Identification of stochastic linear systems in presence of input noise

Most identification methods rely on the assumption that the input is known exactly. However, when collecting data under an identification experiment it may not be possible to avoid noise when measuring the input signal. In the paper some different ways to identify systems from noisy data are discussed. Sufficient conditions for identifiability are given. Also accuracy properties and the computational requirements are discussed. A promising approach is to treat the measured input and output signals as outputs of a multivariable stochastic system. If a prediction error method is applied using this approach the system will be identifiable under mild conditions.

[1]  T. W. Anderson.  Estimation for Autoregressive Moving Average Models in the Time and Frequency Domains , 1977 .

[2]  J. Holmes.  System identification from noise-corrupted measurements , 1968 .

[3]  Torsten Soederstroem,et al.  Some methods for identification of linear systems with noisy input output data , 1979 .

[4]  P. Caines,et al.  Estimation, Identification and Feedback , 1976 .

[5]  Rolf Isermann,et al.  Two-Step Process Identification With Correlation Analysis and Least-Squares Parameter Estimation , 1974 .

[6]  K. Åström.  Introduction to Stochastic Control Theory , 1970 .

[7]  H. Akaike.  Maximum likelihood identification of Gaussian autoregressive moving average models , 1973 .

[8]  E. J. Hannan,et al.  The Estimation of Arma Models , 1975 .

[9]  M. Pagano.  Estimation of Models of Autoregressive Signal Plus White Noise , 1974 .

[10]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[11]  Rolf Isermann,et al.  Identifikation dynamischer Prozesse mittels Korrelation und Parameterschätzung , 1974 .

[12]  Jae S. Lim,et al.  Maximum likelihood parameter estimation of noisy data , 1979, ICASSP.

[13]  F. Smith,et al.  Monte Carlo evaluation of methods for pulse transfer function estimation , 1967 .

[14]  K. Åström,et al.  Numerical Identification of Linear Dynamic Systems from Normal Operating Records , 1966 .

[15]  M. Levin.  Estimation of a system pulse transfer function in the presence of noise , 1964 .

[16]  T. W. Anderson.  Estimation of Linear Functional Relationships: Approximate Distributions and Connections with Simultaneous Equations in Econometrics , 1976 .

[17]  H. Sakai,et al.  Recursive parameter estimation of an autoregressive process disturbed by white noise , 1979 .

[18]  R. Kashyap.  Maximum likelihood identification of stochastic linear systems , 1970 .

[19]  M. Aoki,et al.  On a priori error estimates of some identification methods , 1970 .

[20]  H. Akaike.  Canonical Correlation Analysis of Time Series and the Use of an Information Criterion , 1976 .

[21]  M. S. Ahmed,et al.  Autoregressive models in stochastic approximation algorithms for parameter estimation , 1979 .

[22]  George B. Kleindorfer,et al.  CONSISTENT ESTIMATES OF THE PARAMETERS OF A LINEAR SYSTEM. , 1969 .

[23]  R. Mehra.  Identification and estimation of the error-in-variables model (EVM) in structural form , 1976 .

[24]  Ü. Kotta,et al.  Structure and Parameter Estimation of Multivariable Systems Using Eigenvector Method , 1979 .

[25]  R. Mehra.  On-line identification of linear dynamic systems with applications to Kalman filtering , 1971 .

[26]  Petre Stoica,et al.  Comparison of some instrumental variable methods - Consistency and accuracy aspects , 1981, Autom..

[27]  O. Reiersøl.  Identifiability of a Linear Relation between Variables Which Are Subject to Error , 1950 .

[28]  P. Moran.  Estimating structural and functional relationships , 1971 .

[29]  R. K. Mehra,et al.  Identification of stochastic linear dynamic systems using Kalman filter representation , 1971 .

[30]  Cheng Hsiao,et al.  Identification for a Linear Dynamic Simultaneous Error-Shock Model , 1977 .

[31]  E. Hannan.  The identification of vector mixed autoregressive-moving average system , 1969 .

[32]  D. Humphreys,et al.  Identification of submerged vehicle dynamics through a generalized least squares method , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[33]  E. Hannan.  The estimation of mixed moving average autoregressive systems , 1969 .

[34]  Naresh N. Gupta.  System parameter determination via linear functional estimation , 1971 .

[35]  Lennart Ljung,et al.  Identification of processes in closed loop - identifiability and accuracy aspects , 1977, Autom..

[36]  Katsuhisa Furuta,et al.  Structural Identification and Software Package for Linear Multivariable Systems , 1979 .

[37]  Kenneth Steiglitz,et al.  On system identification from noise-obscured input and output measurements† , 1970 .

[38]  H. Akaike.  Markovian Representation of Stochastic Processes and Its Application to the Analysis of Autoregressive Moving Average Processes , 1974 .

[39]  R. Guidorzi.  Canonical structures in the identification of multivariable systems , 1975, Autom..

[40]  Lennart Ljung,et al.  On The Consistency of Prediction Error Identification Methods , 1976 .

[41]  K. Furuta,et al.  On the identification of time-invariant discrete processes , 1970 .

[42]  P. Sprent,et al.  A Generalized Least‐Squares Approach to Linear Functional Relationships , 1966 .