Gauss-Newton Iteration Research Articles

Indoor Positioning Based on Pedestrian Dead Reckoning and Magnetic Field Matching for Smartphones.

This paper presents an ambient magnetic field map-based matching (MM) positioning algorithm for smartphones in an indoor environment. To improve the low distinguishability of a magnetic field fingerprint at a single point, a magnetic field sequence (MFS) combined with the measured trajectory contour coming from pedestrian dead-reckoning (PDR) is used for MM. Based on the fast approximation of magnetic field gradient, a Gauss-Newton iterative (GNI) method is used to find a rigid transformation that optimally aligns the measured MFS with a reference MFS coming from the magnetic field map. Then, the position of the reference MFS is used to control the position drift error of the inertial navigation system (INS) based PDR by an extended Kalman filter (EKF) and to further improve the accuracy of the trajectory contour. Finally, we conduct several experiments to evaluate the navigation performance of the proposed MM algorithm. The test results show that the position estimation error of the MM algorithm is 0.64 m (RMS) in an office building environment, 1.87 m (RMS) in a typical lobby environment, and 2.34 m (RMS) in a shopping mall environment.

Design and Realization of the Water Resources Carrying Capacity Evaluation Model for Marine Climate Cities

ABSTRACT Yao, L. and Zhang, H., 2018. Design and realization of the water resources carrying capacity evaluation model for marine climate cities. In: Ashraf, M.A. and Chowdhury, A.J.K. (eds.), Coastal Ecosystem Responses to Human and Climatic Changes throughout Asia. To improve the living environment of marine climate cities and the carrying level of water resources under maritime climate conditions, a water resources balance scheduling and cycle control-based evaluation model was proposed. The water balance model of marine climate cities was constructed using Gauss-Newton iteration and the volume square root particle filter method. According to the importance of density function, the confidence interval of the water resources carrying capacity level was analyzed, and the optimal allocation of the water resources carrying capacity based on the particle swarm optimization algorithm was made. Using the reduction coefficient of water resources retention to mechanically control the carrying capacity, the wate...

Quadrangulation through morse-parameterization hybridization

We introduce an approach to quadrilateral meshing of arbitrary triangulated surfaces that combines the theoretical guarantees of Morse-based approaches with the practical advantages of parameterization methods. We first construct, through an eigensolver followed by a few Gauss-Newton iterations, a periodic four-dimensional vector field that aligns with a user-provided frame field and/or a set of features over the input mesh. A field-aligned parameterization is then greedily computed along a spanning tree based on the Dirichlet energy of the optimal periodic vector field, from which quad elements are efficiently extracted over most of the surface. The few regions not yet covered by elements are then upsampled and the first component of the periodic vector field is used as a Morse function to extract the remaining quadrangles. This hybrid parameterization- and Morse-based quad meshing method is not only fast (the parameterization is greedily constructed, and the Morse function only needs to be upsampled in the few uncovered patches), but is guaranteed to provide a feature-aligned quad mesh with non-degenerate cells that closely matches the input frame field over an arbitrary surface. We show that our approach is much faster than Morse-based techniques since it does not require a densely tessellated input mesh, and is significantly more robust than parameterization-based techniques on models with complex features.

Sparse estimation in high-dimensional zero-inflated Poisson regression model

In the high-dimensional zero-inflated Poisson (ZIP) regression model, the traditional Gauss-Newton iteration method and Expectation Maximization (EM) algorithm cannot do the variable selection. We propose an Expectation-Maximization-Regularization (EMR) algorithm. In the E step, we calculate the expected value of the implicit variable under the existing estimated value. In the MR step, the “regularization + likelihood function” method is used. We introduce the elastic net penalty and use the coordinate descent method to obtain the sparse estimate. The simulation results show that the EMR method makes the parameter estimation and variable selection simultaneously, and the estimation accuracy is high. Finally, applying the EMR method to forecast the number of municipal engineering Public-Private-Partnership (PPP) projects in Hebei Province, this model has a strong explanation.

A strong robust observer of distributed drive electric vehicle states based on strong tracking-iterative central difference Kalman filter algorithm

This article proposed a strong robust observer of distributed drive electric vehicle states, including yaw rate, sideslip angle, and longitudinal velocity. Based on strong tracking filter algorithm framework, the proposed observer realized a strong tracking-iterative central difference Kalman filter by introducing a time-varying fade factor into iterative central difference Kalman filter. The introducing of time-varying fade factor assigns approximate orthogonality to residual error, which improves robustness of the observer at mutation conditions. Calculation efficiency and accuracy are improved by applying central difference transformation to approach posterior mean and posterior co-variance. By correcting variance and co-variance with combination of states updating and Gauss–Newton iteration, the observer also achieves high estimation accuracy and convergence rate. Finally, the observer was simulated in vehicle dynamics simulator veDYNA at slalom test and double lane change test with high and low road friction coefficients, respectively. Simulation results have verified that the observer has higher estimation accuracy as well as robustness comparing to extended Kalman filter.

The NLS-based nonlinear grey Bernoulli model with an application to employee demand prediction of high-tech enterprises in China

PurposeThe purpose of this paper is to propose a new method based on nonlinear least squares (NLS) for solving the parameters of nonlinear grey Bernoulli model (NGBM(1,1)) and to verify the proposed model using the case of employee demand prediction of high-tech enterprises in China.Design/methodology/approachFirst of all, minimising the square sum of fitting error of grey differential equation of NGBM(1,1) is taken as the optimisation target and the parameters of classic grey model (GM(1,1)) are set as the initial value of parameter vector. Afterwards, the structural parameters and power exponents are solved by using the Gauss-Newton iteration algorithm so as to calculate the parameters of NGBM(1,1) under given rules for ceasing the algorithm. Finally, by taking the employee demand of high-tech enterprises in the state-level high-tech industrial development zone in China as examples, the validity of the new method is verified.FindingsThe results show that the parameter estimation algorithm based on the NLS method can effectively identify the power exponents of NGBM(1,1) and therefore can favourably adapt to the nonlinear fluctuations of sequences. In addition, the algorithm is superior to the GM(1,1) model, grey Verhulst model, and Quadratic-Exponential smoothing algorithm in terms of the simulation and prediction accuracy.Research limitations/implicationsUnder the framework of solving parameters based on NLS, various aspects of NGBM(1,1) remain to be further investigated including background value, initial condition and variable structural modelling methods.Practical implicationsThe parameter estimation algorithm based on NLS can effectively identify the power exponent of NGBM(1,1) and therefore it can favourably adapt to the nonlinear fluctuation of sequences.Originality/valueAccording to the basic principle of NLS, a new method for solving the parameters of NGBM(1,1) is proposed by using the Gauss-Newton iteration algorithm. Moreover, by conducting the modelling case about employees demand in high-tech enterprises in China, the effectiveness and superiority of the new method are verified.

Position Determination for Moving Transmitter Using Single Station

A common case in location problem is that the terminal is unstable or moving. The classical methods construct equations related to the measurements observed at the individual receivers first, and then solves the problem to localize the source. In this paper, we focus on the moving transmitter localization problem using only one station. The thinking of inverse synthesis aperture is implied, which takes advantage of the motion model to increase the equivalent aperture for higher accuracy. The proposed method formulates the problem through the angle of arrival and Doppler frequency measurements that are obtained from independent observations. After pseudo linearization by ignoring higher order noise terms, the estimator of position and velocity is easily solved through weighted least squares method. The bias reduction (BR) is utilized for lower bias and better root-mean-square error (RMSE). Using the result of BR as an initial solution, the maximum likelihood estimator (MLE) is realized through Gauss–Newton iteration. Theoretical analysis verifies that the BR estimator is efficient, which has Cramer-Rao Lower Bound (CRLB) accuracy if the noise level is mild. While MLE attends CRLB in higher noise situation albeit the possible divergence problem. Simulations indicate the feasibility and validate the advocated performance. The RMSE and bias match the theory very well.

The use of the nonlinear models in the growth of pears of ‘Shinseiki’ cultivar

ABSTRACT: The goal of this study was to elucidate the growth and development of the Asian pear fruit, on the grounds of length, diameter and fresh weight determined over time, using the non-linear Gompertz and Logistic models. The specifications of the models were assessed utilizing the R statistical software, via the least squares method and iterative Gauss-Newton process (DRAPER & SMITH, 2014). The residual standard deviation, adjusted coefficient of determination and the Akaike information criterion were used to compare the models. The residual correlations, observed in the data for length and diameter, were modeled using the second-order regression process to render the residuals independent. The logistic model was highly suitable in demonstrating the data, revealing the Asian pear fruit growth to be sigmoid in shape, showing remarkable development for three variables. It showed an average of up to 125 days for length and diameter and 140 days for fresh fruit weight, with values of 72mm length, 80mm diameter and 224g heavy fat.

Numerical methods for polyline-to-point-cloud registration with applications to patient-specific stent reconstruction.

We present novel numerical methods for polyline-to-point-cloud registration and their application to patient-specific modeling of deployed coronary artery stents from image data. Patient-specific coronary stent reconstruction is an important challenge in computational hemodynamics and relevant to the design and improvement of the prostheses. It is an invaluable tool in large-scale clinical trials that computationally investigate the effect of new generations of stents on hemodynamics and eventually tissue remodeling. Given a point cloud of strut positions, which can be extracted from images, our stent reconstruction method aims at finding a geometrical transformation that aligns a model of the undeployed stent to the point cloud. Mathematically, we describe the undeployed stent as a polyline, which is a piecewise linear object defined by its vertices and edges. We formulate the nonlinear registration as an optimization problem whose objective function consists of a similarity measure, quantifying the distance between the polyline and the point cloud, and a regularization functional, penalizing undesired transformations. Using projections of points onto the polyline structure, we derive novel distance measures. Our formulation supports most commonly used transformation models including very flexible nonlinear deformations. We also propose 2 regularization approaches ensuring the smoothness of the estimated nonlinear transformation. We demonstrate the potential of our methods using an academic 2D example and a real-life 3D bioabsorbable stent reconstruction problem. Our results show that the registration problem can be solved to sufficient accuracy within seconds using only a few number of Gauss-Newton iterations.

Phaseless Recovery Using the Gauss–Newton Method

In this paper, we develop a concrete algorithm for phase retrieval, which we refer to as Gauss-Newton algorithm. In short, this algorithm starts with a good initial estimation, which is obtained by a modified spectral method, and then update the iteration point by a Gauss-Newton iteration step. We prove that a re-sampled version of this algorithm quadratically converges to the solution for the real case with the number of random measurements being nearly minimal. Numerical experiments also show that Gauss-Newton method has better performance over the other algorithms.

Digital Predistortion of Wideband Power Amplifier With Single Undersampling ADC

A novel direct-learning digital predistortion (DPD) of power amplifier (PA) is proposed to alleviate the requirement of an analog-to-digital converter (ADC) in the feedback path. Different from existing undersampling methods, the proposed approach requires only a single ADC running at low sampling rate, which saves one-half hardware cost and avoids the I/Q imbalance problem of the conventional zero-IF feedback structure. First, a modified Gauss-Newton iteration using a low-rate single-branch feedback signal is derived, which justifies the use of single undersampling ADC. Second, a low-complexity time and phase synchronization algorithm based on pattern cross correlation is presented, to align the input and output samples. Experimental results on a 10-W class-AB wideband PA and 100-MHz LTE-A test signal show that the proposed approach can effectively linearize the PA and outperforms other undersampling DPD approaches using the conventional zero-IF feedback structure, in terms of adjacent channel leakage ratio.

Jointly reconstructing ground motion and resistivity for ERT-based slope stability monitoring

Author(s): Boyle, A; Wilkinson, PB; Chambers, JE; Meldrum, PI; Uhlemann, S; Adler, A | Abstract: Electrical resistivity tomography (ERT) is increasingly being used to investigate unstable slopes and monitor the hydrogeological processes within. But movement of electrodes or incorrect placement of electrodes with respect to an assumed model can introduce significant resistivity artefacts into the reconstruction. In this work, we demonstrate a joint resistivity and electrode movement reconstruction algorithm within an iterative Gauss-Newton framework. We apply this to ERT monitoring data from an active slow-moving landslide in the UK. Results show fewer resistivity artefacts and suggest that electrode movement and resistivity can be reconstructed at the same time under certain conditions. A new 2.5-D formulation for the electrode position Jacobian is developed and is shown to give accurate numerical solutions when compared to the adjoint method on 3-D models. On large finite element meshes, the calculation time of the newly developed approach was also proven to be orders of magnitude faster than the 3-D adjoint method and addressed modelling errors in the 2-D perturbation and adjoint electrode position Jacobian.

Probabilistic estimation of reservoir properties by means of wide-angle AVA inversion and a petrophysical reformulation of the Zoeppritz equations

We apply a target-oriented amplitude versus angle (AVA) inversion to estimate the petrophysical properties of a gas-saturated reservoir in offshore Nile Delta. A linear empirical rock-physics model derived from well log data provides the link between the petrophysical properties (porosity, shaliness and saturation) and the P-wave, S-wave velocities and density. This rock-physics model, properly calibrated for the investigated reservoir, is used to re-parameterize the exact Zoeppritz equations. The so derived equations are the forward model engine of a linearized Bayesian AVA-petrophysical inversion that, for each data gather, inverts the AVA of the target reflections to estimate the petrophysical properties of the reservoir layer, keeping fixed the cap-rock properties. We make use of the iterative Gauss-Newton method to solve the inversion problem. For each petrophysical property of interest, we discuss the benefits introduced by wide-angle reflections in constraining the inversion and we compare the posterior probability distributions (PPDs) analytically obtained via a local linearization of the inversion with the PPDs numerically computed with a Markov Chain Monte Carlo (MCMC) method. It results that the porosity is the best resolved parameter and that wide-angle reflections effectively constrain the shaliness estimates but do not guarantee reliable saturation estimates. It also results that the local linearization returns accurate PPDs in good agreement with the MCMC estimates.

GNSS attitude determination method through vectorisation approach

Determining the attitude using GNSS carrier signals is studied. It features an analytical approach to get an estimate as initial guess for iterative algorithms, in three steps. First, baseline vectors are estimated by least-squares method. Second, the constraint of the direction cosine matrix (DCM) is ignored and the least-squares estimates of its 9 elements are solved. Third, a mathematically feasible DCM estimate is extracted from the above estimated free matrix. An error attitude, formulated using the Gibbs vector, is introduced to relate the previously estimated and the true attitude, and the measurement model becomes a nonlinear function of the Gibbs vector. The Gauss-Newton iteration is employed to solve the least-squares problem with this measurement model. The estimate of the roll-pitch-yaw angles and the variance covariance matrix of their estimation errors are extracted from the final solution. Numerical experiments are conducted. With 3 orthogonally mounted 3-meter baselines, 4 visible satellites, and 5-millimeter standard-deviation of the carrier measurements, the accuracy of the analytical solution can be less than 1° in the root mean squared error (RMSE) sense. The convergence of the iteration is rather fast, the RMSE converges after only one iteration, with the converged RMSE less than 0.1°.

Algorithms for estimating the motion of a spacecraft from its state data

Control of processing processes on the state of the spacecraft (SC) is represented by schemes of the invariant control loop of a complex dynamic object. Based on the analysis of the algorithms for estimating the parameters of the translational motion of an aircraft (LA), based on the results of external trajectory measurements, an iterative Gauss-Newton procedure is formulated that implements the approach of directly finding the extremal point of the response surface described by a multidimensional function. Applied to the problem of estimating the initial conditions of motion of an aircraft. The features of the implementation of the algorithm for estimating the initial conditions of the orbital motion of the apparatus based on the method of least squares are investigated.

The Levenberg-Marquardt method to fit parameters in the Monod kinetic model

Mathematical models can describe biochemical processes. Accurately measured data are fundamental for the estimation of the model parameters. This research uses the Monod model describing the bacterial kinetic degradation. The Levenberg-Marquardt method was applied successfully in order to fit the parameters of the model expressing the substrate concentration as a function of time. Hereby the method of steepest ascent and the iterative Gauss-Newton method with its quadratic convergence rate were used to find optimized parameter values of the Monod kinetic model. These results are compared with the results of other minimization methods. Orthogonal error measurement is introduced as uncertainty is present for all variables. This corrected type of error measurement is used to validate the parameter estimations.

The path planning of space manipulator based on Gauss–Newton iteration method

A path planning algorithm based on Gauss–Newton iteration method is proposed for the motion path of space manipulators. The algorithm of space manipulator path planning consists of two optimization aspects, the optimal joint motion target and the trajectory of joint motion, which make the grippers at the end of the space manipulators reach the expected target. First, the inverse solution of the desired state and the joint optimum state of the grippers is supposed to be the minimum value problem, and the Gauss–Newton iterative algorithm is designed to solve the problem. Then, according to the optimal joint target, the sinusoidal trajectory is designed. The path planning solution is transformed into the optimal parameter solution. Based on the optimal sinusoidal trajectory parameters, the path planning of the space manipulator is achieved. Simulation results indicate the correctness and effectiveness of the promoted method.

A modified iterative ensemble Kalman filter data assimilation method

High nonlinearity is a typical characteristic associated with data assimilation systems. Additionally, iterative ensemble based methods have attracted a large amount of research attention, which has been focused on dealing with nonlinearity problems. To solve the local convergence problem of the iterative ensemble Kalman filter, a modified iterative ensemble Kalman filter algorithm was put forward, which was based on a global convergence strategy from the perspective of a Gauss-Newton iteration. Through self-adaption, the step factor was adjusted to enable every iteration to approach expected values during the process of the data assimilation. A sensitivity experiment was carried out in a low dimensional Lorenz-63 chaotic system, as well as a Lorenz-96 model. The new method was tested via ensemble size, observation variance, and inflation factor changes, along with other aspects. Meanwhile, comparative research was conducted with both a traditional ensemble Kalman filter and an iterative ensemble Kalman filter. The results showed that the modified iterative ensemble Kalman filter algorithm was a data assimilation method that was able to effectively estimate a strongly nonlinear system state.

A Gauss–Newton iteration for Total Least Squares problems

The Total Least Squares solution of an overdetermined, approximate linear equation $Ax \approx b$ minimizes a nonlinear function which characterizes the backward error. We show that a globally convergent variant of the Gauss--Newton iteration can be tailored to compute that solution. At each iteration, the proposed method requires the solution of an ordinary least squares problem where the matrix $A$ is perturbed by a rank-one term.

A numerical study concerning brain stroke detection by microwave imaging systems

In this paper, a numerical study devoted to evaluate the application of a microwave imaging method for brain stroke detection is described. First of all, suitable operating conditions for the imaging system are defined by solving the forward electromagnetic scattering problem with respect to simplified configurations and analyzing the interactions between an illuminating electromagnetic wave at microwave frequencies and the biological tissues inside the head. Then, preliminary inversion results are obtained by applying an imaging procedure based on an iterative Gauss-Newton scheme to a realistic model of the human head. The proposed imaging algorithm is able to deal with the nonlinear and ill-posed problem associated to the integral equations describing the inverse scattering problem. The aim of the inversion procedure is related to the determination of the presence of a hemorrhagic brain stroke by retrieving the distributions of the dielectric parameters of the human tissues inside a slice of the head model.