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VARIANCE ASPECTS OF L2-MODEL REDUCTION WHEN UNDERMODELING – THE OUTPUT ERROR CASE
Fredrik Tjärnström
Department of Electrical Engineering,
Linköpings universitet, SE-581 83 Linköping, Sweden.
Email: fredrikt@isy.liu.se
In this contribution, variance properties of L2 model reduction are studied. That is, given an estimated model of high order we study the resulting variance of an L2 reduced approximation. The main result of the paper is showing that estimating a low order output error (OE) model via L2 model reduction of a high order model gives a smaller variance compared to estimating a low order model directly from data in the case of undermodeling. This has previously been shown to hold for FIR (Finite Impulse Response) models, but is in this paper extended to general linear OE models.
Keywords: System identification, Model reduction, Modeling errors, Covariance, System order reduction, Output error identification
Session slot T-Fr-M01: Bias / Variance Issues in Identification/Area code 3a : Modelling, Identification and Signal Processing
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