Journal of Institute of Control, Robotics and Systems (제어로봇시스템학회논문지)

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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A Data Fitting Technique for Rational Function Models Using the LM Optimization Algorithm

LM 최적화 알고리즘을 이용한 유리함수 모델의 데이터 피팅

  • Received : 2011.05.20
  • Accepted : 2011.06.20
  • Published : 2011.08.01
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Abstract

This paper considers a data fitting problem for rational function models using the LM (Levenberg-Marquardt) optimization method. Rational function models have various merits on representing a wide range of shapes and modeling complicated structures by polynomials of low degrees in both the numerator and denominator. However, rational functions are nonlinear in the parameter vector, thereby requiring nonlinear optimization methods to solve the fitting problem. In this paper, we propose a data fitting method for rational function models based on the LM algorithm which is renowned as an effective nonlinear optimization technique. Simulations show that the fitting results are robust against the measurement noises and uncertainties. The effectiveness of the proposed method is further demonstrated by the real application to a 3D depth camera calibration problem.

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References

  1. J. Nocedal and S. J. Wright, Numerical Optimization, Springer, New York, 2006.
  2. S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge Univ. Press, Cambridge, 2004.
  3. V. B. Melas, Functional Approach to Optimal Experimental Design, Springer, New York, 2006.
  4. T. P. Ryan, Modern Regression Methods, Wiely, Hoboken, 2009.
  5. NIST, Engineering Statistics Handbook, http://www.itl.nist.gov/div898/handbook/.
  6. D. Marquardt, "An algorithm for least-squares estimation of nonlinear parameters," SIAM Journal on Applied Mathematics, vol. 11, no. 2, pp. 431-441, 1963. https://doi.org/10.1137/0111030
  7. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++ 3rd Edition, Cambridge Univ. Press, Cambridge, 2007.
  8. K. P. Chong and S. H. Zak, An Introduction to Optimizations, Wiely, New York, 2001.
  9. W. S. Cleveland and S. J. Devlin, "Locally weighted regression: an approach to regression analysis by local fitting," Journal of the American Statistical Association, vol. 83, pp. 596-610, 1988. https://doi.org/10.2307/2289282
  10. PrimeSense, http://www.primesense.com/.
  11. Wikipedia-kinect, http://en.wikipedia.org/wiki/Kinect.

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