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From: stanp <stan.pawl@gmail.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 10:18:06 -0700 (PDT)
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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.

The EKF propagates first and second moments which is essentially
treating the problem like it can be approximated like a linear
Gaussian.

Particle filters come in various flavors and there are versions that
can handle multiplicative noise.