The BeiDou Navigation Satellite System (BDS) features a heterogeneous constellation so that it is difficult to mitigate the multipath in the coordinate-domain. Therefore, mitigating the multipath in the observation-domain becomes more important. Sidereal filtering is commonly used for multipath mitigation, which needs to calculate the orbit repeat time of each satellite. However, that poses a computational challenge and damages the integrity at the end of the multipath model. Therefore, this paper proposes a single-difference model based on the multipath hemispherical map (SD-MHM) to mitigate the BDS-2/BDS-3 multipath in a short baseline. The proposed method is converted from double-difference residuals to single-difference residuals, which is not restricted by the pivot satellite transformation. Moreover, it takes the elevation and the azimuth angles of the satellite as the independent variables of the multipath model. The SD-MHM overcomes the unequal observation time of some satellites and does not require specific hardware. The experimental results show that the SD-MHM reduces the root mean square of the positioning errors by 56.4%, 63.9%, and 67.4% in the east, north, and vertical directions; moreover, it contributes to an increase in the baseline accuracy from 1.97 to 0.84 mm. The proposed SD-MHM has significant advantages in multipath mitigation compared with the advanced sidereal filtering method. Besides, the SD-MHM also features an excellent multipath correction capability for observation data with a period of more than seven days. Therefore, the SD-MHM provides a universal strategy for BDS multipath mitigation.

Due to the existence of environmental or human factors, and because of the instrument itself, there are many uncertainties in point clouds, which directly affect the data quality and the accuracy of subsequent processing, such as point cloud segmentation, 3D modeling, etc. In this paper, to address this problem, stochastic information of point cloud coordinates is taken into account, and on the basis of the scanner observation principle within the Gauss–Helmert model, a novel general point-based self-calibration method is developed for terrestrial laser scanners, incorporating both five additional parameters and six exterior orientation parameters. For cases where the instrument accuracy is different from the nominal ones, the variance component estimation algorithm is implemented for reweighting the outliers after the residual errors of observations obtained. Considering that the proposed method essentially is a nonlinear model, the Gauss–Newton iteration method is applied to derive the solutions of additional parameters and exterior orientation parameters. We conducted experiments using simulated and real data and compared them with those two existing methods. The experimental results showed that the proposed method could improve the point accuracy from 10⁻⁴ to 10⁻⁸ (a priori known) and 10⁻⁷ (a priori unknown), and reduced the correlation among the parameters (approximately 60% of volume). However, it is undeniable that some correlations increased instead, which is the limitation of the general method.

Fundamental systematic errors in point cloud data are inevitable due to a variety of factors, ranging from the external environment during scanning or observation by a terrestrial laser scanner (TLS) to the assembly of the instrument. For low-cost scanners, error terms may be further accentuated and included, in addition to systematic errors, random or even serious errors that directly affect the coordinates of each point in the point cloud, which are directly related to the quality of the point cloud data and subsequent processing. To address the above issues, we attempted to propose a robust target-based self-calibration method for TLS at the algorithmic level without considering the network design and measurement configuration, and derived its solution by normalizing the residual vector and calculating an equivalent covariance matrix based on the IGG III function. After validating the simulated and measured data, the experimental results showed that the proposed self-calibration method could effectively eliminate the random and gross errors associated with the observations; improved the accuracy of the points from centimeter to millimeter level; and increased the accuracy of the corrected checkpoints by 58%, 47%, and 33%, respectively, compared to the three existing methods. However, the proposed method was unable to take into account the attenuation of parameter correlations and further refinement in terms of measurement configurations would be subsequently required.

To address the persistent computational bottlenecks in point cloud registration, this paper proposes a hierarchical grouping strategy named HiGoReg. This method incrementally updates the pose of the source point cloud via a hierarchical mechanism, while adopting a grouping strategy to efficiently conduct recursive parameter estimation. Instead of operating on high-dimensional matrices, HiGoReg leverages previous group estimates and current observations to achieve precise alignment with reduced computational overhead. The method’s effectiveness was validated using both simulated and real-world datasets. The results demonstrate that HiGoReg attains comparable accuracy to traditional batch solutions while significantly improving efficiency, achieving up to 99.79% speedup. Furthermore, extensive experiments confirmed that optimal performance is achieved when each group contains approximately 100 observations. In contrast, excessive grouping could undermine computational efficiency.