Min-Norm based estimators

API references

class doatools.estimation.min_norm.MinNorm(array, wavelength, search_grid, **kwargs)[source]

Bases: doatools.estimation.core.SpectrumBasedEstimatorBase

Creates a spectrum-based Min-Norm estimator.

The Min-Norm spectrum is computed on a predefined-grid, and the source locations are estimated by identifying the peaks.

Parameters:
  • array (ArrayDesign) – Array design.
  • wavelength (float) – Wavelength of the carrier wave.
  • search_grid (SearchGrid) – The search grid used to locate the sources.
  • **kwargs – Other keyword arguments supported by SpectrumBasedEstimatorBase.

Notes

The Min-Norm algorithm is sometimes referred to in the literature as a weighted MUSIC algorithm because it uses weighted eigenspaces.

References

[1] R. Kumaresan and D. W. Tufts, “Estimating the angles of arrival of multiple plane waves,” IEEE Trans. Aerospace Electron. Syst., vol. 19, pp. 134-139, Jan. 1983.

estimate(R, k, **kwargs)[source]

Estimates the source locations from the given covariance matrix.

Parameters:
  • R (ndarray) – Covariance matrix input. The size of R must match that of the array design used when creating this estimator.
  • k (int) – Expected number of sources.
  • return_spectrum (bool) – Set to True to also output the spectrum for visualization. Default value if False.
  • refine_estimates (bool) – Set to True to enable grid refinement to obtain potentially more accurate estimates.
  • refinement_density (int) – Density of the refinement grids. Higher density values lead to denser refinement grids and increased computational complexity. Default value is 10.
  • refinement_iters (int) – Number of refinement iterations. More iterations generally lead to better results, at the cost of increased computational complexity. Default value is 3.
Returns:

A tuple with the following elements.

  • resolved (bool): A boolean indicating if the desired number of sources are found. This flag does not guarantee that the estimated source locations are correct. The estimated source locations may be completely wrong! If resolved is False, both estimates and spectrum will be None.
  • estimates (SourcePlacement): A SourcePlacement instance of the same type as the one used in the search grid, represeting the estimated source locations. Will be None if resolved is False.
  • spectrum (ndarray): An numpy array of the same shape of the specified search grid, consisting of values evaluated at the grid points. Only present if return_spectrum is True.