Non-linear embedding of acoustic cross-spectral density matrices through diffusion maps.

Area of Science:

• Ocean acoustics
• Signal processing
• Geophysics

Background:

• Matched-field source localization relies on cross-spectral density matrices (CSDMs).
• Ocean waveguides introduce stochastic variability affecting acoustic propagation.
• CSDMs can be viewed as points on a high-dimensional Riemannian manifold.

Purpose of the Study:

• To explore the geometric properties of CSDM manifolds for source localization.
• To visualize high-dimensional CSDM spaces using dimensionality reduction.
• To gain insights into the application of geodesic distances for acoustic sensing.

Main Methods:

• Estimation of M x M CSDMs from simulated acoustic fields in a stochastic waveguide.
• Representation of CSDMs as nodes in a weighted graph.
• Application of diffusion maps for non-linear dimensionality reduction and visualization.

Main Results:

• Geodesic distances between CSDMs correlate with source location parameters (range and depth).
• Diffusion maps effectively project the high-dimensional CSDM manifold into a 3D subspace.
• Visualizations reveal geometric relationships and preserve inter-matrix distances.

Conclusions:

• Geodesic distances on CSDM manifolds offer a promising geometric approach for acoustic source localization.
• Dimensionality reduction techniques like diffusion maps facilitate understanding of complex CSDM spaces.
• This geometric framework enhances insights into acoustic sensing in variable ocean environments.