Recursive prediction error parameter estimator for non-linear models

Abstract A recursive prediction error parameter estimation algorithm is derived for systems which can be represented by the NARMAX (non-linear ARMAX) model. A convergence analysis is presented using the differential equation approach, and the new concept of m-invertibility is introduced. The analysis shows that while a highly non-linear process model may be used to capture the non-linearity of the system it is advisable to fit a simple noise model. The results of applying the algorithm to both simulated and real data are included.

[1]  Torsten Söderström.  An On-line Algorithm for Approximate Maximum Likelihood Identificatioin of Linear Dynamic Systems , 1973 .

[2]  J. Gertler,et al.  A recursive (on-line) maximum likelihood identification method , 1974 .

[3]  Lennart Ljung,et al.  On Recursive Prediction Error Identification Algorithms , 1978 .

[4]  C. Granger,et al.  On the invertibility of time series models , 1978 .

[5]  V. Solo.  The convergence of AML , 1979 .

[6]  Eduardo Sontag.  Polynomial Response Maps , 1979 .

[7]  I. J. Leontaritis,et al.  Parameter Estimation Techniques for Nonlinear Systems , 1982 .

[8]  Barry G. Quinn,et al.  Stationarity and invertibility of simple bilinear models , 1982 .

[9]  Lennart Ljung,et al.  Theory and Practice of Recursive Identification , 1983 .

[10]  T. Rao,et al.  An Introduction to Bispectral Analysis and Bilinear Time Series Models , 1984 .

[11]  S. Billings,et al.  Least squares parameter estimation algorithms for non-linear systems , 1984 .

[12]  P. Kumar,et al.  Theory and practice of recursive identification , 1985, IEEE Transactions on Automatic Control.

[13]  S. Billings,et al.  The Practical Identification of Systems with Nonlinearities , 1985 .

[14]  Peter Jones,et al.  Signal processing for control , 1986 .

[15]  L. Ljung,et al.  Recursive identification of bilinear systems , 1987 .

[16]  M. Korenberg,et al.  The nonlinear identification of a heat exchanger , 1987, 26th IEEE Conference on Decision and Control.

[17]  S. A. Billings,et al.  Identification of a non-linear difference equation model of an industrial diesel generator , 1988 .

[18]  Sheng Chen,et al.  Identification of non-linear output-affine systems using an orthogonal least-squares algorithm , 1988 .

[19]  Sheng Chen,et al.  Prediction-error estimation algorithm for non-linear output-affine systems , 1988 .

[20]  Sheng Chen,et al.  Identification of non-linear rational systems using a prediction-error estimation algorithm , 1989 .

[21]  S. A. Billings,et al.  The identification of linear and non-linear models of a turbocharged automotive diesel engine , 1989 .