riecovest.covariance_estimation.est_manifold_tylers_m_estimator_nonorm

riecovest.covariance_estimation.est_manifold_tylers_m_estimator_nonorm(data_noisy_signal, data_noise, rank, start_value=None)

Signal and noise covariance estimation using the log-likelihood of an elliptical distribution.

This is a slight variation of the proposed method of [brunnstroemRobust2024], using a different definition of the log-likelihood.

Parameters:

• data_noisy_signal (ndarray of shape (ambient_dim, num_samples)) – Noisy signal samples.

• data_noise (ndarray of shape (ambient_dim, num_samples)) – Noise samples.

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

• 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.

References

[brunnstroemRobust2024] J. Brunnström, M. Moonen, and F. Elvander, “Robust signal and noise covariance matrix estimation using Riemannian optimization,” presented at the European Signal Processing Conference (EUSIPCO), Sep. 2024