Robust identification of systems with both bias and variance disturbances
The authors present some bounds on the estimation errors for transfer function estimates of discrete-time SISO systems with both random and deterministic disturbances. The random disturbance referred to as ``variance disturbance'' is a martingale difference sequence while the bounded deterministic sequence is called ``bias disturbance''. The system input is an adapted ARMA process. The main result of the note states that the bias disturbance does not upset the \(L^ \infty\) strong consistency of the identification algorithm based on the least-square estimation of discrete transfer function coefficients. Moreover, the authors adopt an input normal realization truncation for model reduction and give bounds on the approximation error for the reduced order transfer function. The estimated transfer function is strongly consistent under some mild conditions on the decaying rate of its coefficients.
scientific article; zbMATH DE number 713517