Most edge AI focuses on prediction tasks on resource-limited edge devices while the training is done at server machines. However, retraining or customizing a model is required at edge devices as the model is becoming outdated due to environmental changes over time. To follow such a concept drift, a neural-network based on-device learning approach is recently proposed, so that edge devices train incoming data at runtime to update their model. In this case, since a training is done at distributed edge devices, the issue is that only a limited amount of training data can be used for each edge device. To address this issue, one approach is a cooperative learning or federated learning, where edge devices exchange their trained results and update their model by using those collected from the other devices. In this paper, as an on-device learning algorithm, we focus on OS-ELM (Online Sequential Extreme Learning Machine) to sequentially train a model based on recent samples and combine it with autoencoder for anomaly detection. We extend it for an on-device federated learning so that edge devices can exchange their trained results and update their model by using those collected from the other edge devices. This cooperative model update is one-shot while it can be repeatedly applied to synchronize their model. Our approach is evaluated with anomaly detection tasks generated from a driving dataset of cars, a human activity dataset, and MNIST dataset. The results demonstrate that the proposed on-device federated learning can produce a merged model by integrating trained results from multiple edge devices as accurately as traditional backpropagation based neural networks and a traditional federated learning approach with lower computation or communication cost.