We introduce geometric and topological methods to develop a new framework for fusing multi-sensor time series. This framework consists of two steps: (1) a joint delay embedding, which reconstructs a high-dimensional state space in which our sensors correspond to observation functions, and (2) a simple orthogonalization scheme, which accounts for tangencies between such observation functions, and produces a more diversified geometry on the embedding space. We conclude with some synthetic and real-world experiments demonstrating that our framework outperforms traditional metric fusion methods.