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 known 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 is usually hard to estimate those state transition and emission probabilities precisely in practice, especially if the training data is not sufficient and the process is not stationary. To this end, we propose nonparametric weak models derived from HMMs to characterize dynamic processes. A weak model does not need the strong requirement for probability specification as in HMMs and it can also characterize non-stationary processes. 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. Furthermore, we analyze how to reduce the size of the hypothesis set by tuning the structure of the emission matrix
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