I tried the version in the link above. It wasn't as robust as the
lmfit.c version. When starting out the sum of squared errors can be
very big and cause floaiting point overflow problems. This occured in
our application when there are 2000+ data points. lmfit.c didn't
have this problem as it had extra code to check the size of the
squared error and kept a couple accumulators to keep them from over
flowing. Finding this problem is how I learned what the algorithm was
doing. I recommend
https://sourceforge.net/projects/lmfit/
The code is ugly c code converted from fortran but it works well and
is easy to implement. If there are other versions that work equally
well then it would be good to hear. This post has saved the world
100s if not 1000s of man hours debugging code.
I don't recommend writing this from scratch if you don't have too.
One's numerical methods and programming techniques better be good.
That is why a bypassed suggesting the books and directed Tom directly
to the code.
Peter Nachtwey

Reply by John Herman●June 17, 20072007-06-17

If you are looking for Levenburg-Marquardt, I would suggest levmar.
http://www.ics.forth.gr/~lourakis/levmar/
You will need the BLAS 1 and LAPACK libraries. I think the code from ATLAS is
the best choice.
In article <1182034526.765823.116870@x35g2000prf.googlegroups.com>,
pnachtwey@gmail.com wrote:

>On Jun 13, 10:53 am, "Tom" <tomda...@yahoo.com> wrote:
>> I am looking for an algorithm to model a system using an ARMA filter. The
>> input and the desired output are available. Is there an iterative algorithm
>> that can give a global optimum solution ? Any good reference ?
>>
>> Regards
>>
>> Tom
>
>You could be more clear about what you want. A quick solution or in
>depth knowledge. I use a minimizing or optimizing algorithm. These
>exist in Scilab as lsqrsolve and optim. In Mathcad I use Minerr. In
>C I use lmfit.c which is c code converted from ancient fortran but it
>works. There are other versions out there that are buggy.
>
>If iterative means on-the-fly there is the recursive least squares
>method but I would be careful with this. In my testing, a fast sample
>rate yields poles close to the unit circle. The poles move around a
>bit while updating and sometimes the poles would cross the unit
>circle. Not good.
>
>What ever method you chose you must make a decision as to how many
>coefficients you need. One can always get a smaller norm or mean
>squared error by adding more coefficients but often the poles in the z
>domain end up on the negative real axis which is an indicator that you
>probably have too many coefficients. I don't use the recursive least
>squares but I do find it interesting how the poles move around and by
>how much.
>
>I read about the Levenberg-Marquardt algorithm in Numerical Recipes in
>C but didn't like the code or the restrictions. After that I found
>tracing through lmfit.c code helpful. I didn't need anything beyond
>this.
>
>Peter Nachtwey
>

Reply by ●June 16, 20072007-06-16

On Jun 13, 10:53 am, "Tom" <tomda...@yahoo.com> wrote:

> I am looking for an algorithm to model a system using an ARMA filter. The
> input and the desired output are available. Is there an iterative algorithm
> that can give a global optimum solution ? Any good reference ?
>
> Regards
>
> Tom

You could be more clear about what you want. A quick solution or in
depth knowledge. I use a minimizing or optimizing algorithm. These
exist in Scilab as lsqrsolve and optim. In Mathcad I use Minerr. In
C I use lmfit.c which is c code converted from ancient fortran but it
works. There are other versions out there that are buggy.
If iterative means on-the-fly there is the recursive least squares
method but I would be careful with this. In my testing, a fast sample
rate yields poles close to the unit circle. The poles move around a
bit while updating and sometimes the poles would cross the unit
circle. Not good.
What ever method you chose you must make a decision as to how many
coefficients you need. One can always get a smaller norm or mean
squared error by adding more coefficients but often the poles in the z
domain end up on the negative real axis which is an indicator that you
probably have too many coefficients. I don't use the recursive least
squares but I do find it interesting how the poles move around and by
how much.
I read about the Levenberg-Marquardt algorithm in Numerical Recipes in
C but didn't like the code or the restrictions. After that I found
tracing through lmfit.c code helpful. I didn't need anything beyond
this.
Peter Nachtwey

Reply by ●June 16, 20072007-06-16

On Jun 14, 6:19 am, BERT <callm...@gmail.com> wrote:

> On Jun 13, 1:53 pm, "Tom" <tomda...@yahoo.com> wrote:
>
> > I am looking for an algorithm to model a system using an ARMA filter. The
> > input and the desired output are available. Is there an iterative algorithm
> > that can give a global optimum solution ? Any good reference ?
>
> > Regards
>
> > Tom
>
> Simon Haykin, "Adaptive Filter Theory"

I don't think that book will help him much. A better book is Ljung and
Sodestrom Theory and Practice of Recursive Estimation, MIT Press 1983.

Reply by ●June 13, 20072007-06-13

On Jun 13, 2:19 pm, BERT <callm...@gmail.com> wrote:

> On Jun 13, 1:53 pm, "Tom" <tomda...@yahoo.com> wrote:
>
> > I am looking for an algorithm to model a system using an ARMA filter. The
> > input and the desired output are available. Is there an iterative algorithm
> > that can give a global optimum solution ? Any good reference ?
>
> > Regards
>
> > Tom
>
> Simon Haykin, "Adaptive Filter Theory"

I wouldn't recommend that book for ARMA modeling; there isn't much any
information on that technique in the text. Haykin (rightfully) points
out that ARMA modeling is in general a nonlinear problem, which is
much more difficult to produce than a model with a simpler AR
structure.
On the other hand, it is, IMO, a great adaptive filtering text.
Jason

Reply by John●June 13, 20072007-06-13

Any optimization criteria is OK as long as the solution is optimal
(unique). In addition samples are available, iterative or non-iterative both
are ok.
Thanks
Tom
"BERT" <callmevc@gmail.com> wrote in message
news:1181758907.555174.71980@i38g2000prf.googlegroups.com...

> On Jun 13, 1:53 pm, "Tom" <tomda...@yahoo.com> wrote:
>> I am looking for an algorithm to model a system using an ARMA filter. The
>> input and the desired output are available. Is there an iterative
>> algorithm
>> that can give a global optimum solution ? Any good reference ?
>>
>> Regards
>>
>> Tom
>
>
> And oh, it might be useful to define what you mean by a "global
> optimum solution" (a.k.a, your optimization criteria).
>

Reply by Eric Jacobsen●June 13, 20072007-06-13

On Wed, 13 Jun 2007 18:56:26 -0000, julius <juliusk@gmail.com> wrote:

>On Jun 13, 1:21 pm, BERT <callm...@gmail.com> wrote:
>> On Jun 13, 1:53 pm, "Tom" <tomda...@yahoo.com> wrote:
>>
>> > I am looking for an algorithm to model a system using an ARMA filter. The
>> > input and the desired output are available. Is there an iterative algorithm
>> > that can give a global optimum solution ? Any good reference ?
>>
>> > Regards
>>
>> > Tom
>>
>> And oh, it might be useful to define what you mean by a "global
>> optimum solution" (a.k.a, your optimization criteria).
>
>And if the original poster defines what he means by "iterative".
>Is it iterative in the samples received, or in terms of solving
>what this "global optimum solution" is?

Yeah, Parks-McLellan is iterative, but it only takes care of the "MA"
part of ARMA.
Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org

Reply by julius●June 13, 20072007-06-13

On Jun 13, 1:21 pm, BERT <callm...@gmail.com> wrote:

> On Jun 13, 1:53 pm, "Tom" <tomda...@yahoo.com> wrote:
>
> > I am looking for an algorithm to model a system using an ARMA filter. The
> > input and the desired output are available. Is there an iterative algorithm
> > that can give a global optimum solution ? Any good reference ?
>
> > Regards
>
> > Tom
>
> And oh, it might be useful to define what you mean by a "global
> optimum solution" (a.k.a, your optimization criteria).

And if the original poster defines what he means by "iterative".
Is it iterative in the samples received, or in terms of solving
what this "global optimum solution" is?

Reply by BERT●June 13, 20072007-06-13

On Jun 13, 1:53 pm, "Tom" <tomda...@yahoo.com> wrote:

> I am looking for an algorithm to model a system using an ARMA filter. The
> input and the desired output are available. Is there an iterative algorithm
> that can give a global optimum solution ? Any good reference ?
>
> Regards
>
> Tom

And oh, it might be useful to define what you mean by a "global
optimum solution" (a.k.a, your optimization criteria).

Reply by BERT●June 13, 20072007-06-13

On Jun 13, 1:53 pm, "Tom" <tomda...@yahoo.com> wrote:

> I am looking for an algorithm to model a system using an ARMA filter. The
> input and the desired output are available. Is there an iterative algorithm
> that can give a global optimum solution ? Any good reference ?
>
> Regards
>
> Tom