Covariance matrix - how to obtain it?

[daqamseh]

Covariance matrix

hi guys,
I am new in signal processing and i have question about how to calculate the covariance matrix. I have signals from 10 sensors arranged in linear line...i want to calculate the covariance matrix of the sensors' responses...the vector generated from these sensors is Z=N x 1 vector with N=number of the sensors.
Is the covariance matrix is just to calculate C=(Z*Z') . This C will be used later to calculate the Energy function using Capon's method to localise the source.
Thanks

 

[s_cihan_tek]

Re: Covariance matrix

Hi,

To calculate the covariance matrix, you need to take multiple measurements for each sensor, because it is not possible to talk about any variance on a single measurement set. Let's say you did M measurements for each sensor, then the number of Z vectors you have will be M. (Z1,Z2,...,ZM).

Then you should calculate the average of these vectors. Let's call this Za.

Then you can calculate the covariance matrix using the following equation.

You need to select the M value as high as possible so that the values in your covariance matrix have any meaning.

Edit: Sorry, i mistyped the equation. The constant in front of the sigma should be 1/(M-1) in your case, not 1/M.

 

[daqamseh]

Re: Covariance matrix

Thanks for your answer...So in this case i have to take few (lets say measurements) for each sensor and then generate this matrix (N x K) where N is is the number os sensors in the array and K is the response of each sensor at different snap shots...am i right....?

Based on above, i will have input matrix from all of the sensors (N x K)...what is the correlation matrix now ...? is it N x 1? or it should be N x N?
may be u take look to this paper..it is almost the same what i plan to do...

**broken link removed**

i missed here that if i want to have the inverse of the correlation matrix, the correlation matrix should be square....so and based of what you explained above if the generated correlation matrix is N x1==> there would be no inverse...


Thanks

 

[s_cihan_tek]

Re: Covariance matrix

Thanks for your answer...So in this case i have to take few (lets say measurements) for each sensor and then generate this matrix (N x K) where N is is the number os sensors in the array and K is the response of each sensor at different snap shots...am i right....?

Yes.

Based on above, i will have input matrix from all of the sensors (N x K)...what is the correlation matrix now ...? is it N x 1? or it should be N x N?
may be u take look to this paper..it is almost the same what i plan to do...

**broken link removed**

Multiplication of a column vector and a row vector will result in a square matrix. NxN in your case.

The equation i wrote is for calculating the covariance matrix. If you want to calculate the correlation matrix, which is a different thing, you should use the equation given in eq. 4 in the paper you mentioned. Please note that in eq 4. the variable N is the number of measurements (which i denoted with M in my previous message), not the number of sensors. The resulting matrix will be AxA where A=number of sensors you have.

i missed here that if i want to have the inverse of the correlation matrix, the correlation matrix should be square....so and based of what you explained above if the generated correlation matrix is N x1==> there would be no inverse...

Look at my answer above.