Unbiased identification of linear stochastic systems from closed loop data

Substantial revisions on the newly proposed bias correction based method are made in the framework of indirect identification of a linear (possibly unstable) plant operating in closed loop with a low-order stabilizing controller. By making a new formulation of a least-squares estimate of an intermediate parameter vector purposely introduced, the modified algorithm is able to achieve a direct yet unbiased closed-loop system estimate in the presence of misspecified noise model. With no prefiltering of the measured data and no identification of an high-order augmented closed-loop system, the computational complexity of the algorithm is significantly reduced. Simulations of identifying an open-loop unstable plant illustrate the promising performance of the modified algorithm in low signal-to-noise ratio environments.