Detectability analysis of detection and estimation of structured action from cluttered data

There is good reason to model an asymmetric threat (a structured action such as a terrorist attack) as an HMM. Thence there is a means (described in earlier work) to detect it via the novel Bernoulli filter paradigm that is emerging as an integrated tracker/track-management tool. This paper details additional progress made to model the detectability of a hidden Markov model (HMM) that is observed in the presence of false measurements or clutter. The ultimate goal of this analysis is to be able to make statements regarding the minimum complexity that an HMM would need to involve in order that it be detectable with reasonable fidelity, as well as upper bounds on the level of clutter (expected number of false measurements) and probability of miss of a relevant observation. Put simply, if a threat modeled as an HMM has (say) three components - transaction O1, followed by O2 and then O3 with modeled delays in between - then this would only be detectable if the delays were very small or if there were very little clutter. A more feasible situation would involve 20 or 30 transactions. To characterize this more fully is the goal of this manuscript.