# Adaptive Algorithm for Fast 3D Characterization of Magnetic Sensors
## 1 Introduction  
Magnetic measurements are becoming increasingly important in many areas, such as health care [1, 2, 3, 4], indoor localization [5, 6, 7], or the investigation of geological conditions of the subsurface [8, 9, 10]. For many of these applications, a detailed forward model of the magnetic sensor is essential for gaining the best possible results when solving inverse problems. In these, a solution for, e.g., a source distribution should be determined by computations based on measured sensor observations. Thus, a characterization of the utilized magnetic sensors is necessary and can be achieved in various ways. The most common evaluation of the sensor includes the impulse or frequency response, a linearity curve, and the sensitivity [11]. The frequency response is the spectral transformation of the impulse response, both of which are used in this paper. Magnetic sensors usually measure one-directional projections of magnetic fields, which means they have a certain directional characteristic (vector magnetometers). This should be considered in a comprehensive characterization of the sensor as well [12]. There exist a variety of established magnetic sensor concepts. Scalar magnetometers like total field optically pumped magnetometers (OPMs) do not need a directional characterization by design; for other vector sensors, e.g., superconducting quantum interference devices (SQUIDs), it is not feasible to use these in a limited characterization setup due to cooling requirements. Otherwise, the directional response of vector magnetometers should be identifiable. Magnetoelectric (ME) sensors, for example, might profit from this, as the sensitive axis of the sensing element does not always coincide with the geometry [13; 14]. Similar problems might occur with other sensor types based on the magnetoresistive (MR) effect or fluxgate magnetometry and should be identified and addressed, especially in areas like array applications where directionality is critical. The directivity of a vector magnetometer can, for example, be assessed by measuring the normalized voltage response of the sensor to a defined magnetic field rotating around the sensing volume [12]. However, this does not account for the whole frequency response of the sensor in different directions. This is captured by the (spatially dependent) frequency response, which usually takes some time for the measurement of a single direction. It is nevertheless of interest to acquire the frequency response of a sensor in all directions to obtain an idea of the limitations and possibilities of a given sensor. A fast characterization of sensors by means of a controlled adaptive algorithm has already been established for underwater transducers [15]. Some adjustments are necessary to apply this method to magnetic sensors for fully automated three dimensional (3D) characterization. In this contribution, we present a fast and robust algorithm for 3D characterization of a magnetic sensor system by estimating the direction-dependent impulse response. The sensor system incorporates the direct analog readout circuitry, as we are interested in characterizing the working behavior of the system and not the sensing element itself. Sensitive-axis frequency responses are typically measured with sine sweeps or noise measurements over a longer period, e.g., in a Helmholtz coil setup. A direct extension of such a measurement concept is often not feasible due to high time requirements and vulnerability to error when it comes to manual modification of the sensor systems alignment. Our proposed method tries to solve these issues. It is schematically visualized in Figure 1.  
Figure 1: Block diagram of overall characterization system. The remainder of this paper is structured as follows: In Section 2, the used hardware setup for characterization as well as the algorithm developed for fast characterization of sensors are presented. Section 3 displays the results of multiple measurements conducted with a fluxgate sensor. Discussion of these follows in Section 4.