This paper presents a correlation-based weighted federated learning approach that combines multimodal-sensing models with knowledge distillation methods. In this case, local models residing on the client devices are regarded as student models and are trained individually, after which their parameters are weighted by the Pearson correlation coefficient before aggregating into a global model. The global model parameters are then distilled by a teacher model on the server. This solution is especially advantageous in cases where edge devices are deployed with weak and heterogeneous configurations, as it permits efficient computational resource management at the clients while still ensuring acceptable performance, aided by a strong teacher model hosted on the server. This solution has demonstrated efficiency when tested on NICT benchmark datasets, and the correlation-based weighted federated learning approach proves to be more stable than traditional FedAvg.