Particle Filtering

Optimal filtering: The filtering problem involves the estimation of the state vector at time k, given all the measurements up to and including time k, which we denote by z1:k. In a Bayesian setting, this problem can be formalized as the computation of the distribution p(xk|z1:k), which can be done recursively in two steps. In the prediction step, p(xk|z1:k−1) is computed from the filtering distribution p(xk−1|z1:k−1) at time k − 1: