Integrating noisy data

T. Prvan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Suppose the parametric form of a curve is not known, but only a set of observations. Quadrature formulae can be used to integrate a function only known from a set of data points. However, the results will be unreliable if the data contains measurement errors (noise). The method presented here fits an even degree piecewise polynomial to the data where all the data points are being used as knot points and the smoothing parameter is optimal for the indefinite integral of the curve which happens to be a smoothing spline. After the smoothing parameter has been chosen, this approach is less computationally expensive than fitting a smoothing spline and integrating.

Original languageEnglish
Pages (from-to)83-87
Number of pages5
JournalApplied Mathematics Letters
Issue number6
Publication statusPublished - 1995
Externally publishedYes


  • Discrete-time smoother
  • Fixed-interval
  • Interpolation smoother
  • Kalman filter
  • Smoothing spline


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