I Have a time series data , containing time, position and error in three column , I want to get the power spectral density of the time series containg the error

The sample time series is like the following:

   Time          position  error
 2005.10822      4.09605  0.00205
 2005.11096      4.09587  0.00210
 2005.11370      4.09601  0.00209
 2005.11644      4.09531  0.00246
 2005.11918      4.09960  0.00272
 2005.12192      4.09812  0.00217
 2005.12466      4.09808  0.00219
 2005.12740      4.09878  0.00229
 2005.13014      4.09790  0.00275
 2005.13287      4.09803  0.00238
 2005.13561      4.10136  0.00278
 2005.13835      4.09995  0.00310
 2005.14109      4.09727  0.00245
 2005.14383      4.09690  0.00228
 2005.14657      4.09782  0.00231
 2005.14931      4.09842  0.00229

Answer 1

[Wayne King]

I'll assume that X is your matrix with 3 columns and the 3rd column is the error vector.

 errvec = X(:,3);
 % if you have the Signal Processing Toolbox
 Pxx = periodogram(errvec,rectwin(length(errvec)));
 plot(10*log10(Pxx))

If you do not have the Signal Processing Toolbox, write back and let me know the length of the error vector (how many elements).

By the way if you are just trying to determine whether the error vector is white noise, I think there are better ways than using the PSD estimate. For an white noise assessment using the cross correlation:

https://www.mathworks.com/help/signal/ug/confidence-intervals-for-sample-autocorrelation.html