This paper presents a stochastic description and evaluation of the ocean acoustics signal for the interpretation of the signal in the frequency domain in order to estimate the modal frequency and dispersion curves of the ocean acoustics signal. Thus, this investigation considered the analysis and simulation of an ocean acoustics time-series in the frequency-domain where the signal in the time-domain was corrupted by white Gaussian noise. With a stochastic property of the measured acoustics signal, we derived the accurate posterior probability distribution of the ocean acoustics modal frequencies and then incorporated a mathematical model of the signal propagating in a dispersive media to obtain a likelihood function for a sequential Bayesian filtering framework that is used for modal frequency and dispersion estimation. Sequential Bayesian filtering, a particle filter in particular, is implemented for frequency and dispersion estimation to test the accuracy of the derived model. Demonstrated via simulation results, the proposed method performs excellent estimation as compared to the conventional MAP estimator especially at high noise level. Finally, evaluated by the Monte Carlo root mean squared errors (MCRMSE), the proposed stochastic model offers excellent tracking results with smaller errors than those provided by the existing methods even in low signal-to-noise ratios (SNRs), illustrating the noise robustness and superiority of the proposed model over the other approaches.

本文对海洋声学信号进行了随机描述和评估，以便在频域中解释该信号，以便估算海洋声学信号的模态频率和色散曲线。因此，本研究考虑了在频域中海洋声学时间序列的分析和仿真，其中时域中的信号被白高斯噪声破坏。利用所测得的声学信号的随机特性，我们得出了海洋声学模态频率的精确后验概率分布，然后合并了在分散介质中传播的信号的数学模型，从而获得了顺序贝叶斯滤波框架的似然函数，即用于模态频率和色散估计。进行顺序贝叶斯滤波，尤其是粒子滤波，以进行频率和频散估计，以测试导出模型的准确性。通过仿真结果表明，与传统的MAP估计器相比，所提出的方法具有出色的估计效果，尤其是在高噪声水平下。最后，通过蒙特卡洛均方根误差（MCRMSE）评估，所提出的随机模型即使在低信噪比（SNR）的情况下，也具有比现有方法所提供的误差小的跟踪结果，且误差较小，从而说明了噪声的鲁棒性以及所提出的模型优于其他方法的优势。与传统的MAP估计器相比，所提出的方法执行效果极佳，尤其是在高噪声水平下。最后，通过蒙特卡洛均方根误差（MCRMSE）评估，所提出的随机模型即使在低信噪比（SNR）的情况下，也具有比现有方法所提供的误差小的跟踪结果，且误差较小，从而说明了噪声的鲁棒性以及所提出的模型优于其他方法的优势。与传统的MAP估计器相比，所提出的方法执行效果极佳，尤其是在高噪声水平下。最后，通过蒙特卡洛均方根误差（MCRMSE）评估，所提出的随机模型即使在低信噪比（SNR）的情况下，也具有比现有方法所提供的误差小的跟踪结果，且误差较小，从而说明了噪声的鲁棒性以及所提出的模型优于其他方法的优势。