The Goodman algorithm
The procedure is well described in Goodman2006[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 Goodman2006 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. The cleaned spectra must be boosted by dividing it by [math]\displaystyle{ 1 - N_V/N_f }[/math] where [math]\displaystyle{ N_V }[/math] is the number of vibration (or other types) of signals used to correct the measured shear spectra and [math]\displaystyle{ N_f }[/math] is the number of fit-segments used to estimate the shear spectrum [2].
References
- ↑ Goodman, L., Levine, E. R., & Lueck, R. G. (2006). On measuring the terms of the turbulent kinetic energy budget from an AUV. Journal of Atmospheric and Oceanic Technology, 23(7), 977-990.
- ↑ Lueck, R. G., D. MacIntyre, and J. MacMillan (2022). The bias in coherent noise removal. Journal of Atmospheric and Oceanic Technology, submitted
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