Compute DOA Functions Using the MUSIC Algorithm

This function calculates the Direction of Arrival (DOA) functions based on the MUSIC algorithm for a given SeaSonde cross-spectra (CS) object. It projects the antenna patterns onto the noise subspace for each Doppler bin and computes single and dual signal solutions, following the MUSIC method.

Usage

seasonder_MUSICComputeDOAProjections(seasonder_cs_object)

Arguments

seasonder_cs_object

An object representing the cross-spectra (CS) data from SeaSonde.

Value

The updated seasonder_cs_object with the MUSIC DOA functions computed and appended.

Details

The function operates as follows:

1. It sets a processing step indicating the start of DOA function computation.

2. Retrieves the Antenna Pattern Measurement (APM) and bearings associated with the CS object.

3. Iteratively computes projections of antenna pattern responses into the noise subspace for each Doppler bin using the MUSIC algorithm. This includes:

   • Initializing storage for projection results.

   • Calculating projections for single (m = 1) and dual (m = 2) signal solutions using the eigenvectors defining the noise subspace.

   • For each bearing, projecting the antenna manifold vector onto the noise subspace, as described by the formula: $$DOA(\theta) = \frac{1}{A^*(\theta) E_n E_n^* A(\theta)}$$ where:

     • \(E_n\) is the eigenvector matrix of the noise subspace.

     • \(A(\theta)\) is the antenna pattern response vector at bearing \(\theta\).

     • \(A^*(\theta)\) is its conjugate transpose.

4. Appends the computed DOA functions to the MUSIC data of the CS object.

5. Updates the processing step to indicate completion.

References

• Paolo, T. de, Cook, T., & Terrill, E. (2007). Properties of HF RADAR Compact Antenna Arrays and Their Effect on the MUSIC Algorithm. OCEANS 2007, 1–10. doi:10.1109/oceans.2007.4449265.

See also

seasonder_compute_antenna_pattern_proyections for computing projections.