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Pervasive computing promotes the integration of smart devices in our living spaces to develop services providing assistance to people. Such smart devices are increasingly relying on cloud-based Machine Learning, which raises questions in terms of security (data privacy), reliance (latency), and communication costs. In this context, Federated Learning (FL) has been introduced as a new machine learning paradigm enhancing the use of local devices. At the server level, FL aggregates models learned locally on distributed clients to obtain a more general model. In this way, no private data is sent over the network, and the communication cost is reduced. Unfortunately, however, the most popular federated learning algorithms have been shown not to be adapted to some highly heterogeneous pervasive computing environments. In this paper, we propose a new FL algorithm, termed FedDist, which can modify models (here, deep neural network) during training by identifying dissimilarities between neurons among the clients. This permits to account for clients' specificity without impairing generalization. FedDist evaluated with three state-of-the-art federated learning algorithms on three large heterogeneous mobile Human Activity Recognition datasets. Results have shown the ability of FedDist to adapt to heterogeneous data and the capability of FL to deal with asynchronous situations.