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Validate Signal Matrix Power Ratios Using MUSIC Algorithm

Source: R/SeaSondeRCS_MUSIC.R
seasonder_MUSICCheckSignalMatrix.Rd

This function implements the P3 test for solutions derived using the MUSIC algorithm. The test evaluates the ratio between the diagonal (P_diag) and off-diagonal (P_off-diag) elements of the signal covariance matrix. Specifically, the ratio is computed as:

Usage

seasonder_MUSICCheckSignalMatrix(seasonder_cs_object)

Arguments

seasonder_cs_object

A SeaSondeRCS object containing MUSIC data (including DOA solutions and power matrices).

Value

The updated SeaSondeRCS object in which:

  • A new column diag_off_diag_power_ratio is added to the MUSIC data.

  • A logical column P3_check indicates if each solution passes the P3 test.

  • The retained_solution field of solutions that fail the test is updated to "single".

Details

Ratio = P_off_diag / P_diag

where P_diag is the product of the absolute values of the diagonal elements and P_off_diag is the square of the absolute value of the upper-left off-diagonal element.

The computed ratio is compared with the threshold parameter (the third element in the MUSIC parameters). For each dual-bearing solution (i.e. when exactly two bearings are present), if the ratio is less than the reciprocal of the threshold, the solution passes the P3 test; otherwise, it is marked as "single".

For each entry in the MUSIC data, the function:

  1. Extracts the covariance matrix power from the dual DOA solution (DOA_sol$dual$P).

  2. Computes the ratio by taking the product of the absolute diagonal elements and the square of the absolute off-diagonal element.

  3. Retrieves the threshold parameter for the P3 test.

  4. Validates each solution by checking that:

    • The solution has exactly two bearings.

    • The computed ratio is available (not NA) and less than 1 divided by the threshold.

  5. Updates the retained_solution field to "single" for solutions that do not pass the test.

See also

seasonder_getSeaSondeRCS_MUSIC to retrieve MUSIC data, seasonder_setSeaSondeRCS_MUSIC to update MUSIC data, and seasonder_getSeaSondeRCS_MUSIC_parameters to retrieve MUSIC parameters.