# LIF-M: A Manifold-Based Approach for 3D Robot Localization in Unstructured Environments
## 5 Experimental Design and Results
### Experimental Results
#### 5.2.2 Trajectory Comparison Results  
To assess the performance of LIF-M in 3D environments, we conducted comparisons with different algorithms and frameworks that have been widely recognized and studied. These comparative frameworks were chosen to ensure the reasonableness and stability of LIF-M. The compared frameworks included LIGO-SAM [11], which is primarily optimization-based; LINS [14], which is based on IESKF, primarily derived from EKF; and a UKF localization framework operating in Euclidean space. The experiments were conducted using a handheld mapping device built on an AGX Xavier platform, with the navigation environment depicted in Figure 4 used for functional testing. The environment was approximately 100 m \(\times\) 100 m in size, resembling a square, and had a significant number of terrain irregularities to challenge the algorithms, particularly in the upper region. Based on the position output data and Figure 5d, it can be observed that the optimization-based methods tend to exhibit weaker precision and more drifted paths for localization in larger scenes. The overall trajectory suggests that filtering demonstrates certain advantages. To ensure data uniformity across sensors, datasets of approximately 460 s, including LiDAR, IMU, and RAC data, were recorded using the rosbag functionality in ROS as the input source for the algorithms. During the recording process, the robot was maintained at a constant speed and encouraged to move in as straight a line as possible. LINS improves the robot's state information by iteratively generating new features using the estimates of the local frame and IESKF. This approach leads to superior performance in overall localization and stability in challenging environments. From Figure 5b,d, it can be inferred that LIF-M exhibits lower oscillations and higher accuracy to a certain extent, akin to LINS. A comparative experiment was conducted between UKF and LIF-M regarding deviations during straight-line motion. Datasets of approximately 10 s were collected along a straight path and the yaw values were compared, as illustrated in Figure 6. LIF-M demon \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Approaches** & **Dsmp (Map/m)** & **Dsmp (Lidar/m)** & **Search Method** & **CPU/\%** & **Mem/Gb** & **Drift** \\ \hline \multirow{6}{*}{NDT-P2D-CUDA} & 0.1 & 0.2 & DIRECT7 & 114 & 1.28 & No \\  & 0.2 & 0.1 & DIRECT7 & 87 & 0.88 & No \\  & 0.2 & 0.2 & DIRECT7 & 103 & 0.88 & Yes \\  & 0.1 & 0.1 & DIRECT7 & 100 & 1.78 & No \\ \hline \multirow{6}{*}{NDT-D2D-CUDA} & 0.1 & 0.2 & DIRECT7 & 92 & 1.28 & No \\  & **0.2** & **0.1** & **DIRECT7** & **79** & **0.88** & **No** \\  & 0.2 & 0.2 & DIRECT7 & 105 & 1.08 & No \\  & 0.1 & 0.1 & DIRECT7 & 95 & 0.88 & No \\ \hline \multirow{6}{*}{NDT-OMP-CPU} & 0.1 & 0.2 & DIRECT1 & 290.4 & 1.52 & Yes \\  & 0.2 & 0.1 & DIRECT1 & 217 & 0.87 & Yes \\ \cline{1-1}  & 0.2 & 0.2 & DIRECT1 & 279.2 & 0.93 & Yes \\ \cline{1-1}  & 0.1 & 0.1 & DIRECT1 & 290.4 & 1.52 & Yes \\ \hline \hline \end{tabular}  
* 1. Dsmp stands for downsampling. 2. The parameters in bold in the table will be used in the overall framework  
\end{table} 
Table 1: Performance evaluation of GPU-based localization. strates smaller angular fluctuation during straight-line motion, with a maximum deviation of around 6\({}^{\circ}\), less than the 10\({}^{\circ}\) oscillation error exhibited by UKF. Analyzing the trajectory shown in Figure 5c, it can be observed that LIF-M's position trajectory is smoother. This is attributed to its representation of sigma points in a group-like manner and calculations performed in the Lie algebra vector space, both of which offer advantages in terms of reducing disturbances and enhancing stability. To clarify the comparison between algorithms, we calculated the absolute trajectory error (ATE) algorithm metrics using the Campus dataset (Figure 4). As shown in Table 2, LIF-M has a lower global error, helping to ensure operation in a variety of challenging environments.