adaptive kalman filtering with dynamics update?

Hey all, I have a quick question about Kalman filtering: I have been
reading about it and I need some opinions about whether Kalman filters are
suitable for my problem at hand: I need to do predictive filtering on a
non-stationary digital signal. There is no noise in the system. Also, I do
not have a dynamic model for the signal, either. On top of that, any
dynamic model that I assume will not be constant since the signal is not
stationary. So I am thinking that the Kalman filter that will be used
requires an adaptive correction on the dynamical model it uses (I could not
find any papers on correcting dynamical model.) The reason why I am
assuming Kalman filters may be helpful in this problem is that they are
used for tracking, and in my case my problem is basically tracking a
signal. So does anyone have any thoughts on whether Kalman filtering would
be applicable to this case? If you could direct me to papers/resources that
would be great. Thanks much in advance.

Oz.

doublehelics wrote:

> Hey all, I have a quick question about Kalman filtering: I have been
> reading about it and I need some opinions about whether Kalman filters are
> suitable for my problem at hand: I need to do predictive filtering on a
> non-stationary digital signal. There is no noise in the system. Also, I do
> not have a dynamic model for the signal, either. On top of that, any
> dynamic model that I assume will not be constant since the signal is not
> stationary. So I am thinking that the Kalman filter that will be used
> requires an adaptive correction on the dynamical model it uses (I could not
> find any papers on correcting dynamical model.) The reason why I am
> assuming Kalman filters may be helpful in this problem is that they are
> used for tracking, and in my case my problem is basically tracking a
> signal. So does anyone have any thoughts on whether Kalman filtering would
> be applicable to this case? If you could direct me to papers/resources that
> would be great. Thanks much in advance.
> 
> Oz.

On Nov 14, 9:38&#4294967295;am, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
> doublehelics wrote:
> > Hey all, I have a quick question about Kalman filtering: I have been
> > reading about it and I need some opinions about whether Kalman filters are
> > suitable for my problem at hand: I need to do predictive filtering on a
> > non-stationary digital signal. There is no noise in the system. Also, I do
> > not have a dynamic model for the signal, either. On top of that, any
> > dynamic model that I assume will not be constant since the signal is not
> > stationary. So I am thinking that the Kalman filter that will be used
> > requires an adaptive correction on the dynamical model it uses (I could not
> > find any papers on correcting dynamical model.) The reason why I am
> > assuming Kalman filters may be helpful in this problem is that they are
> > used for tracking, and in my case my problem is basically tracking a
> > signal. So does anyone have any thoughts on whether Kalman filtering would
> > be applicable to this case? If you could direct me to papers/resources that
> > would be great. Thanks much in advance.
>
> > Oz.

On Nov 14, 9:38&#4294967295;am, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
> doublehelics wrote:
> > Hey all, I have a quick question about Kalman filtering: I have been
> > reading about it and I need some opinions about whether Kalman filters are
> > suitable for my problem at hand: I need to do predictive filtering on a
> > non-stationary digital signal. There is no noise in the system. Also, I do
> > not have a dynamic model for the signal, either. On top of that, any
> > dynamic model that I assume will not be constant since the signal is not
> > stationary. So I am thinking that the Kalman filter that will be used
> > requires an adaptive correction on the dynamical model it uses (I could not
> > find any papers on correcting dynamical model.) The reason why I am
> > assuming Kalman filters may be helpful in this problem is that they are
> > used for tracking, and in my case my problem is basically tracking a
> > signal. So does anyone have any thoughts on whether Kalman filtering would
> > be applicable to this case? If you could direct me to papers/resources that
> > would be great. Thanks much in advance.
>
> > Oz.

Hello, I think there was a problem with the posts. Could you repost these
above? Thanks!

Arif.

>On Nov 14, 9:38=A0am, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
>> doublehelics wrote:
>> > Hey all, I have a quick question about Kalman filtering: I have been
>> > reading about it and I need some opinions about whether Kalman filters
=
>are
>> > suitable for my problem at hand: I need to do predictive filtering on
a
>> > non-stationary digital signal. There is no noise in the system. Also,
I=
> do
>> > not have a dynamic model for the signal, either. On top of that, any
>> > dynamic model that I assume will not be constant since the signal is
no=
>t
>> > stationary. So I am thinking that the Kalman filter that will be used
>> > requires an adaptive correction on the dynamical model it uses (I
could=
> not
>> > find any papers on correcting dynamical model.) The reason why I am
>> > assuming Kalman filters may be helpful in this problem is that they
are
>> > used for tracking, and in my case my problem is basically tracking a
>> > signal. So does anyone have any thoughts on whether Kalman filtering
wo=
>uld
>> > be applicable to this case? If you could direct me to papers/resources
=
>that
>> > would be great. Thanks much in advance.
>>
>> > Oz.
>
>

On Mon, 14 Nov 2011 04:17:09 -0600, doublehelics wrote:

> Hey all, I have a quick question about Kalman filtering: I have been
> reading about it and I need some opinions about whether Kalman filters
> are suitable for my problem at hand: I need to do predictive filtering
> on a non-stationary digital signal. There is no noise in the system.
> Also, I do not have a dynamic model for the signal, either. On top of
> that, any dynamic model that I assume will not be constant since the
> signal is not stationary. So I am thinking that the Kalman filter that
> will be used requires an adaptive correction on the dynamical model it
> uses (I could not find any papers on correcting dynamical model.) The
> reason why I am assuming Kalman filters may be helpful in this problem
> is that they are used for tracking, and in my case my problem is
> basically tracking a signal. So does anyone have any thoughts on whether
> Kalman filtering would be applicable to this case? If you could direct
> me to papers/resources that would be great. Thanks much in advance.

Kalman does not mean "magic" in Hungarian.  Therefor, the Kalman filter 
is not a magic filter.

You need to know something about your system in order to use its past 
behavior to predict its future behavior -- if you have no system 
knowledge, you have no predictive ability unless you have a magic filter.

There are no magic filters.

What the Kalman filter does is answer the question "given what I know 
about this system's past behavior, what is it most likely doing _now_ (or 
what is it going to do in the future, or what was it's state in the past, 
really)".  An actual really-o truly-o _Kalman_ Kalman filter _only_ 
answers this question if the system is discrete time, with perfectly 
known parameters, and whose process variables and measurements are being 
corrupted by Gaussian white noise.  Change any of those conditions, and a 
really-o truly-o Kalman Kalman filter won't work right.

There are a bunch of filters that are colloquially _called_ "Kalman 
filters" but aren't -- Kalman-Bucy filters work in continuous time, so-
called "extended Kalman filters" provide a way of dealing with mild to 
moderately nonlinear systems, etc.

So, what you need for _any_ filter to work, whether it be a Kalman filter 
or a more general filter, is _some_ model of the signal dynamics.  The 
model doesn't have to have known parameters at first, and the parameters 
don't have to stay constant -- but it helps a _lot_ if you can model the 
signal adequately with a signal of constant structure with varying 
parameters, and if you can at least put some bounds on how, and how much, 
the parameters vary.

Once you've done _that_, if you can model the signal as the output of a 
linear system with time-varying parameters, then you can use RLMS 
adaptive filtering (and RLMS is very Kalman-like) to deduce a system 
model from the signal behavior, and you can use that system model to make 
predictions about the future behavior of the signal.

-- 
www.wescottdesign.com

On Mon, 14 Nov 2011 12:44:46 -0600, doublehelics wrote:

> Hello, I think there was a problem with the posts. Could you repost
> these above? Thanks!
> 
> Arif.
> 
>>On Nov 14, 9:38=A0am, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
>>> doublehelics wrote:
>>> > Hey all, I have a quick question about Kalman filtering: I have been
>>> > reading about it and I need some opinions about whether Kalman
>>> > filters
> =
>>are
>>> > suitable for my problem at hand: I need to do predictive filtering
>>> > on
> a
>>> > non-stationary digital signal. There is no noise in the system.
>>> > Also,
> I=
>> do
>>> > not have a dynamic model for the signal, either. On top of that, any
>>> > dynamic model that I assume will not be constant since the signal is
> no=
>>t
>>> > stationary. So I am thinking that the Kalman filter that will be
>>> > used requires an adaptive correction on the dynamical model it uses
>>> > (I
> could=
>> not
>>> > find any papers on correcting dynamical model.) The reason why I am
>>> > assuming Kalman filters may be helpful in this problem is that they
> are
>>> > used for tracking, and in my case my problem is basically tracking a
>>> > signal. So does anyone have any thoughts on whether Kalman filtering
> wo=
>>uld
>>> > be applicable to this case? If you could direct me to
>>> > papers/resources
> =
>>that
>>> > would be great. Thanks much in advance.
>>>
>>> > Oz.

I think that Dave was protesting Vladimir's re-naming of the thread, and 
attempting to re-rename it so that it would read correctly in Google 
Group's broken browser.

Just ignore Vladimir when he gets like that.

-- 
www.wescottdesign.com

Thanks for the info, I agree that my post sounds a little vague, may be i
should have been more clear about what I was trying to ask.

I was merely trying to ask if there is a way to do adaptive predictive
filtering using Kalman's approach (I already looked at adaptive mmse and
rls filtering techniques.) I was just researching whether Kalman filtering
would be applicable and would add anything new to what i am doing. What I
meant by I do not know the system dynamics is basically we do not have an
initial model of how system is behaving, BUT we want to use linear
predictive model. From this point of view, it seems to me like this is more
of a system identification problem. 

From your post I understand that there is a way to do this but its very
similar to other adaptive filtering methods. 

Oz.

>On Mon, 14 Nov 2011 12:44:46 -0600, doublehelics wrote:
>
>> Hello, I think there was a problem with the posts. Could you repost
>> these above? Thanks!
>> 
>> Arif.
>> 
>>>On Nov 14, 9:38=A0am, Vladimir Vassilevsky <nos...@nowhere.com> wrote:
>>>> doublehelics wrote:
>>>> > Hey all, I have a quick question about Kalman filtering: I have
been
>>>> > reading about it and I need some opinions about whether Kalman
>>>> > filters
>> =
>>>are
>>>> > suitable for my problem at hand: I need to do predictive filtering
>>>> > on
>> a
>>>> > non-stationary digital signal. There is no noise in the system.
>>>> > Also,
>> I=
>>> do
>>>> > not have a dynamic model for the signal, either. On top of that,
any
>>>> > dynamic model that I assume will not be constant since the signal
is
>> no=
>>>t
>>>> > stationary. So I am thinking that the Kalman filter that will be
>>>> > used requires an adaptive correction on the dynamical model it uses
>>>> > (I
>> could=
>>> not
>>>> > find any papers on correcting dynamical model.) The reason why I am
>>>> > assuming Kalman filters may be helpful in this problem is that they
>> are
>>>> > used for tracking, and in my case my problem is basically tracking
a
>>>> > signal. So does anyone have any thoughts on whether Kalman
filtering
>> wo=
>>>uld
>>>> > be applicable to this case? If you could direct me to
>>>> > papers/resources
>> =
>>>that
>>>> > would be great. Thanks much in advance.
>>>>
>>>> > Oz.
>
>I think that Dave was protesting Vladimir's re-naming of the thread, and 
>attempting to re-rename it so that it would read correctly in Google 
>Group's broken browser.
>
>Just ignore Vladimir when he gets like that.
>
>-- 
>www.wescottdesign.com
>

On Mon, 14 Nov 2011 15:15:41 -0600, doublehelics wrote:

> Thanks for the info, I agree that my post sounds a little vague, may be
> i should have been more clear about what I was trying to ask.
> 
> I was merely trying to ask if there is a way to do adaptive predictive
> filtering using Kalman's approach (I already looked at adaptive mmse and
> rls filtering techniques.) I was just researching whether Kalman
> filtering would be applicable and would add anything new to what i am
> doing. What I meant by I do not know the system dynamics is basically we
> do not have an initial model of how system is behaving, BUT we want to
> use linear predictive model. From this point of view, it seems to me
> like this is more of a system identification problem.
> 
> From your post I understand that there is a way to do this but its very
> similar to other adaptive filtering methods.

RLS and MMSE are both solving the same problem as a Kalman filter, so you 
would expect them to get the same answer.

I'm pretty sure that they're basically specialized extended Kalman 
filters -- if you had the input to a system and the output and tried to 
find the optimal system identification in the least-squares sense then 
your answer wouldn't approximate a Kalman filter -- it _would be_ a Kalman 
filter.

If you have reason to suspect that the probabilities involved are far 
from being Gaussian, or if your costs are far from being error-squared, 
then "none of the above" may prove to be the best answer.

-- 
www.wescottdesign.com

Yes, I was looking at MMSE and RLS solutions because they tend to have
different convergence characteristics. 

I think I need to learn Kalman filtering theory in more depth to see what
can be done and what cannot, but my main problem is that the signal that we
are trying to model (coming from some biological experiment) is not studied
very well and I am not even sure about how to define the noise in the
signal, let alone how to estimate the noise levels. maybe i could estimate
the noise level (based on some definition) on the fly?? again, maybe not.
my biology friends should be of help there, I hope.

thanks.

Oz.

>On Mon, 14 Nov 2011 15:15:41 -0600, doublehelics wrote:
>
>> Thanks for the info, I agree that my post sounds a little vague, may be
>> i should have been more clear about what I was trying to ask.
>> 
>> I was merely trying to ask if there is a way to do adaptive predictive
>> filtering using Kalman's approach (I already looked at adaptive mmse
and
>> rls filtering techniques.) I was just researching whether Kalman
>> filtering would be applicable and would add anything new to what i am
>> doing. What I meant by I do not know the system dynamics is basically
we
>> do not have an initial model of how system is behaving, BUT we want to
>> use linear predictive model. From this point of view, it seems to me
>> like this is more of a system identification problem.
>> 
>> From your post I understand that there is a way to do this but its very
>> similar to other adaptive filtering methods.
>
>RLS and MMSE are both solving the same problem as a Kalman filter, so you

>would expect them to get the same answer.
>
>I'm pretty sure that they're basically specialized extended Kalman 
>filters -- if you had the input to a system and the output and tried to 
>find the optimal system identification in the least-squares sense then 
>your answer wouldn't approximate a Kalman filter -- it _would be_ a Kalman

>filter.
>
>If you have reason to suspect that the probabilities involved are far 
>from being Gaussian, or if your costs are far from being error-squared, 
>then "none of the above" may prove to be the best answer.
>
>-- 
>www.wescottdesign.com
>