Path: news.mathworks.com!newsfeed-00.mathworks.com!nlpi057.nbdc.sbc.com!prodigy.net!border1.nntp.dca.giganews.com!nntp.giganews.com!postnews.google.com!i76g2000hsf.googlegroups.com!not-for-mail
From: RRogers <rerogers@plaidheron.com>
Newsgroups: sci.stat.math,comp.soft-sys.matlab,sci.engr.control
Subject: Re: Kalman filtering with multiplicative noise
Date: Tue, 22 Jul 2008 06:11:14 -0700 (PDT)
Organization: http://groups.google.com
Lines: 71
Message-ID: <c23fa80c-b7a0-4b27-9afa-7ba254f97163@i76g2000hsf.googlegroups.com>
References: <1309743c-3d5c-4165-9cdb-1ab51892727d@z16g2000prn.googlegroups.com> 
NNTP-Posting-Host: 76.179.99.130
Mime-Version: 1.0
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: 7bit
X-Trace: posting.google.com 1216732274 14395 127.0.0.1 (22 Jul 2008 13:11:14 GMT)
X-Complaints-To: groups-abuse@google.com
NNTP-Posting-Date: Tue, 22 Jul 2008 13:11:14 +0000 (UTC)
Complaints-To: groups-abuse@google.com
Injection-Info: i76g2000hsf.googlegroups.com; posting-host=76.179.99.130; 
User-Agent: G2/1.0
X-HTTP-UserAgent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.8.1.16) 
Bytes: 4497
Xref: news.mathworks.com sci.stat.math:83530 comp.soft-sys.matlab:480938 sci.engr.control:50827



On Jul 21, 7:49 pm, d...@myallit.com wrote:
> On Jul 22, 2:20 am, Tim Wescott <t...@seemywebsite.com> wrote:
>
>
>
> > On Sun, 20 Jul 2008 19:51:02 -0700, dsp wrote:
> > > I'm trying to implement a Kalman filter in MATLAB that will use two
> > > types of measurements: volume and in/out flow rate. For the flow rate,
> > > the measurement error is additive Gaussian, but for the volume the
> > > measurement error is expressed as a percentage of the volume, so that
> > > the volume measurement is less accurate when its value is higher. I
> > > think the measurement model should therefore be:
>
> > > Flow rate measurement model:
> > > z1 = x1 + v1 where v1 ~ N(0,e1)
>
> > > Volume measurement model:
> > > z2 = x2*v2 where v2 ~ N(1,e2)
>
> > > I assumed the volume filtering should be done in the log domain to make
> > > the noise additive but how do I deal with a noise mean of one when the
> > > Kalman filter assumes a mean of zero? And how can I have a Kalman filter
> > > using both the measurements if one is in the log domain and the other
> > > one isn't?
>
> > > I am also dealing with a system where measurements will usually be
> > > missing (they are arriving sequentially) and at an uneven sampling rate,
> > > any other pointers on these too would be appreciated.
>
> > As Ray pointed out these seem to be completely independent measurements,
> > unless V1 and V2 are correlated.
>
> > With any affine system, such as the log-domain volume system, you can
> > subtract out the offset to make the system linear, do your linear
> > processing, then add the offset back in.  I.O.W., calculate log z2 = log
> > x2 + log v2 + 1, then define dlz2 = log z2 - 1, then find your estimated
> > dlz2, then back up to your estimated z2.  (Note that your estimate of z2
> > probably won't be strictly optimal in the mean-squared sense, only your
> > estimate of dlz2 will be.  But you'll certainly be closer than you would
> > by a lot of other means).
>
> > --
> > Tim Wescott
> > Control systems and communications consultinghttp://www.wescottdesign.com
>
> > Need to learn how to apply control theory in your embedded system?
> > "Applied Control Theory for Embedded Systems" by Tim Wescott
> > Elsevier/Newnes,http://www.wescottdesign.com/actfes/actfes.html
>
> My state transition for these two measurements is given by:
>
> F = [dt 1
>      1  0]
>
> where dt is the time step, so as far as I understand it these
> measurements are correlated - if z1 is positive, then z2 will be
> increasing and vice versa.
>
> Doing this in the log domain makes sense, but how can I have one
> measurement in the log domain and the other not? The state transition
> won't make sense.
>
> Equation 2 will actually reach zero quite often, so maybe I need
> multiplicative and additive noise in my measurement model for z2, not
> too sure about that.

I really suggest that you make up a graphical model of the system,
Simulink or Scicos ( I can deal with Scicos), both the physical system
and then the proposed filtering.

RayR