In the architecture, engineering, and construction (AEC) industry, the positioning technology for a mobile construction platform (MCP) is critical to achieve on-site, continuous, large-scale construction. During construction, MCP movement and construction actions seldom occur simultaneously. Therefore, this paper categorizes the MCP into stationary and moving states for positioning studies, respectively. When the platform is stationary, it is positioned using an improved ultra-wideband (UWB) sensor. When the platform is in motion, a single UWB positioning technique cannot meet the required accuracy for positioning, and fusion positioning using both UWB and an inertial measurement unit (IMU) is considered. The experimental results show that compared with only UWB positioning, the improved UWB positioning algorithm improves the positioning accuracy by 53% in the stationary state, and the fused UWB/IMU positioning improves the positioning accuracy by 46% in the moving state. As a result, the positioning accuracy of the MCP is significantly improved regardless of whether it is in a stationary or moving state. Furthermore, this paper integrates the positioning technique with the robotic arm construction technique to successfully simulate an on-site continuous construction of a wooden cabin, which provides the potential for large-scale continuous construction in real-world scenarios in the future.