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Current Derivative Estimation of Non-stationary Processes Based on Metrical Information

  • Elena KochegurovaEmail author
  • Ekaterina Gorokhova
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9330)

Abstract

Demand for estimation of derivatives has arisen in a range of some applied problems. One of the possible approaches to estimating derivatives is to approximate measurement data. The problem of real-time estimation of de-rivatives is investigated. A variation method of obtaining recurrent smoothing splines is proposed for estimation of derivatives. A distinguishing feature of the described method is recurrence of spline coefficients with respect to its segments and locality about measured values inside the segment. Influence of smoothing spline parameters on efficiency of such estimations is studied. Comparative analysis of experimental results is performed.

Keywords

Recurrent algorithm Derivatives estimation Variation smoothing spline 

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References

  1. 1.
    Golubinsky, A.N.: Approximation methods of experimental data and modeling. Herald of Voronezh Institute of MIA Russia 2, 138–143 (2007). (In Russian)Google Scholar
  2. 2.
    Zavyalov, Y.S., Kvasov, B.I., Miroshnichenko, V.L.: Methods of spline functions. Nauka, Moscow (1980). (In Russian)Google Scholar
  3. 3.
    Vershinin, V.V., Zavyalov, Y.S., Pavlov, N.N.: Extreme properties of splines and smoothing problem, p. 102 c. Science, Novosibirsk (1988). (In Russian)Google Scholar
  4. 4.
    Rozhenko, A.I.: Theory and algorithms for variation spline approximation: Dr. Sci. Diss., January 1, 2007, Novosibirsk, p. 231 (2003). (In Russian)Google Scholar
  5. 5.
    Voskoboynikov, Y.E., Kolker, A.B.: Approximation of the contour image smoothing splines. Journal Avtometriya 39(4), 3–12 (2003). (In Russian)Google Scholar
  6. 6.
    Ageev, U.M., Kochegurova, E.A.: Frequency properties of recurrent smoothing splines. Notify of High School, Instrumentmaking 3, 3–8 (1990). (In Russian)Google Scholar
  7. 7.
    Dmitriev, V.I., Ingtem, J.G.: A two-dimensional minimum-derivative spline. Computational Mathematics and Modeling 21, 206–211 (2010). SpringerMathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    De Brabanter, K., De Brabanter, J., De Moor, B.: Derivative Estimation with Local Polynomial Fitting. Journal of Machine Learning Research 14, 281–301 (2013)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Ragozin, D.L.: Error bounds for derivative estimates based on spline smoothing of exact or noise data. Journal of Approximation Theory 37, 335–355 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Kochegurova, E.A., Shebeko, E.V.: Usage of variation smoothing spline in short-term prediction problem. Notify of the Tomsk Polytechnic University 7, 36–39 (2006). T.309, (In Russian)Google Scholar
  11. 11.
    Cao, J., Cai, J.: L. Wang: Estimating Curves and Derivatives with Parametric Penalized Spline Smoothing. Statistics and Computing 22(5), 1059–1067 (2012)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Tomsk Polytechnic UniversityTomskRussian Federation

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