How to obtain time of arrival using MUSIC algorithm

I have a 1-d vector sampled at particular time interval, I want to caluclate the time of arrival between two overlapping echos present in the signal, how to obtain them using Music/ high resolution algorithm.

Answer 1

[Youssef Khmou]

UDBHAV JOSHI,

1.what is the length of the signal ( >7000 ?) ?

2.Did you try ordinary operations : autocorrelation, histogram, PSD, derivative ?

3. Take a look at the spectrum , and see .

concerning the Music algo , what i think is that you need at least 2 targets so you have one source that you need its time of arrival.

So that size(X)=[2 d] and d is the number of snapshots :

R=X*X'/d; % The cross correlation matrix

[U,S,V]=svd( R ); % the Noise and Signal sub matrices

Signal=U(:,1);

noise=U(:,2);

then you scan the time from t0 to t_final :

for t=t0:step:tf

A=exp(j*2*pi*t*F*..... % steering vector

Spec=1./A'*noise*noise'*A';

end

then you plot the Spec vector whose peaks are the TOA,

Warn : this is first suggestion based on DOA, so we wait for better answer

[UDBHAV JOSHI]

By F in steering vector it means sampling frequency or the frequency spacing

[Youssef Khmou]

F is the frequency of the signal itself, whether it is scalar or vector, the sampling frequency is already included in the time "t", F_sampling=1/step.

and of course F_sampling > 2* Max(F) .

Answer 2

[Vijay Shanmugam]

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