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MUSIC algorithm for source localization

Started by riz April 24, 2007
Hi

Does the MUSIC algorithm works for 3D source localization?
As far as I know ,it works for angles of arrival between -90 and 90 for a
microphone array where 0 degrees is the angle at which the source
wavefronts arrive simultaneously at all sensors.How we can apply MUSIC in
3D?
If we cannot,which algorithm is the simplest one to start with;

Riz



_____________________________________
Do you know a company who employs DSP engineers?  
Is it already listed at http://dsprelated.com/employers.php ?
It works in 2D and 3D cases.  You just need to form the steering vectors
accordingly.  I think there are some papers published regarding 2D MUSIC
and you can then extend the idea to 3D.

>Hi > >Does the MUSIC algorithm works for 3D source localization? >As far as I know ,it works for angles of arrival between -90 and 90 for
a
>microphone array where 0 degrees is the angle at which the source >wavefronts arrive simultaneously at all sensors.How we can apply MUSIC
in
>3D? >If we cannot,which algorithm is the simplest one to start with; > >Riz > > > >_____________________________________ >Do you know a company who employs DSP engineers? >Is it already listed at http://dsprelated.com/employers.php ? >
_____________________________________ Do you know a company who employs DSP engineers? Is it already listed at http://dsprelated.com/employers.php ?
On Apr 24, 11:06 am, "riz" <rizwan....@gmail.com> wrote:
> Hi > > Does the MUSIC algorithm works for 3D source localization? > As far as I know ,it works for angles of arrival between -90 and 90 for a > microphone array where 0 degrees is the angle at which the source > wavefronts arrive simultaneously at all sensors.How we can apply MUSIC in > 3D? > If we cannot,which algorithm is the simplest one to start with; > > Riz > > _____________________________________ > Do you know a company who employs DSP engineers? > Is it already listed athttp://dsprelated.com/employers.php?
MUSIC is what is known as the eigenstructure method. It computes the eigenvalues (evals) and eigenvectors (evrs) of the covariance matrix for an array of N elements. If the signals for the sources of interest (usually interference sources whose power is above the noise floor) are uncorrelated, then for a collection of M such sources, there will be M evals (well above) unity. The evrs corresponding to these evals are a basis for the steering vectors for the sources of interest. The remaining evrs have evals of about 1 and they are called the "noise evrs". They are useful because they are orthogonal to all of the steering vectors for the sources. One uses some basic properties of Hermitian matrices (such as the fact that the from different evals are orthogonal) to find the source orientations. One way in which this is done (so called "spectral MUSIC" method) is where one searches the space of all possible orientations for the source, computes the steering vector for each orientation and then takes the reciprocal of the projection of the steering vector onto the subspace spanned by the noise evrs. The term "spectral" is used because when you find an orientation corresponding to one of the sources, it will have a small projection onto the noise subspace and thus the reciprocal of its projection will produce a "spike" or peak that looks like a spectrum. Unfortunately, there are not a lot of good sources that I know of to steer you to, although if you Google "spectral MUSIC" you should find something. GL, M
On Apr 24, 10:06 am, "riz" <rizwan....@gmail.com> wrote:
> Hi > > Does the MUSIC algorithm works for 3D source localization? > As far as I know ,it works for angles of arrival between -90 and 90 for a > microphone array where 0 degrees is the angle at which the source > wavefronts arrive simultaneously at all sensors.How we can apply MUSIC in > 3D? > If we cannot,which algorithm is the simplest one to start with; > > Riz >
How do you express the quantities that you are interested in? MUSIC, ESPRIT, Prony, etc etc etc are just methods for estimating tones (and envelopes) in 1-D. So it depends on the engineer (i.e. you) to figure out how to map the desired quantities into what looks like tones in 1-D. One naive solution to your problem is to have a two arrays: one to find the horizontal angle and one to find the vertical angle. Julius