Time-domain identification using ARMARKOV/Toeplitz models with quasi-Newton update

Recursive identification methods using time-domain data were previously developed by the authors (1997) utilizing a gradient-based identification technique for estimating the Markov parameters of a system. This identification technique utilizes the ARMARKOV representation of a time-invariant finite-dimensional system which relates the current output of a system to past outputs as well as current and past inputs. While the ARMARKOV representation has the same form as an ARMA representation, the ARMARKOV representation explicitly contains Markov parameters of the system. In this paper, we introduce a quasi-Newton method that utilizes a more efficient quasi-Newton update direction to estimate the Markov parameters recursively from time-domain input-output data. The step size is given by an explicit expression analogous to the optimal step size derived for the gradient method