Time-Domain Identification Using ARMARKOV/Toeplitz Models With Quasi-Newton Update

Recursive identification methods using time-domain data have been developed in [l, 21 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. Appropriate "stacking" of time-delayed ARMARKOV representations yields a block-Toeplitz weight matrix which contains Markov parameters and which maps a vector of past outputs and inputs to a vector of current and past outputs. The recursive update law given in El] is based upon a gradient that preserves the block-zero structure of the block-Toeplitz weight matrix. In the presence of a persistent input sequence, this gradient method guarantees that the estimated weight matrix converges to the actual weight matrix. 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.