Inferring Multivariable Delay and Seasonal Structure for Subspace Modeling

Abstract ARX models are used for modeling the multivariable delay structure of a system. A fast order-recursive algorithm is used for factorization of a generalized inverse of a covariance matrix that may be highly illconditioned or singular. The Akaike information criterion (AIC) and generalized likelihood ratio (GLR) tests are used to decide on the most likely multivariable delay structure. Additional synthetic inputs to the system can then be defined if necessary as delayed versions of the system inputs and outputs. Subspace methods such as canonical variate analysis (CVA) are used to identify a state space model. As a result, the state order and total number of estimated parameters of the identified system can be considerably decreased giving reduced parameter estimation and prediction errors.