# A Novel Method of Adaptive Kalman Filter for Heading Estimation Based on an Autoregressive Model
## 7 Experimental Analysis
### Kinematic Experiment
Figure 6 shows local heading error of Figure 4b. In Figure 6a, most errors of Pro and ProA are within 4\({}^{\circ}\), and these errors are smaller than those of Gyr and MGP. In Figure 6b-d, these errors of Pro and ProA are principally less than 5\({}^{\circ}\), and these results of Pro and ProA are superior to those of Gyr and MGP. In Table 2, The RMS of MGP is slightly smaller than that of Gyr, and the mean RMS is decreased by 1.97%. For these two kinematic experiments, the accuracy of heading estimation for MGP is better than that of Gyr, and this conclusion is consistent with that of the literature [22]. We can also see from Table 2 that these accuracies of Pro are better than those of MGP in these four sections. The RMS decrease from 3.45\({}^{\circ}\) to 2.25\({}^{\circ}\) in the local trajectory of mark A, the RMS drops from 3.66\({}^{\circ}\) to 3.28\({}^{\circ}\) in the local trajectory of mark B, the RMS reduces from 5.35\({}^{\circ}\) to 3.39\({}^{\circ}\) in the local trajectory of mark C, and the RMS decreases from 5.51\({}^{\circ}\) to 2.58\({}^{\circ}\) in the local trajectory of mark D. Compared with the mean accuracy of MGP, the mean accuracy of Pro increases by 35.86%. In Table 2, the accuracy of heading estimation is further improved by the adaptive algorithm. The RMS decreases from 2.25\({}^{\circ}\) to 1.70\({}^{\circ}\) in the local trajectory of mark A, the RMS drops from 3.28\({}^{\circ}\) to 2.69\({}^{\circ}\) in the local trajectory of mark B, the RMS reduces from 3.39\({}^{\circ}\) to 2.02\({}^{\circ}\) in the local trajectory of mark C, and the RMS decreases from 2.58\({}^{\circ}\) to 2.19\({}^{\circ}\) in the local trajectory of mark D. Also, the mean of RMS is improved by 25.35% for this kinematic data. Similarly, the biased heading estimation can be observed in Table 2, and the bias of mean for ProA is the smallest among these methods. Compared with these methods of Mag, Gyr and MGP, these methods of Pro and ProA can obtain the higher accuracy of heading estimation. Figure 5: Heading error of local trajectory for HV9: (**a**) Heading error of mark A; (**b**) Heading error of mark B; (**c**) Heading error of mark C; (**d**) Heading error of mark D.  
the position in this section because the heading accuracy is poor, and we designed four programs to obtain the position estimation of these two kinematic experiments. 1. The Gyr is used to calculate heading, and UKF is used for position estimation (Gyr-UKF). 2. The MGP is used to obtain heading, and position is estimated based on UKF (MGP-UKF). 3. The Pro is applied to estimate heading, and position estimation is obtained by UKF (MGP-UKF). 4. The ProA is applied to estimate heading, and UKF is used for position estimation (MGP-UKF). We compare the position estimation of these four methods in this section. Figure 7 shows the position trajectories calculated by the outputs of the HV9. We can see from Figure 7 that these position trajectories of Gyr-UKF and MGP-UKF deviate from the reference with time, and the results of position estimation for these two methods are almost identical. The trajectory is improved by the method of Pro-UKF, and the position trajectory of ProA-UKF is basically the same as that of Pro-UKF. Figure 8 shows these trajectories obtained by XM8. We can see that these trajectories of Gyr-UKF and MGP-UKF deviate from the reference with time, and the trajectory of MGP-UKF is slighter better than that of Gyr-UKF. The trajectory is improved by the method of Pro-UKF, and the trajectory is further improved when ProA is used to estimate heading. Therefore, the trajectory calculated by a ProA-UKF algorithm is more accurate than that obtained by the other three methods. In order to provide a reference at each step, these timestamps were recorded when the tester passed corners, and the coordinates of these corners can be obtained by the reference trajectory and reference heading. The coordinates of each step between these two corners can be calculated by linear interpolation in time.