Mean Square Error in DOA Estimation

Hi all,

I got strucked in calculating the Mean Square Error(MSE) in the DOA
Estimation. Can any one explain me or if you have please send me the
matlab code how to plot MSE for differnt SNR's and if you have any
other matlab code to show the performance of DOA Estimation, Please
Please send it to me.

Thanks in advance 
Chow.

chow wrote:
> Hi all,
>
> I got strucked in calculating the Mean Square Error(MSE) in the DOA
> Estimation. Can any one explain me or if you have please send me the
> matlab code how to plot MSE for differnt SNR's and if you have any
> other matlab code to show the performance of DOA Estimation

Try to get hold of van Trees' "Detection, estimation and
modulation" vol IV, Optimum Array Processing. There are lots
of such plots in that book.

Now, computing the MSE only works with simulated data. You need
to know the true DoA, and then compare that to the estimated DoA.
The comparision gives an error, and from there computing the
MSE of different DoA estimators or SNRs is straight-forward.

Rune

Rune Allnor wrote:
> chow wrote:
> 
>>Hi all,
>>
>>I got strucked in calculating the Mean Square Error(MSE) in the DOA
>>Estimation. Can any one explain me or if you have please send me the
>>matlab code how to plot MSE for differnt SNR's and if you have any
>>other matlab code to show the performance of DOA Estimation
> 
> 
> Try to get hold of van Trees' "Detection, estimation and
> modulation" vol IV, Optimum Array Processing. There are lots
> of such plots in that book.
> 
> Now, computing the MSE only works with simulated data. You need
> to know the true DoA, and then compare that to the estimated DoA.
> The comparision gives an error, and from there computing the
> MSE of different DoA estimators or SNRs is straight-forward.
> 
> Rune
> 


There's also a web page for the vol IV book. I believe it has a number 
of matlab files for the examples.

Sorry I don't have the link handy at present.

Cheers,
David

Rune Allnor <allnor@tele.ntnu.no> wrote:

> Try to get hold of van Trees' "Detection, estimation and
> modulation" vol IV, Optimum Array Processing. There are lots
> of such plots in that book.

I believe I will soon need to brush up on my array signal processing
skills.  A few years ago I spent some time with the book "Array Signal
Processing: Concepts and Techniques", by Don Johnson & Dan Dugeon.  I
did like it at the time, but on the other hand I didn't have much to
compare it with (it was my then advisor's suggestion.)  Are you familiar
with this book?  It seems that this is a hard-to-obtain book these days
-- would you suggest spending time on finding it?  Or is van Trees' book
an adequate book for this purpose?

Thanks,
Henrik

-- 
"On some great and glorious day the plain folks of the land will reach
in their heart's desire at last and the White House will be adorned by
a downright moron."
                             -H.L. Mencken (1880-1956) American Writer 

Henrik Holm wrote:
> Rune Allnor <allnor@tele.ntnu.no> wrote:
>
> > Try to get hold of van Trees' "Detection, estimation and
> > modulation" vol IV, Optimum Array Processing. There are lots
> > of such plots in that book.
>
> I believe I will soon need to brush up on my array signal processing
> skills.  A few years ago I spent some time with the book "Array
Signal
> Processing: Concepts and Techniques", by Don Johnson & Dan Dugeon.  I
> did like it at the time, but on the other hand I didn't have much to
> compare it with (it was my then advisor's suggestion.)  Are you
familiar
> with this book?  It seems that this is a hard-to-obtain book these
days
> -- would you suggest spending time on finding it?  Or is van Trees'
book
> an adequate book for this purpose?

I tried to post a reply to this yesterday, but the post hasn't shown
up on beta-google yet. So I try once more.

First, I don't know the Johnson/Dugeon book, so I can't comment on it.
It is, however, available (as facsimile) through www.amazon.com.
If you liked it before, get a copy of it now before it disappears
from sale. Having a book you know and like is more important than
having the latest or most hyped book. Most people I discuss
array processing with mention this book, so I guess it's not bad.

The van Trees book is not a practitioner's book, it's more of an
academic anthology over all those nifty tricks that can be done
in array processing. The main problem with the van Trees book is
that it skips the basic and suboptimum methods, and focus solely
on the optimum methods. My experience is that the optimum (and
nearly optimum) methods are very tricky to work with. They tend
not to be very robust, neither what problem scope or data quality
are concerned. No library on array processing is complete without
the van Trees book, but it is, in my view, certainly not the first
book to get.

There are a couple of books by Larry Ziomek out, that start from
scratch. The one book I have seen, starts from scratch with
linear arrays and goes on to various forms of planar arrays
and, if my memory serves me correctly, it even mentions 3D arrays.
Ziomek writes with the intention of using the arrays in acoustic
applications, so they may be too biased in the presentation for
others to use. I can't remember Ziomek saying much about practical
implementations.

What little practical implementation stuff on arrays I have seen,
I have found in the book

Burdic: "Underwater Acoustic System Analysis"

(a facsimile of the 1991 edition is available from Peninsula
Publishing, http://www.sound-acoustic-books.com/). This book is
directed towards underwater acoustics applications and is probably
not very useful for people working in other areas.

If you need to dive into implementations, I'd suggest you check
out some journal papers in your field of interest to see what
types of implementations are used or suggested, and use the
key words you find there to search for details in the literature
on adaptive filters.

Rune

Henrik,
The Johnson & Dugeon book is quite good. I would say it covers the 
beginning and intermediate level of Array Processing. These guys also 
have a book on multidimensional signal processing which is also good. 
There is also some common material between the two.

The Van Trees book is more of a reference. To understand some material 
later on you will have to read the first set of chapters. It also covers 
a wide range of array processing (beamforming, adaptive beamforming 
(several methodologies).

I read Rune's post. The Van Trees books are not likely to go out of 
print. I believe earlier volumes are even available in paperback.

To supplement what Rune wrote: a practical book is:
Richard Neilson's - "Sonar Signal Processing" covers LU decomp etc.

A more advanced book (out of print) is Haykin's Array Signal Processing. 
This book is hard to find although you can usually buy some used via 
Amazon or Chapters. This book goes into more advanced performance 
measures ( spatially displursed sources and such).

Hope that helps.

Cheers,
David

Henrik Holm wrote:
> Rune Allnor <allnor@tele.ntnu.no> wrote:
> 
> 
>>Try to get hold of van Trees' "Detection, estimation and
>>modulation" vol IV, Optimum Array Processing. There are lots
>>of such plots in that book.
> 
> 
> I believe I will soon need to brush up on my array signal processing
> skills.  A few years ago I spent some time with the book "Array Signal
> Processing: Concepts and Techniques", by Don Johnson & Dan Dugeon.  I
> did like it at the time, but on the other hand I didn't have much to
> compare it with (it was my then advisor's suggestion.)  Are you familiar
> with this book?  It seems that this is a hard-to-obtain book these days
> -- would you suggest spending time on finding it?  Or is van Trees' book
> an adequate book for this purpose?
> 
> Thanks,
> Henrik
> 

Rune,

I hope you're enjoying the Burdic book :)

Cheers,
David

Rune Allnor wrote:
> Henrik Holm wrote:
> 
>>Rune Allnor <allnor@tele.ntnu.no> wrote:
>>
>>
>>>Try to get hold of van Trees' "Detection, estimation and
>>>modulation" vol IV, Optimum Array Processing. There are lots
>>>of such plots in that book.
>>
>>I believe I will soon need to brush up on my array signal processing
>>skills.  A few years ago I spent some time with the book "Array
> 
> Signal
> 
>>Processing: Concepts and Techniques", by Don Johnson & Dan Dugeon.  I
>>did like it at the time, but on the other hand I didn't have much to
>>compare it with (it was my then advisor's suggestion.)  Are you
> 
> familiar
> 
>>with this book?  It seems that this is a hard-to-obtain book these
> 
> days
> 
>>-- would you suggest spending time on finding it?  Or is van Trees'
> 
> book
> 
>>an adequate book for this purpose?
> 
> 
> I tried to post a reply to this yesterday, but the post hasn't shown
> up on beta-google yet. So I try once more.
> 
> First, I don't know the Johnson/Dugeon book, so I can't comment on it.
> It is, however, available (as facsimile) through www.amazon.com.
> If you liked it before, get a copy of it now before it disappears
> from sale. Having a book you know and like is more important than
> having the latest or most hyped book. Most people I discuss
> array processing with mention this book, so I guess it's not bad.
> 
> The van Trees book is not a practitioner's book, it's more of an
> academic anthology over all those nifty tricks that can be done
> in array processing. The main problem with the van Trees book is
> that it skips the basic and suboptimum methods, and focus solely
> on the optimum methods. My experience is that the optimum (and
> nearly optimum) methods are very tricky to work with. They tend
> not to be very robust, neither what problem scope or data quality
> are concerned. No library on array processing is complete without
> the van Trees book, but it is, in my view, certainly not the first
> book to get.
> 
> There are a couple of books by Larry Ziomek out, that start from
> scratch. The one book I have seen, starts from scratch with
> linear arrays and goes on to various forms of planar arrays
> and, if my memory serves me correctly, it even mentions 3D arrays.
> Ziomek writes with the intention of using the arrays in acoustic
> applications, so they may be too biased in the presentation for
> others to use. I can't remember Ziomek saying much about practical
> implementations.
> 
> What little practical implementation stuff on arrays I have seen,
> I have found in the book
> 
> Burdic: "Underwater Acoustic System Analysis"
> 
> (a facsimile of the 1991 edition is available from Peninsula
> Publishing, http://www.sound-acoustic-books.com/). This book is
> directed towards underwater acoustics applications and is probably
> not very useful for people working in other areas.
> 
> If you need to dive into implementations, I'd suggest you check
> out some journal papers in your field of interest to see what
> types of implementations are used or suggested, and use the
> key words you find there to search for details in the literature
> on adaptive filters.
> 
> Rune
> 

David Kirkland wrote:
> Rune,
>
> I hope you're enjoying the Burdic book :)
>
> Cheers,
> David

I sure do. Thanks for mentioning the PP reprint!

Rune

Rune Allnor <allnor@tele.ntnu.no> wrote:

> First, I don't know the Johnson/Dugeon book, so I can't comment on it.
> It is, however, available (as facsimile) through www.amazon.com.
> If you liked it before, get a copy of it now before it disappears
> from sale. Having a book you know and like is more important than
> having the latest or most hyped book. 

Very good point.  An order is placed.
Thanks for your input, and thanks to David also!

Henrik

-- 
"On some great and glorious day the plain folks of the land will reach
in their heart's desire at last and the White House will be adorned by
a downright moron."
                             -H.L. Mencken (1880-1956) American Writer 

Henrik Holm wrote:
> Rune Allnor <allnor@tele.ntnu.no> wrote:
> 
> 
>>Try to get hold of van Trees' "Detection, estimation and
>>modulation" vol IV, Optimum Array Processing. There are lots
>>of such plots in that book.
> 
> 
> I believe I will soon need to brush up on my array signal processing
> skills.  A few years ago I spent some time with the book "Array Signal
> Processing: Concepts and Techniques", by Don Johnson & Dan Dugeon.  I
> did like it at the time, but on the other hand I didn't have much to
> compare it with (it was my then advisor's suggestion.)  Are you familiar
> with this book?  It seems that this is a hard-to-obtain book these days
> -- would you suggest spending time on finding it?  Or is van Trees' book
> an adequate book for this purpose?
> 
> Thanks,
> Henrik

I've got both books.  I think that Johnson and Dudgeon does a better job 
on some topics such as co-arrays.  Van Trees has a stronger theoretical 
presentation on most topics.