## 4 Experimental Results and Discussions
### Magnetic Localization Evaluation
#### 4.2.1 Magnetic Fields Derived from the \(T\)-Type PM  
Based on the assumption that the noise level at the sensor observation point is constant, the signal-to-noise (SNR) of the sensor array measurements was mainly decided by the magnet-derived magnetic field. Thus, the phenomena in which the magnitude of the magnetic fields becomes quickly weakened with the distance between the magnetic source and the sensor observation point greatly affects the SNR of sensor array measurements. Besides, the coordinate system rotation between the sensing axis frame and the dipole frame will affect the magnitudes of the AMR sensor measurements. Furthermore, both of these have an apparent effect on the magnetic localization results. To demonstrate the improvement brought by the combined \(T\)-type PM in magnetic field distribution, simulation results \begin{table}
\begin{tabular}{c c c c} \hline \hline \(\mathbf{R}_{1}=\left[\begin{array}{cc}0.9994&-0.0319&0.0166\\ 0.0323&0.9992&-0.0225\\ -0.0158&0.0230&0.9996\end{array}\right]\) & \(\mathbf{R}_{2}=\left[\begin{array}{cc}0.9998&-0.0187&0.0103\\ 0.0188&0.9998&-0.0092\\ -0.0101&0.0094&0.9999\end{array}\right]\) \\ \hline \(\mathbf{R}_{3}=\left[\begin{array}{cc}0.9998&-0.0150&-0.0459\\ 0.0144&0.9998&-0.0131\\ 0.0461&0.0124&0.9989\end{array}\right]\) & \(\mathbf{R}_{4}=\left[\begin{array}{cc}0.9999&0.0127&0.0110\\ -0.0123&0.9992&-0.0386\\ -0.0115&0.0384&0.9992\end{array}\right]\) \\ \hline \(\mathbf{R}_{5}=\left[\begin{array}{cc}0.9994&-0.0295&0.0161\\ 0.0300&0.9991&-0.0300\\ -0.0152&0.0305&0.9994\end{array}\right]\) & \(\mathbf{R}_{6}=\left[\begin{array}{cc}0.9996&-0.0248&-0.0147\\ 0.0244&0.9994&-0.0257\\ 0.0153&0.0253&0.9996\end{array}\right]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Sensing axis calibration results. Figure 6: The target trajectories within a 3 \(\times\) 3 \(\times\) 6 cm\({}^{3}\) cube. (**a**) 100 samples on a spiral line; (**b**) 60 samples on a folding line. of the magnetic field magnitude distribution in a limiting case, where the analyzed magnetic field distribution plane is perpendicular to one of the component magnet axes, are presented and discussed. The magnitude distributions \(B\) of magnetic fields derived from the combined \(T\)-type PM and both of its component magnets are compared in Figure 7. As illustrated in Figure 7a, the combined \(T\)-type PM is arranged along the \(y\)-axis (\(d\) = 15 mm, \(\mathbf{m}_{v}\) = (90\({}^{\circ}\), 90\({}^{\circ}\)), \(\mathbf{m}_{h}\) = (90\({}^{\circ}\), 0\({}^{\circ}\))), and the analyzed magnetic fields are distributed on the \(xz\)-plane (30 mm \(\times\) 30 mm). The magnetic field magnitude distributions of the combined \(T\)-type PM and both of its component magnets are presented in Figure 7b-d.  
By comparing Figure 7b,d, there is an apparent enhancement of the magnetic field magnitude level in Figure 7b, which is introduced by the additional orthogonal magnet in Figure 7c. Besides, the uniformity of the area with an equivalent magnitude is improved in Figure 7b compared with Figure 7d. It can be seen that the area with magnitude \(B\)\(>\)4 G along the x-axis is [\(-\)9.3, 9.3] mm and [\(-\)13.2, 13.2] mm in Figure 7b,d respectively, with an increase of about 41.9%. Although the magnetic field magnitude level in Figure 7c is much less than that in Figure 7d, the improvement in magnetic field distribution illustrated in Figure 7b is totally brought about by the combined \(T\)-type PM. From Figure 7, we can find that the promotion of the \(T\)-type PM compensates for the influence brought by the directivity of the magnetic moment caused by the coordinate system rotation between the sensing axis frame and the dipole frame, especially when the sensing axis frame is orthogonal with the dipole frame. Figure 7: Comparisons of the magnitude distributions of magnetic fields derived from the combined \(T\)-type PM and both of its component magnets.