Robust dolphin whistle fundamental frequency tracking via nonlinear least square and segmented adaptive Gaussian process regression

Dolphin whistles represent a primary mode of social communication, characterized by complex frequency modulations. Accurate estimation and tracking of whistle fundamental frequency ( f0) are crucial for understanding dolphin behavior and social interactions. Nevertheless, passive acoustic monitoring (PAM) of dolphins is compromised by marine ambient noise, which degrades f0 tracking accuracy and reduces PAM system effectiveness. To address these challenges, a three-stage approach for dolphin whistle f0 tracking, refered to as enhanced segmented adaptive Gaussian process regression, is proposed. First, a whistle enhancement algorithm based on improved local mean decomposition, effectively suppressing background noise interference, is proposed. Second, a framewise frequency estimation method using a nonlinear least squares (NLS) estimator, accelerated through Toeplitz-plus-Hankel matrix formulation for rapid computation, is developoed. Finally, segmented adaptive Gaussian process regression with Matérn Kernel (ν=3/2) approach to efficiently track the NLS-estimated frequency points is proposed. This method demonstrates suppressing measurement noise while restoring missing whistle f0 points. By leveraging the finite differentiability of the Matérn-3/2 kernel, this method achieves an optimal equilibrium between preserving local trajectory fidelity and maintaining global trend characteristics. Experimental validation using whistle signals from two Tursiops aduncus demonstrates that our proposed f0 tracking method achieves superior accuracy under different signal-to-noise ratios compared to existing approaches.