Convergence analysis of an adaptive algorithm for identifying errors-in-variables systems

Dynamic errors-in-variables (EIV) systems, in which both the output and the input variables are corrupted by noises, are widely used in signal processing, communications, and control engineering. Although a number of different methods for identifying dynamic EIV systems have been proposed, the theoretical analysis of their properties has always been a difficult problem. This paper presents the convergence analysis of an adaptive EIV identification algorithm with no input restrictions. The methods of analysis currently available in literature often assume the input signals to be AR or ARMA process and persistent excitation. This restriction is removed for attenuating excitation in this paper. The convergence rate is derived and it is shown that the adaptive estimation can converge fast to the true system parameters values. Numerical simulations is conducted to demonstrate the theoretical analysis.