Variance analysis of linear SIMO models with spatially correlated noise. (March 2017)

• Record Type: Journal Article
• Authors: Everitt, Niklas; Bottegal, Giulio; Rojas, Cristian R.; Hjalmarsson, Håkan
• Is Part Of: Automatica. Volume 77(2017)
• Page Start: 68
• Page End: 81
• Publication Date: 2017-03
• Subjects: System identification -- Asymptotic variance -- Linear SIMO models -- Least-squares; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2016.11.017
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: In this paper we address the identification of linear time-invariant single-input multi-output (SIMO) systems. In particular, we assess the performance of the prediction error method by quantifying the variance of the parameter estimates. Using an orthonormal representation for the modules composing the SIMO structure, we show that the parameter estimate of a module depends on the model structure of the other modules, and on the correlation structure of the output disturbances. We provide novel results which quantify the variance-error of the parameter estimates for finite model orders, where the effects of noise correlation structure, model structure and input spectrum are visible. In particular, we show that a sensor does not increase the accuracy of a module if common dynamics have to be estimated. When a module is identified using less parameters than the other modules, we derive the noise correlation structure that gives the minimum total variance. The implications of our results are illustrated through numerical examples and simulations.