Re: Kalman filter with elliptical (quadratic) constraint

Jay Goldfarb wrote:
> Note that I made a mistake in the previous post. The measured
> quantities are mx and my.
>
> Jay Goldfarb
>
> [EMAIL PROTECTED] (Jay Goldfarb) wrote in message news:<[EMAIL PROTECTED]>...
>
> > I am struggling with a problem in which the states and measurements
> > are both implicit in a constraint of the form
> >
> > (mx-bx)^2/(1+sx)^2 + (my-by)^2/(1+sy)^2 = 1
> >
> > where mx, bx are measurements and bx, by sx, sy are states to be
> > estimated. The states are generally constant but occassionally exhibit
> > discontinuities, and it is these discontinuities which I would like to
> > track.
> >
> > I have been treating the constraint equation as a
> > "pseudo-measurement".
> >
> > I have tried a standard extended KF, an extended "Bayes" filter, a
> > Schmidt KF (estimating bx and by only) and several variations.
> > Everything I have tried has been unstable. The matrix H*Px*HT (H -
> > Jacobian of constraint, Px state covariance) is very ill-conditioned.
> >
> > I have experimented with various a priori covariances and with both
> > constant and Markov process models (with varying correlation times)
> > for the states.
> >
> > Does anyone have any suggestions as to how to proceed?

Have you tried to transform your state space to another coordinate 
system, like polar coordinates?