Smart Homes need to sense their environment. Augmented appliances can help doing this but sensors are also required. Then, data fusion is used to combine the gathered information. The belief functions theory is adapted for the computation of small pieces of context such as the presence of people or their posture. In our application, we can assume that a lot of sensors are immobile. Also, physical properties of Smart Homes and people can induce belief for more time than the exact moment of measures.
Thus, in this paper, we present a simple way to apply the belief functions theory to sensors and a methodology to take into account the timed evidence using the specificity of mass functions and the discounting operation. An application to presence detection in smart homes is presented as an example.