# Adaptive Algorithm for Fast 3D Characterization of Magnetic Sensors
## 4 Discussion  
Overall, we were able to show the working principle of the algorithm proposed in this contribution together with the dedicated hardware setup built for it. We achieved the goal of estimating directive sensor system behavior by means of its impulse and frequency response model with relatively high directive resolution at short system runtimes. A 1D experiment was performed with two different fixed and adaptive step sizes, the latter controlled by DT and CEA, respectively. We found the expected trade-off for fixed step sizes with a larger step size leading to faster convergence and a smaller step size to a smaller remaining system distance. We were also able to achieve fast convergence and smaller resulting system distance estimates with both adaptive control schemes. The better behavior of the CEA control, with the potential to achieve even lower remaining system distance estimates, shows the control approach's potential and success. However, further investigation of the two distance estimations would be beneficial for a more comprehensive understanding of the algorithm behavior in future work. The DT estimate in this work might also be investigated further with a practically introduced artificial delay instead of relying on assumptions about the sensor ringdown. The 2D experiment was conducted to check the directional control part of the proposed algorithm. Recorded internal signals show similar behavior for the individual adaptation steps and a working logic to change the excitation to the next planned field direction. With a resolution of \(1^{\circ}\) and a target system deviation of \(-78\,\mathrm{dB}\), a full estimation was performed in well under \(8\,\mathrm{min}\). We proposed different frequency-, direction-, and sensor response-dependent visualizations for the resulting estimations, which clearly show the algorithms capacity to model the sensor's cosine-like directivity and low-pass frequency behavior. Due to the chosen design frequency limit for the coil equalizers (\(2\,\mathrm{kHz}\)), the analysis is limited to frequency ranges below this limit. Lastly, the 3D directivity frequency response estimation targeted in this contribution was realized. With \(3^{\circ}\) resolution--120 and 60 steps in azimuth and elevation direction, respectively--and a target system distance of \(-72\,\mathrm{dB}\), the full algorithm run took under \(41\,\mathrm{min}\), which is very fast for the amount of directions with full impulse response estimates. Thus, a lot of directional and frequency response information can be gathered with the proposed method. This suggests the exploitability of the correlation of the response of a  
Figure 13: Histogram visualization of the adaptation time over the directivity positions. A stark increase in adaptation times leading up to the sensor’s insensitive direction is apparent, which is mitigated due to the explained fallback thresholds. The relative frequency of different ranges of adaptation times on the right shows an overall cumulation of most positions in the sub-second range. magnetic sensor to excitation from a directionally similar field. Adaptation times are in general very fast, with a trend of slightly slower adaptation in areas with a larger overall sensor response. A reason for this might be that the sensor's estimated impulse response \(\hat{\mathbf{h}}(n)\) has a higher amplitude for these areas. This might lead to higher remaining noise on the dead-time coefficients and thus a larger DT system distance estimate \(\hat{\Gamma}_{\text{DT}}(n)\), preventing the triggering of the next step by the directional control. Spikes in adaptation time close to the sensor's insensitive direction were expected with an SNR-based threshold in place to mitigate the slowing down of the overall processing. With a different choice of this parameter, the occurrence of these spikes and their respective influence on the overall runtime might be mitigated further. The presented work naturally has limitations that are not within the scope of this contribution.