seasonder_computePowerMatrix {SeaSondeR}R Documentation

Compute Power Matrix

Description

This function calculates the power matrix based on the provided steering vector, eigenvalues, and eigenvectors. The computation differs depending on the number of columns in the steering vector matrix.

Usage

seasonder_computePowerMatrix(eig, a)

Arguments

eig

A list containing the eigenvalues and eigenvectors of a covariance matrix. The list should include:

  • values: A numeric vector of eigenvalues.

  • vectors: A matrix where each column is an eigenvector.

a

A complex matrix representing the steering vector(s). Each column corresponds to a direction of arrival.

Details

The function computes the power matrix using the following steps:

If a has no columns, the function returns NULL.

Value

A complex matrix representing the power matrix, calculated based on the provided eigenvalues, eigenvectors, and steering vectors. If the number of columns in a is zero, the function returns NULL.

Mathematical Formula

For a steering vector matrix a, eigenvectors \text{eigVector}, and eigenvalues \text{eigValues}, the power matrix is calculated as:

P = G_{\text{inv}}^* \cdot \text{diag(eigValues)} \cdot G_{\text{inv}}

where: G = a^* \cdot \text{eigVector} and G_{\text{inv}} is the inverse of G.

References


[Package SeaSondeR version 0.2.8 Index]