We aim to develop data-driven heterogeneous data fusion approaches for unanticipated event/target detection, which will be more robust and immune to model mismatch problems encountered by model-based approaches. Considering the low intrinsic dimensionality of the sensor data, we propose several data-level fusion approaches based on some state-of-the-art dimensionality reduction techniques. For linear sensor measurements, we propose two efficient joint linear subspace tracking approaches. The first joint subspace tracking approach is based on the concept of joint sparsity, compressive sensing techniques, and grid computation, which is suitable when the correlations between data from different sensing modalities are unclear. The second approach is based on the emerging compressive covariance sensing technique, which provides a faster and more accurate solution when explicit models are available for correlations between heterogeneous data streams. For nonlinear data, we propose a joint nonlinear manifold learning based data fusion framework, in which the nonlinear mapping from the target parameters to the measurements is learned and the classifier is trained with heterogeneous data. Computationally efficient online joint nonlinear manifold learning approaches will also be developed for unexpected event/target discovery. The proposed research will be conducted under the guidance of rigorous mathematical/statistical principles.