FPGA Central

Dear all,

I thought to post the message here, because I asked everybody whom I coul
ask and looked in the books I could find and ... because I just want t
talk about it. If you encountered a similar problem, I would reall
appreciate any discussion.

I'm working on implementing Kalman filter in the the numerical cod
(fortran). I have a very large linear system (thousands of equations).
programed steady-state Kalman filter that works more or less OK. I did no
work on model reduction yet, but I'm planning to do it very soon. Th
question, that I want to ask, is about time step choice. To get a nic
noise reduction in my calculations I need to set very small time step (
1 microseconds) . The smaller the time step - the better results are.
would like to get the same good results for the time step of 10
microseconds, if I'm successful then my approach can be used in rea
experiments. My idea is to try tuned up a plant noise (input noise
covariance matrix. Because I work with the full size model, I know inpu
noise covariance matrix exactly. it's 1000*1000 matrix. However, larg
time step introduces some numerical error that may need to be taken int
account too in the plant covariance matrix. I'm tthinking in thi
direction at the moment.

Well, I can talk about it alot. But I think I gave enough information fo
the expert to tell me if I'm on the right track or not. Maybe I need t
focus on model reduction first and then play with time step choice? I d
not know.

Thanks
OKH

PS English is my second language, if I was not clear in my writings
please let me know, I'll try to explain the problem better.

I would look at the noise model first. I would guess that you are
using a guassian noise model. As you run the KF faster, the noise it
sees appears more guassian (that is probably what the ADC noise looks
like). What happens is that most systems will have some sort of
bandlimited noise, and as you sample faster, you need many more data
points to see the true noise structure.

Most KF experts will tell you that if the noise model is correct (and
generally non-guassian), the KF should run better at a slower sampling
rate, and performance will degrade as you increase the sampling rate
(since the noise will start to look guassian).

OKH wrote:
> Dear all,
>
> I thought to post the message here, because I asked everybody whom I could
> ask and looked in the books I could find and ... because I just want to
> talk about it. If you encountered a similar problem, I would really
> appreciate any discussion.
>
> I'm working on implementing Kalman filter in the the numerical code
> (fortran). I have a very large linear system (thousands of equations). I
> programed steady-state Kalman filter that works more or less OK. I did not
> work on model reduction yet, but I'm planning to do it very soon. The
> question, that I want to ask, is about time step choice. To get a nice
> noise reduction in my calculations I need to set very small time step (~
> 1 microseconds) . The smaller the time step - the better results are. I
> would like to get the same good results for the time step of 100
> microseconds, if I'm successful then my approach can be used in real
> experiments. My idea is to try tuned up a plant noise (input noise)
> covariance matrix. Because I work with the full size model, I know input
> noise covariance matrix exactly. it's 1000*1000 matrix. However, large
> time step introduces some numerical error that may need to be taken into
> account too in the plant covariance matrix. I'm tthinking in this
> direction at the moment.
>
> Well, I can talk about it alot. But I think I gave enough information for
> the expert to tell me if I'm on the right track or not. Maybe I need to
> focus on model reduction first and then play with time step choice? I do
> not know.
>
> Thanks
> OKH
>
> PS English is my second language, if I was not clear in my writings,
> please let me know, I'll try to explain the problem better.