How to Make Bias and Variance Errors Insensitive to System and Model Complexity in Identification
2011 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 56, no 1, 100-112 p.Article in journal (Refereed) Published
Solutions to optimal input design problems for system identification are sometimes believed to be sensitive to the underlying assumptions. For example, a wide class of problems can be solved with sinusoidal inputs with the same number of excitation frequencies (over the frequency range (-pi, pi]) as the number of model parameters. The order of the true system is in many cases unknown and, hence, so is the required number of frequencies in the input. In this contribution we characterize when and how the input spectrum can be chosen so that the (asymptotic) variance error of a scalar function of the model parameters becomes independent of the order of the true system. A connection between these robust designs and the solutions of certain optimal input design problems is also made. Furthermore, we show that there are circumstances when using this type of input allows some model properties to be estimated consistently even when the model order is lower than the order of the true system. The results are derived under the assumptions of causal linear time invariant systems operating in open loop and excited by an input signal having a rational spectral factor with all poles and zeros strictly inside the unit circle.
Place, publisher, year, edition, pages
2011. Vol. 56, no 1, 100-112 p.
Asymptotic model accuracy, low-complexity models, optimal input design, robust input design, system identification
Research subject SRA - ICT
IdentifiersURN: urn:nbn:se:kth:diva-7544DOI: 10.1109/TAC.2010.2052294ISI: 000286108800008ScopusID: 2-s2.0-78651323084OAI: oai:DiVA.org:kth-7544DiVA: diva2:12600
Changed title from "Robustness issues in experiment design for system identification".
Updated from submitted to published. QC 201204112007-10-152007-10-152012-04-11Bibliographically approved