applied Hinfinity filtering

Hinfinity filtering is often mentioned by the readers of this group. For
sure, it has theortic advantages over the kalman filter under certain
conditions. Now I encounter the problem of tuning the weighting matrices
and I wonder if you have any cooking recipes, rules of thumb or references
to help. A good startoff for me is trying the covariance matrices of the
corresponding kalman filter for the system to start with but only empirical
tuning is really exhausting

TIA,
Kai

On Sep 11, 7:54 pm, Kai <inva...@invalid.invalid> wrote:
> Hinfinity filtering is often mentioned by the readers of this group. For
> sure, it has theortic advantages over the kalman filter under certain
> conditions. Now I encounter the problem of tuning the weighting matrices
> and I wonder if you have any cooking recipes, rules of thumb or references
> to help. A good startoff for me is trying the covariance matrices of the
> corresponding kalman filter for the system to start with but only empirical
> tuning is really exhausting
>
> TIA,
> Kai

I found myself doing the same as you. Using the same "ratio" as the
noise. In optimal control there are similar issues with weighting
matrices but it is a little more intuative there. One advantage of H
infinity is that it can be applied to deterministic processes too! One
thing I cannot understand is that recently (a few years back) a proof
has been given that LMS minimizes the H infinity norm and NOT the mean-
square error. This being the case, it appears that sure all the
adaptive filter theory of Widrow is well...kinda wrong! Instead of
convergence to the Optimal Wiener, it surely must converge to the H
infinity solution! We have been using H infinity all along...

HardySpicer wrote:

> On Sep 11, 7:54 pm, Kai <inva...@invalid.invalid> wrote:
>> Hinfinity filtering is often mentioned by the readers of this group. For
>> sure, it has theortic advantages over the kalman filter under certain
>> conditions. Now I encounter the problem of tuning the weighting matrices
>> and I wonder if you have any cooking recipes, rules of thumb or
>> references to help. A good startoff for me is trying the covariance
>> matrices of the corresponding kalman filter for the system to start with
>> but only empirical tuning is really exhausting
>>
>> TIA,
>> Kai
> 
> I found myself doing the same as you. Using the same "ratio" as the
> noise. In optimal control there are similar issues with weighting
> matrices but it is a little more intuative there. One advantage of H
> infinity is that it can be applied to deterministic processes too! One
> thing I cannot understand is that recently (a few years back) a proof
> has been given that LMS minimizes the H infinity norm and NOT the mean-
> square error. This being the case, it appears that sure all the
> adaptive filter theory of Widrow is well...kinda wrong! Instead of
> convergence to the Optimal Wiener, it surely must converge to the H
> infinity solution! We have been using H infinity all along...

When I simulate a system comparing Kalman-Filter and Hinfinity-Filter, I get
more or less exacly the same estimation results when appling covariance
matrices=weighting matrices and same initial values. I'm simulating all
kind of noises, systematic errors, whatever. seems to be the same.

if anyone could help bringing some light into the dark I would appreciate.
So far I don't really see the advantage of the Hinfinity estimation
algorithm