Detectability Prediction of Hidden Markov Models with Cluttered Observation Sequences

Abstract

There is good reason to model an asymmetric threat (a structured action such as a terrorist attack) as an HMM whose observations are cluttered. Recently a Bernoulli filter was presented that can process cluttered observations (“transactions”) and is capable of detecting if there is an HMM present, and if so, estimate the state of the HMM. An important question in this context is: when is the HMM-in-clutter problem feasible? In other words, what system properties allow for a solvable problem? In this paper we show that, given a Gaussian approximation of the pdf of the log-likelihood, approximate detection error bounds can be derived. These error bounds allow a prediction of the detection performance, i.e. a prediction of the probability of detection given an “operating point” of transaction-level false alarm rate and miss probability. Simulations show that our analysis accurately predicts detectability of such threats. Our purpose here is to make statements about what sort of threats can be detected, and what quality of ob- servations are necessary that this be accomplished.