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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.

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Authors and Affiliations

  1. Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Yanyu He

  2. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Jin Guo

Authors
  1. Yanyu He
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  2. Jin Guo
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Corresponding author

Correspondence to Jin Guo.

Additional information

This paper was supported in part by the National Natural Science Foundation of China under Grant Nos. 61174042 and 61403027, in part by the National Key Research and Development Program of China (2016YFB0901902), and in part by the Open Research Project under Grant No. 20160105 from SKLMCCS.

This paper was recommended for publication by Editor XIE Lihua.

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He, Y., Guo, J. FIR systems identification under quantized output observations and a large class of persistently exciting quantized inputs. J Syst Sci Complex 30, 1061–1071 (2017). https://doi.org/10.1007/s11424-017-5305-7

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  • DOI: https://doi.org/10.1007/s11424-017-5305-7

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