## 3 Results
### Results and Evaluation of Attitude Estimation  
In order to use the complementary filter, it is necessary to find appropriate values for four parameters: three parameters \(\alpha_{0},e_{1},e_{2}\), and a parameter \(\beta\) for finding parameters \(\beta_{0},c_{1}\) for magnetic disturbance. The \(\alpha_{0},e_{1},e_{2}\) parameters are only related to \(Roll\), \(Pitch\) correction, while \(\beta\) is only related to \(Yav\) correction. Therefore, we evaluated \(\alpha_{0},e_{1},e_{2}\) using the time until \(Roll\), \(Pitch\) becomes stable and evaluated \(\beta\) using the time until \(Yav\) becomes stable. In the complementary filter, increasing \(\alpha_{0}\) means increasing the considered value of the current acceleration. Because the acceleration should be 0 at the moment of stationary, larger \(\alpha_{0}\) indicates shorter time to stability. However, a larger considered value of the current acceleration value means that the estimation error during acceleration and deceleration becomes larger. This point can be somewhat mitigated by setting appropriate values of \(e_{1},e_{2}\); however, if \(\alpha_{0}\) is set too large, then the error is considered to be unacceptable. Hence, we set a new criterion for evaluating the change in attitude during acceleration and deceleration based on the fact that no rotation around the \(Roll\), \(Pitch\) axis occurs when the horizontal plane is moved. Figure 6 shows the results of \(Roll\), \(Pitch\) estimation when the sensor is placed on the horizontal plane and moved back and forth. From Figure 6, it can be seen that rotation around the \(Roll\), \(Pitch\) axis should not occur when the sensor is moved back and forth in the horizontal plane; however, the error is caused by increasing \(\alpha_{0}\), which is the considered value of the current acceleration value. In finding the values of \(e_{1},e_{2}\), we calculate the norm \(RP_{norm}\) of the maximum value of the rotation around \(Roll\), \(Pitch\) axis in the round-trip movement and find \(e_{1},e_{2}\) such that \(RP_{norm}\) becomes as small as possible. Table 4 shows the values of \(RP_{norm}\) when \(e_{1}\) is varied with \(\alpha_{0}=0.4,\ e_{2}=0.1\). Note that \(RP_{norm}\) is the average of ten times. Figure 5: The corrected values of the geomagnetic sensor in each plane (**Left:**\(x-y\); **Center:**\(x-z\); **Right:**\(y-z\)). Figure 6: \(Roll\), \(Pitch\) when the sensor is placed on the horizontal plane and moved back and forth. From Table 4, it can be seen that the error \(RP_{norm}\) becomes smaller by decreasing \(e_{1}\). Table 5 shows the values of \(RP_{norm}\) when \(e_{2}\) is varied with \(\alpha_{0}=0.4,\ e_{1}=0.0001\). Note that \(RP_{norm}\) is the average of ten times. From Table 5, it is found that the error \(RP_{norm}\) becomes smaller by decreasing \(e_{2}\). The smaller \(e_{1},e_{2}\) are, the smaller \(RP_{norm}\) is; however, if \(e_{2}\) is set too small from Equation (29), the value of acceleration is hardly taken into account during acceleration, and a large error is considered to occur in the estimation results during acceleration. Therefore, we use \(e_{2}=0.01\) and set \((e_{1},e_{2})=(0.0001,0.01)\). Table 6 shows the ten averages of \(RP_{norm}\) when \((e_{1},e_{2})=(0.0001,0.01)\) is fixed and \(\alpha_{0}\) is varied. From Table 6, it can be seen that the error \(RP_{norm}\) becomes smaller by decreasing \(\alpha_{0}\). However, the larger \(\alpha_{0}\) is, the shorter the time to stability becomes; thus, we set \(\alpha_{0}=0.2\) to improve the estimation results for both \(RP_{norm}\) and \(t_{stab}\). From the above, the parameters for the correction of \(Roll\), \(Pitch\) are determined to be \(\alpha_{0}=0.2,\ (e_{1},e_{2})=(0.0001,0.01)\). Next, we evaluated how the change in \(\beta\) affects the stability and obtained the parameters. Figure 7 shows the results of attitude estimation when \(\beta=0.01,0.2\) and the sensor is kept stationary.