Convergence properties of bias-eliminating algorithms for errors-in-variables identification

This paper considers the problem of dynamic errors-in-variables identification. Convergence properties of the previously proposed bias-eliminating algorithms are investigated. An error dynamic equation for the bias-eliminating parameter estimates is derived. It is shown that the convergence of the bias-eliminating algorithms is basically determined by the eigenvalue of largest magnitude of a system matrix in the estimation error dynamic equation. When this system matrix has all its eigenvalues well inside the unit circle, the bias-eliminating algorithms can converge fast. In order to avoid possible divergence of the iteration-type bias-eliminating algorithms in the case of high noise, the bias-eliminating problem is re-formulated as a minimization problem associated with a concentrated loss function. A variable projection algorithm is proposed to efficiently solve the resulting minimization problem. A numerical simulation study is conducted to demonstrate the theoretical analysis.