Research on Underwater Sound Source Localization Based on NLM-EEMD and FCM-Generalized Quadratic Correlation

Table 1

Common weighting functions and their characteristics.

Name	Weighting function	Basic features
ROTH		It is equivalent to Wiener filtering, which can effectively suppress areas with high noise power and error-prone signal estimation (i.e., areas with low signal-to-noise ratio) but will expand the peak of the cross-correlation function.
SCOT		It is an improvement on ROTH weighting, considering the effects of both channels, but when , SCOT is equivalent to ROTH, so it will also expand the peak of the cross-correlation function.
PHAT		It is equivalent to whitening filtering, which has a better effect on large signal-to-noise ratios and is suitable for broadband signals. However, when , the correlation function is not a function; in addition, it is weighted by . When the signal energy is small, the denominator approaches 0, thereby increasing the error. It can be improved by adding a fixed constant to the denominator.
Maximum likelihood weighting (ML)		is the modulo-squared coherence function, defined as ; the maximum likelihood weighting function gives a large weight to the frequency band with a large signal-to-noise ratio and a small weight to the frequency band of a small signal-to-noise ratio. In this way, the influence of noise can be better suppressed, and it is the optimal filter in the statistical sense.
HB weighted		It has a suppressing effect on the periodic components in the signal, and the effect is similar to that of direct cross-correlation at low signal-to-noise ratio.
WP weighted		When there are obvious periodic components in the signal, it fails; when the signal-to-noise ratio is low, the performance is not as good as PHAT.