On least-squares identification of stochastic linear systems with noisy input-output data

In a recent paper, two least-squares (LS) based methods, which do not invol ve prefiltering of noisy measurements or parameter extraction, are establis hed for unbiased identification of linear noisy input-output systems. This paper introduces more computationally efficient estimation schemes for the measurement noise variances and develops a new version of two LS based algo rithms in combination with the bias correction technique. The proposed two algorithms work directly with the underlying noisy system, thereby being su bstantially different from the previous methods that need to actually ident ify an augmented system. It is shown that a significant saving in the compu tational cost can be achieved by this better way of implementation of the t wo LS-based algorithms while at almost no sacrifice of the parameter estima tion accuracy. The performance of the proposed two identification algorithm s and comparisons with their predecessors are substantiated using simulatio n data. Copyright (C) 1999 John Wiley & Sons, Ltd.