In wearable-sensor-based activity recognition, it is often assumed that the training and test samples follow the same data distribution. This assumption neglects practical scenarios where the activity patterns inevitably vary from person to person. To solve this problem, transfer learning and domain adaptation approaches are often leveraged to reduce the gaps between different participants. Nevertheless, these approaches require additional information (i.e., labeled or unlabeled data, meta-information) from the target domain during the training stage. In this paper, we introduce a novel method named Generalizable Independent Latent Excitation (GILE) for human activity recognition, which greatly enhances the cross-person generalization capability of the model. Our proposed method is superior to existing methods in the sense that it does not require any access to the target domain information. Besides, this novel model can be directly applied to various target domains without re-training or fine-tuning. Specifically, the proposed model learns to automatically disentangle domain-agnostic and domain-specific features, the former of which are expected to be invariant across various persons. To further remove correlations between the two types of features, a novel Independent Excitation mechanism is incorporated in the latent feature space. Comprehensive experimental evaluations are conducted on three benchmark datasets to demonstrate the superiority of the proposed method over the state-of-the-art solutions.