The Goodman algorithm
The procedure is well described in Goodman2006.
Focusing on one specific direction, one can simply:
- compute the coherence squared [math]\displaystyle{ Coh(f) }[/math] between the observed velocity or shear frequency spectrum [math]\displaystyle{ E_{obs}(f) }[/math] and the vibration frequency spectrum [math]\displaystyle{ E_{vib}(f) }[/math].
- and remove it from [math]\displaystyle{ E_{obs}(f) }[/math] using [math]\displaystyle{ E_{clean}(f)=E_{obs}(f)(1-Coh(f)) }[/math]
where [math]\displaystyle{ E_{clean}(f) }[/math] is the corrected velocity 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 directions used to correct the observed signal should be included in the quality control flag.
To obtain statistical significance, it is recommended to compute the coherence/cross-spectra over 7 segments (see section 8.2).
