On two methods for identifying dynamic errors-in-variables systems

Identification of dynamic errors-in-variables systems, where both inputs and outputs are affected by errors (measurement noises), is a fundamental problem of great interest in many areas, such as process control, econometrics, astronomical data reduction, image processing, etc. This field has received increased attention within several decades. Many solutions have been proposed with different approaches. In this thesis, the focus is on some specific problems concerning two time domain methods for identifying linear dynamic errors-in-variables systems. The thesis is divided into four parts. In the first part, a general introduction to the problem of identifying errors-in-variables systems and different approaches to solve the problem are given. Also, a summary of the contributions and some topics for future works are presented. The second part of the thesis considers the instrumental variables based approaches. They are studied under the periodic excitation condition. The main motivation is to analyze what type of instrumental variables should be chosen to maximally utilize the information of the periodic measurements. A particular overdetermined instrumental variable estimator is proposed, which can achieve optimal performance without weighting. The asymptotic convergence properties of the Bias-eliminating least squares (BELS) methods are investigated in the third part. By deriving an error dynamics equation for the parameter estimates, it is shown that the convergence of the bias-eliminating algorithms is determined by the largest magnitude of the eigenvalues of the system matrix. To overcome the possible divergence of the iteration-type bias-eliminating algorithms under very low signal-to-noise ratio, we reformulate the bias-elimination problem as a minimization problem and develop a variable projection algorithm to perform consistent parameter estimation. Part four contains an analysis of the accuracy properties of the BELS estimates. It is shown that the estimated system parameters and the estimated noise variances are asymptotically Gaussian distributed. An explicit expression for the normalized asymptotic covariance matrix of the estimated system parameters and the estimated noise variances is derived