Joined: Dec 2001
Mon May 20, 13 03:32 PM
Originally posted by: frame
Nobody has hints?
However, even a simpler thing would be very useful to me.
How should I adjust the usual kalman (bucy) filter when the unobservable state is correlated with the observable signal?
e.g. I want to filter x with dx = -k x dt + s dB and I observe y with dy = x dt + b dW and dB and dW are correlated.
I don't know anything about the Kalman filter, but I see a discussion in Oksendahl's SDE book.
He says that
dX = (f1 X + f2 Y) dt + C dB1
dY = (g1 X + g2 Y) dt + D dB2
with X unobserved and Y observed, is amenable to such a filter and gives refs.
Here (B1, B2) are uncorrelated Brownians. I am using capital letters for his variables and small letters for yours.
Now your last eqn pair (with small case variable) could be transformed to Oksendahl's form by keeping
the observed Y = y and defining a new unobservable X = x - A y and choosing A appropriately.
Edited: Mon May 20, 13 at 04:18 PM by Alan