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Volumn 58, Issue 1, 2011, Pages 53-83

Error analysis of Jacobi derivative estimators for noisy signals

Author keywords

Error bound; Jacobi orthogonal polynomials; Numerical differentiation; Stochastic integrals; Stochastic process

Indexed keywords


EID: 80051544745     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-011-9447-8     Document Type: Article
Times cited : (49)

References (40)
  • 2
    • 0029293540 scopus 로고
    • A class of second-order integrators and low-pass differentiators
    • Al-Alaoui, M. A.: A class of second-order integrators and low-pass differentiators. IEEE Trans. Circuits Syst. I 42(4), 220-223 (1995).
    • (1995) IEEE Trans. Circuits Syst. I , vol.42 , Issue.4 , pp. 220-223
    • Al-Alaoui, M.A.1
  • 4
    • 0036741835 scopus 로고    scopus 로고
    • Time-varying high-gain observers for numerical differentiation
    • Chitour, Y.: Time-varying high-gain observers for numerical differentiation. IEEE Trans. Automat. Contr. 47, 1565-1569 (2002).
    • (2002) IEEE Trans. Automat. Contr. , vol.47 , pp. 1565-1569
    • Chitour, Y.1
  • 5
    • 0033349279 scopus 로고    scopus 로고
    • Discrete-time implementation of high-gain observers for numerical differentiation
    • Dabroom, A. M., Khalil, H. K.: Discrete-time implementation of high-gain observers for numerical differentiation. Int. J. Control 72, 1523-1537 (1999).
    • (1999) Int. J. Control , vol.72 , pp. 1523-1537
    • Dabroom, A.M.1    Khalil, H.K.2
  • 7
    • 33646489320 scopus 로고    scopus 로고
    • Analyse non standard du bruit
    • Fliess, M.: Analyse non standard du bruit. C. R. Acad. Sci. Paris Ser. I 342, 797-802 (2006).
    • (2006) C.R. Acad. Sci. Paris Ser. I , vol.342 , pp. 797-802
    • Fliess, M.1
  • 10
    • 84930350670 scopus 로고    scopus 로고
    • Closed-loop parametric identification for continuous-time linear systems via new algebraic techniques
    • In: Garnier, H., Wang, L. (eds.) Springer. Available at
    • Fliess, M., Sira-Ramírez, H.: Closed-loop parametric identification for continuous-time linear systems via new algebraic techniques. In: Garnier, H., Wang, L. (eds.) Identification of Continuous-Time Models from Sampled Data, pp. 363-391. Springer (2008). Available at http://hal. inria. fr/inria-00114958/en/.
    • (2008) Identification of Continuous-Time Models from Sampled Data , pp. 363-391
    • Fliess, M.1    Sira-Ramírez, H.2
  • 12
    • 0000527993 scopus 로고
    • Regularization of a non-characteristic Cauchy problem for a parabolic equation
    • Hào, D. N., Schneider, A., Reinhardt, H. J.: Regularization of a non-characteristic Cauchy problem for a parabolic equation. Inverse Problems 11, 1247-1264 (1995).
    • (1995) Inverse Problems , vol.11 , pp. 1247-1264
    • Hào, D.N.1    Schneider, A.2    Reinhardt, H.J.3
  • 14
    • 0345690108 scopus 로고    scopus 로고
    • Online exact differentiation and notion of asymptotic algebraic observers
    • Ibrir, S.: Online exact differentiation and notion of asymptotic algebraic observers. IEEE Trans. Automat. Contr. 48, 2055-2060 (2003).
    • (2003) IEEE Trans. Automat. Contr. , vol.48 , pp. 2055-2060
    • Ibrir, S.1
  • 15
    • 1642525853 scopus 로고    scopus 로고
    • Linear time-derivatives trackers
    • Ibrir, S.: Linear time-derivatives trackers. Automatica 40, 397-405 (2004).
    • (2004) Automatica , vol.40 , pp. 397-405
    • Ibrir, S.1
  • 16
    • 0034510447 scopus 로고    scopus 로고
    • New finite difference formulas for numerical differentiation
    • Khan, I. R., Ohba, R.: New finite difference formulas for numerical differentiation. J. Comput. Appl. Math. 126, 269-276 (2000).
    • (2000) J. Comput. Appl. Math. , vol.126 , pp. 269-276
    • Khan, I.R.1    Ohba, R.2
  • 17
    • 0142137682 scopus 로고    scopus 로고
    • Higher-order sliding modes, differentiation and output-feedback control
    • Levant, A.: Higher-order sliding modes, differentiation and output-feedback control. Int. J. Control 76, 924-941 (2003).
    • (2003) Int. J. Control , vol.76 , pp. 924-941
    • Levant, A.1
  • 18
    • 0003398168 scopus 로고
    • Englewood Cliffs: Prentice-Hall
    • Lanczos, C.: Applied Analysis. Prentice-Hall, Englewood Cliffs (1956).
    • (1956) Applied Analysis
    • Lanczos, C.1
  • 19
    • 77950857207 scopus 로고    scopus 로고
    • Error analysis for a class of numerical differentiator: application to state observation
    • Available at
    • Liu, D. Y., Gibaru, O., Perruquetti, W.: Error analysis for a class of numerical differentiator: application to state observation. In: 48th IEEE Conference on Decision and Control, China (2009). Available at http://hal. inria. fr/inria-00437129/en/.
    • (2009) In: 48th IEEE Conference on Decision and Control, China
    • Liu, D.Y.1    Gibaru, O.2    Perruquetti, W.3
  • 21
    • 79951517828 scopus 로고    scopus 로고
    • Differentiation by integration with Jacobi polynomials
    • doi:10.1016/j.cam.2010.12.023. Available at
    • Liu, D. Y., Gibaru, O., Perruquetti, W.: Differentiation by integration with Jacobi polynomials. J. Comput. Appl. Math. (2010). doi: 10. 1016/j. cam. 2010. 12. 023. Available at http://hal. inria. fr/inria-00550160.
    • (2010) J. Comput. Appl. Math
    • Liu, D.Y.1    Gibaru, O.2    Perruquetti, W.3
  • 22
    • 0003981320 scopus 로고
    • 3rd edn., New York: van Nostrand
    • Loève, M.: Probability Theory, 3rd edn. van Nostrand, New York (1963).
    • (1963) Probability Theory
    • Loève, M.1
  • 23
    • 0039165486 scopus 로고
    • Finite-part integrals and the Euler-Maclaurin expansion
    • R. V. M. Zahar (Ed.), Basel: Birkhäuser
    • Lyness, J. N.: Finite-part integrals and the Euler-Maclaurin expansion. In: Zahar, R. V. M. (ed.) Approximation and Computation, Int. Ser. Numer. Math., vol. 119, pp. 397-407. Birkhäuser, Basel (1994).
    • (1994) Approximation and Computation, Int. Ser. Numer. Math., Vol. 119 , pp. 397-407
    • Lyness, J.N.1
  • 24
    • 77349099714 scopus 로고    scopus 로고
    • Parameter estimation for signals described by differential equations
    • Mboup, M.: Parameter estimation for signals described by differential equations. Appl. Anal. 88, 29-52 (2009).
    • (2009) Appl. Anal. , vol.88 , pp. 29-52
    • Mboup, M.1
  • 26
    • 63349102453 scopus 로고    scopus 로고
    • Numerical differentiation with annihilators in noisy environment
    • Mboup, M., Join, C., Fliess, M.: Numerical differentiation with annihilators in noisy environment. Numer. Algorithms 50(4), 439-467 (2009).
    • (2009) Numer. Algorithms , vol.50 , Issue.4 , pp. 439-467
    • Mboup, M.1    Join, C.2    Fliess, M.3
  • 28
    • 0032021199 scopus 로고    scopus 로고
    • Discrete mollification and automatic numerical differentiation
    • Murio, D. A., Mejía, C. E., Zhan, S.: Discrete mollification and automatic numerical differentiation. Comput. Math. Appl. 35, 1-16 (1998).
    • (1998) Comput. Math. Appl. , vol.35 , pp. 1-16
    • Murio, D.A.1    Mejía, C.E.2    Zhan, S.3
  • 29
    • 37249009051 scopus 로고    scopus 로고
    • Numerical differentiation for the second order derivatives of functions of two variables
    • Nakamura, G., Wang, S., Wang, Y.: Numerical differentiation for the second order derivatives of functions of two variables. J. Comput. Appl. Math. 212, 341-358 (2008).
    • (2008) J. Comput. Appl. Math. , vol.212 , pp. 341-358
    • Nakamura, G.1    Wang, S.2    Wang, Y.3
  • 30
    • 0030291928 scopus 로고    scopus 로고
    • A new approach to numerical differentiation and integration
    • Qu, R.: A new approach to numerical differentiation and integration. Math. Comput. 24(10), 55-68 (1996).
    • (1996) Math. Comput. , vol.24 , Issue.10 , pp. 55-68
    • Qu, R.1
  • 31
    • 33845729972 scopus 로고    scopus 로고
    • Approximating noncausal IIR digital filters having arbitrary poles, including new Hilbert transformer designs, via forward/backward block recursion
    • Rader, C. M., Jackson, L. B.: Approximating noncausal IIR digital filters having arbitrary poles, including new Hilbert transformer designs, via forward/backward block recursion. IEEE Trans. Circuits Syst. I 53(12), 2779-2787 (2006).
    • (2006) IEEE Trans. Circuits Syst. I , vol.53 , Issue.12 , pp. 2779-2787
    • Rader, C.M.1    Jackson, L.B.2
  • 32
    • 0035592056 scopus 로고    scopus 로고
    • On stable numerical differentiation
    • Ramm, A. G., Smirnova, A. B.: On stable numerical differentiation. Math. Comput. 70, 1131-1153 (2001).
    • (2001) Math. Comput. , vol.70 , pp. 1131-1153
    • Ramm, A.G.1    Smirnova, A.B.2
  • 36
    • 33747612193 scopus 로고    scopus 로고
    • A simple improved velocity estimation for low-speed regions based on position measurements only
    • Su, Y. X., Zheng, C. H., Mueller, P. C., Duan, B. Y.: A simple improved velocity estimation for low-speed regions based on position measurements only. IEEE Trans. Control Syst. Technol. 14, 937-942 (2006).
    • (2006) IEEE Trans. Control Syst. Technol. , vol.14 , pp. 937-942
    • Su, Y.X.1    Zheng, C.H.2    Mueller, P.C.3    Duan, B.Y.4
  • 38
    • 0036905596 scopus 로고    scopus 로고
    • A numerical differentiation method and its application to reconstruction of discontinuity
    • Wang, Y., Jia, X., Cheng, J.: A numerical differentiation method and its application to reconstruction of discontinuity. Inverse Problems 18, 1461-1476 (2002).
    • (2002) Inverse Problems , vol.18 , pp. 1461-1476
    • Wang, Y.1    Jia, X.2    Cheng, J.3
  • 39
    • 77949485977 scopus 로고    scopus 로고
    • Numerical differentiation for high orders by an integration method
    • Wang, Z., Wen, R.: Numerical differentiation for high orders by an integration method. J. Comput. Appl. Math. 234, 941-948 (2010).
    • (2010) J. Comput. Appl. Math. , vol.234 , pp. 941-948
    • Wang, Z.1    Wen, R.2
  • 40
    • 17444367366 scopus 로고    scopus 로고
    • Reconstruction of numerical derivatives from scattered noisy data
    • Wei, T., Hon, Y. C., Wang, Y.: Reconstruction of numerical derivatives from scattered noisy data. Inverse Problems 21, 657-672 (2005).
    • (2005) Inverse Problems , vol.21 , pp. 657-672
    • Wei, T.1    Hon, Y.C.2    Wang, Y.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.