I. Introduction
Recent years, security robots have emerged in large numbers with the demand for various special operations. Similarly, due to the unique shape of petrochemical pipelines a suitable robot is urgently needed to achieve the detection of welds[1], [2] on them. The petrochemical pipeline inspection robot is prone to detachment or difficulty moving forward due to its need to run on the curved surface of the pipeline. Therefore, it is inevitable to install an inertial measurement unit to determine the current posture and position of the robot, while the error of the IMU will greatly affect the stability of the robot's operation on the pipeline. Therefore, multi-sensor navigation systems using high precision and accuracy filters for state estimation have long been essential. The complexity and diversity of the robot's working environment, coupled with the characteristics of the robot's structure can cause various difficulties in data measurement. In last decades, two more excellent classes of algorithms have been developed for the solution of this problem: the Kalman filter (KF)[3] and the complementary filter (CF)[4], [5].