Bayes Filters

1. The Bayes Filter Algorithm

The most general algorithm for calculating beliefs is given by the Bayes Filter algorithm.

The general algorithm for Bayes filtering

• recursive
• $bel(x_t)$ at time $t$ is calculated from the belief $bel(x_{t-1})$ at the time $t-1$

input

• belief bel at time $t-1$
• most recent control $u_t$
• most recent measuremnt $z_t$

output

• belief bel$(x_t)$ at time t

The Bayes filter algorithm possesses two essential steps.

• update step (, control update, or prediction)
• measurment update