> 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