Gauss-Newton Iteration Research Articles

Image reconstruction and bladder stimulation using electrical impedance tomography

Impedance tomography (EIT) is an imaging technique that harnesses differences in electrical conductivity to visualize the interior of objects. Despite limitations such as low resolution and nonlinearity of current distribution, its potential in medicine and industry is a source of fascination. The research in this work is a step towards unlocking this potential, focusing on improving the quality of EIT image reconstruction, particularly in bladder modeling. A key element is regularization techniques, including Laplace matrices and the iterative Gauss-Newton algorithm, which balance matching accuracy and image smoothness. In the practical part, simulations were conducted on dense and sparse meshes. Modeling the urinary bladder as a rotational ellipse significantly influences the interpretation of data by algorithms, a crucial factor for the accuracy of reconstruction. Various electrode configurations were also analyzed, revealing the impact of their arrangement on electrical properties and imaging quality. Iterative testing led to identifying optimal electrode placement and grid configuration, underscoring the importance of precise modeling for obtaining high-quality images. The results underscore the critical role of appropriately selecting the regularization parameter in minimizing reconstruction errors.

Sampling free iterative PCE filter for state and parameter estimation of nonlinear dynamical systems

We present a novel filter for state and parameter estimation in non-linear dynamical systems, based on a generalised Kalman filter formulation. To achieve a sampling-free implementation, polynomial chaos expansion (PCE) and a Galerkin projection method are utilized for the propagation of uncertainties through the system dynamics. The non-linear dynamics of the system are then linearised by a sequence of Gauss-Newton iterations in combination with linear Kalman updates. Additionally, we introduce a new square root implementation of the PCE-based filter. The proposed filter is evaluated on the Lorenz-63 and Lorenz-84 models for the task of simultaneous state and parameter estimation and is compared with two related approaches. Finally, the computational complexity of our square-root implementation is compared against two existing square root approaches.

Estimation of Soil Characteristic Parameters for Electric Mountain Tractor Based on Gauss–Newton Iteration Method

Future field work tasks will require mountain tractors to pass through rough terrain with limited human supervision. The wheel–soil interaction plays a critical role in rugged terrain mobility. In this paper, an algorithm for the estimation of soil characteristic parameters based on the Simpson numerical integration method and Gauss–Newton iteration method is presented. These parameters can be used for passability prediction or in a traction control algorithm to improve tractor mobility and to plan safe operation paths for autonomous navigation systems. To verify the effectiveness of the solving algorithm, different initial values and soils were selected for simulation calculations of soil characteristic parameters such as internal friction angle, settlement index, and the joint parameter of soil cohesion modulus and friction modulus. The results show that the error was kept within 2%, and the calculation time did not exceed 0.84 s, demonstrating high robustness and real-time performance. To test the applicability of the algorithm model, further research was conducted using different wheel parameters of electric mountain tractors under wet clay conditions. The results show that these parameters also have high accuracy and stability with only a few iterations. Thus, the estimation algorithm can meet the requirements of quickly and accurately identifying soil characteristic parameters during tractor operation. A criterion for the passability of wheeled tractors through unknown terrain is proposed, utilizing identified soil parameters.

Enhanced Moving Source Localization with Time and Frequency Difference of Arrival: Motion-Assisted Method for Sub-Dimensional Sensor Networks

Localizing a moving source by Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA) commonly requires at least N+1 sensors in N-dimensional space to obtain more than N pairs of TDOAs and FDOAs, thereby establishing more than 2N equations to solve for 2N unknowns. However, if there are insufficient sensors, the localization problem will become underdetermined, leading to non-unique solutions or inaccuracies in the minimum norm solution. This paper proposes a localization method using TDOAs and FDOAs while incorporating the motion model. The motion between the source and sensors increases the equivalent length of the baseline, thereby improving observability even when using the minimum number of sensors. The problem is formulated as a Maximum Likelihood Estimation (MLE) and solved through Gauss–Newton (GN) iteration. Since GN requires an initialization close to the true value, the MLE is transformed into a semidefinite programming problem using Semidefinite Relaxation (SDR) technology, while SDR results in a suboptimal estimate, it is sufficient as an initialization to guarantee the convergence of GN iteration. The proposed method is analytically shown to reach the Cramér–Rao Lower Bound (CRLB) accuracy under mild noise conditions. Simulation results confirm that it achieves CRLB-level performance when the number of sensors is lower than N+1, thereby corroborating the theoretical analysis.

Dimensionless Analysis of the Spatial–Temporal Coupling Characteristics of the Surrounding Rock Temperature Field in High Geothermal Roadway Realized by Gauss–Newton Iteration Method

Understanding the time–space coupling characteristics of the surrounding rock temperature field in high geothermal roadways is essential for controlling heat damage in mines. However, current research primarily focuses on individually analyzing the temperature changes in the surrounding rock of roadways, either over time or space. Therefore, the Gauss–Newton iteration method is employed to model the coupling relationship between temperature, time, and space. The results demonstrate that the dual coupling function describing the temperature field of the surrounding rock in both time and space provides a more comprehensive characterization of the temperature variations. Over time, as ventilation duration increases, the fitting degree of the characteristic curve steadily rises, and the characteristic curve descends overall. In the spatial dimension, the fitting degree of the characteristic curve gradually decreases with the rise of the dimensionless radius, and the characteristic curve ascends overall. Additionally, as thermal conductivity increases, the fitting degree of the characteristic curve steadily rises.

A hybrid of iterative Gauss–Newton and one-dimensional convolutional neural network for high-resolution electrical impedance tomography

We developed a processing method using benefits of both iterative Gauss–Newton (IGN) and a one-dimensional convolutional neural network (1D-CNN) for high-resolution electrical impedance tomography. The proposed method logically combines conductivity images reconstructed by different methods. The accuracies of the mathematical IGN method, 1D-CNN method, and the proposed method were compared. Utilizing the ideal potential data obtained through simulations, along with the experimental potential data derived from cement samples, we reconstruct the conductivity distribution. When utilizing the simulation data, the IGN method produces larger errors in the reconstructed images as the size of the foreign object decreases. The proposed method reconstructs the position and size more accurately than the IGN and 1D-CNN methods. When utilizing the experimental data, 1D-CNN and proposed methods were more accurate in terms of the position and size than the IGN method.

Iterated Orthogonal Simplex Cubature Kalman Filter and Its Applications in Target Tracking

In order to increase a nonlinear system’s state estimate precision, an iterated orthogonal simplex cubature Kalman filter (IOSCKF) is presented in this study for target tracking. The Gaussian-weighted integral is decomposed into a spherical integral and a radial integral, which are approximated using the spherical simplex-radial rule and second-order Gauss–Laguerre quadrature rule, respectively, and result in the novel simplex cubature rule. To decrease the high-order error terms, cubature points with appropriate weights are taken from the cubature rule and processed using the provided orthogonal matrix. The structure supporting the nonlinear Kalman filter incorporates the altered points and weights and the calculation steps; from this, the updated time and measurement can be inferred. The Gauss–Newton iteration is employed repeatedly to adjust the measurement update until the termination condition is met and the IOSCKF is attained. The proposed algorithms are applied in target tracking, including CV target tracking and spacecraft orbit tracking, and the simulation results reveal that the IOSCKF can achieve higher accuracy compared to the CKF, SCKF, and OSCKF. In spacecraft orbit tracking simulation, compared with the SCKF, the position tracking accuracy and velocity tracking accuracy of the OSCKF are increased by 2.21% and 1.94%, respectively, which indicates that the orthogonal transformation can improve the tracking accuracy. Furthermore, compared with the OSCKF, the position tracking accuracy and velocity tracking accuracy of the IOSCKF are increased by 2.71% and 2.97%, respectively, which indicates that the tracking accuracy can be effectively improved by introducing iterative calculation into the measurement equation, thus verifying the effectiveness of the method presented in this paper.

GAUSS-NEWTON METHOD APPLICATION IN THE PROBLEM OF PHASE FUNCTION RECONSTRUCTING FROM HILBERTOGRAMS

The problem of phase function reconstructing in Hilbert diagnostics of gaseous, condensed and reacting media is discussed in the work. The method for reconstructing the phase disturbances structure of a probing light field, based on the iterative Gauss-Newton al- gorithm, is proposed.This method does not require the second derivatives determination and greatly reduces the number of calculations.It consists in the sequential selection of a complex phase profile, which is specified by the sum of third degree Bezier curves, and the hilbertogram calculation in order to minimize the root-mean-square error between the experimental and reconstructed hilbertograms. The Jacobi matrix for the nonlinear integral operator of Hilbert visualization is calculated. The proposed algorithm was tested on test functions.The devel- opment of the method and its applications is associated with the application of the algorithm to the processing of experimental results.

Метод Гаусса-Ньютона в задаче оптимизации расчёта осесимметричной фазовой функции по данным гильберт-диагностики

A method for reconstructing phase disturbances of a probing light field using the iterative Gauss-Newton algorithm is discussed as part of the Hilbert diagnostics development of gaseous, condensed and reacting media. In this case, the need to determine second derivatives is eliminated, which simplifies the calculations. The method consists of selecting a phase profile, which is specified by a Bezier curve, and hilbertogram calculating. The coincidence of the reference and reconstructed hilbertograms serves as a criterion for the results reliability. The Jacobian matrix for the nonlinear integral operator of Hilbert visualization is obtained. The algorithm is analyzed using a test function. The method development is associated with the algorithm application to the processing of experimental results, including the reconstruction of complex structures in which the phase function is described by several Bezier polynomials.

A sandwich resonant bar method with transfer matrices for measuring the elastic parameters of rock at low frequency

Abstract Rocks and other geological materials have appreciable dispersion in their elastic properties. Rock elastic parameters within the same frequency range as the logging frequency band (1–20 kHz) should be determined to facilitate reservoir prediction and interpretation of logging data. This study suggests a technique for determining the elastic characteristics of rock cores at low frequencies using a sandwich resonant bar by integrating transfer matrices into the one-dimensional transmission model. The frequency response expression of the sandwich resonant bar is derived analytically and then the response is simulated accurately based on this expression. Numerical results show that the first two-order longitudinal resonance frequencies are approximately linearly related to the inverse of the sample's Young's modulus and the density, respectively. In addition, an inversion algorithm based on Gauss–Newton iteration, which converges faster and more efficiently, is proposed in this paper. The residuals between the model's first two resonant frequencies and the simulated results are used as the error function, and the elasticity parameters that minimize the error function are the best estimate for creating the model. This research is valuable for measuring rock elastic parameters accurately in the kilohertz range, which is of practical significance in dispersion-related studies relating to rock cores.

Sensing Method for Wet Spraying Process of Tunnel Wall Based on the Laser LiDAR in Complex Environment.

In tunnel lining construction, the traditional manual wet spraying operation is labor-intensive and can be challenging to ensure consistent quality. To address this, this study proposes a LiDAR-based method for sensing the thickness of tunnel wet spray, which aims to improve efficiency and quality. The proposed method utilizes an adaptive point cloud standardization processing algorithm to address differing point cloud postures and missing data, and the segmented Lamé curve is employed to fit the tunnel design axis using the Gauss-Newton iteration method. This establishes a mathematical model of the tunnel section and enables the analysis and perception of the thickness of the tunnel to be wet sprayed through comparison with the actual inner contour line and the design line of the tunnel. Experimental results show that the proposed method is effective in sensing the thickness of tunnel wet spray, with important implications for promoting intelligent wet spraying operations, improving wet spraying quality, and reducing labor costs in tunnel lining construction.

Proposal of a non-linear model to adjust in vitro gas production at different incubation times

This work aims to propose a new model named Gompertz-Von Bertalanffy bicompartmental (GVB), a combination of the models Gompertz and Von Bertalanffy. The GVB models is applied to fit the kinetic curve of cumulative gas production (CGP) of four foods (SS – sunflower silage; CS – corn silage; and the mixtures 340SS – 660 gkg-1 of corn silage and 340 gkg-1 of sunflower silage; and 660SS – 340 gkg-1 of corn silage and 660 gkg-1 of sunflower silage). The GVB fit is compared to models Logistic-Von Bertalanffy bicompartmental (LVB) and bicompartmental logistic (BL). All the process studied employed the semi-automatic “in vitro” technique of producing gases used in ruminant nutrition. The gas production readout was performed at times 2, 4, 6, 8, 10, 12, 15, 19, 24, 30, 48, 72, and 96 h. The data generated were used to estimate the models’ parameters by the least squared method with the iterative Gauss-Newton process. The data fit quality of the models was verified using the adjusted coefficient of determination criterion (), mean residual square (MRS), Akaike information criterion (AIC), and mean absolute deviation (MAD). Among the analyzed models, the LVB model presented the best quality of fit evaluators for CS. In contrast, the GVB model showed better quality of fit to describe CGP over time for 340SS, 660SS, and SS, presenting the highest values of () and the lowest values of MSR, AIC, and MAD.

Real-Time Scan-to-Map Matching Localization System Based on Lightweight Pre-Built Occupancy High-Definition Map

High-precision and robust localization in GNSS-denied areas is crucial for autonomous vehicles and robots. Most state-of-the-art localization methods are based on simultaneous localization and mapping (SLAM) with a camera or light detection and ranging (LiDAR). However, SLAM will suffer from drift during long-term running without loop closure or prior constraints. Lightweight, high-precision environmental maps have gradually become an indispensable part of future autonomous driving. In order to solve the problem of real-time global localization for autonomous vehicles and robots, we propose a precise and robust LiDAR localization system based on a pre-built, occupied high-definition (HD) map called the Extended QuadTree (EQT) map. It makes use of a planar quadtree for block division and a Z-sequence index structure within the block cells. Then, a four-level occupancy probability cell value model is adopted. It will save about eight times the storage space compared with Google Cartographer, and the EQT map can be extended to store other information. For efficient scan-to-map matching with our specialized EQT map, the Bursa linearized model is used in the Gauss–Newton iteration of our algorithm, which makes the calculation of partial derivatives fast. All the above improvements lead to optimal storage and efficient querying for real-time scan-to-map matching localization. Field tests in an industrial park and road environment prove that positioning accuracy of about 6–13 cm and attitude accuracy of about 0.15° were achieved using a VLP-16 LiDAR. They also show that the method proposed in this paper is significantly better than the NDT method. For the long and narrow environment of an underground mine tunnel, high-resolution maps are also helpful for accurate and robust localization.

Intelligent Prediction Method for Heat Dissipation State of Converter Heatsink

Currently, the offline manual periodic detection method is a well-established practice in detecting the thermal state of the converter heatsink. This method, however, is huge in maintenance costs. To lower maintenance costs and improve maintenance efficiency in detecting the thermal dissipation state, this paper proposes an intelligent online prediction scheme based on Gauss-Newton iteration method. Firstly, the power loss model of the power module is established according to the characteristics of IGBT and FWD. The power loss of the power device is then calculated in real time with the voltage and current parameters of the converter. Next, the transient thermal model of the heatsink is established based on thermodynamics theory. And the calculation method of steady thermal resistance of heatsink based on Gauss-Newton iteration method is proposed according to the model. The transient thermal impedance data allow for timely prediction of thermal resistance of the heatsink and characterize the thermal state of the heatsink. Finally, with the help of DSP28377D, an experimental platform is built to verify the scheme. Results show that this method can realize intelligent prediction of thermal state online.

Indoor Camera Pose Estimation from Room Layouts and Image Outer Corners.

To support indoor scene understanding, room layouts have been recently introduced that define a few typical space configurations according to junctions and boundary lines. In this paper, we study camera pose estimation from eight common room layouts with at least two boundary lines that is cast as a PnL (Perspective-n-Line) problem. Specifically, the intersecting points between image borders and room layout boundaries, named image outer corners (IOCs), are introduced to create additional auxiliary lines for PnL optimization. Therefore, a new PnL-IOC algorithm is proposed which has two implementations according to the room layout types. The first one considers six layouts with more than two boundary lines where 3D correspondence estimation of IOCs creates sufficient line correspondences for camera pose estimation. The second one is an extended version to handle two challenging layouts with only two coplanar boundaries where correspondence estimation of IOCs is ill-posed due to insufficient conditions. Thus the powerful NSGA-II algorithm is embedded in PnL-IOC to estimate the correspondences of IOCs. At the last step, the camera pose is jointly optimized with 3D correspondence refinement of IOCs in the iterative Gauss-Newton algorithm. Experiment results on both simulated and real images show the advantages of the proposed PnL-IOC method on the accuracy and robustness of camera pose estimation from eight different room layouts over the existing PnL methods. The code is available at https://github.com/XiaoweiChenOSU/PnL-IOC.

3D minimum-structure inversion of controlled-source EM data using unstructured grids

In this study, a minimum-structure inversion procedure for controlled-source electromagnetic data that parameterizes the Earth model in terms of an unstructured tetrahedral grid is presented. To minimize the objective function defining the inversion problem Gauss–Newton iterations are used. Iterative solvers are employed for the solution of the system of equations at each Gauss–Newton step. These solvers do not need the matrix to be explicitly formed to solve the linear system, and hence, these kinds of solvers ensure memory efficiency of the developed algorithm. For the forward-modelling problem, a potentials formulation, in which the electric field is expressed in terms of vector and scalar potentials and the relevant partial differential equations are the Helmholtz and conservation of charge equations, is discretized by the finite-element method. This decomposition results in a well conditioned matrix equation compared to the E-field equation and gives a more natural description of electromagnetic phenomena. The linear system of equations for the forward-modelling problem is solved by a direct solver. The advantage of this type of solver is that the factorization that is generated, which takes up the bulk of the solution time for this system, can be reused when solving for multiple right-hand sides. This is important for the efficient calculation of the matrix–vector products in the above-mentioned Gauss–Newton systems. Two synthetic examples are given to illustrate the capabilities and efficiency of the presented procedure. In the first example, inversion of a dataset generated over a geometric shaped conductive body for a flat Earth’s surface is presented. In the second example, a realistic scenario is given. This example shows that topography and a realistic ore body can be naturally and effectively handled by unstructured grids.

Interval Q factor estimation based on an improved frequency shift method

To characterize seismic attenuation information quantitatively, the qualify factor Q is routinely used in seismic exploration. To obtain a more reliable Q value than the peak frequency shift (PFS) method, the improved frequency shift (IFS) method computes the peak frequency by the centroid frequency (CF) to improve the noise immunity. However, the IFS method assumes all wavelets are the standard Ricker shape and ignores the effect of attenuation on the wavelet, which greatly affects the accuracy of estimated Q values, especially in interlayer computations. Some analytical methods try to replace the original hypothesis with attenuated Ricker wavelets, but there are too many mathematical approximations, resulting in inaccurate analytical results. Here, a new formula is derived by matching the spectrums with the attenuated Ricker wavelets. The peak frequencies (PFs) of the reference and attenuated wavelet are calculated by the Gauss-Newton iteration method. Combined with fitted PFs, we derive another new formula to calculate the interval-Q value directly. With these modifications, the PFS improved (PFSI) method not only improves the accuracy of the Q factor but also has noise robustness. The synthetic data tests and field data application demonstrate the feasibility and effectiveness of the proposed method.

Convolutional neural network based displacement gradients estimation for a full-parameter initial value guess of digital image correlation

The selection of initial value in digital image correlation (DIC) has significant influence on the search efficiency of image subpixel displacement and the algorithmic convergence speed. An accurate and reasonable initial value can reduce the number of iterations of subsequent IC-GN optimization, accelerate the convergence of the results, and avoid the divergence of the algorithm in the iterative process. This paper proposes a full-parameter initial value estimation method based on a regression convolution neural network with multithreaded calculation. The proposed method sequentially uses the integer-pixel estimation based on neighborhood search, the subpixel estimation based on surface fitting and the first-order displacement gradients estimation based on a regressive convolutional neural network to achieve the initial value estimation of inverse compositional Gauss-Newton (IC-GN) iteration. Experimental results show that the iteration times of the proposed method are reduced by about 30% compared with the integer-pixel initial value estimation method. In the process of IC-GN iteration, the computational efficiency of CPU multithreaded calculation is nearly twice higher as that of the single-thread method. It can not only improve the accuracy of the initial value estimation but also has high adaptability, which can adapt to selecting different subset sizes or different speckle patterns. This study provides a reference for the effect of iterative initial value optimization on efficiency and accuracy in DIC.

Gauss–Newton iteration method for radial basis function-based postdistortions in visible light communication systems

In visible light communication systems, the inherent nonlinear characteristics of light-emitting diodes (LEDs) are the primary source of signal distortion. To alleviate the nonlinear effect of the LED and improve the system reliability, the polynomial method is used to construct the postdistorter. With strong processing ability and high solution accuracy, radial basis function (RBF) interpolation can also be used to alleviate the nonlinear effect. In terms of the iterative implementations, recursive least squares (RLS) algorithm has been widely adopted, but performance loss exists with the solution since RLS is initially proposed for linear regressions. Aiming at the nonlinear characteristics of post distortions, Gauss–Newton (GN) method is investigated to accomplish the iterations in this paper, where Taylor series expansion is used to approximate the nonlinear regression model. Simulation results show that the RBF can obtain better bit error ratio performance than polynomial, and the proposed GN iterations have significantly better performance compared to RLS in mitigating the nonlinear effect of LED.

Reflection-based traveltime and waveform inversion with second-order optimization

Reflection-based inversion that aims to reconstruct the low-to-intermediate wavenumbers of the subsurface model, can be a complementary to refraction-data-driven full-waveform inversion (FWI), especially for the deep target area where diving waves cannot be acquired at the surface. Nevertheless, as a typical nonlinear inverse problem, reflection waveform inversion may easily suffer from the cycle-skipping issue and have a slow convergence rate, if gradient-based first-order optimization methods are used. To improve the accuracy and convergence rate, we introduce the Hessian operator into reflection traveltime inversion (RTI) and reflection waveform inversion (RWI) in the framework of second-order optimization. A practical two-stage workflow is proposed to build the velocity model, in which Gauss-Newton RTI is first applied to mitigate the cycle-skipping problem and then Gauss-Newton RWI is employed to enhance the model resolution. To make the Gauss-Newton iterations more efficiently and robustly for large-scale applications, we introduce proper preconditioning for the Hessian matrix and design appropriate strategies to reduce the computational costs. The example of a real dataset from East China Sea demonstrates that the cascaded Hessian-based RTI and RWI have good potential to improve velocity model building and seismic imaging, especially for the deep targets.