Why are errors-in-variables problems often tricky?

There are several identification methods designed for the errors-in-variables problem. In this paper we focus on discussing the underlying assumptions for several of these methods. Some assumptions are shown to have far reaching consequences. For example, if the noise-free input happens to be periodic, simple estimators that give consistent parameter estimates of the system parameters can easily be designed. If the variances of the input and output noises are unknown, some structural assumption must be added for the system dynamics to be identifiable. On the other hand, should the ratio between output noise variance and input noise variance be known, it is possible not only to estimate the system parameters consistently, but also to combine this with a reasonable estimate of the unperturbed input.

[1]  Fredrik Gustafsson,et al.  Time-domain identification of dynamic errors-in-variables systems using periodic excitation signals , 1999 .

[2]  Torsten Söderström,et al.  Why are errors-in-variables problems often tricky? , 2003, ECC.

[3]  Identifiability in dynamic errors-in-variables models , 1983 .

[4]  Torsten Söderström,et al.  Perspectives on errors-in-variables estimation for dynamic systems , 2002, Signal Process..

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

[6]  S. S. Wilks,et al.  Linear Regression Analysis of Economic Time Series. , 1938 .

[7]  T. Söderström,et al.  Study of a bias-free least squares parameter estimator , 1995 .

[8]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[9]  Wayne A. Fuller,et al.  Measurement Error Models , 1988 .

[10]  T. Söderström,et al.  Bias correction in least-squares identification , 1982 .

[11]  Torsten Söderström,et al.  Identification of stochastic linear systems in presence of input noise , 1981, Autom..

[12]  Gerd Vandersteen,et al.  Frequency-domain system identification using non-parametric noise models estimated from a small number of data sets , 1997, Autom..

[13]  Sabine Van Huffel,et al.  Recent advances in total least squares techniques and errors-in-variables modeling , 1997 .

[14]  Sabine Van Huffel,et al.  Comparison of total least squares and instrumental variable methods for parameter estimation of transfer function models , 1989 .

[15]  W. Zheng.  On least‐squares identification of stochastic linear systems with noisy input–output data , 1999 .