Weak process models for robust process detection

Many defense and security applications involve the detection of a dynamic process. A process model describes the state transitions of an object, which evolves in time according to specific know laws. Given a process model, the process detection problem is to identify the existence of such a process in large amount of observation data. While Hidden Markov Models (HMMs) are widely used to characterize dynamic processes, it's usually hard to estimate those state transition and emission probabilities precisely in practice, especially if we don't have sufficient training data. An inaccurate process model could lead to high false alarm and misdetection rates and the inference result could be misleading in the decision-making process. To this end, we propose nonparametric weak models derived from HMMs to characterize dynamic processes. A weak model doesn't need the strong requirement for probability specification as in HMMs. In this paper, we analyze the properties of such weak models and propose recursive algorithms to compute the hypotheses of the hidden state sequence and the size of the hypothesis set. Further we analyze how to control the size of the hypothesis set by increasing the number of sensors to tune the structure of the emission matrix.