Horizontal Directional Drilling Positioning Based on Strong Tracking Adaptive Kalman Filter

Aiming at the problem that the traditional drilling rig positioning method requires manual walking tracking and strict environmental requirements, this paper proposes an improved algorithm of strong tracking adaptive Kalman filter (STAEKF) based on ground mobile magnetic beacon, which reduces the requirements for the environment. Firstly, a magnetic field measurement model based on the far-field conditions of ground magnetic beacon is established, and then the STAEKF algorithm is introduced and improved for mobile magnetic beacon positioning. Finally, the effectiveness of the proposed method is verified by simulation experiments. The results show that the STAEKF exhibits an X-axis positioning error of 0.007 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$m$</tex>, a Y-axis positioning error of 0.0068 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$m$</tex>, and a Z-axis positioning error of 0.0061 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$m$</tex> during single-point positioning. Its positioning accuracy and convergence speed are superior to those of the EKF and AEKF. Under this paper's simulation conditions, the drill bit's relative distances on the X and Y axis from the magnetic beacon track's geometric center should be within 6m, and its depth within 11m. Beyond these ranges, the positioning error will rise significantly, exceeding 0.5m. In dynamic positioning, the Mean Absolute Percentage Error (MAPE) of STAEKF can reach 0.645%, and the Root Mean Square Error (RMSE) can reach 0.078 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$m$</tex>, which are better than those of the EKF and AEKF.