logo

SCIENCE CHINA Information Sciences, Volume 62, Issue 5: 052203(2019) https://doi.org/10.1007/s11432-018-9604-0

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

More info
  • ReceivedJun 6, 2018
  • AcceptedSep 5, 2018
  • PublishedApr 2, 2019

Abstract

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.


Acknowledgment

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).


References

[1] Ljung L. Perspectives on system identification. Annu Rev Control, 2008, 34: 1--12. Google Scholar

[2] Ljung L. System Identification: Theory for the User. 2nd ed. Englewood Cliffs: Prentice-Hall, 1999. Google Scholar

[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, 1967. Google Scholar

[4] Astrom K J. Maximum likelihood and prediction error methods. Automatica, 1980, 16: 551-574 CrossRef Google Scholar

[5] Kalman R E. A New Approach to Linear Filtering and Prediction Problems. J Basic Eng, 1960, 82: 35-45 CrossRef Google Scholar

[6] Ho Y, Lee R. A Bayesian approach to problems in stochastic estimation and control. IEEE Trans Autom Control, 1964, 9: 333-339 CrossRef Google Scholar

[7] Anderson T W, Taylor J B. Some Experimental Results on the Statistical Properties of Least Squares Estimates in Control Problems. Econometrica, 1976, 44: 1289-1302 CrossRef Google Scholar

[8] Le Yi Wang , Ji-Feng Zhang , Yin G G. System identification using binary sensors. IEEE Trans Autom Control, 2003, 48: 1892-1907 CrossRef Google Scholar

[9] Wang L Y, Zhang J F, Yin G, et al. System Identification with Quantized Observations. Boston: Birkhäuser, 2010. Google Scholar

[10] Godoy B I, Goodwin G C, Agüero J C. On identification of FIR systems having quantized output data. Automatica, 2011, 47: 1905-1915 CrossRef Google Scholar

[11] Zhao Y, Bi W, Wang T. Iterative parameter estimate with batched binary-valued observations. Sci China Inf Sci, 2016, 59: 052201 CrossRef Google Scholar

[12] Bottegal G, Hjalmarsson H, Pillonetto G. A new kernel-based approach to system identification with quantized output data. Automatica, 2017, 85: 145-152 CrossRef Google Scholar

[13] Wang J, Zhang Q. Identification of FIR Systems Based on Quantized Output Measurements: A Quadratic Programming-Based Method. IEEE Trans Automat Contr, 2015, 60: 1439-1444 CrossRef Google Scholar

[14] Yu C, Zhang C, Xie L. Blind system identification using precise and quantized observations. Automatica, 2013, 49: 2822-2830 CrossRef Google Scholar

[15] Zhao Y, Wang L Y, Yin G G. Identification of Wiener systems with binary-valued output observations. Automatica, 2007, 43: 1752-1765 CrossRef Google Scholar

[16] Zhao Y, Zhang J F, Wang L Y. Identification of Hammerstein Systems with Quantized Observations. SIAM J Control Optim, 2010, 48: 4352-4376 CrossRef Google Scholar

[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: 129208. Google Scholar

[18] White F E. Data Fusion Lexicon. Joint Directors of Laboratories, Technical Panel for $C^3$. 1991. Google Scholar

[19] Lawrence A K. Sensor and Data Fusion Concepts and Applications. 2nd ed. Bellingham: SPIE Optical Engineering press, 1999. Google Scholar

[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--107. Google Scholar

[21] Han C Z, Zhu H Y, Duan Z S. Multi-Source Information Fusion. Beijing: Tsinghua University Press, 2006. Google Scholar

[22] Costa O L V. Linear minimum mean square error estimation for discrete-time Markovian jump linear systems. IEEE Trans Autom Control, 1994, 39: 1685-1689 CrossRef Google Scholar

[23] Marelli D E, Fu M. Distributed weighted least-squares estimation with fast convergence for large-scale systems.. Automatica, 2015, 51: 27-39 CrossRef PubMed Google Scholar

[24] Li X R. Optimal linear estimation fusion for multisensor dynamic systems. The Workshop on Multiple Hypothesis Tracking -- a Tribute To Sam Blackman. 2003. Google Scholar

[25] Sun S L, Deng Z L. Multi-sensor optimal information fusion Kalman filter. Automatica, 2004, 40: 1017-1023 CrossRef Google Scholar

[26] Deng Z, Zhang P, Qi W. The accuracy comparison of multisensor covariance intersection fuser and three weighting fusers. Inf Fusion, 2013, 14: 177-185 CrossRef Google Scholar

[27] Ferguson T S. A Course in Large Sample Theory. New York: Chapman and Hall, 1996. Google Scholar

[28] Bi W, Kang G, Zhao Y. 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: 294-309 CrossRef PubMed Google Scholar

  • Figure 1

    (Color online) Two FIR systems have same periodic inputs. (a) The estimation results of parameter $\theta$ including $\hat{\theta}_{N_1}$ (LS), $\hat{\theta}_{N_2}$ (set-value) and $\hat{\theta}_Q$ (QCCE); (b) the asymptotic efficiency of estimation error of the QCCE by the evaluation criterion $E(\hat{\theta}_Q-\theta)^{\rm~T}(\hat{\theta}_Q-\theta)$ with 500 replicated simulations.

  • Figure 2

    (Color online) Two FIR systems have different periodic inputs and the sample size of precise observations is fixed. (a) The estimation results of parameter $\theta$ including $\hat{\theta}_{N_2}$ (set-value) and $\hat{\theta}_Q$ (QCCE); (b) the asymptotic efficiency of estimation error of the QCCE by the evaluation criterion $E(\hat{\theta}_Q-\theta)^{\rm~T}(\hat{\theta}_Q-\theta)$ with 500 replicated simulations.

Copyright 2020 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有

京ICP备18024590号-1