Journal of Systems Science and Complexity

, Volume 30, Issue 5, pp 1061–1071 | Cite as

FIR systems identification under quantized output observations and a large class of persistently exciting quantized inputs

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Abstract

This paper investigates the FIR systems identification with quantized output observations and a large class of quantized inputs. The limit inferior of the regressors’ frequencies of occurrences is employed to characterize the input’s persistent excitation, under which the strong convergence and the convergence rate of the two-step estimation algorithm are given. As for the asymptotical efficiency, with a suitable selection of the weighting matrix in the algorithm, even though the limit of the product of the Cramér-Rao (CR) lower bound and the data length does not exist as the data length goes to infinity, the estimates still can be asymptotically efficient in the sense of CR lower bound. A numerical example is given to demonstrate the effectiveness and the asymptotic efficiency of the algorithm.

Keywords

Asymptotic efficiency FIR system identification quantized input quantized output observations 
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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  2. 2.School of Automation and Electrical EngineeringUniversity of Science and Technology BeijingBeijingChina

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