Trajectory reconstruction of subsurface pipes for salt discharge in saline–alkali soils based on an improved EKF and adaptive gradient optimization

Abstract The laying trajectory of saline–alkali land subsurface pipes for salt discharge plays a crucial role in assessing the efficiency of saline–alkali land reclamation. Due to the complex soil conditions of saline–alkali land and the physical properties of the subsurface pipes, directly reconstructing the trajectory using an inertial measurement unit (IMU) often fails to achieve sufficient accuracy. To address this issue, this paper proposes a trajectory reconstruction method for saline–alkali land subsurface pipes based on an improved extended Kalman filter (EKF) and adaptive gradient optimization. This method integrates accelerometer and gyroscope data using the proposed dynamic weighted threshold EKF (DWTEKF). The dynamic weighted threshold control module adjusts the noise covariance matrix to reduce the impact of inaccurate initial state information on subsequent attitude estimation. Meanwhile, this paper proposes an adaptive gradient descent algorithm with suppression factors and dynamic step sizes (AGDSD). This algorithm adaptively adjusts the step size to optimize the gradient direction estimate and incorporates a suppression factor through discriminant testing to reduce the influence of pipe oscillations, thus improving the robustness of attitude estimation and trajectory reconstruction. Experimental results show that the DWTEKF algorithm exhibits excellent performance in noise suppression and signal fidelity. Compared to traditional adaptive gradient descent algorithm (AGDA) and standard gradient descent algorithm (GDA), the AGDSD algorithm improves the average attitude error by 44.02% and 57.31%, respectively. Furthermore, the proposed trajectory reconstruction method significantly enhances trajectory fitting accuracy, successfully validating the effectiveness of the method.