6.1.2. Runtime Performance Analysis

Meanwhile, our experiments proved that the time consumption of our scan-to-map module is significantly reduced from Table 3. Four algorithms have this module which is the most time-consuming. So, we choose the cost time of this module for comparison. The bold and italic values indicate the minimum time consumption. We can see the obvious advantage of our algorithm.

**Table 3.** The time consumption (ms) in seven datasets. All are recorded in the same platform.


LOAM and LeGo-LOAM use a scan-to-scan match to provide odometry, which means using the current scan and last scan to do the scan matching, and the result offers an initial guess for mapping. LIO-SAM and our system use IMU pre-integration, which is of high frequency, and we use the back-end result to suppress IMU drift. Even more, thanks to the edge points extracted from the rod-shaped information and the planar points extracted from the ground surface information, many outliers are not in the operation. Accuracy and speed are greatly improved.

We still choose street\_01 for analysis. Table 4 shows the number of frames four systems processed.

**Table 4.** The scan-to-map frames in street\_01.


Figure 14 shows the processing time of each frame. We can clearly see the lowest cost time of our system. In ALOAM, the mapping module uses the global map and map maintenance is time-consuming. LeGo-LOAM and LIO-SAM are the same, which apply Levenberg–Marquardt algorithm [32] of 30 iterations for optimization. Our algorithm uses faster and more accurate graph optimization model to solve the scan-to-map module (see Sections 4.2 and 4.3).

**Figure 14.** Processing time of each scan. The red is obviously lower than other three.

The computationally-efficient system is meaningful for mobile terminal and other platforms with limited computing resources.

#### *6.2. Validation of Our Datasets*

To further test our system, LIDAR has less beams and IMU is of different quality. We set up a sensor suite composed of a VLP16 Velodyne and an ADIS16488 IMU (see Figure 15). Sensors have hardware time synchronization because of GPS pulse per second (PPS). RTK/IMU combined navigation results are used as the truth value, which is after NovAtel Inertial Explorer software post-processing. Our aim is to prove the versatility of our algorithm. We pick two typical scenarios. One is in a campus (dataset\_01) and the other is on a city road (datasetet\_02).

In dataset\_01, (see Figure 16) the speed of our car is about 6 m/s. There is rich feature, but there is accumulated error in long-term run. Various weeds, leaves and other environmental factors affect the positioning accuracy.

Dataset\_02 was collected in the wide urban road (see Figure 17) and the speed of our car is about 14 m/s. It contains a large number of buildings. Dynamic objects will affect the point cloud matching accuracy. The density of point cloud in open space is small and it is difficult to have a good performance on localization.

**Figure 15.** Our sensor suite. All have hardware time synchronization (**a**) IMU is in the LIDAR below. Integrated navigation device is used to gain ground truth. (**b**) The device is mounted on top of the vehicle.

(**a**)

**Figure 16.** *Cont*.

**Figure 16.** Trajectory and mapping are generated by our system. (**a**) Our trajectory and ground truth. Different colors represent the error values. (**b**) The mapping result is rendered with LIDAR intensity value from the top view during the positioning process. (**c**) The top panel is the specific real-word environment picked out of the whole trajectory. The bottom panel shows the detail from LIDAR mapping correspond to the top panel.

**Figure 17.** *Cont*.

**Figure 17.** Trajectory and mapping in dataset\_02. (**a**) Our trajectory and ground truth in the urban road. (**b**) The mapping result is rendered with LIDAR intensity value from bird-eye view. (**c**) The road scene.

In feature-rich areas(dataset\_01), we can conclude that LIDAR will have good performance than the wide-open spaces(dataset\_02) from the Table 5. The bold and italic values indicate the minimum error. Compared with the LIO-SAM, the RMSE in the study increases by 24.2% in dataset\_01 and 25.0% in dataset\_02.

**Table 5.** Absolute trajectory error (ATE) RMSE (m) in our real-word experiments.


In the Figures 16a and 17a, they show the corresponding trajectories of the two datasets and different colors represent the error values. In the Figures 16b and 17b, the global reconstruction of the two scenes is built. Due to the multiple constraints of the back-end optimization, we obtain a globally consistent point cloud map. According to Equation (19), the robustness and reliability of the map can be guaranteed. The map shows the structural details in the bottom panel of Figure 16c. We can clearly see the cars and the trunk of the tree in the dataset in bird-eye view. In the Figure 17c, the wide roads have great influence for LIDAR slam (see Table 5). However, our algorithm can also reduce the error.

The time performance is consistent with the M2DGR dataset analysis (see Section 6.1.2). In dataset\_01, due to the features' richness in campus scenes, the feature information relationship in scan-to-map needs much time for calculation. However, the average time consumption is 64.379 ms, which can satisfy the real-time requirement (LIDAR is 10 HZ sampling frequency), and the average time consumption is 25.874 ms in the road test in the dataset\_02, which is computationally efficient. Our system can achieve a good estimation result with less time cost.

#### **7. Conclusions and Future Perspectives**

According to the datasets and our own data experiments, compared to LIDAR only positioning (ALOAM), the positioning accuracy and robustness is significantly improved. Then only IMU data helps the point cloud to remove distortion (LeGo-LOAM), the tightly coupled LIO has lower drift, and compared to LIO-SAM, segmentation and clustering are used to mark feature information. The point cloud matching is more accurate and the runtime of scan-to-map module is much less.

In this paper, we propose an improved LIO system. Firstly, it makes reasonable use of the feature information of point cloud and effectively improves the accuracy of point cloud matching. Point cloud registration is carried out after marking rod-shaped and planar feature information which is different from the existing LIDAR-inertial integration scheme. The optimized edge points and planar points extraction modes reduce the computation of scan-to-map and improve the real-time performance. Secondly, prediction of IMU odometry and correction of LIDAR odometry improve the accuracy and frequency of the mapping module, which is inspired by LIO-SAM. Comparing this to the front-end odometry in traditional scan-to-scan mode, the tightly coupled mode of system greatly improves the performance of LIO. Thirdly, the scan-to-map based on the graph optimization model is of great significance to speed up the solution and decrease error. Therefore, the system does not apply the Levenberg–Marquardt algorithm, which is adopted in Lego-LOAM and LIO-SAM. Fourthly, the robust back-end optimization system including effective loop closure suppress the cumulative drift of LIO odometry, and IMU measurements residuals add more constraints information between IMU and LIDAR measurements compared to LIO-SAM. The optimization mode based on sliding window ensure full use of sensors information under real-time conditions. Experiments show that the real-time performance and accuracy of our algorithm exceed that of most state-of-the-art systems in various typical environments.

It can be seen from Table 2 that the positioning accuracy (RMSE) can be improved by 25–78% (the average increment is 64.45%) in the M2DGR street datasets compared to the current tightly coupled LIDAR SLAM algorithms (LIO-SAM). After optimizing the extraction mode of edge points and planar points, our system processes more frames and takes less time on average, effectively improving real-time performance. In our actual scene datasets, the RMSE in the study increases by 24.4% in dataset\_01 and 25.0% in dataset\_02.

We draw a conclusion that we propose the low drift and high real-time LIDAR-inertial positioning and mapping system, which is of great importance in indoor locating and other GNSS occlusion area. At the same time, it can provide high precision point cloud image for scene understanding in automatic system. For the back-end optimization framework, we can easily add other measurements such as GNSS for global restriction.

In the future, we noticed that it is necessary to improve the initialization process to reduce initial error. It is very important to judge the rod-shaped feature information and the planar feature information in the research process of this paper. This work gets thresholds according to experience temporarily. We will focus on online threshold estimation and adaptive threshold selection. Also, it is worth mentioning that LIO system is prone to Z direction drift in the large scene. Then more constraints will be introduced to suppress drift in our next step. Furthermore, according to the recent study [33–36], the positioning and mapping system based on solid state LIDAR can significantly reduce the hardware cost. Therefore, the research of solid-state LIDAR- inertial system is worth exploring.

**Author Contributions:** Conceptualization, H.L., S.P., W.G. and C.M.; methodology, H.L.; software, F.J. and C.M.; validation, S.P. and F.J.; formal analysis, H.L. and C.M.; investigation, W.G. and F.J.; resources, S.P., W.G. and H.L.; writing—original draft preparation, H.L. and X.L.; writing—review and editing, W.G. and X.L.; supervision, S.P. and W.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research study was funded by the National Key Research and Development Program of China (No. 2021YFB3900804), the Research Fund of Ministry of Education of China and China Mobile, (No. MCM20200J01) and the Fundamental Research Funds for the Central Universities (No. 2242021R41134).

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
