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!y38g2000hsy.googlegroups.com!not-for-mail
From: RRogers <rerogers@plaidheron.com>
Newsgroups: comp.soft-sys.matlab,sci.stat.math,sci.engr.control,comp.dsp
Subject: Re: Kalman filtering with multiplicative noise
Date: Tue, 22 Jul 2008 05:54:42 -0700 (PDT)
Organization: http://groups.google.com
Lines: 41
Message-ID: <63e1a774-10ed-4995-94d8-9bf1ad566376@y38g2000hsy.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 1216731283 4231 127.0.0.1 (22 Jul 2008 12:54:43 GMT)
X-Complaints-To: groups-abuse@google.com
NNTP-Posting-Date: Tue, 22 Jul 2008 12:54:43 +0000 (UTC)
Complaints-To: groups-abuse@google.com
Injection-Info: y38g2000hsy.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: 3017
Xref: news.mathworks.com comp.soft-sys.matlab:480927 sci.stat.math:83529 sci.engr.control:50825 comp.dsp:245422



On Jul 21, 8:06 pm, d...@myallit.com wrote:
> On Jul 21, 5:35 pm, "Bruno Luong" <b.lu...@fogale.fr> wrote:
>
> > d...@myallit.com wrote in message
>
> > You might consider Extended Kalman filtering (EKF). Be aware
> > about the eventual non-stability of the scheme.
>
> What do you mean by the eventual non-stability? I did look at the EKF,
> there is some simple sample MATLAB code here:http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objec...
>
> But in the first few lines of this script it says:
>
> % for nonlinear dynamic system:
> %           x_k+1 = f(x_k) + w_k
> %           z_k   = h(x_k) + v_k
> % where w ~ N(0,Q) meaning w is gaussian noise with covariance Q
> %       v ~ N(0,R) meaning v is gaussian noise with covariance R
>
> so the EKF looks appropriate for non-linear process models and
> measurement models that can be represented by any arbitrary functions
> f(x) and h(x), but the noise is still assumed to be additive.

If you change the second equation to log's, and if the log(v2) was
adequately described by a normal distribution then the noise would be
additive and the non-linearity would pushed into the x2/z2 and it
seems that the EKF could deal with it.    In terms of the wikipedia
article and your state equation
z1=x1+v1
lz2=lx2+lv2

and presumptively
x1'=dt*lx1+exp(lx2)+v1
lx2'=log(x1)+lv2

You should really presume these state equations are wrong!  Without
the differential equations including the noise terms I really can't
get a handle on them mentally ( I usually get the first go round wrong
anyway).

RayR