On the equivalence of time and frequency domain maximum likelihood estimation

Agüero, Juan C.; Yuz, Juan I.; Goodwin, Graham C.; Delgado, Ramón A.

doi:10.1016/j.automatica.2009.10.038

Cited by 58 publications

(31 citation statements)

References 31 publications

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“…In these expressions, O(x) stands for ordo(x): a function that goes to zero at least as fast as x. It is most important for the rest of this paper to understand that (4) is an exact relation [16], [17], [18], [19] that is valid for both discrete and continuous time systems. The finite record length requires the use of a transient term in (2), and it turns out that the leakage errors of the DFT are modelled by very similar terms in the frequency domain.…”

Section: A Set-upmentioning

confidence: 99%

“…All contributions up to degree R in (19) are covered by the polynomial model of degree R and hence do not contribute to the error E F . The first term that contributes to the error E F is the term of degree R + 2 in F e (∆) (19), keeping in mind the discussion in the first part of this section on even and odd contributions.…”

Section: B Normalised Second Order Systemmentioning

confidence: 99%

“…The first term that contributes to the error E F is the term of degree R + 2 in F e (∆) (19), keeping in mind the discussion in the first part of this section on even and odd contributions. In the matrix products in (27), sums like…”

Section: B Normalised Second Order Systemmentioning

confidence: 99%

“…The deviations are due to the fact that higher order terms should be included in (20) for larger values of B LP M /B 3dB . Since the terms in the Taylor series in (19) have alternating signs, the next term that should be included will lower the theoretical error which explains the too conservative estimate for higher values of B LP M /B 3dB . For values close to 1 the Taylor series is no longer converging.…”

Section: A Study Of the Normalised Problemmentioning

confidence: 99%

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Bounding the Polynomial Approximation Errors of Frequency Response Functions

Schoukens

Vandersteen

Pintelon

et al. 2013

IEEE Trans. Instrum. Meas.

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Abstract-Frequency response function (FRF) measurements take a central place in the instrumentation and measurement field because many measurement problems boil down to the characterisation of a linear dynamic behaviour. The major problems to be faced are leakage-and noise errors. The local polynomial method (LPM) was recently presented as a superior method to reduce the leakage errors with several orders of magnitude while the noise sensitivity remained the same as that of the classical windowing methods. The kernel idea of the LPM is a local polynomial approximation of the FRF and the leakage errors in a small frequency band around the frequency where the FRF is estimated. Polynomial approximation of FRF's is also present in other measurement and design problems. For that reason it is important to have a good understanding of the factors that influence the polynomial approximation errors. This article presents a full analysis of this problem, and delivers a rule of thumb that can be easily applied in practice to deliver an upper bound on the approximation error of FRF's. It is shown that the approximation error for lowly damped systems is bounded by (BLP M /B 3dB ) R+2 with BLP M the local bandwidth of the LPM, R the degree of the local polynomial that is selected to be even (user choices), and B 3dB the 3 dB bandwidth of the resonance, which is a system property.

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Section: A Set-upmentioning

confidence: 99%

Section: B Normalised Second Order Systemmentioning

confidence: 99%

Section: B Normalised Second Order Systemmentioning

confidence: 99%

Section: A Study Of the Normalised Problemmentioning

confidence: 99%

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Bounding the Polynomial Approximation Errors of Frequency Response Functions

Schoukens

Vandersteen

Pintelon

et al. 2013

IEEE Trans. Instrum. Meas.

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“…It is most important for the rest of this paper to understand that (3) is an exact relation [4], [21]- [23]. The notation O(N −α ), called "ordo," stands for a variable that goes to zero at least as fast as N −α .…”

Section: V(t) = H(q)e(t)mentioning

confidence: 99%

Estimation of the FRF Through the Improved Local Bandwidth Selection in the Local Polynomial Method

Thummala

Schoukens

2012

IEEE Trans. Instrum. Meas.

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Abstract-This paper presents a nonparametric method to measure an improved frequency response function (FRF) of a linear dynamic system excited by a random input. Recently, the local polynomial method (LPM) has been proposed as a technique to reduce the leakage errors on FRF measurements. The noise sensitivity of the LPM was similar to that of the classical windowing methods, while the leakage rejection is improved from an O(N −1 ) to an O(N −3 ). This paper shows a methodology, to automatically tune the parameter of the LPM, viz., the local bandwidth that sets how many neighboring frequency lines are combined in a single-point estimate, to get lower noise sensitivity by increasing the smoothening of the original LPM, without any user interaction. The balance between noise reduction and bias error will be automatically retrieved.

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2012

System Identification

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On the equivalence of time and frequency domain maximum likelihood estimation

Cited by 58 publications

References 31 publications

Bounding the Polynomial Approximation Errors of Frequency Response Functions

Bounding the Polynomial Approximation Errors of Frequency Response Functions

Estimation of the FRF Through the Improved Local Bandwidth Selection in the Local Polynomial Method

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