I found that the submarine noise is mainly related to the central frequency but I cannot figure out a clear definition for the central frequency.
Again I would suggest you to go back to your sources, as your question is unclear... (I guess you don't have a degree in acoustics)
To set the scene, the underwater noise of a submarine vessel is commonly expressed in third octave band analysis, each of them with a central frequency associated with the averaged noise energy in the band, expressed in "equivalent sound level" (Pa/square root of Hz x bandwidth, in a dB scale commonly referenced to 1microPa, but it is to be checked as it is not an universal reference as is for airborne acoustics the 2E-5Pa reference). The ship signature is generally normalized at a distance of 1m, assuming a monopole radiation in an infinite medium (no surface or seafloor reflection), allowing to consider a sound pressure decay invert to the actual distance (1/r propagation attenuation). These mentions should appear in the scales of the acoustic signature graphs.
I guess it is from this that your source refers to "central frequencies"
You can do the same with any other bandpass (1 octave, 1/10 of octave...) again allocating the noise level to the central frequency of the band.
(Because all these are logarithmic frequency bands, the central frequency is not the mid frequency between the lower and higher frequency of the analysis band).
The use of 1/3 octave analysis is only relevant if there are no dominant tones in the signature (which is the case for a well designed and well maintained low signature vessel)
In air spectral analysis of subjectve «brightness» or «darkness» a term «spectral centeroid» is used. I do not know if it is relevant for submarine sounds, but it is one of the used psychoacoustic terms in listening experiments.
https://en.wikipedia.org/wiki/Spectral_centroid
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