Non-linear minimum variance state-space-based estimation for discrete-time multi-channel systems

Author(s): M.J. Grimble
DOI: 10.1049/iet-spr.2009.0064

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Author(s): M.J. Grimble ¹
- Affiliations: 1: Industrial Control Centre, University of Strathclyde, Glasgow, UK
Source: Volume 5, Issue 4, July 2011, p. 365 – 378
DOI: 10.1049/iet-spr.2009.0064 , Print ISSN 1751-9675, Online ISSN 1751-9683

A new state equation and non-linear operator-based approach to estimation is introduced for discrete-time multi-channel systems. This is a type of deconvolution or inferential estimation problem, where a signal enters a communications channel involving both non-linearities and transport delays. The measurements are corrupted by a coloured noise signal, which is correlated with the signal to be estimated both at the inputs and outputs of the channel. The communications channel may include either static or dynamic non-linearities represented in a general non-linear operator form. The optimal non-linear estimator is derived in terms of the state equations and non-linear operators that describe the system. The algorithm is relatively simple to derive and to implement in the form of a recursive algorithm. The main advantage of the approach is the simplicity of the non-linear estimator theory and the straightforward structure of the resulting solution. The results may be applied to the solution of channel equalisation problems in communications or fault detection problems in control applications.

References

1. 1)
  - X. Liu , J.W. Sun , D. Liu . Nonlinear multifunctional sensor signal reconstruction based on total least squares. J. Phys. Conf. Ser. , 281 - 286
2. 2)
  - B.D.O. Anderson , J.B. Moore , S.G. Loo . Spectral factorization of time-varying covariance functions. IEEE Trans. Inf. Theory , 550 - 557
3. 3)
  - M.J. Grimble . (2006) Robust industrial control: optimal design approach for polynomial systems.
4. 4)
  - M.J. Grimble . Non-linear generalised minimum variance feedback, feedforward and tracking control. Automatica , 957 - 969
5. 5)
  - J.G. Proakis . (1995) Digital communications.
6. 6)
  - P. Celka , N.J. Bershad , J.M. Vesin . Stochastic gradient identification of polynomial Wiener systems: analysis and application. IEEE Trans. Signal Process. , 301 - 313
7. 7)
  - N.E. Wiener . (1949) Extrapolation, interpolation, and smoothing of stationary time series, with engineering applications.
8. 8)
  - K. Aström . (1970) Introduction to stochastic control theory.
9. 9)
  - Frank, H., Richard, D.: `The Gaussian particle filter for diagnosis of non-linear systems', Proc. 14th Int. Conf. on Principles of Diagnosis, June 2003, Washington, DC, USA, p. 65–70.
10. 10)
  - A. Doucet , S. Godsill , C. Andreu . On sequential Monte-Carlo sampling methods for Bayesian filtering. Stat. Comput. , 197 - 208
11. 11)
  - Grimble, M.J., Majecki, P.: `Nonlinear generalised minimum variance control under actuator saturation', IFAC World Congress, Friday 8 July 2005, Prague.
12. 12)
  - M.J. Grimble . Mutlichannel optimal linear deconvolution filters and strip thickness estimation from gauge measurements. ASME J. Dyn. Syst., Meas. Control , 165 - 174
13. 13)
  - P.M. Djuric , J.H. Kotecha , J. Zhang . Particle filtering. IEEE Signal Process. Mag. , 5 , 19 - 38
14. 14)
  - Grimble, M.J.: ` design of optimal linear filters', Proc. MTNS Conf., 1987, Phoenix, Arizona, p. 553–540, in Byrnes C.I., Martin C.F. Saeks R.E. (Eds.); 1988, North Holland, Amsterdam.
15. 15)
  - J.B. Moore , B.D.O. Anderson . Solution of a time-varying Wiener filtering problem. Electron. Lett. , 562 - 563
16. 16)
  - P. Celka , N.J. Bershad , J.M. Vesin . Fluctuation analysis of stochastic gradient identification of polynomial Wiener systems. IEEE Trans. Signal Process. , 6 , 1820 - 1825
17. 17)
  - T.J. Moir . Optimal deconvolution smoother. IEE Proc. , 13 - 18
18. 18)
  - S. Pinter , X.N. Fernando . Equalization of multiuser wireless CDMA downlink considering transmitter nonlinearity using Walsh codes. EURASIP J. Wirel. Commun. Netw. , 1
19. 19)
  - M.J. Grimble , S. Ali Naz . Nonlinear minimum variance estimation for discrete-time multi-channel systems. IEEE Trans. Signal Process. , 7 , 2437 - 2444
20. 20)
  - R.E. Ziemer , R.L. Peterson . (1992) Introduction to digital communication.
21. 21)
  - M.J. Grimble . (2001) Industrial control systems design.
22. 22)
  - Berggren, P.: `Cylinder individual lambda feedback control in an SI engine', 1996, MSc, Linkoping, Perkovic, A..
23. 23)
  - M.J. Grimble , A. El Sayed . Solution of the H∞ optimal linear filtering problem for discrete-time systems. IEEE Trans. Signal Process. , 7 , 1092 - 1104
24. 24)
  - S.S. Haykin . (1983) Communication systems.
25. 25)
  - M.J. Grimble , M.A. Johnson . (1988) Optimal multivariable control and estimation theory.
26. 26)
  - F. Cadini , E. Zio . Application of particle filtering for estimating the dynamics of nuclear systems. IEEE Trans. Nucl. Sci. , 2 , 748 - 757
27. 27)
  - Kalman, R.E.: `New methods in Wiener filtering theory', Proc. Symp. on Engineering Applications of Random Function Theory and Probability, 1961, p. 270–388.
28. 28)
  - J.C. Gomez , E. Baeyens . Hammerstein and Wiener model identification using rational orthonormal bases. Lat. Am. Appl. Res., oct./dic. , 4 , 449 - 456
29. 29)
  - Ali Naz, S., Grimble, M.J.: `Design and real time implementation of nonlinear minimum variance filter', UKACC Conf., September 2008, Manchester.
30. 30)
  - S.S. Jiang , A. Sawchuk . Noise updating repeated Wiener filter and other adaptive noise smoothing filters using local image statistics. Appl. Opt. , 2326 - 2337
31. 31)
  - M.J. Grimble , K.A. Jukes , D.P. Goodall . Nonlinear filters and operators and the constant gain extended Kalman filter. IMA J. Math. Control Inf. , 359 - 386
32. 32)
  - Grimble, M.J.: `NMV optimal estimation for nonlinear discrete-time multi-channel systems', 46thIEEE Conf. on Decision and Control, 12–14 December 2007, New Orleans, p. 4281–4286.
33. 33)
  - J.C. Gómez , E. Baeyens . Identification of block-oriented nonlinear systems using orthonormal bases. J. Process Control , 6 , 685 - 697
34. 34)
  - R.E. Kalman . A new approach to linear filtering and prediction problems. J Basic Eng. , 34 - 45
35. 35)
  - N.J. Bershad , P. Celka , S. McLaughlin . Analysis of stochastic gradient identification of Wiener-Hammerstein systems for nonlinearities with Hermite polynomial expansions. IEEE Trans. Signal Process. , 1060 - 1072
36. 36)
  - T. Kailath . Fredholm resolvents, Wiener-Hopf equations, and Riccati differential equations. IEEE Trans. Inf. Theory , 665 - 672
37. 37)
  - H. Kwakernaak , R. Sivan . (1991) Modern signals and systems.

Non-linear minimum variance state-space-based estimation for discrete-time multi-channel systems

Non-linear minimum variance state-space-based estimation for discrete-time multi-channel systems

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