Point cloud fitting plays an important role in various applications of laser scanning technology. Currently, the most dominant algorithms are the linear least squares (LS) method and the Random Sample Consensus (RANSAC) algorithm, in which the random noises of the point cloud coordinates and the influence of the corresponding stochastic model cannot be fully considered. In this study, the mathematical model of point cloud fitting is uniformly described using the nonlinear Gauss-Helmert (NGH) model, in which the nonlinear relationship between the measurements and parameters as well as the effects of all random errors can be considered. In addition, the covariance matrix of point cloud coordinates obtained from the precision of the original measurements is employed to construct the corresponding stochastic model. By further introducing an equivalent weight scheme of robust estimation, a novel point cloud fitting method is proposed based on the robust NGH (RNGH) model. Unlike the previous studies, the RNGH-based algorithm can effectively resist the negative effects of outliers with a full consideration of all random errors in various linear and nonlinear fitting problems. To verify the performance of the proposed RNGH, comparative experiments of point cloud fitting are employed in both simulated and real-world scenarios, respectively. The results demonstrate that the proposed point cloud fitting algorithm has significant advantages over LS and RANSAC in terms of the accuracy and robustness.

The new generation of SAR satellites is serving our long-standing demand for high-resolution crustal deformation over various scales. However, the reliability of InSAR measurements is still limited by varying tropospheric conditions between acquisitions, especially when mapping slow-deforming interseismic deformation. We propose here a new phase-based approach for mapping interseismic deformation using short-period interferograms. Our method formulates the InSAR phase after topographic correction as the sum of three components: (1) spatiotemporally varied turbulent tropospheric phase, (2) topography-correlated stratified tropospheric phase, and (3) interseismic-related deformation assumed to be accumulated at a constant rate. We simultaneously solve for the parameters in the model to avoid overestimating the tropospheric phases, especially when interseismic deformation and tropospheric delays are both coupled with elevation in space. Synthetic tests and practical applications to easternmost Altyn Tagh fault demonstrate that the new method can effectively recover the small-amplitude interseismic deformation caused by fault motion even when the interferograms are dominated by strong tropospheric delays.

Datum transformations are a fundamental issue in geodesy, Global Positioning System (GPS) science and technology, geographical information science (GIS), and other research fields. In this study, we establish a general total least squares (TLS) theory which allows the errors-in-variables model with different constraints to formulate all transformation models, including affine, orthogonal, similarity, and rigid transformations. Through the adaptation of the transformation models to the constrained TLS problem, the nonlinear constrained normal equation is analytically derived, and the transformation parameters can be iteratively estimated by fixed-point formulas. We also provide the statistical characteristics of the parameter estimator and the unit of precision of the control points. Two examples are given, as well as an analysis of the results on how the estimated quantities vary when the number of constraints becomes larger.

Variance component estimation (VCE) is widely applied to adjust random models in the fusion processing of multiple classes of observations. In our previous study, the least squares variance component estimation (LS-VCE) for the classical Gauss-Markov (GM) model was extended to a universal adjustment model: nonlinear Gauss-Helmert (GH) model. However, due to its limited ability to resist outliers, the accuracy of the estimated variance components and parameters will be negatively affected in the presence of outliers. In this paper, the variance inflation principle of robust estimation is further introduced based on our previous study and a robust LS-VCE method for the nonlinear GH model is proposed. To avoid the emergence of negative variance components, the non-negative estimation of the variance components is achieved as well. Unlike the existing studies, the new method can simultaneously mitigate the negative influence of outliers while reasonably adjusting the relative weighting ratios among different classes of observations in the nonlinear GH model. Finally, case studies of point cloud fitting based on original observations and geodetic symmetric transformation are carried out to validate the performance of the proposed method. The results show that when the observations are polluted by outliers, the accuracy of the parameters obtained by the new method has considerable improvement compared with that from the generalized total least squares and the LS-VCE method for the nonlinear GH model. Since the linear/nonlinear GM and errors-in-variables (EIV) models can be treated as the special cases of the nonlinear GH model, the proposed method possesses a wide range of applicability.