Pervasive computing promotes the integration of connected electronic devices in our living environments in order to deliver advanced services. Interest in machine learning approaches for engineering pervasive applications has increased rapidly. Recently federated learning (FL) has been proposed. It has immediately attracted attention as a new machine learning paradigm promoting the use of edge servers. This new paradigm seems to fit the pervasive environment well. However, federated learning has been applied so far to very specific applications. It still remains largely conceptual and needs to be clarified and tested. Here, we present experiments performed in the domain of Human Activity Recognition (HAR) on smartphones which exhibit challenges related to model convergence.