An exact and stable algebraic solution based on solving a quartic equation with respect to the cosine function of the reduced latitude is proposed to transform Cartesian into geodetic coordinates. The unique proper root of the equation appropriate to the transformation is chosen from all possible roots by rigorous analyses and the singular region of the transformation that in which there at least one component of the geodetic coordinates is indeterminate or non-single-valued characteristics are determined strictly. The new algorithm does not need any approximation and the instability problems incurred in other algebraic solutions are overcome. For practical applications, the algorithm performs comparably to that of [Vermeille, H., 2011. An analytical method to transform geocentric into geodetic coordinates. Journal of geodesy, 85 (2), 105–117.] and shows a certain superiority in the singular disc over Vermeille's algorithm.

To address scale-like errors in local point clouds caused by pitch angle errors in unmanned aerial vehicle-borne LiDAR bathymetry (UAV-ALB) systems, this study proposes a correction method based on scanline keypoint constraints. First, the point cloud is traversed using scanline information to extract geometric keypoint features from each scanline. Next, a scale-like error correction model is constructed based on the distance differences between keypoints at the start and end of overlapping scanlines, and the pitch angle correction value is estimated using a forward–backward fusion approach. The estimated correction is then applied to the attitude data, and the point cloud is reprocessed. This procedure is iterated until the convergence criterion is satisfied. Experimental results show that, after correction, the horizontal root mean square errors (RMSE) of the two datasets decrease from 0.217 and 0.283 m to 0.025 and 0.030 m, respectively, while the elevation RMSE values decrease from 0.227 and 0.241 m to 0.006 and 0.004 m, respectively. These results demonstrate that the proposed method effectively mitigates scale-like errors in UAV-ALB point clouds and substantially improves their geometric consistency and elevation accuracy.

To improve the data quality of underwater point clouds acquired by UAV-borne LiDAR bathymetry, a scanline-based sliding window filtering method is proposed based on an analysis of scanline data characteristics. Scanline data of underwater point clouds are first extracted from raw point clouds, and the radius outlier removal algorithm is employed to eliminate outliers. Taking the acquisition time of scanline points as the X-axis and elevation as the Y-axis, a 3D problem is simplified into a 2D representation, and a sliding window is constructed along the scanline. Robust least-squares fitting is applied within the window. The median absolute deviation of the fitting residuals is adopted to calculate the terrain feature values for quantifying the terrain complexity, followed by an adaptive filtering threshold determination according to terrain feature values. Fine filtering of the individual scanlines is performed using a point-by-point sliding window. Experimental results demonstrate that the proposed method is adaptable to various terrain conditions, achieving a noise recall rate ≥ 96%, an overall filtering accuracy ≥99%, and an F1-score ≥ 0.9. Particularly, the precision rate in flat-water areas reached 97.37%. Overall, the proposed filtering method effectively separates noise points while preserving detailed terrain features and supports UAV-borne LiDAR bathymetry for mapping complex shallow-water regions.