ABSTRACT
In the time updating process, the state p(xk | Zk−1) at time step k considering all the observations up to time step k−1 is determined. While in the observation updating process the posterior distribution of the state p(xk|Zk) using measurements Zk is determined using Bayes’ rule as shown below
p p
( | ) ( | ) (p | ) ( | ) (p | )
Z x x x
(3)
The above equation shows an optimal Bayesian solution to the filtering problem. If F and H are linear and all other densities are Gaussian the Kalman Filter is an optimal solution. For nonlinear problems other techniques can be used, e.g. Extended Kalman Filter or the Unscented Kalman Filter. In this paper SMCS is used since the observation equation is nonlinear so that a closed-form solution is not possible.
