The variations of non-parametric estimates in closed-loop

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    It is known that non-parametric transfer function estimates in closed-loop often have infinite variance. We characterise the probability density function of such estimates under the assumption that the corresponding closed-loop system estimate has complex normal distribution in the frequency domain. The probability density function can be described as a horseshoe encircling the inverse of the controller, with a global maximum on the line between the true value and the inverse of the controller. The expected value of the absolute value of such estimates is finite, and we propose it as a measure of variation. We also derive and discuss new expressions for the variance when an exclusion zone is introduced around the singularity. © 2003 Elsevier Ltd. All rights reserved.
    Original languageEnglish
    Pages (from-to)1849-1863
    Number of pages14
    Issue number11
    Publication statusPublished - Nov 2003


    • Closed-loop identification
    • Empirical transfer function estimate
    • Frequency response
    • Non-parametric identification
    • Spectral estimation


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