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Parameter Estimation Based on Set-valued Signals: Theory and Application

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Abstract

This paper summarizes the parameter estimation of systems with set-valued signals, which can be classified to three catalogs: one-time completed algorithms, iterative methods and recursive algorithms. For one-time completed algorithms, empirical measure method is one of the earliest methods to estimate parameters by using set-valued signals, which has been applied to the adaptive tracking of periodic target signals. The iterative methods seek numerical solutions of the maximum likelihood estimation, which have been applied to both complex diseases diagnosis and radar target recognition. The recursive algorithms are constructed via stochastic approximation and stochastic gradient methods, which have been applied to adaptive tracking of non-periodic signals.

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References

  1. 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. Annals of Human Genetics, 79(4): 294–309 (2015)

    Article  Google Scholar 

  2. Bourgois, L., Juillard, J. Convergence analysis of an online approach to parameter estimation problems based on binary noisy observations. Automatica, 48(11): 2837–2842 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bradfield, J.P., Taal, H.R., Timpson, N.J., et al. A genome-wide association meta-analysis identifies new childhood obesity loci. Nature Genetics, 44(5): 526–531 (2012)

    Article  Google Scholar 

  4. Brailsford, A.D., Yussouff, M., Logothetis, E.M. Theory of gas sensors. Sensors and Actuators B Chemical, 13(1): 135–138 (1993)

    Article  Google Scholar 

  5. Fang, J., Li, H. Distributed adaptive quantization for wireless sensor networks: From delta modulation to maximum likelihood. IEEE Transactions on Signal Processing, 56(10): 5246–5257 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Florez, J. C. A genome-wide association study of treated A1C. Diabetes, 59(2): 332–334 (2010)

    Article  Google Scholar 

  7. Godoy, B.I., Goodwin, G.C., Agüero, J.C., Marelli, D., Wigren, T. On identification of FIR systems having quantized output data. Aotomatica, 47(9): 1905–1915 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Guo, J., Zhang, J.F., Zhao, Y.L. Adaptive tracking control of a class of first-oder systems with binary-valued observations and fixed thresholds. Journal of Systems Science and Complexity, 5(6): 1041–1051 (2012)

    Article  MATH  Google Scholar 

  9. Guo, J., Zhang, J.F., Zhao, Y.L. Adaptive tracking control of a class of first-oder systems with binary-valued observations and time-varying thresholds. IEEE Transactions on Automatic Control, 56(12): 2991–2996 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Guo, J., Zhao, Y.L. Identification of the gain system with quantized observations and bounded persistent excitations. Science China Information Sciences, 57(1): 012205:1–012205: 15 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  11. Guo, J., Zhao, Y.L. Recursive projection algorithm on FIR system identification with binary-valued observations. Automatica, 49(11): 3396–3401 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  12. Jafari, K., Juillard, J., Colinet, E. A recursive system identification method based on binary measurements. In: Proceedings of 49th IEEE Conference on Decision and Control, Atlanta, 2010: 1154–1158

    Google Scholar 

  13. Kang, G.L., Bi, W.J., Zhao, Y.L., et al. A new system identification approach to identify genetic variants in sequencing studies for a binary phenotype. Human Heredity, 78(2): 104–116 (2014)

    Article  Google Scholar 

  14. Knott, E.F., Shaeffer, J.F., Tuley, M.T. Radar Cross Section, 2nd ed. SciTech Publishing Inc, Raleigh, 2004

    Google Scholar 

  15. Li, J., Alregib, G. Rate-constrained distributed estimation in wireless sensor networks. IEEE Transactions on Signal Processing, 55(5): 1634–1643 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  16. Song, Q.J. Recursive identification of systems with binary-valued outputs and with ARMA noises. Automatica, 93: 106–113 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  17. Wang, L.Y., Yin, G.G. Asymptotically efficient parameter estimation using quantized output observations. Automatica, 43(7): 1178–1191 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  18. Wang, L.Y., Yin, G.G., Zhang, J.F., Zhao, Y.L. System identification with quantized observations. MA: Birkhauser, Boston, 2010

    Book  MATH  Google Scholar 

  19. Wang, L.Y., Zhang, J.F., Yin, G.G. System identification using binary sensors. IEEE Transactions on Automatic Control, 48(11): 1892–1907 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  20. Wang, T., Bi, W.J., Zhao, Y.L., Xue, W.C. Radar target recognition algorithm based on RCS observation sequence—set-valued identification method. Journal of Systems Science and Complexity, 29(3): 1–16 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  21. Wang, T., Tan, J.W., Zhao, Y.L. Asymptotically efficient non-truncated identification for FIR systems with binary-valued outputs. Science China Information Sciences, doi: 10.1007/sll432-018-9646-7 (2018)

    Google Scholar 

  22. You, K.Y. Recursive algorithms for parameter estimation with adaptive quantizer. Automatica, 52: 192–201 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  23. Zhang, H., Wang, T., Zhao, Y.L. Asymptotically Efficient Recursive Identification of FIR Systems with Binary Observations. IEEE Transactions on Systems, Man and Cybernetics: Systems, submitted.

  24. Zhao, Y.L., Bi, W.J., Wang, T. Iterative parameter estimate with batched binary-valued observations. Science China Information Sciences, 59(5): 1–18 (2016)

    Article  Google Scholar 

  25. Zhao, Y.L., Guo, J., Zhang, J.F. Adaptive tracking control of linear systems with binary-valued observations and periodic target. Automatica, 58(5): 1293–1298 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  26. Zhao, Y.L., Wang, L.Y., Yin, G.G., Zhang, J.F. Identification of Wiener systems with binary-valued output observations. Automatica, 43: 1752–1765 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  27. Zhao, Y.L., Zhang, J.F., Wang, L.Y., Yin, G. Identification of Hammerstein systems with quantized observations. SIAM Journal on Control and Optimization, 48(7): 4352–4376 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. The Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Ting Wang, Hang Zhang & Yan-long Zhao

Authors
  1. Ting Wang
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  2. Hang Zhang
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  3. Yan-long Zhao
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Corresponding author

Correspondence to Yan-long Zhao.

Additional information

Supported by the National Natural Science Foundation of China (Nos. 61803370, 61622309), the China Postdoctoral Science Foundation (No. 2018M630216), and the National Key Research and Development Program of China (No. 2016YFB0901902).

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Wang, T., Zhang, H. & Zhao, Yl. Parameter Estimation Based on Set-valued Signals: Theory and Application. Acta Math. Appl. Sin. Engl. Ser. 35, 255–263 (2019). https://doi.org/10.1007/s10255-019-0822-x

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  • DOI: https://doi.org/10.1007/s10255-019-0822-x

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