Nonlinear Blind Parameter Estimation

This note deals with parameter estimation of nonlinear continuous-time models when the input signals of the corresponding system are not measured. The contribution of the note is to show that, with simple priors about the unknown input signals and using derivatives of the output signals, one can perform the estimation procedure. As an illustration, we consider situations where the simple priors, e.g., independence or Gaussianity of the unknown inputs, is assumed.

[1]  R. Landau,et al.  Numerical Differentiation , 2019, Numerical Methods.

[2]  R. Murray,et al.  Flat systems, equivalence and trajectory generation , 2003 .

[3]  E. Oja,et al.  Independent Component Analysis , 2001 .

[4]  Christian Jutten,et al.  Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture , 1991, Signal Process..

[5]  Pierre Comon.  Independent component analysis - a new concept? signal processing , 1994 .

[6]  J. Grizzle,et al.  On numerical differentiation algorithms for nonlinear estimation , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[7]  Emanuel Parzen,et al.  Stochastic Processes , 1962 .

[8]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[9]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

[10]  Russell H. Lambert,et al.  OVERDETERMINED BLIND SOURCE SEPARATION: USING MORE SENSORS THAN SOURCE SIGNALS IN A NOISY MIXTURE , 2000 .

[11]  Eric Moulines,et al.  A blind source separation technique using second-order statistics , 1997, IEEE Trans. Signal Process..

[12]  Jean-François Cardoso,et al.  Equivariant adaptive source separation , 1996, IEEE Trans. Signal Process..

[13]  Jessy W. Grizzle,et al.  Interpolation and numerical differentiation for observer design , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[14]  C. Heyde,et al.  Quasi-likelihood and its application , 1997 .

[15]  Franck Plestan,et al.  Synthesis of nonlinear observers via structural analysis and numerical differentiation , 1999, 1999 European Control Conference (ECC).

[16]  Bradford F. Kimball,et al.  Sufficient Statistical Estimation Functions for the Parameters of the Distribution of Maximum Values , 1946 .

[17]  Sidney C. Port,et al.  Probability, Random Variables, and Stochastic Processes—Second Edition (Athanasios Papoulis) , 1986 .

[18]  K. Pearson.  Contributions to the Mathematical Theory of Evolution , 1894 .

[19]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[20]  J. Cardoso.  Infomax and maximum likelihood for blind source separation , 1997, IEEE Signal Processing Letters.

[21]  Eric Walter,et al.  Identification of Parametric Models: from Experimental Data , 1997 .

[22]  Luc Jaulin,et al.  Applied Interval Analysis , 2001, Springer London.

[23]  Didier Maquin,et al.  Sliding mode multiple observer for fault detection and isolation , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[24]  Dinh-Tuan Pham,et al.  Blind separation of instantaneous mixtures of nonstationary sources , 2001, IEEE Trans. Signal Process..

[25]  Ramon E. Moore.  Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.

[26]  H. Sira-Ramirez,et al.  On the output feedback control of a synchronous generator , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[27]  Akira Sano,et al.  Identification of a dynamical system with input nonlinearity , 1999 .

[28]  George K. Kokkinakis,et al.  Improving simultaneous speech recognition in real room environments using overdetermined blind source separation , 2001, INTERSPEECH.

[29]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[30]  Er-Wei Bai,et al.  Identification of linear systems with hard input nonlinearities of known structure , 2002, Autom..