The manufacturing process demands customization, flexibility, and agility, which introduce new challenges for product assembly. One such challenge involves identifying the assembly state on-site without relying on markers. In this paper, an unmarked identification method is proposed for product assembly states. Firstly, assembly sites are captured by a depth camera. Secondly, an offline template library is constructed based on the product's digital model using a multi-view projection method. Thirdly, A shape vector descriptor is employed for both the digital templates and the product's point cloud. Finally, open source assembly models are used for experimentation, demonstrating the proposed method’s effectiveness in recognizing assembly states.