riecovest.covariance_estimation.est_manifold_airm

riecovest.covariance_estimation.est_manifold_airm(scm_noisy_signal, scm_noise, rank, alpha=0.5, start_value=None)

Signal and noise covariance estimation using the affine-invariant Riemannian metric distance.

Parameters:

• scm_noisy_signal (ndarray of shape (ambient_dim, ambient_dim)) – Sample covariance matrix of the noisy signal.

• scm_noise (ndarray of shape (ambient_dim, ambient_dim)) – Sample covariance matrix of the noise.

• rank (int) – Rank of the signal covariance matrix.

• alpha (float, optional) – Weighting parameter between the noisy signal and the noise. Default is 0.5.

• start_value (tuple of ndarrays, optional) – Initial value for the optimization. If None, the optimization starts from a random point.

Returns:

• Rx (ndarray of shape (ambient_dim, ambient_dim)) – Estimated signal covariance matrix.

• Rv (ndarray of shape (ambient_dim, ambient_dim)) – Estimated noise covariance matrix.