11.6 Computing Probabilistic Information States

The probabilistic I-states can be quite complicated in practice because each element of ${\cal I}_{prob}$ is a probability distribution or density function. Therefore, substantial effort has been invested in developing efficient techniques for computing probabilistic I-states efficiently. This section can be considered as a continuation of the presentations in Sections 11.2.3 (and part of Section 11.4, for the case of continuous state spaces). Section 11.6.1 covers Kalman filtering, which provides elegant computations of probabilistic I-states. It is designed for problems in which the state transitions and sensor mapping are linear, and all acts of nature are modeled by multivariate Gaussian densities. Section 11.6.2 covers a general sampling-based planning approach, which is approximate but applies to a broader class of problems. One of these methods, called particle filtering, has become very popular in recent years for mobile robot localization.