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Fitting circles to data with correlated noise

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  • Chernov, N.
  • Sapirstein, P.N.

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.

Suggested Citation

  • Chernov, N. & Sapirstein, P.N., 2008. "Fitting circles to data with correlated noise," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5328-5337, August.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:12:p:5328-5337
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    References listed on IDEAS

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    1. Berman, Mark, 1989. "The asymptotic statistical behaviour of some estimators for a circular structural model," Statistics & Probability Letters, Elsevier, vol. 7(5), pages 413-416, April.
    2. Chernov, N. & Lesort, C., 2004. "Statistical efficiency of curve fitting algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 47(4), pages 713-728, November.
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    Cited by:

    1. Al-Sharadqah, A. & Ho, K.C., 2018. "Constrained Cramér–Rao Lower Bound in Errors-In Variables (EIV) models: Revisited," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 118-126.
    2. Greco, Luca & Pacillo, Simona & Maresca, Piera, 2023. "An impartial trimming algorithm for robust circle fitting," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    3. Ulric Lund, 2013. "Monte Carlo maximum likelihood circle fitting using circular density functions," Computational Statistics, Springer, vol. 28(2), pages 393-411, April.
    4. Liu, Xin & Yue, Rong-Xian & Wong, Weng Kee, 2018. "D-optimal design for the heteroscedastic Berman model on an arc," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 131-141.
    5. Zvi Drezner & Jack Brimberg, 2014. "Fitting concentric circles to measurements," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(1), pages 119-133, February.

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