# Kalman filter with elliptical (quadratic) constraint

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?
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Note that I made a mistake in the previous post. The measured quantities are mx and my.
Jay Goldfarb
snipped-for-privacy@gci.net (Jay Goldfarb) wrote in message

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Jay Goldfarb wrote:

Have you tried to transform your state space to another coordinate system, like polar coordinates?
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snipped-for-privacy@gci.net (Jay Goldfarb) writes:

It seems to me that the linearization (since A=0) is bound to be unobservable, thus (I think) the Kalman Filter can not work?
Lars