An output error identification method of projected gradient search is proposed for the parameter estimation
of linear time-invariant(LTI) state-space models. The system parameters are estimated by optimizing an output-error
cost function. The nonuniqueness of the fully parameterized state-space system is resolved by restricting the update of
the parameters to the tangent space to the manifold of observationally equivalent state-space systems. In addition, the
regularization parameter is adaptively determined by considering the local linear approximation of the output error. Moreover,
the relation between the computational load and system properties such as the observability and controllability is also
discussed in detail. Finally, simulation results show the effectiveness of the proposed method.