question regarding capon's method

[daqamseh]

capon's method

Hi guys,

I have question regarding capon's method....I have array of sensors arranged in linear line...i used model to calculate the flow field over 2D grid points (x and y direction) as my tamplate. Based on Capon's method i used the measurements of my array covariance matrix (R) as well as the tamplate data (S) over the grid points to find the energy of each point as E=1/(S^H*R^-1*S). Then i plotted the E matrix as function of x and y...Unfortunatly, i didn't get what i am expecting....i mean to localize the source...anybody ca help in that.

Just to confirm...R^-1 is the inverse matrix of R...am i right?

Thanks

 

[marzouki]

Re: capon's method

Hi guys,

I have question regarding capon's method....I have array of sensors arranged in linear line...i used model to calculate the flow field over 2D grid points (x and y direction) as my tamplate. Based on Capon's method i used the measurements of my array covariance matrix (R) as well as the tamplate data (S) over the grid points to find the energy of each point as E=1/(S^H*R^-1*S). Then i plotted the E matrix as function of x and y...Unfortunatly, i didn't get what i am expecting....i mean to localize the source...anybody ca help in that.

Just to confirm...R^-1 is the inverse matrix of R...am i right?

Thanks

I can help you better if you give explicitly your steering vector, grid separation and noise power. Otherwise, try your program on a dererminist covariance matrix to find where the bug is located. Run a Bertlett beamformer in parallel to check your covariance matrix.

 

[daqamseh]

Thanks for ur answer....
Actually, i am using model based steering vector (Dipole flow field)...and 1cm as grid seperation. I am using the same model to feed signal to the code as experimental data with some noise, The noise, i am feeding, is random noise with different signal-to-noise ratios to test the rebustness of the localization...To be honest with you, this is the first time i treating with source localization and signal processing ...so if u have any nice literature to study about this topic this would be nice from you.

Regards

 

[marzouki]

By grid separation I mean angular grid. For example if you apply Capon in 2D and if your steering vector is symmetric in theta, the grid is (pi/N)[0,1,...,N-1]. If the noise variance is small and the steering vector length is high your N has to allow you to detect the angle of arrival. The best way is to check your algorithm with a theta = j*pi/N; where j belongs to [0,N-1]. Then you should find a high spectrum value at this angle and week ones at the others. Choose also a lamda/2 separation antenna array to find just one spectrum maxima.
You can also fix the noise covariance matrix (determinist one) and test your Capon with a determinst (Signal + Noise Covariance matrix): R = a*a' + N0*I
where a is the steering vector with the actual AOA, N0 is the noise power and I is the identity matrix. ' means conjugate of the transpose.
I don't have in mind a special reference. The first Capon paper is the best one in my sense.

 

[daqamseh]

Thanks...i will try to manage that....