Recursive Identification of Errors-in-Variables Systems Based on the Correlation Analysis

Abstract

This paper considers a single-input single-output linear dynamic system, whose input and output are corrupted by Gaussian white measurement noises with zero means and unknown variances; the parameter estimation of such a system is a typical errors-in-variables (EIV) system identification problem. This paper proposes the correlation function-based two-step identification methods for the EIV systems. In order to obtain the unbiased parameter estimates of the EIV system, we derive the correlation function equation by using the correlation analysis method and adopt the least squares method and the instrumental variable method to recursively compute the parameter estimates of the model, resulting in the unbiased parameter estimates of the EIV systems. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed algorithms.

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References

  1. 1.

    J.C. Agüero, G.C. Goodwin, Identifiability of errors in variables dynamic systems. Automatica 44(2), 371–382 (2008)

    MathSciNet  MATH  Google Scholar 

  2. 2.

    F. Cairone, D. Mirabella, P. Cabrales, M. Intaglietta, M. Bucolo, Quantitative analysis of spatial irregularities in RBCs flows. Chaos Solitons Fract. 115, 349–355 (2018)

    Google Scholar 

  3. 3.

    Y. Cao, H. Lu, T. Wen, A safety computer system based on multi-sensor data processing. Sensors 19(4), 818 (2019)

    Google Scholar 

  4. 4.

    Y. Cao, L.C. Ma, S. Xiao et al., Standard analysis for transfer delay in CTCS-3. Chin. J. Electron. 26(5), 1057–1063 (2017)

    Google Scholar 

  5. 5.

    Y. Cao, Y.K. Sun, G. Xie, T. Wen, Fault diagnosis of train plug door based on a hybrid criterion for IMFs selection and fractional wavelet package energy entropy. IEEE Trans. Veh. Technol. 68(8), 7544–7551 (2019)

    Google Scholar 

  6. 6.

    Y. Cao, Z. Wang, F. Liu, P. Li, G. Xie, Bio-inspired speed curve optimization and sliding mode tracking control for subway trains. IEEE Trans. Veh. Technol. 68(7), 6331–6342 (2019)

    Google Scholar 

  7. 7.

    Y. Cao, Y. Zhang, T. Wen, P. Li, Research on dynamic nonlinear input prediction of fault diagnosis based on fractional differential operator equation in high-speed train control system. Chaos 29(1), 013130 (2019)

    Google Scholar 

  8. 8.

    Y.F. Chang, C.J. Sun, Y. Qiu, Effective notch stress method for fatigue assessment of sheet alloy material and bi-material welded joints. Thin-Walled Struct. 151, 106745 (2020)

    Google Scholar 

  9. 9.

    Y.F. Chang, G.S. Zhai, B. Fu, L.L. Xiong, Quadratic stabilization of switched uncertain linear systems: a convex combination approach. IEEE-CAA J. Autom. Sin. 6(5), 1116–1126 (2019)

    MathSciNet  Google Scholar 

  10. 10.

    M.T. Chen, F. Ding, R.M. Lin et al., Maximum likelihood least squares-based iterative methods for output-error bilinear-parameter models with colored noises. Int. J. Robust Nonlinear Control (2020). https://doi.org/10.1002/rnc.5081

  11. 11.

    Z.W. Chen, X.X. Zhang, H. Xiong et al., Dissolved gas analysis in transformer oil using Pt-doped WSe2 monolayer based on first principles method. IEEE Access 7, 72012–72019 (2019)

    Google Scholar 

  12. 12.

    A. Dankers, P.M.J. Van Den Hof, X. Bombios et al., Errors-in-variables identification in dynamic networks—consistency results for an instrumental variable approach. Automatica 62, 39–50 (2015)

    MathSciNet  MATH  Google Scholar 

  13. 13.

    I. Dassios, A practical formula of solutions for a family of linear non-autonomous fractional nabla difference equations. J. Comput. Appl. Math. 339, 317–328 (2018)

    MathSciNet  MATH  Google Scholar 

  14. 14.

    I. Dassios, D. Baleanu, Caputo and related fractional derivatives in singular systems. Appl. Math. Comput. 337, 591–606 (2018)

    MathSciNet  MATH  Google Scholar 

  15. 15.

    J. Ding, Z.X. Cao, J.Z. Chen et al., Weighted parameter estimation for Hammerstein nonlinear ARX systems. Circuits Syst. Signal Process. 39(4), 2178–2192 (2020)

    Google Scholar 

  16. 16.

    J. Ding, J.Z. Chen, J.X. Lin, G.P. Jiang, Particle filtering-based recursive identification for controlled auto-regressive systems with quantised output. IET Control Theory Appl. 13(14), 2181–2187 (2019)

    Google Scholar 

  17. 17.

    J. Ding, J.Z. Chen, J.X. Lin, L.J. Wan, Particle filtering based parameter estimation for systems with output-error type model structures. J. Franklin Inst. 356(10), 5521–5540 (2019)

    MathSciNet  MATH  Google Scholar 

  18. 18.

    F. Ding, L. Lv, J. Pan et al., Two-stage gradient-based iterative estimation methods for controlled autoregressive systems using the measurement data. Int. J. Control Autom. Syst. 18(4), 886–896 (2020)

    Google Scholar 

  19. 19.

    F. Ding, F.F. Wang, L. Xu, M.H. Wu, Decomposition based least squares iterative identification algorithm for multivariate pseudo-linear ARMA systems using the data filtering. J. Franklin Inst. 354(3), 1321–1339 (2017)

    MathSciNet  MATH  Google Scholar 

  20. 20.

    F. Ding, X. Zhang, L. Xu, The innovation algorithms for multivariable state-space models. Int. J. Adapt. Control Signal Process 33(11), 1601–1608 (2019)

    MathSciNet  Google Scholar 

  21. 21.

    R. Diversi, Bias-eliminating least-squares identification of errors-in-variables models with mutually correlated noises. Int. J. Adapt. Control Signal Process. 27(10), 915–924 (2013)

    MathSciNet  MATH  Google Scholar 

  22. 22.

    B. Fu, C.X. Ouyang, C.S. Li, J.W. Wang, E. Gul, An improved mixed integer linear programming approach based on symmetry diminishing for unit commitment of hybrid power system. Energies 12(5), Article Number: 833 (2019)

  23. 23.

    Y.B. Gao, F. Xiao, J.X. Liu, R.C. Wang, Distributed soft fault detection for interval type-2 fuzzy-model-based stochastic systems with wireless sensor networks. IEEE Trans. Ind. Inf. 15(1), 334–347 (2019)

    Google Scholar 

  24. 24.

    L. Geng, R.B. Xiao, Control and backbone identification for the resilient recovery of a supply network utilizing outer synchronization. Appl. Sci. 10(1), 313 (2020)

    Google Scholar 

  25. 25.

    L. He, H. Lin, Q. Zou, D.J. Zhang, Accurate measurement of pavement deflection velocity under dynamic loads. Autom. Constr. 83, 149–162 (2017)

    Google Scholar 

  26. 26.

    D. Kreiberg, T. Söderström, F.Y. Wallentin, Errors-in-variables system identification using structural equation modeling. Automatica 66, 218–230 (2016)

    MathSciNet  MATH  Google Scholar 

  27. 27.

    X.Y. Li, Y. Gao, B.Y. Wu, Approximate solutions of Atangana–Baleanu variable order fractional problems. AIMS Matt. 5(3), 2285–2294 (2020)

    MathSciNet  Google Scholar 

  28. 28.

    H.Y. Li, Y.B. Gao, L.G. Wu, H.K. Lam, Fault detection for T–S fuzzy time-delay systems: delta operator and input–output methods. IEEE Trans. Cybern. 45(2), 229–241 (2015)

    Google Scholar 

  29. 29.

    M.H. Li, X.M. Liu, The least squares based iterative algorithms for parameter estimation of a bilinear system with autoregressive noise using the data filtering technique. Sig. Process. 147, 23–34 (2018)

    Google Scholar 

  30. 30.

    M.H. Li, X.M. Liu, Auxiliary model based least squares iterative algorithms for parameter estimation of bilinear systems using interval-varying measurements. IEEE Access 6, 21518–21529 (2018)

    Google Scholar 

  31. 31.

    M.H. Li, X.M. Liu et al., 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. Int. J. Adapt. Control Signal Process. 33(7), 1189–1211 (2019)

    MathSciNet  MATH  Google Scholar 

  32. 32.

    M.Y. Liu, I. Dassios, G. Tzounas, F. Milano, Stability analysis of power systems with inclusion of realistic-modeling WAMS delays. IEEE Trans. Power Syst. 34(1), 627–636 (2019)

    Google Scholar 

  33. 33.

    S.Y. Liu, F. Ding, L. Xu et al., Hierarchical principle-based iterative parameter estimation algorithm for dual-frequency signals. Circuits Syst. Signal Process 38(7), 3251–3268 (2019)

    Google Scholar 

  34. 34.

    L.J. Liu, F. Ding, L. Xu et al., Maximum likelihood recursive identification for the multivariate equation-error autoregressive moving average systems using the data filtering. IEEE Access 7, 41154–41163 (2019)

    Google Scholar 

  35. 35.

    N. Liu, S. Mei, D. Sun, W. Shi, J. Feng, Y.M. Zhou, F. Mei, J. Xu, Y. Jiang, X.A. Cao, Effects of charge transport materials on blue fluorescent organic light-emitting diodes with a host-dopant system. Micromachines 10(5), Article Number: 344 (2019)

  36. 36.

    H. Liu, Q.X. Zou, Z.P. Zhang, Energy disaggregation of appliances consumptions using ham approach. IEEE Access 7, 185977–185990 (2019)

    Google Scholar 

  37. 37.

    L.L. Lv, S.Y. Tang, L. Zhang, Parametric solutions to generalized periodic Sylvester bimatrix equations. J. Frankl. Inst. 357(6), 3601–3621 (2020)

    MathSciNet  MATH  Google Scholar 

  38. 38.

    J.X. Ma, F. Ding, Filtering-based multistage recursive identification algorithm for an input nonlinear output-error autoregressive system by using the key term separation technique. Circuits Syst. Signal Process. 36(2), 577–599 (2017)

    MATH  Google Scholar 

  39. 39.

    P. Ma, F. Ding, New gradient based identification methods for multivariate pseudo-linear systems using the multi-innovation and the data filtering. J. Frankl. Inst. 354(3), 1568–1583 (2017)

    MathSciNet  MATH  Google Scholar 

  40. 40.

    F.Y. Ma, C.C. Fu, J. Yang, Q.Z. Yang, Control strategy for adaptive active energy harvesting in sediment microbial fuel cells. J. Energy Eng. 146(1), 04019034 (2020)

    Google Scholar 

  41. 41.

    H. Ma, J. Pan et al., Partially-coupled least squares based iterative parameter estimation for multi-variable output-error-like autoregressive moving average systems. IET Control Theory Appl. 13(18), 3040–3051 (2019)

    Google Scholar 

  42. 42.

    J.X. Ma, W.L. Xiong, J. Chen et al., Hierarchical identification for multivariate Hammerstein systems by using the modified Kalman filter. IET Control Theory Appl. 11(6), 857–869 (2017)

    MathSciNet  Google Scholar 

  43. 43.

    F.Y. Ma, Y.K. Yin, W. Chen, Reliability analysis of power and communication network in drone monitoring system. IEICE Trans. Commun. E102B(10), 1991–1997 (2019)

    Google Scholar 

  44. 44.

    F.Y. Ma, Y.K. Yin, M. Li, Start-up process modelling of sediment microbial fuel cells based on data driven. Math. Problems Eng. 2019, 7403732 (2019)

    Google Scholar 

  45. 45.

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

    Google Scholar 

  46. 46.

    F. Milano, I. Dassios, Small-signal stability analysis for non-index 1 Hessenberg form systems of delay differential-algebraic equations. IEEE Trans. Circuits Syst. 63(9), 1521–1530 (2016)

    MathSciNet  Google Scholar 

  47. 47.

    J. Pan, X. Jiang, X.K. Wan, W. Ding, A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems. Int. J. Control Autom. Syst. 15(3), 1189–1197 (2017)

    Google Scholar 

  48. 48.

    J. Pan, W. Li, H.P. Zhang, Control algorithms of magnetic suspension systems based on the improved double exponential reaching law of sliding mode control. Int. J. Control Autom. Syst. 16(6), 2878–2887 (2018)

    Google Scholar 

  49. 49.

    W.X. Shi, N. Liu, Y.M. Zhou, X.A. Cao, Effects of postannealing on the characteristics and reliability of polyfluorene organic light-emitting diodes. IEEE Trans. Electron Devices 66(2), 1057–1062 (2019)

    Google Scholar 

  50. 50.

    T. Söderström, Errors-in-variables methods in system identification. Automatica 43(6), 939–958 (2007)

    MathSciNet  MATH  Google Scholar 

  51. 51.

    T. Söderström, System identification for the errors-in-variables problem. Trans. Inst. Meas. Control 34(7), 780–792 (2012)

    Google Scholar 

  52. 52.

    T. Söderström, A generalized instrumental variable estimation method for errors-in-variables identification problems. Automatica 47(8), 1656–1666 (2011)

    MathSciNet  MATH  Google Scholar 

  53. 53.

    T. Söderström, U. Soverini, Errors-in-variables identification using maximum likelihood in the frequency domain. Automatica 79, 131–143 (2017)

    MathSciNet  MATH  Google Scholar 

  54. 54.

    Z.D. Su, Y. Li, G.C. Yang, Dietary composition perception algorithm using social robot audition for Mandarin Chinese. IEEE Access 8, 8768–8782 (2020)

    Google Scholar 

  55. 55.

    S.S. Tian, X.X. Zhang, S. Xiao et al., Application of C6F12O/CO2 mixture in 10 kV medium-voltage switchgear. IET Sci. Meas. Technol. 13(9), 1225–1230 (2019)

    Google Scholar 

  56. 56.

    A. Vicari, A. Ciraudo, C.D. Negro, A. Hérault, Lava flow simulations using discharge rates from thermal infrared satellite imagery during the 2006 Etna eruption. Nat. Hazards 50(3), 539–550 (2009)

    Google Scholar 

  57. 57.

    L.J. Wan, F. Ding, Decomposition- and gradient-based iterative identification algorithms for multivariable systems using the multi-innovation theory. Circuits Syst. Signal Process. 38(7), 2971–2991 (2019)

    Google Scholar 

  58. 58.

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

    Google Scholar 

  59. 59.

    Y.J. Wang, F. Ding, M.H. Wu, Recursive parameter estimation algorithm for multivariate output-error systems. J. Frankl. Inst. 355(12), 5163–5181 (2018)

    MathSciNet  MATH  Google Scholar 

  60. 60.

    L.J. Wang, B.Y. Feng, Y. Wang et al., Bidirectional short-circuit current blocker for DC microgrid based on solid-state circuit breaker. Electronics 9(2), 306 (2020)

    Google Scholar 

  61. 61.

    L.J. Wang, J. Guo, C. Xu, T.Z. Wu, H.P. Lin, Hybrid model predictive control strategy of supercapacitor energy storage system based on double active bridge. Energies 12(11), 2134 (2019)

    Google Scholar 

  62. 62.

    L. Wang, H. Liu, L.V. Dai, Y.W. Liu, Novel method for identifying fault location of mixed lines. Energies 11(6), Article Number: 1529 (2018)

  63. 63.

    L. Wang, J. Wu, X.S. Zhan, T. Han, H. Yan, Fixed-time bipartite containment of multi-agent systems subject to disturbance. IEEE Access 8, 77679–77688 (2020)

    Google Scholar 

  64. 64.

    H.J. Wang, F.M. Zhang, Bifurcations, ultimate boundedness and singular orbits in a unified hyperchaotic lorenz-type system. Discrete Contin. Dyn. Syst. Ser. B 25(5), 1791–1820 (2020)

    MATH  Google Scholar 

  65. 65.

    T.Z. Wu, X. Shi, L. Liao, C.J. Zhou, H. Zhou, Y.H. Su, A capacity configuration control strategy to alleviate power fluctuation of hybrid energy storage system based on improved particle swarm optimization. Energies 12(4), Article Number: 642 (2019)

  66. 66.

    T.Z. Wu, F.C. Ye, Y.H. Su et al., Coordinated control strategy of DC microgrid with hybrid energy storage system to smooth power output fluctuation. Int. J. Low-Carbon Technol. 15(1), 46–54 (2020)

    Google Scholar 

  67. 67.

    L. Xu, The damping iterative parameter identification method for dynamical systems based on the sine signal measurement. Signal Process. 120, 660–667 (2016)

    Google Scholar 

  68. 68.

    L. Xu, The parameter estimation algorithms based on the dynamical response measurement data. Adv. Mech. Eng. 9(11), 1–12 (2017). https://doi.org/10.1177/1687814017730003

    Article  Google Scholar 

  69. 69.

    L. Xu, L. Chen, W.L. Xiong, Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration. Nonlinear Dyn. 79(3), 2155–2163 (2015)

    MathSciNet  Google Scholar 

  70. 70.

    L. Xu, W.L. Xiong et al., Hierarchical parameter estimation for the frequency response based on the dynamical window data. Int. J. Control Autom. Syst. 16(4), 1756–1764 (2018)

    Google Scholar 

  71. 71.

    G.C. Yang, Z.J. Chen, Y. Li, Z.D. Su, Rapid relocation method for mobile robot based on improved ORB-SLAM2 algorithm. Remote Sens. 11(2), 149 (2019)

    Google Scholar 

  72. 72.

    C.C. Yin, C.W. Wang, The perturbed compound Poisson risk process with investment and debit interest. Methodol. Comput. Appl. Probab. 12(3), 391–413 (2010)

    MathSciNet  MATH  Google Scholar 

  73. 73.

    C.C. Yin, Y.Z. Wen, Optimal dividend problem with a terminal value for spectrally positive Levy processes. Insur. Math. Econ. 53(3), 769–773 (2013)

    MATH  Google Scholar 

  74. 74.

    C.C. Yin, Y.Z. Wen, Exit problems for jump processes with applications to dividend problems. J. Comput. Appl. Math. 245, 30–52 (2013)

    MathSciNet  MATH  Google Scholar 

  75. 75.

    C.C. Yin, Y.Z. Wen, An extension of Paulsen-Gjessing’s risk model with stochastic return on investments. Insur. Math. Econ. 52(3), 469–476 (2013)

    MathSciNet  MATH  Google Scholar 

  76. 76.

    C.C. Yin, Y.Z. Wen, Y.X. Zhao, On the optimal dividend problem for a spectrally positive levy process. Astin Bull. 44(3), 635–651 (2014)

    MathSciNet  MATH  Google Scholar 

  77. 77.

    C.C. Yin, K.C. Yuen, Optimality of the threshold dividend strategy for the compound Poisson model. Stat. Probab. Lett. 81(12), 1841–1846 (2011)

    MathSciNet  MATH  Google Scholar 

  78. 78.

    C.C. Yin, K.C. Yuen, Exact joint laws associated with spectrally negative Levy processes and applications to insurance risk theory. Front. Math. China 9(6), 1453–1471 (2014)

    MathSciNet  MATH  Google Scholar 

  79. 79.

    C.C. Yin, K.C. Yuen, Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs. J. Ind. Manag. Optim. 11(4), 1247–1262 (2015)

    MathSciNet  MATH  Google Scholar 

  80. 80.

    C.P. Yu, L. Ljung, A. Wills, M. Verhaegen, Constrained subspace method for the identification of structured state-space models. IEEE Trans. Autom. Control (2020). https://doi.org/10.1109/TAC.2019.2957703

    Article  Google Scholar 

  81. 81.

    X. Zhang, F. Ding, Hierarchical parameter and state estimation for bilinear systems. Int. J. Syst. Sci. 51(2), 275–290 (2020)

    MathSciNet  Google Scholar 

  82. 82.

    X. Zhang, F. Ding, Adaptive parameter estimation for a general dynamical system with unknown states. Int. J. Robust Nonlinear Control 30(4), 1351–1372 (2020)

    MathSciNet  Google Scholar 

  83. 83.

    X. Zhang, F. Ding, E.F. Yang, State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors. Int. J. Adapt. Control Signal Process. 33(7), 1157–1173 (2019)

    MathSciNet  MATH  Google Scholar 

  84. 84.

    X. Zhang, F. Ding, L. Xu, Recursive parameter estimation methods and convergence analysis for a special class of nonlinear systems. Int. J. Robust Nonlinear Control 30(4), 1373–1393 (2020)

    MathSciNet  Google Scholar 

  85. 85.

    Y. Zhang, M.M. Huang, T.Z. Wu, F. Ji, Reconfigurable equilibrium circuit with additional power supply. Int. J. Low-Carbon Technol. 15(1), 106–111 (2020)

    Google Scholar 

  86. 86.

    Y.L. Zhang, X.W. Li, G.Y. Zhao, B. Lu, C.C. Cavalcante, Signal reconstruction of compressed sensing based on alternating direction method of multipliers. Circuits Syst. Signal Process. 39(1), 307–323 (2020)

    Google Scholar 

  87. 87.

    E.L. Zhang, R. Pintelon, J. Schoukens, Errors-in-variables identification of dynamic systems excited by arbitrary non-white input. Automatica 49(10), 3032–3041 (2013)

    MathSciNet  MATH  Google Scholar 

  88. 88.

    G.Z. Zhang, X.X. Zhang, H.T. Cheng, J. Tang, Ladder-Wise calculation method for z-coordinate of transformer PD source based on planar layout UHF antenna sensors. IEEJ Trans. Electr. Electron. Eng. 15(3), 340–345 (2020)

    Google Scholar 

  89. 89.

    Y. Zhang, X.X. Zhang, Y. Li et al., AC breakdown and decomposition characteristics of environmental friendly gas C5F10O/Air and C5F10O/N-2. IEEE Access 7, 73954–73960 (2019)

    Google Scholar 

  90. 90.

    N. Zhao, Joint optimization of cooperative spectrum sensing and resource allocation in multi-channel cognitive radio sensor networks. Circuits Syst. Signal Process. 35(7), 2563–2583 (2016)

    MATH  Google Scholar 

  91. 91.

    N. Zhao, Y. Liang, Y. Pei, Dynamic contract incentive mechanism for cooperative wireless networks. IEEE Trans. Veh. Technol. 67(11), 10970–10982 (2018)

    Google Scholar 

  92. 92.

    X.L. Zhao, Z.Y. Lin, B. Fu, L. He, 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. J. Electr. Eng. Technol. 14(3), 1075–1086 (2019)

    Google Scholar 

  93. 93.

    X.L. Zhao, Z.Y. Lin, B. Fu, L. He, 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 11(12), 3325 (2018)

    Google Scholar 

  94. 94.

    X.L. Zhao, F. Liu, B. Fu, F. Na, Reliability analysis of hybrid multi-carrier energy systems based on entropy-based Markov model. J. Risk Reliab. 230(6), 561–569 (2016)

    Google Scholar 

  95. 95.

    N. Zhao, M.H. Wu, J.J. Chen, Android-based mobile educational platform for speech signal processing. Int. J. Electr. Eng. Educ. 54(1), 3–16 (2017)

    Google Scholar 

  96. 96.

    W.X. Zheng, A bias correction method for identification of linear dynamic errors in variables models. IEEE Trans. Autom. Control 47(7), 1142–1147 (2002)

    MathSciNet  MATH  Google Scholar 

  97. 97.

    W.X. Zheng, Transfer function estimation form noisy input and output data. Int. J. Adapt. Control Signal Process. 12, 365–380 (1998)

    MATH  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 61873111), the 111 Project (B12018) and by Key Program Special Fund in XJTLU (No. KSF-E-12).

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Fan, S., Ding, F. & Hayat, T. Recursive Identification of Errors-in-Variables Systems Based on the Correlation Analysis. Circuits Syst Signal Process 39, 5951–5981 (2020). https://doi.org/10.1007/s00034-020-01441-7

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Keywords

  • Parameter estimation
  • EIV system
  • Correlation analysis
  • Least squares
  • Instrumental variable