## 1 Introduction  
Simultaneous localization and mapping (SLAM) provides the mobile robot the ability to set up a model of the working space and to localize itself, and it is the most important ability for a truly autonomous robot able to operate within real-world environments. There are several main kinds of sensors widely used for SLAM research or applications, such as cameras [1], RGBD sensors [2], LiDAR [3], and even the fusion of different kinds of sensors [4]. Each kind of sensor has its own advantages and limitations. The camera-based methods are easy to be affected by illumination or seasons changing. Comparatively, LiDAR has the advantages of high precision, good real-time performance, and strong anti-interference ability, so the LiDAR-based SLAM has been widely used in many practical applications, such as autonomous vehicles, home service robots, and automatic guided vehicles in civilian areas. Generally, LiDAR-based SLAM can be separated into two stages according to the information processing: the front-end stage and the back-end stage. In the front-end stage, currently observed scanning data is matched with the previously scanned one, which is the very fundamental step in SLAM--data association (DA). There are usually two strategies for data association: scan-to-scan matching-based [5; 6] and scan-to-map matching-based [7]. Scan-to-scan matching-based DA is commonly used to compute the relative motion between two consecutive scanning results. The matching process is to adjust the pose of the current scan to make sure an overlap exists as much as possible between current scan and reference scan. For example, the HG-SLAM method in reference [8] adopts a scan-to-scan matching strategy and Iterative Closest Point (ICP) [9] is used to compute the rigid transformation between adjacent scanning frames. The advantage of scan-to-scan matching strategy is that it has a lower computational cost because only two frames are considered. However, due to the noise data and many other factors, the result is prone to quickly accumulating errors. On the other hand, scan-to-map matching-based DA is to align the current scan with the existing map. For example, Hector SLAM [7] takes a scan-to-map matching strategy to solve the data association problem, where the current frame is aligned with the entire map to achieve the rigid transformation from the current scanning set to the built map, which uses the Gauss-Newton method to solve the nonlinear optimization problems. Usually, to further improve the stability, the features extracted from scanned points can be used for matching [6]. The cumulative error is limited in this case and a higher precision mapping result can be achieved for small-scale environments. Because the current scan will be matched with the whole or part of the existing map, it has a higher computational cost compared with scan-to-scan matching. Based on the initial pose estimation results obtained in the front-end stage, some optimization methods are applied to improve the accuracy and robustness of SLAM results in the back-end stage. Particle filter-based [10] or graph-based optimization are two popular methods used for nonlinear optimization in SLAM. The graph-based method [11; 12] uses a collection of nodes to represent the poses and features; the edges in the graph are the results generated by DA from observations, also regarded as the constraints and different optimization methods can be applied to minimize the error expressed by the constraints. Loop closure detection (LCD) when a robot revisits a place plays a very important role in SLAM [13; 14]. It will be used as a constraint for global optimization and can reduce the accumulated error. LCD is heavily dependent on the DA results. In HG-SLAM [8], a hierarchical loop closure method based on a local map [15; 16; 17] is proposed. The optimization in the back-end stage can usually enhance the results, but it needs a good initial value to start over, or it will fall into the local minimum or even be unable to converge.