Convergence of bias-eliminating least-squares algorithms for identification of dynamic errors-in-variables systems

The problem of dynamic errors-in-variable identification is studied in this paper. We investigate asymptotic convergence properties of the previous bias-eliminating algorithms. We first derive an error dynamic equation for the bias-eliminating parameter estimates. We then show that the asymptotic convergence of the bias-eliminating algorithms is basically determined by the eigenvalue of the largest magnitude of a system matrix in the estimation error dynamic equation. Moreover, the bias-eliminating algorithms possess desired convergence when all the eigenvalues of the system matrix in the estimation error dynamic equation fall strictly inside the unit circle. Given possible divergence of the iteration-type bias-eliminating algorithms under very low SNR (signalto-noise ratio) values at the system input and output, we re-formulate the bias-elimination problem as a minimization problem associated with a concentrated loss function and develop a variable projection algorithm to efficiently solve the resulting minimization problem. Finally, we illustrate and verify the theoretical results through stochastic simulations.