Mathematical Considerations for Unmanned Aerial Vehicle Navigation in the Magnetic Field of Two Parallel Transmission Lines

This publication deals with the navigation of unmanned aerial vehicles (UAVs) moving in the magnetic field of two long, straight, parallel conductors, which is of high interest for several new technical applications. How the position and orientation of the UAV can be calculated using a minimal number of only three three-axis magnetometers are discussed. It is shown that the angles can be determined without the knowledge of the conductor currents and the magnetic field equations, but only by combining the sensor measurements with the rotation matrix and exploiting a characteristic property of the magnetic field. Furthermore, different strategies were investigated to determine the respective sensor positions. An analytical solution was derived from the nonlinear magnetic field equations, which promises a low computational time. It is shown that for a given sensor, several solutions exist, from which the correct one has to be selected. Therefore, a specific detection method is introduced. Once the solution is known, the UAV location can be determined. Finally, the overall algorithm was tested by simulations far from and near the conductors with superimposed typical magnetic noise.