Discrete Bayes Filter

The discrete Bayes filter is a special case of the general Bayes filter. Because the states are discrete, the integral in the general Bayes filter becomes a summation. The implementation is straightforward and is given as follows:

(source: Probabilistic Robotics)

The key is to define the states. If the physical states are continuous, discretization is required. The number of the states is obviously an important parameter. The larger the state number, the more accurate the estimation is. On the other hand, with large state number, it's expensive to compute.