Forecasting method in multilateration accuracy based on laser tracker measurement

Multilateration based on a laser tracker (LT) requires the measurement of a set of points from three or more positions. Although the LTs' angular information is not used, multilateration produces a volume of measurement uncertainty. This paper presents two new coefficients from which to determine whether the measurement of a set of points, before performing the necessary measurements, will improve or worsen the accuracy of the multilateration results, avoiding unnecessary measurement, and reducing the time and economic cost required. The first specific coefficient measurement coefficient (MCLT) is unique for each laser tracker. It determines the relationship between the radial and angular laser tracker measurement noise. Similarly, the second coefficient is related with specific conditions of measurement beta. It is related with the spatial angle between the laser tracker positions a and its effect on error reduction. Both parameters MCLT and beta are linked in error reduction limits. Beside these, a new methodology to determine the multilateration reduction limit according to the multilateration technique of an ideal laser tracker distribution and a random one are presented. It provides general rules and advice from synthetic tests that are validated through a real test carried out in a coordinate measurement machine.