Multi-sensor fusion method based on FFR-FK for 3D trajectory measurement of underground pipelines

•A 3D trajectory measurement method for pipelines based on inertial navigation.•A high-reliability measurement algorithm based on multiple sensors.•An algorithm based on the fusion of time forward and time reverse Kalman filter.•A time-saving method that only needs one trip from inlet to outlet of pipeline.•A high-precision algorithm that can correct sensor errors. The three-dimensional (3D) trajectory measurement of underground pipelines is the basis for establishing an underground pipeline network system. Mastering the trajectory of underground pipelines can reduce damage to old pipelines during construction. Traditional pipeline measurement methods have limitations in terms of depth and environment, leading to the inability to obtain accurate information on the pipeline trajectory. In this study, a forward and reverse Kalman filtering fusion measurement algorithm based on MEMS-IMU, MEMS magnetometer, and the odometer was proposed. First, a 16-dimensional Kalman filtering model was established according to the motion mode and working environment of the pipeline measurement instruments; Secondly, based on the 16-dimensional Kalman filtering model, the data of multi-sensors were fused according to the forward and reverse time order respectively. Thus, two kinds of 3D trajectories of the pipeline were obtained. One is the time order, the other one is the reverse time order. Thirdly, in order to get the optimal measurement results of the 3D trajectory of the pipeline, the forward and reverse measurement results were fused according to the covariance matrix of the forward and reverse Kalman filter. Finally, a ground simulation experiment and an underground pipelines experiment with a MEMS sensor (PA-IMU488B) were performed to verify the feasibility of the method. In the ground simulation experiment, the maximum relative error in the plane is 0.14%, and the maximum relative error in the vertical is 0.28%. In the experiment of underground drainage pipelines, the maximum relative error in the plane is 0.22%, and the maximum relative error in the vertical is 0.12%. This method proposed by this study uses one set of data twice which can make the measurement results more accurate. Above all, the sensors used in this method are all cheap and low precision. Moreover, the measuring equipment only needs to travel through the pipe from the entrance to the exit and doesn’t need to go back from the exit to the entrance. Therefore, the method proposed by this study is a hi