Parallel Algorithms for Solving Inverse Gravimetry Problems: Application for Earth’s Crust Density Models Creation

The paper describes a method of gravity data inversion, which is based on parallel algorithms. The choice of the density model of the initial approximation and the set on which the solution is sought guarantees the stability of the algorithms. We offer a new upward and downward continuation algorithm for separating the effects of shallow and deep sources. Using separated field of layers, the density distribution is restored in a form of 3D grid. We use the iterative parallel algorithms for the downward continuation and restoration of the density values (by solving the inverse linear gravity problem). The algorithms are based on the ideas of local minimization; they do not require a nonlinear minimization; they are easier to implement and have better stability. We also suggest an optimization of the gravity field calculation, which speeds up the inversion. A practical example of interpretation is presented for the gravity data of the Urals region, Russia.

An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation

In this paper, for the first time the inverse problem of reconstructing the time-dependent potential (TDP) and displacement distribution in the hyperbolic problem with periodic boundary conditions (BCs) and nonlocal initial supplemented by over-determination measurement is numerically investigated. Though the inverse problem under consideration is ill-posed by being unstable to noise in the input data, it has a unique solution. The Crank–Nicolson-finite difference method (CN-FDM) along with the Tikhonov regularization (TR) is applied for calculating an accurate and stable numerical solution. The programming language MATLAB built-in lsqnonlin is used to solve the obtained nonlinear minimization problem. The simulated noisy input data can be inverted by both analytical and numerically simulated. The obtained results show that they are accurate and stable. The stability analysis is performed by using Fourier series.

A general framework for modeling and dynamic simulation of multibody systems using factor graphs

In this paper, we present a novel general framework grounded in the factor graph theory to solve kinematic and dynamic problems for multibody systems. Although the motion of multibody systems is considered to be a well-studied problem and various methods have been proposed for its solution, a unified approach providing an intuitive interpretation is still pursued. We describe how to build factor graphs to model and simulate multibody systems using both, independent and dependent coordinates. Then, batch optimization or a fixed lag smoother can be applied to solve the underlying optimization problem that results in a highly sparse nonlinear minimization problem. The proposed framework has been tested in extensive simulations and validated against a commercial multibody software. We release a reference implementation as an open-source C++ library, based on the GTSAM framework, a well-known estimation library. Simulations of forward and inverse dynamics are presented, showing comparable accuracy with classical approaches. The proposed factor graph-based framework has the potential to be integrated into applications related with motion estimation and parameter identification of complex mechanical systems, ranging from mechanisms to vehicles, or robot manipulators.

A high-speed and high-efficiency imaging polarimeter based on ferroelectric liquid crystal retarders: Design and test

Polarimeters play a key role in investigating solar magnetic fields. In this paper, a High speed and high efficiency Imaging POlarimeter (HIPO) is proposed based on a pair of ferroelectric liquid crystal retarders (FLCs), with the ultimate goal of measuring magnetic fields of prominences and filaments from the ground. A unique feature of the HIPO is that it enables high cadence polarization measurements covering a wide field of view (FOV); the modulation frequency of the HIPO is able to achieve ∼100 Hz, which greatly suppresses the seeing-induced crosstalk, and the maximum FOV can reach 62″ × 525″. Additionally, FLC retardances under low and high states were calibrated individually and found to have a slight discrepancy, which is neglected in most works. Based on FLC calibration results, an optimization was performed using a constrained nonlinear minimization approach to obtain the maximum polarimetric efficiency. Specifically, optimized efficiencies of the Stokes Q, U, and V are well balanced and determined as (ξQ, ξU, ξV) = (0.5957, 0.5534, 0.5777), yielding a total efficiency of 0.9974. Their practical efficiencies are measured as (ξQ′, ξU′, ξV′) = (0.5934, 0.5385, 0.5747), slightly below the optimized values but still resulting in a high total efficiency of 0.9861. The HIPO shows advantages in terms of modulation frequency and polarimetric efficiency compared with most other representative ground-based solar polarimeters. In the observations, measurement accuracy is found to be better than 2.7 × 10−3 by evaluating full Stokes Hα polarimetry results of the chromosphere. This work lays a foundation for the development of high-speed and high-accuracy polarimeters for our next-generation solar instruments.

Optimal Design of Bus Stop Locations Integrating Continuum Approximation and Discrete Models

Although transit stop location problem has been extensively studied, the two main categories of modeling methodologies, i.e., discrete models and continuum approximation (CA) ones, seem have little intersection. Both have strengths and weaknesses, respectively. This study intends to integrate them by taking the advantage of CA models’ parsimonious property and discrete models’ fine consideration of practical conditions. In doing so, we first employ the state-of-the-art CA models to yield the optimal design, which serves as the input to the next discrete model. Then, the stop location problem is formulated into a multivariable nonlinear minimization problem with a given number of stop location variables and location constraint. The interior-point algorithm is presented to find the optimal design that is ready for implementation. In numerical studies, the proposed model is applied to a variety of scenarios with respect to demand levels, spatial heterogeneity, and route length. The results demonstrate the consistent advantage of the proposed model in all scenarios as against its counterparts, i.e., two existing recipes that convert CA model-based solution into real design of stop locations. Lastly, a case study is presented using real data and practical constraints for the adjustment of a bus route in Chengdu (China). System cost saving of 15.79% is observed by before-and-after comparison.

Accuracy estimates of regularization methods and conditional well-posedness of nonlinear optimization problems

We investigate the nonlinear minimization problem on a convex closed set in a Hilbert space. It is shown that the uniform conditional well-posedness of a class of problems with weakly lower semicontinuous functionals is the necessary and sufficient condition for existence of regularization procedures with accuracy estimates uniform on this class. We also establish a necessary and sufficient condition for the existence of regularizing operators which do not use information on the error level in input data. Similar results were previously known for regularization procedures of solving ill-posed inverse problems.

A ROBUST METHOD FOR FUNDAMENTAL MATRIX ESTIMATION WITH RADIAL DISTORTION

Fundamental Matrix Estimation is of vital importance in many vision applications and is a core part of 3D reconstruction pipeline. Radial distortion makes the problem to be numerically challenging. We propose a novel robust method for radial fundamental matrix estimation. Firstly, two-sided radial fundamental matrix is deduced to describe epipolar geometry relationship between two distorted images. Secondly, we use singular value decomposition to solve the final nonlinear minimization solutions and to get the outliers removed by multiplying a weighted matrix to the coefficient matrix. In every iterative step, the criterion which is the distance between feature point and corresponding epipolar line is used to determine the inliers and the weighted matrix is update according to it. The iterative process has a fast convergence rate, and the estimation result of radial fundamental matrix remains stable even at the condition of many outliers. Experimental results prove that the proposed method is of high accuracy and robust for estimating the radial fundamental matrix. The estimation result of radial fundamental matrix could be served as the initialization for structure from motion.