A geometric approach to variance analysis in system identification: Linear Time-Invariant Systems

This paper addresses the problem of quantifying the model error ("variance-error") in estimates of linear time invariant systems. Building on the results in H. Hjalmarsson and J. Martensson (2007), we present an explicit method to construct an expression for the asymptotic variance of system properties such as impulse response coefficients, system gain, or the performance of some (control) application where the identified model is used. The expression is such that the individual impacts of model structure, model order and experimental conditions become visible. The technique is used to derive asymptotic variance expressions for a number of system properties.