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Generalized Cross Correlation

Started by George W November 4, 2004
Thanks Jerry,

I have Googled the subject :o).  The technique is cited often for
determining the location of an acoustic audio signal source based on TDOA.
My application is similar except I'm determining the location of a radio
transmitter using TDOA where the signal arrives at a receiver via different
paths.  The equipment in both paths will have closely matched
characteristics but differences may be caused by propagation effects that
can't be controlled.

The references I found don't give numbers on achievable time resolution at
audio frequencies.  Can anyone  give me a rough estimate?  I can afford
several seconds of sampling time, if needed.  Is the 1 usec resolution I'm
trying to get reasonably achievable?

George


"Jerry Avins" <jya@ieee.org> wrote in message
news:2u9p7nF27irohU1@uni-berlin.de...
> George W wrote: > > > I have a need to measure the relative delay between two audio signals > > arriving at a receiver via different paths. The audio signals are
standard
> > 3 kHz audio bandwidths containing voice or music. One could arrive as
much
> > as 1 msec before or after the other. I'd like to be able to measure the > > difference in time of arrival between the two signals down to 1 usec if > > that's possible. > > > > Any suggestions? I'm thinking of using a 180 degree phase shifter and > > adjusting a variable delay line for a null when the signals are summed. > > > > Thanks. > > > > George > > Different paths imply some reflection. You will get a very mushy null > unless the path properties are perfectly matched in frequency and phase > responses. "Ain't gonna happen." Correlate. I understand how to do that > in time, but a frequency approach is better. > > Jerry > -- > Engineering is the art of making what you want from things you can get. > &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
If you are trying to estimate time-delay (TDOA) between to signals using cross-correlation - forget it. Cross-correlation only works well when both signals are white. You need what has been termed Generalised Cross Correlation. The Hanan Thomson Transform,SCOT -Smoothed Covariance and so on.Most of them are based on FFTs but also the coherence.This sharpens the cross-correlation when there are multiple delays otherwise you do get a smudging. Besy way is to work out the cross-spectral density and weight this with the required function (for example the SCOT method) - then do an inverse FFT to get back to cross-correlation.There are numerous papers on this - search the IEEE or just Google for Generalized Cross Correlation TDOA.I have tried this and it works pretty well though it still has its problems.Ordinary Cross Correlation is next to useless.
George W wrote:

> Thanks Jerry, > > I have Googled the subject :o). The technique is cited often for > determining the location of an acoustic audio signal source based on TDOA. > My application is similar except I'm determining the location of a radio > transmitter using TDOA where the signal arrives at a receiver via different > paths. The equipment in both paths will have closely matched > characteristics but differences may be caused by propagation effects that > can't be controlled. > > The references I found don't give numbers on achievable time resolution at > audio frequencies. Can anyone give me a rough estimate? I can afford > several seconds of sampling time, if needed. Is the 1 usec resolution I'm > trying to get reasonably achievable? > > George
Time delay measurements work. In fact, one way or another, they are the only way I can think of.
> > If you are trying to estimate time-delay (TDOA) between to signals using > cross-correlation - forget it. Cross-correlation only works well when both > signals are white.
Why? with an adequate SNR, the spectral content of the signal shouldn't be an issue. Cross correlation is simply a way to measure the amount of time the signal from one path needs to be delayed in order to match up with the signal from the other.
> You need what has been termed Generalised Cross Correlation. The Hanan > Thomson Transform,SCOT -Smoothed Covariance and so on.Most of them are based > on FFTs but also the coherence.This sharpens the cross-correlation when > there are multiple delays otherwise you do get a smudging. > Besy way is to work out the cross-spectral density and weight this with the > required function (for example the SCOT method) - then do an inverse FFT to > get back to cross-correlation.There are numerous papers on this - search the > IEEE or just Google for Generalized Cross Correlation TDOA.I have tried this > and it works pretty well though it still has its problems.Ordinary Cross > Correlation is next to useless.
Well sure. If there are more than two paths, correlating only two signals can't paint the whole picture. Loran techniques might have some useful hints, but there, the path directions are widely different. Jerry P.S. What happened to the rest of the thread? -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;