Encyclopedia of Systems and Control

2015 Edition
| Editors: John Baillieul, Tariq Samad

Nonparametric Techniques in System Identification

  • Rik Pintelon
  • Johan Schoukens
Reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5058-9_109


This entry gives an overview of classical and state-of-the-art nonparametric time and frequency-domain techniques. In opposition to parametric methods, these techniques require no detailed structural information to get insight into the dynamic behavior of complex systems. Therefore, nonparametric methods are used in system identification to get an initial idea of the model complexity and for model validation purposes (e.g., detection of unmodeled dynamics). Their drawback is the increased variability compared with the parametric estimates. Although the main focus of this entry is on the classical identification framework (estimation of dynamical systems operating in open loop from known input, noisy output observations), the reader will also learn more about (i) the connection between transient and leakage errors, (ii) the estimation of dynamical systems operating in closed loop, (iii) the estimation in the presence of input noise, and (iv) the influence of nonlinear distortions on the linear framework. All results are valid for discrete- and continuous-time systems. The entry concludes with some user choices and practical guidelines for setting up a system identification experiment and choosing an appropriate estimation method.


Best linear approximation Correlation method Empirical transfer function estimate Errors-in-variables Feedback Frequency response function Gaussian process regression Impulse transient response modeling method Local polynomial method Local rational method Noise (co)variances Noise power spectrum Spectral analysis 
This is a preview of subscription content, log in to check access.



This work is sponsored by the Research Foundation Flanders (FWO-Vlaanderen), the Flemish Government (Methusalem Fund, METH1), the Belgian Federal Government (Interuniversity Attraction Poles programme IAP VII, DYSCO), and the European Research Council (ERC Advanced Grant SNLSID).


  1. Antoni J, Schoukens J (2007) A comprehensive study of the bias and variance of frequency-response-function measurements: optimal window selection and overlapping strategies. Automatica 43(10):1723–1736MathSciNetGoogle Scholar
  2. Bendat JS, Piersol AG (1980) Engineering applications of correlations and spectral analysis. Wiley, New YorkGoogle Scholar
  3. Blackman RB, Tukey JW (1958) The measurement of power spectra from the point of view of communications engineering – Part II. Bell Syst Tech J 37(2):485–569MathSciNetGoogle Scholar
  4. Brillinger DR (1981) Time series: data analysis and theory. McGraw-Hill, New YorkGoogle Scholar
  5. Broersen PMT (2004) Mean square error of the empirical transfer function estimator for stochastic input signals. Automatica 40(1):95–100MathSciNetGoogle Scholar
  6. Carter GC, Nuttall AH (1980) On the weighted overlapped segment averaging method for power spectral estimation. Proc IEEE 68(10):1352–1353Google Scholar
  7. Chen T, Ohlsson H, Ljung L (2012) On the estimation of transfer functions, regularizations and Gaussian processes – revisited. Automatica 48(8): 1525–1535MathSciNetGoogle Scholar
  8. Enqvist M, Ljung L (2005) Linear approximations of nonlinear FIR systems for separable input processes. Automatica 41(3):459–473MathSciNetGoogle Scholar
  9. Eykhoff P (1974) System identification. Wiley, New YorkGoogle Scholar
  10. Godfrey K (1993) Perturbation signals for system identification. Prentice-Hall, Englewood CliffsGoogle Scholar
  11. Hägg P, Hjalmarsson H (2012) Non-parametric frequency response function estimation using transient impulse response modelling. Paper presented at the 16th IFAC symposium on system identification, Brussels, 11–13 July, pp 43–48Google Scholar
  12. Heath WP (2007) Choice of weighting for averaged nonparametric transfer function estimates. IEEE Trans Autom Control 52(10):1914–1920MathSciNetGoogle Scholar
  13. Ljung L (1999) System identification: theory for the user, 2nd edn. Prentice-Hall, Upper Saddle RiverGoogle Scholar
  14. McKelvey T, Guérin G (2012) Non-parametric frequency response estimation using a local rational model. Paper presented at the 16th IFAC symposium on system identification, Brussels, 11–13 July, pp 49–54Google Scholar
  15. Pillonetto G, Chiuso A, De Nicolao G (2011) Prediction error identification of linear systems: a nonparametric Gaussian regression approach. Automatica 47(2):291–305MathSciNetGoogle Scholar
  16. Pintelon R, Schoukens J (2012) System identification: a frequency domain approach, 2nd edn. IEEE, Piscataway/Wiley, HobokenGoogle Scholar
  17. Schoukens J, Rolain Y, Pintelon R (2006) Analysis of windowing/leakage effects in frequency response function measurements. Automatica 42(1):27–38MathSciNetGoogle Scholar
  18. Stenman A, Gustafsson F, Rivera DE, Ljung L, McKelvey T (2000) On adaptive smoothing of empirical transfer function estimates. Control Eng Pract 8(11):1309–1315Google Scholar
  19. Welch PD (1967) The use of the fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans Audio Electroacoust 15(2):70–73MathSciNetGoogle Scholar
  20. Wellstead PE (1981) Non-parametric methods of system identification. Automatica 17(1):55–69MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  1. 1.Department ELECVrije Universiteit BrusselBrusselsBelgium