Using subwindows of 5 secs in the beamformer, so that, with a bandwidth of 1Hz, 7 coefficients are obtained in generating the CSDM. Since a Hanning window is employed, the effective number of degrees of freedom is ~5. The CSDM is actually averaged over four subwindows, (no overlapping), so an output estimate occurs every twenty seconds. This relatively short time is used to capture the transient nature of the signals. The total number of DOFs is ~20. The next two images show a k-omega plot of the Conventional and Capon results for one 20 second interval:
We see a direct broadside arrival, which is smeared over all angles in the conventional estimate, but is resolved in the adaptive, at about 7 Hz. Following this we can see a trace of two arrivals at plus/minus 18 degrees in the 16 to 23Hz range.
To get a more comprehensive view, it is interesting to use a series of small 7 second windows when beamforming this data. This increases the number of DOFs since NFFT increases to 2048 (1024 was used for 5 second windows). The number of coefficents in a subwindow, 1Hz band, becomes 15. If we divide the entire file into four sections, and compute four incoherent sums of the results for these small windows, we obtain the following four figures:
Times 0 -> 300 seconds
Times 300 -> 550 seconds,
Times 550 -> 800 seconds
Times 800 -> 1050 seconds
The BMF_E input parameter file used for the beamformer in one of these runs is:
319144437V1.mat 1 0 1
.003333333 0 1090 800 1050 500
-90 90
1e-2 1500
319144437V1_Positions
7 7 7 7
A new routine, Merge_kf2.m, is then used to sum the individual estimates, and to remap the result into k-omega space.
The separation of the arrival of the chirps into two directions near 17Hz is easier to see, when the file is averaged over smaller intervals. Results in the 300 through 550 second time section are pretty much obscured by the strong arrival at 500s. The ~7Hz arrival is smeared in the conventional, but is tightened up in the adaptive results. The MVDR usually appears cleaner than the Capon ("MLM") result.
Perhaps one could argue that the symmetric angles of arrival of the 17Hz chirps change in the 15 minute duration of this file: The angles on either side of broadside are more separated at the beginning of the file, and are close to each other near the end of the file, arguably because of decreasing range to the source.