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 involve prefiltering of noisy measurements or parameter extraction, are established 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 algorithms in combination with the bias correction technique. The proposed two algorithms work directly with the underlying noisy system, thereby being substantially different from the previous methods that need to actually identify an augmented system. It is shown that a significant saving in the computational cost can be achieved by this better way of implementation of the two LS-based algorithms while at almost no sacrifice of the parameter estimation accuracy. The performance of the proposed two identification algorithms and comparisons with their predecessors are substantiated using simulation data.