This paper addresses the problem of tracking and diagnosing complex
systems with mixtures of discrete and continuous variables.
This problem is a difficult one, particularly when the system dynamics are
nondeterministic, not all aspects of the system are directly observed, and
the sensors are subject to noise.  In this paper, we propose a new approach
to this task, based on the framework of <I>hybrid dynamic Bayesian
networks (DBN)</I>.  These models contain both continuous variables
representing the state of the system and discrete variables representing
discrete changes such as failures; they can model a variety of faults,
including burst faults, measurement errors, and gradual drifts.  We present
a novel algorithm for tracking in hybrid DBNs, that deals with the
challenges posed by this difficult problem.  We demonstrate how the
resulting algorithm can be used to detect faults in a complex system.
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