seasonder_MUSICCovDecomposition {SeaSondeR}R Documentation

Eigen Decomposition of the MUSIC Covariance Matrix

Description

Performs the eigen decomposition of a MUSIC covariance matrix to obtain the eigenvalues and eigenvectors. This decomposition is a critical step in the MUSIC algorithm for spectral estimation and direction finding, as it enables the identification of the signal and noise subspaces.

Usage

seasonder_MUSICCovDecomposition(seasonder_cs_object)

Arguments

seasonder_cs_object

A SeaSondeRCS object containing the covariance matrices derived from cross-spectra data.

Details

The covariance matrix represents one Doppler cell of the averaged cross-spectra of three received signals. This matrix captures the summation of signals from all bearings (plus noise) received by the antennas. To estimate the direction of arrival (DOA), the covariance matrix is subjected to eigenvalue decomposition (diagonalization) to estimate the signal and noise subspaces.

In practical HF radar systems, there are two primary sources of noise:

  1. System (thermal) noise: Generated by the receiving equipment and assumed to be uncorrelated between antennas.

  2. Spatial noise field: Includes wind-wave noise and current noise, modeled as Gaussian, which introduces correlation.

The eigenvalue decomposition produces:

Based on the largest eigenvalues:

The signal and noise subspaces are orthogonal. This decomposition facilitates identifying the signal's direction by finding the antenna manifold that best fits the signal subspace.

Value

An updated SeaSondeRCS object where each Doppler cell includes the eigenvalues and eigenvectors of its covariance matrix. The eigenvalues are sorted in descending order, and the eigenvectors are aligned accordingly. The updates include:

References

Paolo, T. de, Cook, T. & Terrill, E. Properties of HF RADAR Compact Antenna Arrays and Their Effect on the MUSIC Algorithm. OCEANS 2007 1–10 (2007) doi:10.1109/oceans.2007.4449265.

See Also

seasonder_MUSICComputeCov for computing the covariance matrix.


[Package SeaSondeR version 0.2.8 Index]