Mean-squared errors

API references

doatools.performance.mse.ecov_music_1d(array, sources, wavelength, P, sigma, n_snapshots=1, perturbations='all', return_mode='full')[source]

Computes the asymptotic covariance matrix of the estimation errors of the classical MUSIC algorithm.

Parameters:

  • array (ArrayDesign) – Array design.

  • wavelength (float) – Wavelength of the carrier wave.

  • sources (FarField1DSourcePlacement) – Source locations.

  • p (float or ndarray) –

    The power of the source signals. Can be

    1. A scalar if all sources are uncorrelated and share the same power.

    2. A 1D numpy array if all sources are uncorrelated but have different powers.

    3. A 2D numpy array representing the source covariance matrix.

  • sigma (float) – Variance of the additive noise.

  • n_snapshots (int) – Number of snapshots. Default value is 1.

  • perturbations (str) – Specifies which perturbations are considered when constructing the steering matrix. Possible values include 'all', 'known', and 'none'. Default value is 'all'. See steering_matrix() for more details.

  • return_mode (str) –

    Can be one of the following:

    1. 'full': returns the full covariance matrix.

    2. 'diag': returns only the diagonals of the covariance matrix.

    3. 'mean_diag': returns the mean of the diagonals of the covariance matrix.

    Default value is 'full'.

Returns:

Depending on 'return_mode', can be the full covariance matrix, the diagonals of the covariance matrix, or the mean of the diagonals of the covariance matrix.

References

[1] P. Stoica and A. Nehorai, “MUSIC, maximum likelihood, and Cramér-Rao bound: further results and comparisons,” IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 38, no. 12, pp. 2140-2150, Dec. 1990.

[2] P. Stoica and A. Nehorai, “MUSIC, maximum likelihood, and Cramér-Rao bound,” IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 37, no. 5, pp. 720-741, May 1989.

doatools.performance.mse.ecov_coarray_music_1d(array, sources, wavelength, p, sigma, n_snapshots=1, return_mode='full')[source]

Computes the asymptotic covariance matrix of the estimation errors of the coarray-based MUSIC algorithm, SS-MUSIC or DA-MUSIC.

Parameters:

  • array (ArrayDesign) – Array design.

  • wavelength (float) – Wavelength of the carrier wave.

  • sources (FarField1DSourcePlacement) – Source locations.

  • p (float or ndarray) –

    The power of the source signals. Can be

    1. A scalar if all sources are uncorrelated and share the same power.

    2. A 1D numpy array if all sources are uncorrelated but have different powers.

    3. A 2D numpy array representing the source covariance matrix. Only the diagonal elements will be used.

  • sigma (float) – Variance of the additive noise.

  • n_snapshots (int) – Number of snapshots. Default value is 1.

  • return_mode (str) –

    Can be one of the following:

    1. 'full': returns the full covariance matrix.

    2. 'diag': returns only the diagonals of the covariance matrix.

    3. 'mean_diag': returns the mean of the diagonals of the covariance matrix.

    Default value is 'full'.

Returns:

Depending on 'return_mode', can be the full covariance matrix, the diagonals of the covariance matrix, or the mean of the diagonals of the covariance matrix.

References

[1] M. Wang and A. Nehorai, “Coarrays, MUSIC, and the Cramér-Rao Bound,” IEEE Transactions on Signal Processing, vol. 65, no. 4, pp. 933-946, Feb. 2017.