System Identification via Weighted Subspace Fitting

This paper presents a new method for the identification of linear systems parameterised by state space models. The method relies on the concept of subspace-fitting, in which the goal is to find a particular input/output data model parameterized by the state matrices that best fits, in the least-squares sense, the dominant subspace of the measured data. Central to this approach is the idea that a weighting may be applied to the observed dominant subspace in order to emphasize certain directions where the signal-to-noise ratio is highest. This has the advantage of making the algorithm robust to systems that are nearly unobservable, or to those whose state space has not been sufficiently excited. Some empirical results are included to validate the algorithm and illustrate its advantages over previous techniques. In addition to presenting the theory and implementation of the new method, this paper also illustrates some interesting connections between state space data models and those encountered in processing the signals received by an array of sensors.