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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.

The development of underwater high-precision navigation technology is of great significance for the application of autonomous underwater vehicles (AUVs). Traditional long baseline (LBL) positioning systems require pre-deployment and the calibration of multiple beacons, which consumes valuable time and manpower. In contrast, the range-only single-beacon (ROSB) positioning technology can help autonomous underwater vehicles (AUVs) obtain accurate position information by deploying only one beacon. This method greatly reduces the time and workload of deploying beacons, showing high application potential and cost ratio. Given the operational constraints of AUV open-ocean navigation with single-beacon weak observations and absence of valid a priori positioning data in calibration zones, a multi-sensor underwater virtual beacon localization framework was established, proposing a differential Chan–Gauss–Newton (DCGN) methodology for submerged vehicles. Based on inertial navigation, the method uses the distance measurement information from a single beacon and observations from multiple sensors, such as the Doppler velocity log (DVL) and pressure sensor, to obtain accurate position estimates by discriminating the initial position of multiple hypotheses. A simulation experiment and lake test show that the proposed method not only significantly improves the positioning accuracy and convergence speed, but also shows high reliability.

This study addressed the problem of localization in an ultrawide-band (UWB) network, where the positions of both the access points and the tags needed to be estimated. We considered a fully wireless UWB localization system, comprising both software and hardware, featuring easy plug-and-play usability for the consumer, primarily targeting sport and leisure applications. Anchor self-localization was addressed by two-way ranging, also embedding a Gauss–Newton algorithm for the estimation and compensation of antenna delays, and a modified isolation forest algorithm working with low-dimensional set of measurements for outlier identification and removal. This approach avoids time-consuming calibration procedures, and it enables accurate tag localization by the multilateration of time difference of arrival measurements. For the assessment of performance and the comparison of different algorithms, we considered an experimental campaign with data gathered by a proprietary UWB localization system.

Malaria is one of the world׳s most widespread parasitic diseases. The parasitic protozoans of the genus Plasmodium have developed resistance to several antimalarial drugs. Some patients are therefore infected by two or more strains with different levels of antimalarial drug sensitivity. We previously developed a model to estimate the drug concentration (IC50) that inhibits 50% of the growth of the parasite isolated from a patient infected with one strain. We propose here a new Two-Slopes model for patients infected by two strains. This model involves four parameters: the proportion of each strain and their IC50, and the sigmoidicity parameter. To estimate the parameters of this model, we have developed a new algorithm called PGBO (Population Genetics-Based Optimizer). It is based on the Metropolis–Hasting algorithm and is implemented in the statistical software R. We performed a simulation study and defined three evaluation criteria to evaluate its properties and compare it with three other algorithms (Gauss–Newton, Levenberg–Marquardt, and a simulated annealing). We also evaluated it using in vitro data and three ex vivo datasets from the French Malaria Reference Center. Our evaluation criteria in the simulation show that PGBO gives good estimates of the parameters even if the concentration design is poor. Moreover, our algorithm is less sensitive than Gauss–Newton algorithms to initial values. Although parameter estimation is good, interpretation of the results can be difficult if the proportion of the second strain is close to 0 or 1. For these reasons, this approach cannot yet be implemented routinely. •We model the antimalarial sensitivity in a blood sample with two strains of parasite.•We develop a Metropolis–Hasting algorithm to estimate parameters of the model.•We compare our estimation results with three other algorithms.•We evaluate our algorithm on a simulation study, on in vitro and ex vivo data.•For poor concentration design, our algorithm gives accurate results.

Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra.

Atmospheric phase error is the main factor affecting the accuracy of ground-based synthetic aperture radar (GB-SAR). The atmospheric phase screen (APS) may be very complicated, so the atmospheric phase correction (APC) model is very important; in particular, the parameters to be estimated in the model are the key to improving the accuracy of APC. However, the conventional APC method first performs phase unwrapping and then removes the APS based on the least-squares method (LSM), and the general phase unwrapping method is prone to introducing unwrapping error. In particular, the LSM is difficult to apply directly due to the phase wrapping of permanent scatterers (PSs). Therefore, a novel methodology for estimating parameters of the APC model based on the maximum likelihood estimation (MLE) and the Gauss-Newton algorithm is proposed in this paper, which first introduces the MLE method to provide a suitable objective function for the parameter estimation of nonlinear far-end and near-end correction models. Then, based on the Gauss-Newton algorithm, the parameters of the objective function are iteratively estimated with suitable initial values, and the Matthews and Davies algorithm is used to optimize the Gauss-Newton algorithm to improve the accuracy of parameter estimation. Finally, the parameter estimation performance is evaluated based on Monte Carlo simulation experiments. The method proposed in this paper experimentally verifies the feasibility and superiority, which avoids phase unwrapping processing unlike the conventional method.

This article presents a new class of nonnormal linear mixed models that provide an efficient estimation of subject-specific disease progression in the analysis of longitudinal data from the Modification of Diet in Renal Disease (MDRD) trial. This new analysis addresses the previously reported finding that the distribution of the random effect characterizing disease progression is negatively skewed. We assume a log-gamma distribution for the random effects and provide the maximum likelihood inference for the proposed nonnormal linear mixed model. We derive the predictive distribution of patient-specific disease progression rates, which demonstrates rather different individual progression profiles from those obtained from the normal linear mixed model analysis. To validate the adequacy of the log-gamma assumption versus the usual normality assumption for the random effects, we propose a lack-of-fit test that clearly indicates a better fit for the log-gamma modeling in the analysis of the MDRD data. The full maximum likelihood inference is also advantageous in dealing with the missing at random (MAR) type of dropouts encountered in the MDRD data.

Local scour around bridge piers is one of the primary causes of structural failure in bridges. Therefore, this study focuses on addressing the estimation of maximum scour depth (dsm), which is essential for safe and resilient bridge design. Many studies in the last eight decades have included metadata collection and developed around 80 empirical formulas using various scour-affecting parameters of different ranges. To date, a total of 33 formulas have been comparatively analyzed and ranked based on their predictive accuracy. In this study, novel formulas using semi-empirical methods and gene expression programming (GEP) have been developed alongside an artificial neural network (ANN) model to accurately estimate dsm using 768 observed data points collected from published work, along with eight newly conducted experimental data points in the laboratory. These new formulas/models are systematically compared with 74 empirical literature formulas for their predictive capability. The influential parameters for predicting dsm are flow intensity, flow shallowness, sediment gradation, sediment coarseness, time, constriction ratio, and Froude number. Performances of the formulas are compared using different statistical metrics such as the coefficient of determination, Nash–Sutcliffe efficiency, mean bias error, and root-mean-squared error. The Gauss–Newton method is employed to solve the nonlinear least-squares problem to develop the semi-empirical formula that outperforms the literature formulas, except the formula from GEP, in terms of statistical performance metrics. However, the feed-forward ANN model outperformed the semi-empirical model during testing and validation phases, respectively, with higher CD (0.790 vs. 0.756), NSE (0.783 vs. 0.750), lower RMSE (0.289 vs. 0.301), and greater prediction accuracy (64.655% vs. 61.935%), providing approximately 15–18% greater accuracy with minimal errors and narrower uncertainty bands. Using user-friendly tools and a strong semi-empirical model, which requires no coding skills, can assist designers and engineers in making accurate predictions in practical bridge design and safety planning.

PurposeThis paper aims to propose a fast and robust 3D point set registration method for pose estimation of assembly features with few distinctive local features in the manufacturing process.Design/methodology/approachThe distance between the two 3D objects is analytically approximated by the implicit representation of the target model. Specifically, the implicit B-spline surface is adopted as an interface to derive the distance metric. With the distance metric, the point set registration problem is formulated into an unconstrained nonlinear least-squares optimization problem. Simulated annealing nested Gauss-Newton method is designed to solve the non-convex problem. This integration of gradient-based optimization and heuristic searching strategy guarantees both global robustness and sufficient efficiency.FindingsThe proposed method improves the registration efficiency while maintaining high accuracy compared with several commonly used approaches. Convergence can be guaranteed even with critical initial poses or in partial overlapping conditions. The multiple flanges pose estimation experiment validates the effectiveness of the proposed method in real-world applications.Originality/valueThe proposed registration method is much more efficient because no feature estimation or point-wise correspondences update are performed. At each iteration of the Gauss–Newton optimization, the poses are updated in a singularity-free format without taking the derivatives of a bunch of scalar trigonometric functions. The advantage of the simulated annealing searching strategy is combined to improve global robustness. The implementation is relatively straightforward, which can be easily integrated to realize automatic pose estimation to guide the assembly process.

In the last few decades, the demand for three-dimensional (3-D) inversions for magnetotelluric data has significantly driven the progress of 3-D codes. There are currently a lot of new 3-D inversion and forward modeling codes. Some, such as the WSINV3DMT code of the author, are available to the academic community. The goal of this paper is to summarize all the important issues involving 3-D inversions. It aims to show how inversion works and how to use it properly. In this paper, I start by describing several good reasons for doing 3-D inversion instead of 2-D inversion. The main algorithms for 3-D inversion are reviewed along with some comparisons of their advantages and disadvantages. These algorithms are the classical Occam’s inversion, the data space Occam’s inversion, the Gauss–Newton method, the Gauss–Newton with the conjugate gradient method, the non-linear conjugate gradient method, and the quasi-Newton method. Other variants are based on these main algorithms. Forward modeling, sensitivity calculations, model covariance and its parallel implementation are all necessary components of inversions and are reviewed here. Rules of thumb for performing 3-D inversion are proposed for the benefit of the 3-D inversion novice. Problems regarding 3-D inversions are discussed along with suggested topics for future research for the developers of the next decades.