FIR Systems Identification Under Quantized Output Observations and a Large Class of Persistently Exciting Quantized Inputs

HE Yanyu,GUO Jin

Journal of Systems Science & Complexity ›› 2017, Vol. 30 ›› Issue (5) : 1061-1071.

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PDF(316 KB)
Journal of Systems Science & Complexity ›› 2017, Vol. 30 ›› Issue (5) : 1061-1071. DOI: 10.1007/s11424-017-5305-7

FIR Systems Identification Under Quantized Output Observations and a Large Class of Persistently Exciting Quantized Inputs

  • HE Yanyu1 , GUO Jin2
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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 Cram´er-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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HE Yanyu , GUO Jin. FIR Systems Identification Under Quantized Output Observations and a Large Class of Persistently Exciting Quantized Inputs. Journal of Systems Science and Complexity, 2017, 30(5): 1061-1071 https://doi.org/10.1007/s11424-017-5305-7
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