  The problem of situational awareness (SAW) is investigated from the
probabilistic modeling point of view. Taking the situation as a hidden
variable, we introduce a hidden Markov model (HMM) and an extended state space
model (ESSM) to mathematically express the dynamic evolution law of the
situation and the relationships between the situation and the observable
quantities. We use the Gaussian mixture model (GMM) to formulate expert
knowledge, which is needed in building the HMM and ESSM. We show that the ESSM
model is preferable as compared with HMM, since using ESSM, we can also get a
real time estimate of the pivot variable that connects the situation with the
observable quantities. The effectiveness and efficiency of both models are
tested through a simulated experiment about threat surveillance.
