With the continuous advancement of automation and safety demands for special operating conditions in the industrial field, wall-climbing robots are gradually replacing traditional manual high-altitude work. To address the issues of low positioning accuracy, yaw deviation, and large operation errors during grinding and spraying in industrial scenarios such as shipbuilding and petrochemical industries, this paper proposes an improved least squares fitting arc algorithm to calculate the robot's position. Additionally, a fusion of LiDAR and an Inertial Measurement Unit (IMU) is used to provide navigation for the robot. To verify the feasibility of this method, an experimental test was conducted with a five-wheeled permanent magnet wall-climbing robot on a metal surface, and experimental data were collected. The results indicate that the proposed method achieves a positioning accuracy of 96.85% within a working range of 10 meters, with the fixed trajectory navigation error controlled within ±4cm, which meets the practical operational requirements of industrial scenarios.