Quadratically constrained least squares identification

We investigate the consistency of parameter estimates obtained from least squares identification with a quadratic parameter constraint. For generality, we consider infinite impulse response systems with arbitrarily colored output noise. In the case of finite data, we show that there always exists a generally indefinite quadratic constraint that yields the true parameters of the system when a persistency condition is satisfied. When the autocorrelation matrix of the output noise is known to within a scalar multiple, we show that the QCLS estimator is consistent. Furthermore, we develop a heuristic iterative method for applying QCLS identification when the noise statistics are unknown. Finally, we give an example comparing this method to standard least squares identification, as well as an instrumental variable technique