MATLAB: I think no one will be able to answer this………

Question

How to get the noise component in a GPS time series applying MLE technique. The paper I have followed is http://onlinelibrary.wiley.com/doi/10.1029/1998JB900033/pdf. I having the time series data. The time series is attached. The first column is the time column, second is the signal and third is the standard deviation

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Best Answer
    

    

								

								
Your question is ill-defined:
You have not presented enough info.
1. Is the middle column the noisy signal?
2. Is the noise supposed to be
 a. additive?
 b. zero-mean?
 c. constant variance?
 d. Gaussian distributed?
If so, how was the variance measured? In particular, how many points were used to estimate each tabulated value?
						    
						
		
    
        

    

Related Solutions
MATLAB: How to apply Maximum likelihood estimation technique to characterize the amplitude of noise in a given time series

								

								
Im just guessing here, but since the least square fit of your time function (inverse fourier?) is a maximum likelihood estimator of your signal model (assuming gaussian noise), then the sum of residuals should be a measure for the amount of noise?
						    
						
MATLAB: How to decompose following gps time series ?? Please help me

								

								
OK, I suspected but then didn't check, that was dumb of me..
So with that in mind:
    resid = y-yfit;
    % find the DFT of the residuals
    residDFT = fft(resid);
    Fs = 1;
    freq = 0:Fs/length(resid):Fs/2;
    residDFT = residDFT(1:floor(length(resid)/2)+1);
    plot(freq(1:100),abs(residDFT(1:100)))
You'll see the biggest peak at a frequency of 0.002 cycles/day, which is a period of 500 days. Looks to me like the next most prominent peak is at 0.0059 cycles/day which is a period of almost 170 days (169.89).
I think if you fit those two frequencies using the Fourier coefficients along with the linear model fitted above, you'll have a very good fit to the data.
						    
						
        
        

            
            
            
Related Question
        
    

Answer 1

Your question is ill-defined:

You have not presented enough info.

1. Is the middle column the noisy signal?

2. Is the noise supposed to be

 a. additive?
 b. zero-mean?
 c. constant variance?
 d. Gaussian distributed?

If so, how was the variance measured? In particular, how many points were used to estimate each tabulated value?