Skip to main content
SpringerLink
Log in

Correlation Analysis-based Stochastic Gradient and Least Squares Identification Methods for Errors-in-variables Systems Using the Multiinnovation

  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper deals with the identification problem of discrete-time linear time-invariant errors-in-variables systems for the case of the colored output noise. Based on the correlation analysis, the multi-innovation theory is introduced to the errors-in-variables systems where both input and output data are noisy. A correlation analysis-based multi-innovation stochastic gradient algorithm and a correlation analysis-based multi-innovation least squares algorithm are proposed by means of the multi-innovation theory in order to improve the parameter accuracy. The simulation results confirm that these two algorithms are effective.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. Wang, J. F. Jiao, and S. Yin, “A kernel direct decomposition-based monitoring approach for nonlinear quality-related fault detection,” IEEE Transactions on Industrial Informatics, vol. 13, no. 4, pp. 1565–1574, August 2017.

    Article  Google Scholar 

  2. X. Zhang, F. Ding, and E. F. Yang, “State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors,” International Journal of Adaptive Control and Signal Processing, vol. 33, no. 7, pp. 1157–1173, July 2019.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Pan, W. Li, and H. P. Zhang, “Control algorithms of magnetic suspension systems based on the improved double exponential reaching law of sliding mode control,” International Journal of Control Automation and Systems, vol. 16, no. 6, pp. 2878–2887, December 2018.

    Article  Google Scholar 

  4. F. Ding, L. Lv, J. Pan, X. K. Wan, and X. B. Jin, “Two-stage gradient-based iterative estimation methods for controlled autoregressive systems using the measurement data,” International Journal of Control Automation and Systems, vol. 18, no. 4, pp. 886–896, April 2020.

    Article  Google Scholar 

  5. J. Pan, X. Jiang, X. K. Wan, and W. Ding, “A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems,” International Journal of Control Automation and Systems, vol. 15, no. 3, pp. 1189–1197, June 2017.

    Article  Google Scholar 

  6. H. Ma, J. Pan, F. Ding, L. Xu, and W. Ding, “Partially-coupled least squares based iterative parameter estimation for multi-variable output-error-like autoregressive moving average systems,” IET Control Theory and Applications, vol. 13, no. 18, pp. 3040–3051, December 2019.

    Article  Google Scholar 

  7. Y. Zhang, M. M. Huang, T. Z. Wu, and F. Ji, “Reconfigurable equilibrium circuit with additional power supply,” International Journal of Low-Carbon Technologies, vol. 15, no. 1, pp. 106–111, February 2020.

    Article  Google Scholar 

  8. L. Geng and R. B. Xiao, “Control and backbone identification for the resilient recovery of a supply network utilizing outer synchronization,” Applied Sciences, vol. 10, no. 1, p. 313, January 2020.

    Article  Google Scholar 

  9. L. J. Wang, B. Y. Feng, Y. Wang, T. Z. Wu, and H. P. Lin, “Bidirectional short-circuit current blocker for DC micro-grid based on solid-state circuit breaker,” Electronics, vol. 9, no. 2, p. 306, February 2020.

    Article  Google Scholar 

  10. L. J. Wang, J. Guo, C. Xu, T. Z. Wu, and H. P. Lin, “Hybrid model predictive control strategy of supercapacitor energy storage system based on double active bridge,” Energies, vol. 12, no. 11, p. 2134, June 2019.

    Article  Google Scholar 

  11. L. Tang, G. J. Liu, M. Yang, F. Y. Li, F. P. Ye, and C. Y. Li, “Joint design and torque feedback experiment of rehabilitation robot,” Advances in Mechanical Engineering, vol. 12, no. 5, pp. 1–11, May 2020.

    Article  Google Scholar 

  12. T. Söderström, “Identification of stochastic linear systems in presence of input noise,” Automatica, vol. 17, no. 5, pp. 713–725, September 1981.

    Article  MathSciNet  MATH  Google Scholar 

  13. M. K. Masoud and H. Mohammad, “Identification of EIV models with coloured input-output noise: Combining PEM and covariance matching method,” International Journal of Systems Science, vol. 49, no. 8, pp. 1738–1747, June 2018.

    Article  MathSciNet  Google Scholar 

  14. D. Kreiberg, T. Söderström, and F. Y. Wallentin, “Errors-in-variables system identification using structural equation modeling,” Automatica, vol. 66, pp. 218–230, April 2016.

    Article  MathSciNet  MATH  Google Scholar 

  15. M. Hong, T. Söderström, and W. X. Zheng, “A simplified form of the bias-eliminating least squares method for errors-in-variables identification,” IEEE Transactions on Automatic Control, vol. 52, no. 9, pp. 1754–1756, September 2007.

    Article  MathSciNet  MATH  Google Scholar 

  16. K. Mahata, “An improved bias-compensation approach for errors-in-variables model identification,” Automatica, vol. 43, no. 8, pp. 1339–1354, August 2007.

    Article  MathSciNet  MATH  Google Scholar 

  17. T. Söderström, “A generalized instrumental variable estimation method for errors-in-variables identification problems,” Automatica, vol. 47, no. 8, pp. 1656–1666, August 2011.

    Article  MathSciNet  MATH  Google Scholar 

  18. T. Söderström, “Errors-in-variables methods in system identification,” Automatica, vol. 43, no. 6, pp. 939–958, June 2007.

    Article  MathSciNet  MATH  Google Scholar 

  19. W. X. Zheng, “A bias correction method for identification of linear dynamic errors in variables models,” IEEE Transactions on Automatic Control, vol. 47, no. 7, pp. 1142–1147, July 2002.

    Article  MathSciNet  MATH  Google Scholar 

  20. T. Söderström, “Extending the Frisch scheme for errors-in-variables identification to correlated output noise,” International Journal of Adaptive Control and Signal Processing, vol. 22, no. 1, pp. 55–73, February 2008.

    Article  MathSciNet  MATH  Google Scholar 

  21. F. Y. Ma, C. C. Fu, J. Yang, and Q. Z. Yang, “Control strategy for adaptive active energy harvesting in sediment microbial fuel cells,” Journal of Energy Engineering, vol. 146, no. 1, Article Number: 04019034, February 2020.

  22. M. H. Li, X. M. Liu, and F. Ding, “The filtering-based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle,” International Journal of Adaptive Control and Signal Processing, vol. 33, no. 7, pp. 1189–1211, July 2019.

    Article  MathSciNet  MATH  Google Scholar 

  23. X. Zhang and F. Ding, “Hierarchical parameter and state estimation for bilinear systems,” International Journal of Systems Science, vol. 51, no. 2, 275–290, 2020.

    Article  MathSciNet  Google Scholar 

  24. J. X. Ma, W. L. Xiong, J. Chen, and F. Ding, “Hierarchical identification for multivariate Hammerstein systems by using the modified Kalman filter,” IET Control Theory and Applications, vol. 11, no. 6, pp. 857–869, April 2017.

    Article  MathSciNet  Google Scholar 

  25. J. X. Ma and F. Ding, “Filtering-based multistage recursive identification algorithm for an input nonlinear output-error autoregressive system by using key the term separation technique,” Circuits Systems and Signal Processing, vol. 36, no. 2, pp. 577–599, February 2017.

    Article  MATH  Google Scholar 

  26. M. H. Wu, R. Chen, and Y. Tong, “Shadow elimination algorithm using color and texture features,” Computational Intelligence and Neuroscience, vol. 2020, Article ID. 2075781, January 2020.

  27. F. Y. Ma, Y. K. Yin, and M. Li, “Start-up process modelling of sediment microbial fuel cells based on data driven,” Mathematical Problems in Engineering, vol. 2019, Article ID. 7403732, 2019.

  28. S. J. Fan, F. Ding, and T. Hatyat, “Recursive identification of errors-in-variables systems based on the correlation analysis,” Circuits Systems and Signal Processing, 2020. DOI: https://doi.org/10.1007/s00034-020-01441-7

  29. L. J. Liu, F. Ding, L. Xu, J. Pan, A. Alsaedi, and T. Hayat, “Maximum likelihood recursive identification for the multivariate equation-error autoregressive moving average systems using the data filtering,” IEEE Access, vol. 7, pp. 41154–41163, 2019.

    Article  Google Scholar 

  30. Y. J. Wang, F. Ding, and M. H. Wu, “Recursive parameter estimation algorithm for multivariate output-error systems,” Journal of the Franklin Institute, vol. 355, no. 12, pp. 5163–5181, August 2018.

    Article  MathSciNet  MATH  Google Scholar 

  31. Y. F. Chang, G. S. Zhai, B. Fu, and L. L. Xiong, “Quadratic stabilization of switched uncertain linear systems: A convex combination approach,” IEEE-CAA Journal of Automatica Sinica, vol. 6, no. 5, pp. 1116–1126, September 2019.

    Article  MathSciNet  Google Scholar 

  32. Y. F. Chang, C. J. Sun, and Y. Qiu, “Effective notch stress method for fatigue assessment of sheet alloy material and bi-material welded joints,” Thin-Walled Structures, vol. 151, p. 106745, June 2020.

    Article  Google Scholar 

  33. L. He, H. Lin, Q. Zou, and D. J. Zhang, “Accurate measurement of pavement deflection velocity under dynamic loads,” Automation in Construction, vol. 83, pp. 149–162, November 2017.

    Article  Google Scholar 

  34. F. Y. Ma, Y. K. Yin, and W. Chen, “Reliability analysis of power and communication network in drone monitoring system,” IEICE Transactions on Communications, vol. E102B, no. 10, pp. 1991–1997, October 2019.

    Article  Google Scholar 

  35. P. Ma and F. Ding, “New gradient based identification methods for multivariate pseudo-linear systems using the multi-innovation and the data filtering,” Journal of the Franklin Institute, vol. 354, no. 3, pp. 1568–1583, February 2017.

    Article  MathSciNet  MATH  Google Scholar 

  36. F. Ding, F. F. Wang, L. Xu, and M. H. Wu, “Decomposition based least squares iterative identification algorithm for multivariate pseudo-linear ARMA systems using the data filtering,” Journal of the Franklin Institute, vol. 354, no. 3, pp. 1321–1339, February 2017.

    Article  MathSciNet  MATH  Google Scholar 

  37. F. Y. Ma, Y. K. Yin, S. P. Pang, J. X. Liu, and W. Chen, “A data-driven based framework of model optimization and neural network modeling for microbial fuel cells,” IEEE Access, vol. 7, pp. 162036–162049, 2019.

    Article  Google Scholar 

  38. C. M. Jiang, A. Zada, M. T. Senel, and T. X. Li, “Synchronization of bidirectional N-coupled fractional-order chaotic systems with ring connection based on antisymmetric structure,” Advances in Difference Equations, vol. 2019, no. 1, Article Number: 456, October 2019.

  39. F. Ding, “Several multi-innovation identification methods,” Digital Signal Processing, vol. 20, no. 4, pp. 1027–1039, July 2010.

    Article  Google Scholar 

  40. J. Ding, J. Z. Chen, J. X. Lin, and G. P. Jiang, “Particle filtering-based recursive identification for controlled autoregressive systems with quantised output,” IET Control Theory and Applications, vol. 13, no. 14, pp. 2181–2187, September 2019.

    Article  Google Scholar 

  41. J. Ding, Z. X. Cao, J. Z. Chen, and G. P. Jiang, “Weighted parameter estimation for Hammerstein nonlinear ARX systems,” Circuits Systems and Signal Processing, vol. 39, no. 4, pp. 2178–2192, April 2020.

    Article  Google Scholar 

  42. L. J. Wan and F. Ding, “Decomposition- and gradient-based iterative identification algorithms for multivariable systems using the multi-innovation theory,” Circuits Systems and Signal Processing, vol. 38, no. 7, pp. 2971–2991, July 2019.

    Article  Google Scholar 

  43. S. Y. Liu, F. Ding, L. Xu, and T. Hayat, “Hierarchical principle-based iterative parameter estimation algorithm for dual-frequency signals,” Circuits Systems and Signal Processing, vol. 38, no. 7, pp. 3251–3268, July 2019.

    Article  Google Scholar 

  44. X. K. Wan, Y. Li, C. Xia, M. H. Wu, J. Liang, and N. Wang, “A T-wave alternans assessment method based on least squares curve fitting technique,” Measurement, vol. 86, pp. 93–100, May 2016.

    Article  Google Scholar 

  45. H. Liu, Q. X. Zou, and Z. P. Zhang, “Energy disaggregation of appliances consumptions using ham approach,” IEEE Access, vol. 7, pp. 185977–185990, 2019.

    Article  Google Scholar 

  46. L. Wang, H. Liu, L. V. Dai, and Y. W. Liu, “Novel method for identifying fault location of mixed lines,” Energies, vol. 11, no. 6, Article Number: 1529, June 2018.

  47. F. Ding, H. B. Chen, and M. Li, “Multi-innovation least squares identification methods based on the auxiliary model for MISO systems,” Applied Mathematics and Computation, vol. 187, no. 2, pp. 658–668, April 2007.

    Article  MathSciNet  MATH  Google Scholar 

  48. C. C. Yin and C. W. Wang, “The perturbed compound Poisson risk process with investment and debit interest,” Methodology and Computing in Applied Probability, vol. 12, no. 3, pp. 391–413, September 2010.

    Article  MathSciNet  MATH  Google Scholar 

  49. C. C. Yin and K. C. Yuen, “Optimality of the threshold dividend strategy for the compound Poisson model,” Statistics & Probability Letters, vol. 81, no. 12, pp. 1841–1846, December 2011.

    Article  MathSciNet  MATH  Google Scholar 

  50. C. C. Yin and Y. Z. Wen, “Optimal dividend problem with a terminal value for spectrally positive Levy processes,” Insurance Mathematics & Economics, vol. 53, no. 3, pp. 769–773, November 2013.

    Article  MathSciNet  MATH  Google Scholar 

  51. C. C. Yin and Y. Z. Wen, “Exit problems for jump processes with applications to dividend problems,” Journal of Computational and Applied Mathematics, vol. 245, pp. 30–52, June 2013.

    Article  MathSciNet  MATH  Google Scholar 

  52. C. C. Yin and Y. Z. Wen, “An extension of Paulsen-Gjessing’s risk model with stochastic return on investments,” Insurance Mathematics & Economics, vol. 52, no. 3, pp. 469–476, May 2013.

    Article  MathSciNet  MATH  Google Scholar 

  53. C. C. Yin, Y. Z. Wen, and Y. X. Zhao, “On the optimal dividend problem for a spectrally positive levy process,” Astin Bulletin, vol. 44, no. 3, pp. 635–651, September 2014.

    Article  MathSciNet  MATH  Google Scholar 

  54. C. C. Yin and K. C. Yuen, “Exact joint laws associated with spectrally negative Levy processes and applications to insurance risk theory,” Frontiers of Mathematics in China, vol. 9, no. 6, pp. 1453–1471, December 2014.

    Article  MathSciNet  MATH  Google Scholar 

  55. C. C. Yin and K. C. Yuen, “Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs,” Journal of Industrial and Management Optimization, vol. 11, no. 4, pp. 1247–1262, October 2015.

    Article  MathSciNet  MATH  Google Scholar 

  56. W. X. Shi, N. Liu, Y. M. Zhou, and X. A. Cao, “Effects of postannealing on the characteristics and reliability of polyfluorene organic light-emitting diodes,” IEEE Transactions on Electron Devices, vol. 66, no. 2, pp. 1057–1062, February 2019.

    Article  Google Scholar 

  57. N. Liu, S. Mei, D. Sun, W. Shi, J. Feng, Y. M. Zhou, F. Mei, J. Xu, Y. Jiang, and X. A. Cao, “Effects of charge transport materials on blue fluorescent organic light-emitting diodes with a host-dopant system,” Micromachines, vol. 10, no. 5, Article Number: 344, May 2019.

  58. T. Z. Wu, X. Shi, L. Liao, C. J. Zhou, H. Zhou, and Y. H. Su, “A capacity configuration control strategy to alleviate power fluctuation of hybrid energy storage system based on improved particle swarm optimization,” Energies, vol. 12, no. 4, Article Number: 642, February 2019.

  59. T. Z. Wu, F. C. Ye, Y. H. Su, Y. B. Wang, and S. Riffat, “Coordinated control strategy of DC microgrid with hybrid energy storage system to smooth power output fluctuation,” International Journal of Low-Carbon Technologies, vol. 15, no. 1, pp. 46–54, February 2020.

    Article  Google Scholar 

  60. X. L. Zhao, Z. Y. Lin, B. Fu, L. He, and C. S. Li, “Research on the predictive optimal PID plus second order derivative method for AGC of power system with high penetration of photovoltaic and wind power,” Journal of Electrical Engineering & Technology, vol. 14, no. 3, pp. 1075–1086, May 2019.

    Article  Google Scholar 

  61. N. Zhao, “Joint optimization of cooperative spectrum sensing and resource allocation in multi-channel cognitive radio sensor networks,” Circuits Systems and Signal Processing, vol. 35, no. 7, pp. 2563–2583, July 2016.

    Article  MATH  Google Scholar 

  62. S. N. Chiu and C. C. Yin, “Passage times for a spectrally negative Levy process with applications to risk theory,” Bernoulli, vol. 11, no. 3, pp. 511–522, June 2005.

    MathSciNet  MATH  Google Scholar 

  63. N. Zhao, M. H. Wu, and J. J. Chen, “Android-based mobile educational platform for speech signal processing,” International Journal of Electrical Engineering Education, vol. 54, no. 1, pp. 3–16, January 2017.

    Article  Google Scholar 

  64. N. Zhao, Y. Liang, and Y. Pei, “Dynamic contract incentive mechanism for cooperative wireless networks,” IEEE Transactions on Vehicular Technology, vol. 67, no. 11, pp. 10970–10982, November 2018.

    Article  Google Scholar 

  65. X. L. Zhao, F. Liu, B. Fu, and F. Na, “Reliability analysis of hybrid multi-carrier energy systems based on entropy-based Markov model,” Proceedings of the Institution of Mechanical Engineers Part O-Journal of Risk and Reliability, vol. 230, no. 6, pp. 561–569, December 2016.

    Article  Google Scholar 

  66. X. L. Zhao, Z.Y. Lin, B. Fu, L. He, and F. Na, “Research on automatic generation control with wind power participation based on predictive optimal 2-degree-of-freedom PID strategy for multi-area interconnected power system,” Energies, vol. 11, no. 12, Article Number: 3325, December 2018.

  67. Y. Cao, Z. Wang, F. Liu, P. Li, and G. Xie, “Bio-inspired speed curve optimization and sliding mode tracking control for subway trains,” IEEE Transactions on Vehicular Technology, vol. 68, no. 7, pp. 6331–6342, July 2019.

    Article  Google Scholar 

  68. Y. Cao, Y. K. Sun, G. Xie, and T. Wen, “Fault diagnosis of train plug door based on a hybrid criterion for IMFs selection and fractional wavelet package energy entropy,” IEEE Transactions on Vehicular Technology, vol. 68, no. 8, pp. 7544–7551, August 2019.

    Article  Google Scholar 

  69. Y. Cao, Y. Zhang, T. Wen, and P. Li, “Research on dynamic nonlinear input prediction of fault diagnosis based on fractional differential operator equation in high-speed train control system,” Chaos, vol. 29, no. 1, Article Number: 013130, January 2019.

  70. Y. Cao, L. C. Ma, S. Xiao, X. Zhang, W. Xu, “Standard analysis for transfer delay in CTCS-3,” Chinese Journal of Electronics, vol. 26, no. 5, pp. 1057–1063, September 2017.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, P. R. China

    Shujun Fan, Ling Xu & Feng Ding

  2. School of Internet of Things Technology, Wuxi Vocational Institute of Commerce, Wuxi, 214153, P. R. China

    Ling Xu

  3. College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao, 266061, P. R. China

    Feng Ding

  4. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Ahmed Alsaedi & Tasawar Hayat

Authors
  1. Shujun Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ling Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Feng Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ahmed Alsaedi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Tasawar Hayat
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Feng Ding.

Additional information

Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Joseph Kwon under the direction of Editor Jay H. Lee. This work was supported by the National Natural Science Foundation of China (No. 61873111), Qing Lan Project, the 333 project of Jiangsu Province (No. BRA2018328) and the 111 Project (B12018).

Shujun Fan was born in Nantong (Jiangsu Province, China) in 1996. She received her B.Sc. degree from Jinling Institute of Technology (Nanjing, China) in 2018. She is currently a Master’s student in the School of Internet of Things Engineering, Jiangnan University (Wuxi, China). Her interests include system modeling, system identification and parameter estimation.

Ling Xu was born in Tianjin, China. She received her Master’s and Ph.D. degrees from the Jiangnan University (Wuxi, China), in 2005 and 2015, respectively. She is a Post-Doctoral Fellow at the Jiangnan University and has been an Associate Professor since 2015. She is a Colleges and Universities “Blue Project” Young Teacher (Jiangsu, China). Her research interests include process control, parameter estimation and signal modeling.

Feng Ding received his B.Sc. degree from the Hubei University of Technology (Wuhan, China) in 1984, and his M.Sc. and Ph.D. degrees both from the Tsinghua University, in 1991 and 1994, respectively. He has been a professor in the School of Internet of Things Engineering at the Jiangnan University (Wuxi, China) since 2004. His current research interests include model identification and adaptive control. He authored five books on System Identification.

Ahmed Alsaedi obtained his Ph.D. degree from Swansea University (UK) in 2002. He has a broad experience of research in applied mathematics. His fields of interest include dynamical systems, nonlinear analysis involving ordinary differential equations, fractional differential equations, boundary value problems, mathematical modeling, biomathematics, Newtonian and Non-Newtonian fluid mechanics. He served as the chairman of the mathematics department at KAU and presently he is serving as director of the research program at KAU. Under his great leadership, this program is running quite successfully and it has attracted a large number of highly rated researchers and distinguished professors from all over the world. He is also the head of NAAM international research group at KAU.

Tasawar Hayat was born in Khanewal, Punjab. He is a Distinguished National Professor and Chairperson of Mathematics Department at Quaid-I-Azam University and renowned worldwide for his seminal, diversified and fundamental contributions in models relevant to physiological systems, control engineering. He has a honor of being fellow of Pakistan Academy of Sciences, Third World Academy of Sciences (TWAS) and Islamic World Academy of Sciences in the mathematical Sciences.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fan, S., Xu, L., Ding, F. et al. Correlation Analysis-based Stochastic Gradient and Least Squares Identification Methods for Errors-in-variables Systems Using the Multiinnovation. Int. J. Control Autom. Syst. 19, 289–300 (2021). https://doi.org/10.1007/s12555-019-0970-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-019-0970-z

Keywords

Search

Navigation