# Kinematic In Situ Self-Calibration of a Backpack-Based Multi-Beam LiDAR System
## 1 Introduction
LiDAR self-calibration can remove the systematic errors inherent in the sensor and thus improve the overall accuracy of point cloud by reducing the Root Mean Square Error (RMSE) associated with registration and check points [24]. It also can reduce the need for point cloud outlier removal as a post-processing step. In the case of MBL, various studies in the literature have performed self-calibration using modified manufacturer-based calibration parameters. They also have confirmed the potential of applying these sensors as a basis for obtaining a highly accurate mobile mapping platform. A calibration of Velodyne HDL-64E, which is Velodyne's first generation of MBL consisting of 64 laser channels, can be found in the literature. Static calibration of Velodyne HDL-64E using plane-based targets achieved a 3D RMSE up to 0.013 m [25], while optimization-based calibration showed standard deviations of planar data from 0.006 to 0.037 m [26]. Moreover, minimizing the discrepancies between the point cloud and pattern planes attained 0.0156 m of point cloud accuracy [27]. In addition to the installed target-based approaches, the static on-site re-calibration approach using planes accomplished 0.013 m of planar misclosure [28]. Besides, the kinematic calibration of HDL-64E on a moving vehicle attained 0.023 m of planar RMS residuals [29]. Velodyne HDL-32E mounted on a vehicle, which consists of 32 laser channels, was also calibrated using cylinder-based self-calibration and improved the accuracy level to 0.008 m in static mode and 0.014 m in kinematic mode [30]. The calibration of the most recent generation of MBL by Velodyne, VLP-16, showed 0.025 m of planar RMSE residuals [31]. However, the system parameters may still be inconsistent, even after self-calibration, due to the instability inherent in the scanning system. Temporal stability analysis of an MBL demonstrated that the measurement stability is slightly higher than the quantization level, which stresses the need for periodic re-calibration of the LiDAR sensor to maintain a high level of accuracy [32]. Since measurement stability analysis showed inconsistency in range observation, there is a chance that the calibration parameters might change during data acquisition. As a result, periodic in situ calibration should be performed to increase and maintain the heightened overall accuracy of the point cloud for a backpack-based MBL system. This leads to our objective of the study, which is the kinematic self-calibration method that can be performed continually during the data acquisition. In this respect, this study aimed to perform kinematic in situ self-calibration of a backpack-based MBL system for the purposes of easy, efficient and frequent periodical self-calibration prior to data acquisition. First, self-calibration was conducted with simulation datasets to examine the minimum network configuration for the in situ self-calibration of backpack-based MBL system. Second, based on the analysis from the simulation experiments, reals datasets were acquired using our own backpack system. The accuracy of the results was analyzed by investigating planar misclosure after the adjustment, the correlations between parameters, measurement residuals, and the standard deviation of the estimated parameters. The remainder of this study is organized as follows. Section 2 presents the configuration and specifications of the sensor system used in this study. Section 3 covers the mathematical models, which are an observation model, a systematic error model, a functional model, and a least squares solution for the adjustment. Section 4 outlines the experimental set-ups and the calibration datasets for the investigation of the minimum network configuration and observation requirements. It also includes the results of the experiments and accuracy analysis. Section 5 provides a discussion of the proposed method in terms of accuracy and benefits. In conclusion, Section 6 summarizes the findings of the study along with possible future work.