposed in this paper. The spatial similarity of measurement errors is qualitatively analyzed based on the mathematical model, and quantitative analysis is presented by means of simulation and semivariogram. We then model the error similarity, and an error-estimation model for target points is established with the radius basis function neural network and regularized extreme learning machine. The experiments are conducted to verify error similarity and the applicability and accuracy of the estimation model in practice. The results show that error similarity does exist in practical measurements, and the proposed method can reduce the absolute measurement error to less than 0.03 mm (2 sigma<i). The method is applicable for measurements in different environments since the compensated point sets are almost coincident.