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 | <ref name="goodmanetal2006">{{Cite journal | ||
|authors= L. Goodman, E. Levine and R. Lueck | |authors= L. Goodman, E. Levine and R. Lueck | ||
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|pages= 977-990 | |pages= 977-990 | ||
|doi= 10.1175/JTECH1889.1 | |doi= 10.1175/JTECH1889.1 | ||
}}</ref> | }}</ref>. | ||
Focusing on one specific direction, one specific shear probe, one can simply: | Focusing on one specific direction, one specific shear probe, one can simply: | ||
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- 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> | - 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>E_{\mathrm{clean}}(f)</math> is the corrected shear frequency spectrum. Equation 3 in | 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 fft-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. | ||
The vibration-coherent noise removal algorithm biases low the spectrum of shear in a frequency independent manner | |||
<ref name="luecketal2022">{{Cite journal | <ref name="luecketal2022">{{Cite journal | ||
|authors= R. G. Lueck, D. MacIntyre, and J. MacMillan | |authors= R. G. Lueck, D. MacIntyre, and J. MacMillan | ||
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|paper_or_booktitle= The bias in coherent noise removal | |paper_or_booktitle= The bias in coherent noise removal | ||
|year= 2022 | |year= 2022 | ||
|doi=TBD | |||
}}</ref>. | }}</ref>. | ||
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return to [[Flow chart for shear probes]] | 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
- and remove the vibration-coherent content of the shear spectrum using
where
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
