Hi, Marc,
I have one question about Capon's method. I used three fk 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
One question about Capon's method!
One question about Capon's method!
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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
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
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.e4, 1e.3, 1.e2 and 1.e1)
bye
Matthias
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.e4, 1e.3, 1.e2 and 1.e1)
bye
Matthias