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Huang et al. Complex Eng Syst 2023;3:2 I http://dx.doi.org/10.20517/ces.2022.43 Page 17 of 20

Figure 13. Comparison between our algorithm, LOAM and the ground truth.

Table 2. Localization error
Algorithm RMSE Min APE error Max APE error
Algorithm of this paper 4.3361m 0.6679m 15.1492m
LOAM 12.5518m 1.1545m 21.8804m

v
u
t
1 Õ 2
RMSE = APE (25)

=1
The absolute pose error (APE) considers only translational errors:

APE =
trans( −1 , )
(26)
,
In this study, the EVO [41] toolkit is used to evaluate the trajectory error of the proposed localization algorithm,
and the results are shown in Table 2.

Figure 13 shows the comparison of the effect of the proposed algorithm and the LOAM algorithm. The pro-
posed localization algorithm has a more significant improvement compared to the pure LOAM distance meter.
As seen, the error in the localization effect of incorporating the HD map remains small most of the time. A
horizontal offset can be seen in the upper left part of the road where the HD map does not exist. Because
the leftmost road is long and has a particular curvature, the localization of the fused HD map needs to be
improved for the forward direction. The LiDAR odometer has a large offset on the lower left side of the road,