The asymptotic variance of the PBSIDopt algorithm

Abstract

It is well-known that system identification is a valuable technique to obtain compact models for controller design and prediction. Subspace identification methods are of interest since they solely rely on tools from linear algebra and their ability to directly work with data generated by systems with multiple inputs and outputs. With respect to other methods (e.g. Prediction Error (PE)), subspace methods do not have straightforward asymptotic variance expressions. However, recently some papers appeared with asymptotic variance expressions for a certain class of identification algorithms that merge ideas from PE and subspace methods. In this paper we derive the asymptotic variance expression for the PBSIDopt algorithm and derive manageable expressions under some reasonable assumptions. We conclude the paper with two simulation examples where we show the strength of the proposed method.