The life span of ordinary people is increasing steadily and many developed countries are facing the big challenge of dealing with an ageing population at greater risk of impairments and cognitive disorders, which hinder their quality of life. Monitoring human activities of daily living (ADLs) is important in order to identify potential health problems and apply corrective strategies as soon as possible. Towards this long term goal, the research here presented is a first step to monitor ADLs using 3D sensors in an Ambient Assisted Living (AAL) environment. In particular, the work here presented adopts a new 3D Qualitative Trajectory Calculus (QTC3D) to represent human actions that belong to such activities, designing and implementing a set of computational tools (i.e. Hidden Markov Models) to learn and classify them from standard datasets. Preliminary results show the good performance of our system and its potential application to a large number of scenarios, including mobile robots for AAL.