Dynamic Three-dimensional Ocean Sound Speed Field Reconstruction Using Bayesian Streaming Sparse Tensor Decomposition

Reconstructing a three-dimensional (3D) ocean sound speed field (SSF) from sparse and noisy measurements is crucial for various applications in ocean acoustics, including acoustic communication and target localization. Principles of classical SSF reconstruction algorithms (e.g., linear interpolation and geostatistical methods) are similar to those of machine learning theory, such as linear and Gaussian process regression. They can be uniformly regarded as supervised regression models, which learn the mapping from the geographical locations to the sound speed output. From a unified machine learning perspective, these supervised regression- based reconstruction approaches exhibit several limitations. They are sensitive to noise and incur high computational costs, requiring complete SSF reconstruction when updating partial sound speed data. Thus, online Bayesian learning is feasible to update the SSF. When a new batch of data is observed, dynamic SSF reconstruction occurs without requiring the integration of new data with old, ensuring that all observation data are used only once. To preserve the 3D structure of the SSF, Tucker decomposition is used to characterize the 3D SSF in the model, and a sparse prior is added to each element of the core tensor to reduce model complexity and the risk of overfitting. Numerical results obtained using real ocean SSF data demonstrate that the method performs excellently for dynamic SSF reconstruction.