Fitting circles to data with correlated noise

Authors:
N. Chernov;P. N. Sapirstein
Affiliations:
Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, United States;Department of the History of Art and Archaeology, Cornell University, Ithaca, NY 14853, United States
Venue:
Computational Statistics & Data Analysis
Year:
2008

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Abstract

We study the problem of fitting circles to scattered data. Unlike many other studies, we assume that the noise is (strongly) correlated; we adopt a particular model where correlations decay exponentially with the distance between data points. Our main results are formulas for the maximum likelihood estimates and their covariance matrix. Our study is motivated by (and applied to) arcs collected during archeological field work.