## 2 Methodology  
Before describing the proposed methodology for lightweight laser scanner performance assessment, it is important to review the kinematic MMS positioning equation. The mapping frame coordinates (\(m\)) of a point p, \(r_{p}^{m}(t)\), observed by an MMS, can be expressed as follows:  
\[\mathbf{r}_{p}^{m}(t)=\mathbf{r}_{b}^{m}(t)+\mathbf{R}_{b}^{m}(t)\Big{\{}\mathbf{a}_{IMU/s}^{b} +\mathbf{R}_{s}^{b}\mathbf{r}_{p}^{s}(t)\Big{\}} \tag{1}\]  
where \(\mathbf{r}_{b}^{m}(t)\) is the position of the body frame (\(b\)) origin; \(\mathbf{R}_{b}^{m}(t)\) is the body frame attitude matrix, which is parameterized in terms of the time-varying roll, pitch and yaw angles, and represents the rotational transformation from the body frame to the mapping frame; \(\mathbf{a}_{IMU/s}^{b}\) is the lever arm offset vector between the sensor (laser scanner) frame (s) and the body frame (the IMU axes); \(\mathbf{R}_{s}^{b}\) is the boresight matrix, parameterized in terms of three Cardan angles, which represents the rotation from the sensor frame to the body frame; and \(\mathbf{r}_{p}^{s}(t)\) is the position vector of point \(p\) in the sensor frame. For a Velodyne laser scanner, the vector \(\mathbf{r}_{p}^{s}(t)\) is a function of the observed range, rotation angle and the vertical angle of each of its 16 lasers as well the scanner's interior calibration parameters. Additional details about the laser scanner are given later. All quantities are considered to time-varying except for the elements of the boresight matrix and the lever arm vector, which are pre-calibrated and treated as constants. The mapping frame in this project was the 3 TM projection with central meridian 114\({}^{\circ}\) west. The point coordinates given by Equation (1) are prone to many error sources. If the mounting parameters (boresight and lever arm) have been accurately calibrated, then the errors can be attributed to the navigation and laser scanner systems. MMS position and orientation can be severely biased in GNSS-denied and high-multipath environments like urban canyons. They can rapidly vary with time if a low-cost IMU is used. The accuracy assessment methodology is based on spatial comparison of an MMS (kinematic) point cloud and a GNSS/IMU-independent (static) point cloud. The kinematic point cloud possesses variable spatial accuracy at different temporal points due to the nature of the MMS data collection. For instance, areas with sufficient GNSS coverage feature high spatial quality, while areas with a lack of GNSS coverage may feature lower spatial quality, depending on the aiding provided by the IMU for the navigation solution. On the other hand, the static point cloud possesses almost constant accuracy since it is based on a precise multi-station terrestrial laser scanning survey that does not rely on kinematic GNSS/IMU position and orientation estimates. A spatial comparison between the kinematic point cloud and the static one will indicate any discrepancies between the two datasets. One famous way to derive spatial discrepancies between point clouds is by conducting 3D registration [26]. The well-known iterative closest point method [17] can handle registration between point clouds from different sources and with variable point density. The application of the ICP-registration results in six Helmert transformation parameters (i.e., three translations and three rotation angles), which are used as the accuracy measure for the spatial quality of the kinematic point cloud. The scale parameter is not solved for using the ICP since the laser scanners preserve unit scale factor. If the kinematic point cloud has a high spatial quality, it will match the static point cloud and the values of the six transformation parameters will be close to zeroes following the ICP registration. Any differences between the two point-clouds will be indicated by large, non-zero values for the transformation parameters. For a rigorous accuracy assessment, the kinematic point cloud is divided into temporal slices prior to the registration.