Sampling in Factored Dynamic Systems
In many real-world situations, we are interested in monitoring the evolution of a complex situation over time. For example, we may be monitoring a patient’s vital signs in an intensive care unit (Dagum and Galper 1995), analyzing a complex freeway traffic scene with the goal of controlling a moving vehicle (Huang, Koller, Malik, Ogasawara, Rao, Russell and Weber 1994), localizing a robot in a complex environment (Fox, Burgard and Thrun 1999) (see also Murphy and Russell (2001: this volume)), or tracking motion of non-rigid objects in a cluttered visual scene (Isard and Blake 1998a). We treat such systems as being in one of a possible set of states, where the state changes over time. We model the states as changing at discrete time intervals, so that x t is the state of the system at time t. In most systems, we model the system states as having some internal structure: the system state is typically represented by some vector of variables X = (X 1,...,X n ), where each X i takes on values in some space Dom[X i ]. The possible states x are assignments of values to the variables X. In a traffic surveillance application, the state might contain variables such as the vehicle position, its velocity, the weather, and more.
KeywordsBayesian Network Belief State Multivariate Gaussian Distribution Dynamic Bayesian Network Conditional Probability Distribution
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