Forgetting factor for discrete linear kalman filter

On Tue, 07 Apr 2009 20:31:16 GMT, Ben Jackson <ben@ben.com> wrote:

>On 2009-04-07, Muzaffer Kal <kal@dspia.com> wrote:
>> On Tue, 07 Apr 2009 09:59:06 -0500, "adrian116"
>><adrianchang116@hotmail.com> wrote:
>>>>One possibility is to update the covariance estimate in the following
>>>>manner
>>>>R(n) =3D (1-lambda)R(n-1) + lambda * x*x'
>>>>
>>>
>>>Thanks David, what is the 3D in the equation?
>>
>> There is no 3D in the equation. That's your news client adding some
>> markup to the text in the post.
>
>Actually it's *your* news client doign [SIC] MIME encoding and his client

I think your reply is to the wrong person.

>
>One possibility is to update the covariance estimate in the following
>manner
>R(n) =3D (1-lambda)R(n-1) + lambda * x*x'
>
>where lambda is a scalar and x is a vector and x' is the transpose of
>x.
>
>Hope that helps.
>
>Cheers,
>David
>

Do you mind to tell me how do you derive such a euqations and what the
symbols represent for?
THX

>
>Since my experience with Kalman filters includes no moving windows, 
>unless you're doing some serious smoothing, all I can do is point you to

>the book.
>
>You may want to answer my question about how what you're doing compares 
>to the Wikipedia article -- you don't seem to be realizing a standard 
>Kalman filter, hence any questions you ask should have a _lot_ more 
>background on what you really are doing.
>
>-- 
>http://www.wescottdesign.com
>

I may need to have a talk with my teacher to answer you question. Thank
You

adrian116 schrieb:
> Dear all, 
> 
>        I am doing a final year project to estimate the power consumption
> of a chiller plant. I have built a basic model by using Kalman Filter and
> get a result with some percent of error.
> 
> For my model, I used a moving windows say 60 sets of data, then calculated
> the parameters to be estimated from these data sets. Use these a,b,c,d,e
> and the measurement of 61set of data to estimation the power at t=61. So
> a,b,c,d,e calculated from 2-61sets of data sets and measurement of 62 set
> of data are used to determine the power at t=62 and so on.
> 
> For this case, I need to handle all 60 sets in the moving windows each
> time. It seems strange and time consumption.
> 
> My teacher asked me try to introduce forgetting factor to my model. But i
> have searched many material in the web and didn't find any help. Do you
> guys have any idea?
> 
> Thank You.
> 
> 

I do not know what your really trying to approach. As far as I know the 
Kalman Filter is supposed to predict and filter at each measurement 
step. If you are using averaging windows you induce correlation in time 
which violates the assumption of the Kalman Filter that you have white 
noise. In some cases that correlation does not matter if your data is 
very noisy and the process you are trying to estimate is very slowly 
changing. (In your case the change should be not significant within 60 
measurements than you are ok with your method)
If you want to keep your windowing and use a forgetting factor you 
should use a different window. Google for weighted averages...