A continuous-time model-based approach for activity recognition in pervasive environments

We present a model-based approach to Activity Recognition (AR) in Ambient Assisted Living (AAL). The approach leverages an a-priori stochastic model termed Continuous Time Hidden Semi-Markov Model (CT-HSMM), capturing the continuous-time durations of activities and inter-event times. The model is enhanced according to the observed statistics, associating the events with an occurrence probability, and the sojourn time and the inter-event time in each activity with a continuous-time Probability Density Function (PDF), allowing effective fitting of observed durations through non-Markovian distributions. The model is updated at run-time according to a sequence of time-stamped observations, exploiting the method of stochastic state classes to perform transient analysis and derive a measure of likelihood that an activity is currently performed. The approach supports both online AR, predicting the activity performed at time t using only the events observed until that time, and offline AR, applying a Forward-Backward procedure that exploits all the events observed before and after time t. The approach is experimented on a real data set of the literature, providing performance measures that can be compared with those of offline Hidden Markov Models (HMMs) and offline Hidden Semi-Markov Models (HSMMs).