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### One question about Capon's method!

Posted: **Wed Jul 30, 2008 2:18 am**

by **leedward**

Hi, Marc,

I have one question about Capon's method. I used three f-k beamformers to analyze the field testing data. They are conventional FDBF, Capon's and MUSIC methods. But Capon's method gave more scattered dispersion curves. Have you had this problem? The details can be seen in the attachment. Let me know if you have any question. Thanks for your time.

leedward

Posted: **Mon Aug 04, 2008 12:32 pm**

by **admin**

Hi,

Usually, Capon's estimator can give very good velocities with a nice high resolution. However, for certain cases (especially noisy noise wave fields?), I also observed that Capon's estimator was not as robust as conventional BF. For a single source wave field, you should not get this kind of scattering.

As far as I understood your problem, you are dealing with a line of sensors. How many sensors do you process? Have you ever looked at the singularity of the inversed matrix with Capon's estimator? In Geopsy module, I first decompose the cross correlation matrix into its eigenvectors. If last vectors are too small (some threshold I can't remember, see in the code), some messages are issued in log window, and no computation is performed (null array oupput). You can obtain a singular matrix if they are a lot of sensors and if you are not processing enough time (e.g. for active source experiments). The more sensors you have, the longer time you have to consider. If you chose the frequency averaging to compute the cross correlation matrix, you have to adjust the frequency band width instead. Another alternative is to add white noise (on the diagonal terms of the matrix) before the inversion.

Marc

### Capon's method & instability

Posted: **Wed Aug 13, 2008 7:10 pm**

by **mao**

Dear leedward,

have you tried a small damping on your cross spectral matrix before

inverting. I think you can try easily a simple diagonal loading and you will

get more stable results then - it will come at the expense of

reduced resolution capabilities. The reponse will look then in between the

undamped Capon's estimator and the BF - the shape resembles more

the undamped Capon's est. case, but the peak gets smeared and broader

tending to BF response. In case you try with the matlab scripts

I would be interested to see the change of Capon estimate with damping

value (something like 1.e-4, 1e.-3, 1.e-2 and 1.e-1)

bye

Matthias