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The paper addresses the vehicle-to-X (V2X) data fusion for cooperative or collective perception (CP). This emerging and promising intelligent transportation systems (ITS) technology has enormous potential for improving efficiency and safety of road transportation. Recent advances in V2X communication primarily address the definition of V2X messages and data dissemination amongst ITS stations (ITS-Ss) in a traffic environment. Yet, a largely unsolved problem is how a connected vehicle (CV) can efficiently and consistently fuse its local perception information with the data received from other ITS-Ss. In this paper, we present a novel data fusion framework to fuse the local and V2X perception data for CP that considers the presence of cross-correlation. The proposed approach is validated through comprehensive results obtained from numerical simulation, CARLA simulation, and real-world experimentation that incorporates V2X-enabled intelligent platforms. The real-world experiment includes a CV, a connected and automated vehicle (CAV), and an intelligent roadside unit (IRSU) retrofitted with vision and lidar sensors. We also demonstrate how the fused CP information can improve the awareness of vulnerable road users (VRU) for CV/CAV, and how this information can be considered in path planning/decision making within the CAV to facilitate safe interactions.