## 1 Introduction  
Magnetic field-based navigation is an old discipline that had its beginnings in the 20 th Century [1]. Magnetic fields have several advantages over other physical quantities. For example, unlike electromagnetic waves, they are not subject to multipath effects or fading because they do not reflect off surfaces. This allows for much higher accuracy. In addition, they are not attenuated when passing through magnetically neutral materials, making magnetic field-based navigation ideal for use between obstacles, at night, or in difficult weather conditions such as snow or fog. A large number of publications exist dealing with techniques for object navigation and localization. Depending on the application, they all use one or more distributed magnetic field sources that emit an alternating magnetic signal. This is usually sampled and measured by several sensors, which may be from different technologies. By combining these measurement data with the mathematical model of the source used, the position and orientation of the observed object are then determined. This can be divided into four different types of sources. The first type is a simple rectangular or circular coil that typically has a large number of turns. It represents the basic element for the construction of more complex coil types and is often referred to as a dipole, since above a minimum distance from the winding, its magnetic field distribution can be described by the equations of a magnetic dipole. In various research projects [2, 3, 4, 5, 6], such as MILPS (magnetic indoor local positioning system), multiple coils mounted on walls are used to locate cell phones and robots in buildings or patients in hospitals. Other use cases include the navigation of medical instrumentsinside the human body [7] or the localization of an implantable transponder for intensity-modulated radiation therapy [8]. In addition, several projects have investigated how these coils can be used to locate trapped persons as quickly as possible [9; 10; 11; 12]. These could be buried miners or avalanche victims, who can be found by the emitted signal from a small coil worn close to the body. Another interesting topic is the detection of buried landmines in old war zones, also known as humanitarian demining [13; 14]. This involves the use of hand-held coils such as metal detectors. Finally, a new application has emerged with the advent of the electric vehicle age. In the context of inductive charging, the receiver coil mounted on the underbody of the car must be positioned relatively precisely above the transmitter coil in the parking lot, as shown in Figure 1. Since this is very difficult for the driver to achieve, the MPPS (magnetic pulse positioning system) was developed in [15]. Here, the transmitting coil in the ground emits a low-frequency pulsed magnetic signal that allows precise localization by the vehicle in the sub-centimeter range. The next two coil types consist of two or three base coils wound orthogonally to each other. An example of a three-axis magnetic field source is shown in Figure 2.  
For two-axis sources, the coils carry phase quadrature currents that produce a rotating magnetic dipole [1; 16; 17]. Together with phase detection algorithms and amplitude evaluation, the object position and also the orientation can be determined. For three-axis sources, all source axes are successively excited with currents of the same frequency and phase. In this way, each axis generates an equivalent dipole of arbitrary orientation [18; 19; 20]. The three sensor responses are linearly independent and provide sufficient information to determine both the sensor position and its orientation. The last type of source to be mentioned is a long wire with an alternating signal. In [21; 22; 23], its magnetic field was used to allow an underwater vehicle to locate and track a buried underwater cable. Until now, however, no attention has been paid to magnetic sources consisting of two long parallel conductors.