The Goodman algorithm: Difference between revisions
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The procedure is well described in [https://journals.ametsoc.org/view/journals/atot/23/7/jtech1889_1.xml | The procedure is well described in [https://journals.ametsoc.org/view/journals/atot/23/7/jtech1889_1.xml Goodman et al. 2006] | ||
<ref name="goodmanetal2006">{{Cite journal | |||
|authors= L. Goodman, E. Levine and R. Lueck | |||
|journal_or_publisher= J. Atmos. Oceanic Technol. | |||
|paper_or_booktitle= On measuring the terms of the turbulent kinetic energy budget from an AUV | |||
|year= 2006 | |||
|volume= 23 | |||
|pages= 977-990 | |||
|doi= 10.1175/JTECH1889.1 | |||
}}</ref>. | |||
Focusing on one specific direction, one specific shear probe, one can simply: | |||
- compute the coherence squared <math> | - compute the coherence squared <math>\Gamma^2(f)</math> between the observed velocity or shear frequency spectrum <math>E_{\mathrm{obs}}(f)</math> and the vibration frequency spectrum <math>E_{\mathrm{vib}}(f)</math>. | ||
- and remove | - and remove the vibration-coherent content of the shear spectrum using <math>E_{\mathrm{clean}}(f)=E_{\mathrm{obs}}(f)(1-\Gamma^2(f))</math> | ||
where <math> | where <math>E_{\mathrm{clean}}(f)</math> is the corrected shear frequency spectrum. Equation 3 in [https://journals.ametsoc.org/view/journals/atot/23/7/jtech1889_1.xml Goodman et al. 2006] presents the formalism for a correction using multiple directions (multivariate approach). The multivariate approach is more efficient and, almost a requirement for powered vehicles like AUVs. The number of vibration (or acceleration) signals used to correct the observed spectra of shear should be included in the quality control flag. | ||
To obtain statistical significance, it is recommended to compute the coherence/cross-spectra over 7 segments ( | To obtain statistical significance, it is recommended to compute the coherence/cross-spectra over 7 fft-segments. The vibration-coherent noise removal algorithm [[The_bias_induced_by_the_Goodman_algorithm| biases low]] the spectrum of shear in a frequency independent manner, and can be corrected using the number of vibration (or other types) of signals used to correct the measured shear spectra and the number of fit-segments used to estimate the shear spectrum. | ||
<ref name="luecketal2022">{{Cite journal | |||
|authors= R. G. Lueck, D. MacIntyre, and J. MacMillan | |||
|journal_or_publisher= J. Atmos. Oceanic Technol. | |||
|paper_or_booktitle= The bias in coherent noise removal | |||
|year= 2022 | |||
|doi=TBD | |||
}}</ref>. | |||
==References== | |||
<references /> | |||
---------------------------- | |||
return to [[Flow chart for shear probes]] | |||
[[Category:Shear probes]] | |||
Latest revision as of 15:46, 7 June 2024
The procedure is well described in Goodman et al. 2006 [1]. Focusing on one specific direction, one specific shear probe, one can simply:
- compute the coherence squared [math]\displaystyle{ \Gamma^2(f) }[/math] between the observed velocity or shear frequency spectrum [math]\displaystyle{ E_{\mathrm{obs}}(f) }[/math] and the vibration frequency spectrum [math]\displaystyle{ E_{\mathrm{vib}}(f) }[/math].
- and remove the vibration-coherent content of the shear spectrum using [math]\displaystyle{ E_{\mathrm{clean}}(f)=E_{\mathrm{obs}}(f)(1-\Gamma^2(f)) }[/math]
where [math]\displaystyle{ E_{\mathrm{clean}}(f) }[/math] is the corrected shear frequency spectrum. Equation 3 in Goodman et al. 2006 presents the formalism for a correction using multiple directions (multivariate approach). The multivariate approach is more efficient and, almost a requirement for powered vehicles like AUVs. The number of vibration (or acceleration) signals used to correct the observed spectra of shear should be included in the quality control flag.
To obtain statistical significance, it is recommended to compute the coherence/cross-spectra over 7 fft-segments. The vibration-coherent noise removal algorithm biases low the spectrum of shear in a frequency independent manner, and can be corrected using the number of vibration (or other types) of signals used to correct the measured shear spectra and the number of fit-segments used to estimate the shear spectrum. [2].
References
- ↑ L. Goodman and E. Levine and R. Lueck. 2006. On measuring the terms of the turbulent kinetic energy budget from an AUV. J. Atmos. Oceanic Technol.. doi:10.1175/JTECH1889.1
- ↑ R. G. Lueck, D. MacIntyre and and J. MacMillan. 2022. The bias in coherent noise removal. J. Atmos. Oceanic Technol.. doi:TBD
return to Flow chart for shear probes
