  In identification of dynamical systems, the prediction error method using a
quadratic cost function provides asymptotically efficient estimates under
Gaussian noise and additional mild assumptions, but in general it requires
solving a non-convex optimization problem. An alternative class of methods uses
a non-parametric model as intermediate step to obtain the model of interest.
Weighted null-space fitting (WNSF) belongs to this class. It is a weighted
least-squares method consisting of three steps. In the first step, a high-order
ARX model is estimated. In a second least-squares step, this high-order
estimate is reduced to a parametric estimate. In the third step, weighted least
squares is used to reduce the variance of the estimates. The method is flexible
in parametrization and suitable for both open- and closed-loop data. In this
paper, we show that WNSF provides estimates with the same asymptotic properties
as PEM with a quadratic cost function when the model orders are chosen
according to the true system. Also, simulation studies indicate that WNSF may
be competitive with state-of-the-art methods.
