Explicit expression of the parameter bias in identification of Laguerre models from step responses

Abstract This paper delivers an analysis of the least-squares estimation of the Laguerre coefficients of a linear discrete-time system from step response data. The original contribution consists in an explicit formula for the bias error on the estimated coefficients due to the under-modelling of the system. The formula, jointly with some a-priori information on the neglected dynamics, can be used to construct bounds on this error. The results presented in this paper are illustrated with a simulation example.