Kalman Filter for predicing the center of a filter

jim wrote:
> 
> Mat wrote:
> 
>> I want a smoothed estimate of the current raw value relative to my
>> filter window. Extrapolation of an unknown next signal is "not
>> required".
>>
> 
> I don't understand. You are asking for a algorithm that would predict
> the output of a filter? You apparently have the data and you have the
> filter. Where's the problem?

The output of the filter is delayed by some amount that depends on the 
filter. Some filters are more "prompt" than linear-phase filters. 
(Minimum-phase filters are the most prompt of all.) Mat wants to predict 
when the delay begins what the output is likely to be after the delay 
period has elapsed.

Jerry
-- 
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
���������������������������������������������������������������������

jim wrote:
> Mat wrote:
>
> >
> > I want a smoothed estimate of the current raw value relative to my
> > filter window. Extrapolation of an unknown next signal is "not
> > required".

I do not have the filter.  My question are aimed at which filter might
be more suitable as stated above -- or whether anyone else is
currently using the filter for a similiar task.  If I can confirm
either of the two remaining interpolation methods or other
suggestions are suitable then I will move forward.

Mat

> I don't understand. You are asking for a algorithm that would predict
> the output of a filter? You apparently have the data and you have the
> filter. Where's the problem?
>
> -jim
>
>
> > >   3. You wish a "good" prediction of the next value(s) from the noisy
> > >      source so that you can apply a suitable correction.
> >
> > I'm looking for an interpolation method and/or a suitable prediction
> > method than can estimate what the "known population" within
> > my raw data would be in a smoothed format. I suspect this
> > reduces to interpolation of all known raw values in a filter window
> > to smoothed values. It appears that kriging and Gaussian
> > Process Regression are frequently used for this process but
> > there might be other interpolation methods that work just as well.
> >
> > Does anyone doing interpolation or something similiar to what I've
> > described know of models that might be suitable for this purpose?
> >
> > Mat
> >
> > >   4. *THE GOTCHA* You have an appropriately sensitive detector of mismatch
> > >      between "predicted" and "actual" value to signal when you should
> > >      change compensating algorithm.
> > >
> > > I'm not attempting to claim "solution" but only "better" definition.
> > >
> > >
> > > A side question to group
> > > "Am I thinking in useful directions for solving my own problems?"
>
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Mat skrev:
> It appears that Kriging Interpolation or Gaussian Process Regression
> are very similar and smooth data using information about how the
> points are statistically deviation over the period of interest.  I feel
> either of these two processes might be more suitable for my purpose
> since the end results would be a set of smoothed value via
> interpolation.
>
> Does anyone has any practical experience with either of these methods?

I have only seen Kriging mentioned as a tool with 2D scattered data.
You have been deliberately vague about your data, so this is one
detail that confuses me. Regression models might be good
interpolators; as extrapolators they tend not to perform quite as well.


The common denominator of the two is that they work in batch
mode, i.e. all relevant data need to be available when you start
the processing. If processing delay is an issue -- and it seems
it is, in your application -- then I see no obvious way to incorporate
such methods.

Without knowing more about the application, I think the Kalman
filter/predictor is the best you can do for filtering and predicting
adaptive processes. 

Rune

Mat skrev:
> It appears that Kriging Interpolation or Gaussian Process Regression
> are very similar and smooth data using information about how the
> points are statistically deviation over the period of interest.  I feel
> either of these two processes might be more suitable for my purpose
> since the end results would be a set of smoothed value via
> interpolation.
>
> Does anyone has any practical experience with either of these methods?

I have only seen Kriging mentioned as a tool with 2D scattered data.
You have been deliberately vague about your data, so this is one
detail that confuses me. Regression models might be good
interpolators; as extrapolators they tend not to perform quite as well.


The common denominator of the two is that they work in batch
mode, i.e. all relevant data need to be available when you start
the processing. If processing delay is an issue -- and it seems
it is, in your application -- then I see no obvious way to incorporate
such methods.

Without knowing more about the application, I think the Kalman
filter/predictor is the best you can do for filtering and predicting
adaptive processes. 

Rune

Mat wrote:
> 
> jim wrote:
> > Mat wrote:
> >
> > >
> > > I want a smoothed estimate of the current raw value relative to my
> > > filter window. Extrapolation of an unknown next signal is "not
> > > required".
> 
> I do not have the filter.  My question are aimed at which filter might
> be more suitable as stated above -- or whether anyone else is
> currently using the filter for a similiar task.  If I can confirm
> either of the two remaining interpolation methods or other
> suggestions are suitable then I will move forward.

Yes many people use filters to smooth data. There is no "estimate",
"prediction" or "interpolation" involved. Those words don't make any
sense to me in the context of what it sounds like you want to do.

	What I think you may be asking is - can I take my data set run it thru
a filter that smoothes it and then have the output so that it lines up
with the input. That is, you wish perhaps to construct a graph of your
data such that the smoothed version and unsmoothed version appear
together (no delay) so that you can see exactly how they correspond. If
that is your goal then it is not at all difficult to acheive.

-jim

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Jerry Avins wrote:

> 
> The output of the filter is delayed by some amount that depends on the
> filter. Some filters are more "prompt" than linear-phase filters.
> (Minimum-phase filters are the most prompt of all.) Mat wants to predict
> when the delay begins what the output is likely to be after the delay
> period has elapsed.

What do you mean "predict"? Is someone going to design this filter? Does
he want to know where he can find a crystal ball that will tell him what
the filter this person is going to design will look like?

-jim

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jim wrote:
> Jerry Avins wrote:
>
> >
> > The output of the filter is delayed by some amount that depends on the
> > filter. Some filters are more "prompt" than linear-phase filters.
> > (Minimum-phase filters are the most prompt of all.) Mat wants to predict
> > when the delay begins what the output is likely to be after the delay
> > period has elapsed.

The following url has an explanation for kriging.
http://en.wikipedia.org/wiki/Kriging

And more importantly it show a graph of one-dimensional data
interpolation by Kriging,   Following is the explanation they provide.

"A set of values are then observed, each value associated with a
spatial location. Now, a new value can be predicted at any new spatial
location, by combining the Gaussian prior with a Gaussian likelihood
function for each of the observed values. The resulting posterior
distribution is also a Gaussian, with a mean and covariance that can be
simply computed from the observed values, "

Now I have a regression consultant who will soon try to explore whether
his techniques will be useful on the solution that been posed and
rephrased several times.  If Kalman is more practical than the two
interpolation methods mentioned several times I'll find a consultant
in this area -- but if interpolation is more durable that will be my
next direction.  So at this point I'm looking very broadly to find
the modeling solution others are using for the task described. My
regression consultant is not involved with Gaussian Process
Regression which I understand is a more generalized form related
to Kriging.

If you do a google search on "predict the smoothed filter" or similiar
wording you will find that when the raw value are know -- that it's
possible to predict their smoothed values.  Take a look at the
background of people in this area and you will find they are using
mathematical models and not crystal balls. It looks like most of
this work is going on outside of the DSP field  -- so I can
understand if the idea seems foriegn.

Mat


> What do you mean "predict"? Is someone going to design this filter? Does
> he want to know where he can find a crystal ball that will tell him what
> the filter this person is going to design will look like?
>
> -jim
>
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jim wrote:
> 
> Jerry Avins wrote:
> 
>> The output of the filter is delayed by some amount that depends on the
>> filter. Some filters are more "prompt" than linear-phase filters.
>> (Minimum-phase filters are the most prompt of all.) Mat wants to predict
>> when the delay begins what the output is likely to be after the delay
>> period has elapsed.
> 
> What do you mean "predict"? Is someone going to design this filter? Does
> he want to know where he can find a crystal ball that will tell him what
> the filter this person is going to design will look like?

The filter itself will have been designed once and for all. He wants a 
crystal ball that will tell him what the output of the filter will be 
after the data enter the filter but before the filtered result emerges. 
Within limits, that may be feasible.

Jerry
-- 
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
���������������������������������������������������������������������

Jerry Avins wrote:
> jim wrote:
> >
> > Jerry Avins wrote:
> >
> >> The output of the filter is delayed by some amount that depends on the
> >> filter. Some filters are more "prompt" than linear-phase filters.
> >> (Minimum-phase filters are the most prompt of all.) Mat wants to predi=
ct
> >> when the delay begins what the output is likely to be after the delay
> >> period has elapsed.
> >
> > What do you mean "predict"? Is someone going to design this filter? Does
> > he want to know where he can find a crystal ball that will tell him what
> > the filter this person is going to design will look like?

I really do appreciate the comments on Kalman filters and will pursue
this model further.  Apparently the two interpolation methods which
take a different approach to obtain the same end are too far away
from the more common use of DSP to go much further here.  And it
makes sense in a field that most pay for the level of smoothness with
a lag penalty that tools are model that try a loophole approach are
questionable.  I spend over 75% of my signal modeling efforts on
noise issues in my domain  and 25% on making sure that I avoid
signal lags.  It's not hard for me to believe that someone who has
spend much of their efforts on avoiding filter lags has techniques
that works because the persistent person will generally find a
solution.

Mat

> The filter itself will have been designed once and for all. He wants a
> crystal ball that will tell him what the output of the filter will be
> after the data enter the filter but before the filtered result emerges.
> Within limits, that may be feasible.
>
> Jerry
> --
>         "The rights of the best of men are secured only as the
>         rights of the vilest and most abhorrent are protected."
>             - Chief Justice Charles Evans Hughes, 1927
> =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF

On Oct 6, 4:03 pm, "Mat" <math_st...@comcast.net> wrote:
> It may have been better to say that I want to use my raw data to
> predict the smoothed trend without any lag.

Maybe I'm missing the point, but why don't you consider computing a
smoothed trend from only the past samples, as in an exponential window
going back into the past?  That has zero lag.

> So I would like to
> know if I could use something like a Kalman filter to develop
> a model to do this on say 1000 to 5000 data points which
> would have enough predictive powers to predict the smoothed
> values using my raw data. I know prediction issues are often
> dealt with from the statistical viewpoint using regression and
> similar models.
>
> Can Kalman or some other dsp algorithm be trained on
> raw data to predict filtered values with zero lag?