Least Squares Association of Geometrical Features by Automatic Differentiation

Least squares association of geometrical features plays an important role in geometrical product specification and verification. Most existing algorithms for the least squares association today usually do not give the covariance matrix associated with the parameters of the respective geometrical fea...

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Bibliographic Details
Published in:Key engineering materials 2010-01, Vol.437, p.222-226
Main Authors: Lin, Jia Chun, Krystek, Michael Paul, Shi, Zhao Yao
Format: Article
Language:English
Subjects:
Algorithms
Complexity
Covariance matrix
Differentiation
Errors
Least squares method
Mathematical analysis
Product specifications
Quotients
Risk
Citations: Items that this one cites
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Summary:Least squares association of geometrical features plays an important role in geometrical product specification and verification. Most existing algorithms for the least squares association today usually do not give the covariance matrix associated with the parameters of the respective geometrical feature. The reason is that the complexity of these algorithms can be very high, because partial differential quotients are needed. If the necessary partial difference quotients are calculated by hand and subsequently coded into an algorithm, there is a high risk to introduce unwillingly errors. This paper shows how the least squares algorithm can automatically be generated solely from the equation specifying the distance function of the measured points from the geometrical feature.
ISSN:1013-9826
1662-9795
1662-9795
DOI:10.4028/www.scientific.net/KEM.437.222