FIR system identification with set-valued and precise observations from multiple sensors

  • Hang Zhang
  • Ting Wang
  • Yanlong ZhaoEmail author
Research Paper


This paper considers the system identification problem for FIR (finite impulse response) systems with set-valued and precise observations received from multiple sensors. A fusion estimation algorithm based on some suitable identification algorithms for different types of observations is proposed. In particular, least square method is chosen for FIR systems with precise observations, while empirical measure method and EM algorithm are chosen for FIR systems with set-valued observations in the cases of periodic and general system inputs, respectively. Then, the quasi-convex combination estimator (QCCE) fusing the two different estimators by a linear combination with appropriate weights is constructed. Furthermore, the convergence properties are theoretically analyzed in terms of strong consistency and asymptotic efficiency. The fused estimator QCCE is proved to achieve the Cramér-Rao (CR) lower bound asymptotically under periodic inputs. Extensive numerical simulations validate the superiority of the fusion estimation algorithm under both periodic and general inputs.


system identification FIR system set-valued precise fusion estimation quasi-convex combination estimator 



This work was supported by National Key Research and Development Program of China (Grant No. 2016YFB0901902), National Natural Science Foundation of China (Grant Nos. 61803370, 61622309), and National Key Basic Research Program of China (973 Program) (Grant No. 2014CB845301).


  1. 1.
    Ljung L. Perspectives on system identification. Annu Rev Control, 2008, 34: 1–12CrossRefGoogle Scholar
  2. 2.
    Ljung L. System Identification: Theory for the User. 2nd ed. Englewood Cliffs: Prentice-Hall, 1999zbMATHGoogle Scholar
  3. 3.
    Clarke D W. Generalized least squares estimation of the parameters of a dynamic model. In: Proceeding of IFAC Symposium on Identification in Automatic Control Systems, Prague, 1967Google Scholar
  4. 4.
    Astrom K J. Maximum likelihood and prediction error methods. Automatica, 1980, 16: 551–574CrossRefzbMATHGoogle Scholar
  5. 5.
    Kalman R E. A new approach to linear filtering and prediction problems. J Basic Eng, 1960, 82: 35–45CrossRefGoogle Scholar
  6. 6.
    Ho Y, Lee R. A Bayesian approach to problems in stochastic estimation and control. IEEE Trans Autom Control, 1964, 9: 333–339MathSciNetCrossRefGoogle Scholar
  7. 7.
    Anderson T W, Taylor J B. Some experimental results on the statistical properties of least squares estimates in control problems. Econometrica, 1976, 44: 1289–1302CrossRefGoogle Scholar
  8. 8.
    Wang L Y, Zhang J F, Yin G G. System identification using binary sensors. IEEE Trans Autom Control, 2003, 48: 1892–1907MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Wang L Y, Zhang J F, Yin G G, et al. System Identification with Quantized Observations. Boston: Birkhäuser, 2010CrossRefzbMATHGoogle Scholar
  10. 10.
    Godoy B I, Goodwin G C, Agüero J C, et al. On identification of FIR systems having quantized output data. Automatica, 2011, 47: 1905–1915MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Zhao Y L, Bi W J, Wang T. Iterative parameter estimate with batched binary-valued observations. Sci China Inf Sci, 2016, 59: 052201CrossRefGoogle Scholar
  12. 12.
    Bottegal G, Hjalmarsson H, Pillonetto G. A new kernel-based approach to system identification with quantized output data. Automatica, 2017, 85: 145–152MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Wang J D, Zhang Q H. Identification of FIR systems based on quantized output measurements: a quadratic programming-based method. IEEE Trans Autom Control, 2015, 60: 1439–1444MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Yu C P, Zhang C S, Xie L H. Blind system identification using precise and quantized observations. Automatica, 2013, 49: 2822–2830MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Zhao Y L, Wang L Y, Yin G G, et al. Identification of Wiener systems with binary-valued output observations. Automatica, 2007, 43: 1752–1765MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Zhao Y L, Zhang J F, Wang L Y, et al. Identification of Hammerstein systems with quantized observations. SIAM J Control Optim, 2010, 48: 4352–4376MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Wang T, Tan J W, Zhao Y L. Asymptotically efficient non-truncated identification for FIR systems with binary-valued outputs. Sci China Inf Sci, 2018, 61: 129208MathSciNetCrossRefGoogle Scholar
  18. 18.
    White F E. Data Fusion Lexicon. Joint Directors of Laboratories, Technical Panel for C 3. 1991.
  19. 19.
    Lawrence A K. Sensor and Data Fusion Concepts and Applications. 2nd ed. Bellingham: SPIE Optical Engineering Press, 1999Google Scholar
  20. 20.
    Boström H, Andler S F, Brohede M, et al. On the definition of information fusion as a field of research. Neoplasia, 2008, 13: 98–107Google Scholar
  21. 21.
    Han C Z, Zhu H Y, Duan Z S. Multi-Source Information Fusion. Beijing: Tsinghua University Press, 2006Google Scholar
  22. 22.
    Costa O L V. Linear minimum mean square error estimation for discrete-time Markovian jump linear systems. IEEE Trans Autom Control, 1994, 39: 1685–1689MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Marelli D E, Fu M. Distributed weighted least-squares estimation with fast convergence for large-scale systems. Automatica, 2015, 51: 27–39MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Li X R. Optimal linear estimation fusion for multisensor dynamic systems. In: Proceedings of the Workshop on Multiple Hypothesis Tracking — A Tribute to Sam Blackman, 2003Google Scholar
  25. 25.
    Sun S L, Deng Z L. Multi-sensor optimal information fusion Kalman filter. Automatica, 2004, 40: 1017–1023MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Deng Z L, Zhang P, Qi W J, et al. The accuracy comparison of multisensor covariance intersection fuser and three weighting fusers. Inf Fusion, 2013, 14: 177–185CrossRefGoogle Scholar
  27. 27.
    Ferguson T S. A Course in Large Sample Theory. New York: Chapman and Hall, 1996CrossRefzbMATHGoogle Scholar
  28. 28.
    Bi W J, Kang G L, Zhao Y L, et al. SVSI: fast and powerful set-valued system identification approach to identifying rare variants in sequencing studies for ordered categorical traits. Ann Human Genets, 2015, 79: 294–309CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Key Laboratory of Systems and Control, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  2. 2.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina

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