EKF process/noise modeling with non-additive noise

Hi,

I am trying to model an EKF where the noise is not simply additive and
I am not sure how to begin. Perhaps someone could give some
pointers...

To explain my model I start with a simple linear (and very common)
discrete model:

x(k) = x(k-1) + dt * xd(k-1) + dt^2/2 * v(k)
xd(k) = xd(k-1) + dt * v(k)

where,

x =>position
xd => speed
v => noise
dt=> time step

On my non-linear model, the discrete speed equation is modified to be:

xd(k) = xd(k-1) * sqrt(v(k))

How would I go about redefining the effect of this multiplicative
noise on the position equation?



.