Efficient Algorithms for Structured Self-Calibration Problems.

摘要

Self-calibration techniques have been used extensively in co-ordinate metrology. At their most developed, they are able to extract all systematic error behaviour associated with the measuring instrument as well as determining the geometry of the artefact being measured. However, this is generally at the expense of introducing extra parameters leading to moderately large observation matrices. Fortunately, these matrices tend to have sparse, block structure in which the nonzero elements are confined to much smaller submatrices. This structure can be exploited either in direct approaches in which QR factorisations are performed or in iterative algorithms which depend on matrix- vector multiplications. In this paper, we describe self-calibration approaches associated with high accuracy, dimensional assessment by co-ordinate measuring systems, highlighting how the associated optimisation problems can be presented compactly and solved efficiently. The self-calibration techniques lead to uncertainties significantly smaller than can be expected from standard methods.