I am wondering about the effectiveness or optimality of Kalman smoother algorithm for multiplicative state space model with gaussian errors. Can I still use the standard linear gaussian kalman smoother algorithm if I have an interaction between a deterministic and a stochastic elements of the state vector in the measurement equation?
observation equation: Y(t)=A(t)X(t)+w(t), state equation: X(t+1)=ϕX(t)+v(t), A(t+1)=A(t)
I personally doubt so and am considering nonlinear state space model techniques. However, I have little experience on this matter and will appreciate any suggestions, thoughts and references on how to proceed. Many thanks in advance and sorry if the question has been previously been asked!
