Nonlinear Least-squares Approach Research Articles

Determination of the X-Auger electron spectroscopy evolution of indium in InSb by linear and nonlinear least squares approaches

X-ray photoelectron spectroscopy is a major and valuable chemical analysis technique that can bring a wide range of information if one takes time to carefully interpret the spectra. In particular, many metrological developments deal with the modeling of photoelectron peaks while X-Auger transitions still remain hardly exploited. Here, an innovative approach examining these spectral features in a complementary way is presented and illustrated on a concrete case dealing with chemical changes of indium in the InSb semiconductor during its air aging. Indium contains an extensive range of photopeaks along the energy scale, meaning electrons emitted from different escape depths are present on the same widescan spectrum, and, thus, information from different depths is accessible. Specifically, this study focuses on indium’s X-Auger electron spectroscopy (X-AES) transitions and decomposition to track the outer surface chemistry evolution of the InSb semiconductor. To this end, we compared linear and nonlinear least-squares approaches to decompose In M4,5N4,5N4,5 X-AES transition and demonstrate oxide growth progression. For both approaches, we applied the vectorial method (also known as the informed amorphous sample model) to retrieve the different chemical environments present during air aging. Linear and nonlinear least-squares approaches were both found to yield comparable results, with a comparative error of less than 10%. Over time, a progressive growth of the oxide layer was demonstrated, ranging from 0.3 ± 0.2 to 2.9 ± 0.2 nm using the X-AES transitions. Additionally, decomposition of the In 3d and In 4d photoelectron peaks showed a lower thickness of oxide with time due to the lesser surface sensitivity of these peaks.

A New RF Sensing Framework for Human Detection Through the Wall

A recent trend for human activity recognition, fall detection, health-care applications, etc., which is using the non-contact radio-frequency (RF) signals, is known as the RF sensing. State-of-the-art radar and Wi-Fi based human sensing systems utilize high bandwidth and require high computational burden. In this paper, a machine learning (ML) framework is proposed for device-free through-the-wall (TTW) human detection using narrow-band continuous RF signals that are transmitted and captured by low-cost software-defined radio (SDR) modules. To be more realistic the double TTW scenario, where both transmitter and receiver are placed outside the walls of the monitored area, is considered. Three different classes are defined as empty (human-free), moving human, and additionally the static human (only breathing, not moving) which addresses the unconscious or sleeping person. In this framework, the variance of the respiratory rate (RR) estimates of the subject and overall signal variances are used as distinguishing features. RR estimates are obtained using nonlinear least-squares (NLS) approach. It is shown in the experiments conducted with real measurements from different environments that the proposed ML framework achieves over 99% classification accuracy using a Decision Tree (DT) classifier. In addition, it is also shown that the proposed framework achieves over 95% accuracy in a completely different environment where the model is not trained. This indicates that the proposed ML framework can be applied generally without requiring specific re-training for different environments and conditions.

Deep learning-based Accelerated and Noise-Suppressed Estimation (DANSE) of quantitative Gradient-Recalled Echo (qGRE) magnetic resonance imaging metrics associated with human brain neuronal structure and hemodynamic properties.

The purpose of the current study was to introduce a Deep learning-based Accelerated and Noise-Suppressed Estimation (DANSE) method for reconstructing quantitative maps of biological tissue cellular-specific, R2t*, and hemodynamic-specific, R2', metrics of quantitative gradient-recalled echo (qGRE) MRI. The DANSE method adapts a supervised learning paradigm to train a convolutional neural network for robust estimation of R2t* and R2' maps with significantly reduced sensitivity to noise and the adverse effects of macroscopic (B0 ) magnetic field inhomogeneities directly from the gradient-recalled echo (GRE) magnitude images. The R2t* and R2' maps for training were generated by means of a voxel-by-voxel fitting of a previously developed biophysical quantitative qGRE model accounting for tissue, hemodynamic, and B0 -inhomogeneities contributions to multigradient-echo GRE signal using a nonlinear least squares (NLLS) algorithm. We show that the DANSE model efficiently estimates the aforementioned qGRE maps and preserves all the features of the NLLS approach with significant improvements including noise suppression and computation speed (from many hours to seconds). The noise-suppression feature of DANSE is especially prominent for data with low signal-to-noise ratio (SNR ~ 50-100), where DANSE-generated R2t* and R2' maps had up to three times smaller errors than that of the NLLS method. The DANSE method enables fast reconstruction of qGRE maps with significantly reduced sensitivity to noise and magnetic field inhomogeneities. The DANSE method does not require any information about field inhomogeneities during application. It exploits spatial and gradient echo time-dependent patterns in the GRE data and previously gained knowledge from the biophysical model, thus producing high quality qGRE maps, even in environments with high noise levels. These features along with fast computational speed can lead to broad qGRE clinical and research applications.

Nonlinear least-squares estimation of shear elasticity and shear viscosity in viscoelastic media

Rapid simulations of three-dimensional (3D) shear wave propagation in viscoelastic media with a Kelvin-Voigt model are enabled by Green’s functions accelerated with graphics processing unit parallelization and high-performance computing resources. Cross-correlation analysis of the wave motion yields an estimate of shear elasticity, where the errors in the estimated values increase with rising shear viscosity. To reduce errors in the shear elasticity estimates, a nonlinear least-squares routine that accounts for the effects of propagation, attenuation, and dispersion is applied to 3D simulated shear wave data in viscoelastic media. The nonlinear least-squares approach also yields an estimate of the shear viscosity when applied to simulated particle velocity waveforms. Post-processing, cross-correlation analysis, and the nonlinear least-squares routine are evaluated on a desktop computer using MATLAB. Estimation of viscoelastic parameters is performed at the focal depth for several combinations of shear elasticity and shear viscosity. The errors in the estimated shear elasticities obtained from the nonlinear least-squares routine and cross-correlation are determined as a function of the input shear elasticity and shear viscosity values. The estimates provided by the nonlinear least-squares routine for shear elasticity and shear viscosity are shown to approach the simulation input values for each combination of viscoelastic parameters.

A general framework for spatial GARCH models

In time-series analysis, particularly in finance, generalized autoregressive conditional heteroscedasticity (GARCH) models are widely applied statistical tools for modelling volatility clusters (i.e., periods of increased or decreased risk). In contrast, it has not been considered to be of critical importance until now to model spatial dependence in the conditional second moments. Only a few models have been proposed for modelling local clusters of increased risks. In this paper, we introduce a novel spatial GARCH process in a unified spatial and spatiotemporal GARCH framework, which also covers all previously proposed spatial ARCH models, exponential spatial GARCH, and time-series GARCH models. In contrast to previous spatiotemporal and time series models, this spatial GARCH allows for instantaneous spill-overs across all spatial units. For this common modelling framework, estimators are derived based on a non-linear least-squares approach. Eventually, the use of the model is demonstrated by a Monte Carlo simulation study and by an empirical example that focuses on real estate prices from 1995 to 2014 across the postal code areas of Berlin. A spatial autoregressive model is applied to the data to illustrate how locally varying model uncertainties (e.g., due to latent regressors) can be captured by the spatial GARCH-type models.

Angular Velocity Estimation and Error-Covariance Analysis from Accelerometers Using Least Squares

In this work angular velocity solutions are presented from accelerometers. Two main formulations are presented. The first is based on using multiple vector sets of accelerometers, and the second is based on using multiple single-axis accelerometers. Linear least-squares approaches are derived for both, along with error-covariance expressions for the angular velocity estimates. Nonlinear least-squares approaches are also derived for both, which also provide the Cramér–Rao lower bound as a byproduct. All approaches have a sign ambiguity in the angular velocity solutions, which is resolved using a simple linear Kalman filter. Simulation results are shown to compare the formulations, along with the linear and nonlinear least-squares solutions.

Potential field data interpretation to detect the parameters of buried geometries by applying a nonlinear least-squares approach

Potential field data interpretation to detect the parameters of buried geometries by applying a nonlinear least-squares approach

Modeling of measles epidemic with optimized fractional order under Caputo differential operator

Abstract Memory is an important characteristic of an epidemic. One of such memory dependent and highly contagious viral diseases is measles that is also responsible for more than 140,000 deaths in 2018 in various regions of Asia and Africa. In order to better understand the transmission dynamics of measles, we have developed a new epidemiological model while considering both integer and fractional order operators and presented comparison. The Caputo fractional model has a unique solution with the positively invariant region. On the basis of basic reproduction number R 0 , stability analysis is discussed and sensitivity of parameters is investigated using PRCC global technique. Not only parameters but fractional order χ is also optimized via nonlinear least-squares approach with availability of statistical data obtained from WHO. Various simulations in terms of time series plots, 3D meshes and contours are carried out to observe effects of parameters on dynamics of the epidemic wherein it is said to be persistent for χ → 0 demonstrating the role being played by Caputo fractional derivative towards measles dynamics.

Free-water DTI estimates from single b-value data might seem plausible but must be interpreted with care.

Free-water elimination DTI (FWE-DTI) has been used widely to distinguish increases of free-water partial-volume effects from tissue's diffusion in healthy aging and degenerative diseases. Because the FWE-DTI fitting is only well-posed for multishell acquisitions, a regularized gradient descent (RGD) method was proposed to enable application to single-shell data, more common in the clinic. However, the validity of the RGD method has been poorly assessed. This study aims to quantify the specificity of FWE-DTI procedures on single-shell and multishell data. Different FWE-DTI fitting procedures were tested on an open-source in vivo diffusion data set and single-shell and multishell synthetic signals, including the RGD and standard nonlinear least-squares methods. Single-voxel simulations were carried out to compare initialization approaches. A multivoxel phantom simulation was performed to evaluate the effect of spatial regularization when comparing between methods. To test the algorithms' specificity, phantoms with two different types of lesions were simulated: with altered mean diffusivity or with modified free water. Plausible parameter maps were obtained with RGD from single-shell in vivo data. The plausibility of these maps was shown to be determined by the initialization. Tests with simulated lesions inserted into the in vivo data revealed that the RGD approach cannot distinguish free water from tissue mean-diffusivity alterations, contrarily to the nonlinear least-squares algorithm. The RGD FWE-DTI method has limited specificity; thus, its results from single-shell data should be carefully interpreted. When possible, multishell acquisitions and the nonlinear least-squares approach should be preferred instead.

Fast stable parameter estimation for linear dynamical systems

Dynamical systems describe changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for the drivers and impediments of the processes. Extracting these governing equations from data is a central challenge in many diverse areas of science and engineering. A methodology for estimating the solution; and the parameters of linear dynamical systems from incomplete and noisy observations of the processes is introduced. Building on the parameter cascading approach, where a linear combination of basis functions approximates the implicitly defined solution of the dynamical system. The systems’ parameters are estimated so that this approximating solution adheres to the data. By taking advantage of the linearity of the system, the parameter cascading estimation procedure is simplified, and by developing a new iterative scheme, fast and stable computation is achieved. An illustrative example obtains a linear differential equation that represents real data from biomechanics. A comparison of the proposed approach with popular methods for estimating the parameters of linear dynamical systems, namely, the non-linear least-squares approach, simulated annealing, parameter cascading and smooth functional tempering reveals a considerable reduction in computation and an improved bias and sampling variance.

Spectral Calibration Algorithm for the Geostationary Environment Monitoring Spectrometer (GEMS)

The Geostationary Environment Monitoring Spectrometer (GEMS) onboard the Geostationary Korean Multi-Purpose Satellite 2B was successfully launched in February 2020. GEMS is a hyperspectral spectrometer measuring solar irradiance and Earth radiance in the wavelength range of 300 to 500 nm. This paper introduces the spectral calibration algorithm for GEMS, which uses a nonlinear least-squares approach. Sensitivity tests for a series of unknown algorithm parameters such as spectral range for fitting, spectral response function (SRF), and reference spectrum were conducted using the synthetic GEMS spectrum prepared with the ground-measured GEMS SRF. The test results show that the required accuracy of 0.002 nm is achievable provided the SRF and the high-resolution reference spectrum are properly prepared. Such a satisfactory performance is possible mainly due to the inclusion of additional fitting parameters of spectral scales (shift, squeeze, and high order shifts) and SRF (width, shape and asymmetry). For the application to the actual GEMS data, in-orbit SRF is to be monitored using an analytic SRF function and the measured GEMS solar irradiance, while a reference spectrum is going to be selected during the instrument in-orbit test. The calibrated GEMS data is expected to be released by the end of 2020.

Simultaneous identification of timewise terms and free boundaries for the heat equation

PurposeThe purpose of this paper is to provide an insight and to solve numerically the identification of timewise terms and free boundaries coefficient appearing in the heat equation from over-determination conditions.Design/methodology/approachThe formulated coefficient identification problem is inverse and ill-posed, and therefore, to obtain a stable solution, a nonlinear Tikhonov regularization least-squares approach is used. For the numerical discretization, the finite difference method combined with a regularized nonlinear minimization is performed using the MATLAB subroutine lsqnonlin.FindingsThe numerical results presented for two examples show the efficiency of the computational method and the accuracy and stability of the numerical solution even in the presence of noise in the input data.Research limitations/implicationsThe mathematical formulation is restricted to identify coefficients in unknown components dependent on time, and this may be considered as a research limitation. However, there is no research implication to overcome this, as the known input data is also limited to single temperature in heat equation with Stefan conditions, and the first- and second-order heat moments measurements at a particular time location.Practical implicationsAs noisy data are inverted, the study models real situations in which practical measurements are inherently contaminated with noise.Social implicationsThe identification of the timewise terms and free boundaries will be of great interest in the heat transfer community and related fluid flow applications.Originality/valueThe current investigation advances previous studies, which assumed that the coefficient multiplying the lower order temperature term depends on time. The knowledge of this physical property coefficient is very important in heat transfer and fluid flow. The originality lies in the insight gained by performing for the numerical simulations of inversion to find the timewise terms and free boundaries coefficient dependent on time in the heat equation from noisy measurements.

Semiautomated Parallel RAFT Copolymerization of Isoprene with Glycidyl Methacrylate.

Copolymerization of isoprene (IP) with glycidyl methacrylate (GMA) was performed under RAFT (reversible addition-fragmentation chain-transfer) polymerization conditions in a platform for high-output experimentation. Covering the range between 1 and 0.2 molar fraction of IP in the feed, four sets of reactions were carried out at 10, 15, 20, and 30 h at 115 °C. The kinetic data obtained were used to estimate the reactivity ratios using a nonlinear least-squares approach (NLLS). Reactivity ratios rGMA = 0.61 and rIP = 0.74 indicate that both monomers tend to crosspropagate in agreement with known literature values. Concerning the RAFT study, relatively good control and livingness of the copolymerization was observed except for the experiment in which IP represents 20 mol % in the feed. 1H NMR characterization confirmed the presence of both monomers in the final copolymer, particularly the presence of the epoxy ring of GMA which is susceptible to post polymerization reactions. Finally, preliminary results on the hydrogenation of various polymers are discussed.

Bayesian pharmacokinetic modeling of dynamic contrast-enhanced magnetic resonance imaging: validation and application

Tracer-kinetic analysis of dynamic contrast-enhanced magnetic resonance imaging data is commonly performed with the well-known Tofts model and nonlinear least squares (NLLS) regression. This approach yields point estimates of model parameters, uncertainty of these estimates can be assessed e.g. by an additional bootstrapping analysis. Here, we present a Bayesian probabilistic modeling approach for tracer-kinetic analysis with a Tofts model, which yields posterior probability distributions of perfusion parameters and therefore promises a robust and information-enriched alternative based on a framework of probability distributions. In this manuscript, we use the quantitative imaging biomarkers alliance (QIBA) Tofts phantom to evaluate the Bayesian tofts model (BTM) against a bootstrapped NLLS approach. Furthermore, we demonstrate how Bayesian posterior probability distributions can be employed to assess treatment response in a breast cancer DCE-MRI dataset using Cohen’s d. Accuracy and precision of the BTM posterior distributions were validated and found to be in good agreement with the NLLS approaches, and assessment of therapy response with respect to uncertainty in parameter estimates was found to be excellent. In conclusion, the Bayesian modeling approach provides an elegant means to determine uncertainty via posterior distributions within a single step and provides honest information about changes in parameter estimates.

Nonlinear least square approach for range estimation based on attenuation of EM waves in seawater using world ocean data from 1955 to 2012

SummaryIn this research paper, we estimated absorption loss (Lα) and spreading loss (Lo) based on electromagnetic (EM) waves propagation, considering multiple seawater depth (1101) points from surface to 5500 m distributed uniformly with 5‐m difference. Estimation of parameters aforementioned was done based on world ocean data (WOD13) from the National Center for Environmental Information (NCEI) averaged between 1955 and 2012 along decades for basic parameters of seawater T (Co) and S (ppt) up to 5500‐m depth vertically and also across (41 088) latitude/longitude points for all oceans that includes Indian, Pacific, Southern, Atlantic, and Arctic horizontally. We also computed another important factor that contributes in overall path loss (LUW), loss due to polarization of EM fields between transmitter Tx and receiver Rx such as antenna polarization factor (Lϕ). Lϕ (dB) along with Lα (dB) and Lo (dB) by substituting into basic propagation model for EM waves in seawater helps us to predict efficiently accurate achievable range (Rest) using nonlinear least square (NLLS) approximation combined with Lambert transformation considering nonlinear exponential PT (dBm) decay. Moreover, predicted Rest (m) helps us to minimize mean error (mean(e(t))) by adapting to actual range R (m) using NLLS approach. Simulation tool MATLAB has been used for implementation of NLLS approach and performance analysis.

A novel nonlinear least-squares approach to highly maneuvering target tracking

Abstract Trajectories of aerial and marine vehicles are typically made of a succession of smooth trajectories, linked by abrupt changes, i.e. maneuvers. Notably, modern highly maneuvering targets are capable of very brutal changes in the heading, with accelerations of up to 15 g . As a result, we model the target behavior using piecewise deterministic Markov models, driven by parameters that jump at unknown times. Over the past years, real-time (or incremental) optimization-based smoothing methods have become a popular alternative to nonlinear filters, such as the Extended Kalman Filter (EKF), owing to the successive relinearizations that mitigate the linearization errors that inherently affect the EKF estimates. In the present paper, we propose to combine such methods for tracking the target during non-jumping phases with a probabilistic approach to detect jumps. Our algorithm is shown to compare favorably to the state-of-the-art Interacting Multiple Model (IMM) algorithm, especially in terms of target's velocity estimation, on a set of meaningful and challenging trajectories.

Nonlinear Least-Squares Approach for Large-Scale Algebraic Riccati Equations

We propose a new optimization approach for solving large-scale continuous-time algebraic Riccati equations with a low-rank right-hand side. First, we project the problem onto a Krylov-type low-dime...

Genetic algorithm with Gaussian function for optimal P-wave morphology in electrocardiography for atrial fibrillation patients

Atrial fibrillation (AF), which is a rapid-irregular heartbeat and shows abnormal heart rhythm of the supraventricular tachycardia class, has proved to increase the risks of heart failure, dementia, and stroke. To detection AF, P-wave morphology in electrocardiography (ECG) is suggested to be a strong indicator. To make computerized detection possible, most approaches decompose the ensemble of signals into a finite set of features and establish the relation between symptoms and values of features. Therefore, the disease can be asserted solely by the values of the decomposed features. For early diagnosis of AF, this study develops a hybrid Taguchi-genetic algorithm (HTGA) that facilitates Gaussian decomposition in ECG signals, because P-wave morphology can be well approximated by a family of Gaussian functions. The HTGA optimizes features with minimized performance index of the normalized root mean square error. With accurate decomposition in characterizing parameter values of P-wave morphology, the performance of disease classification improves by using appropriate feature set. Our experiments indicate that the proposed HTGA with Gaussian function obtains a better fit to the actual P-wave compared to the conventional nonlinear least-squares approaches.

Performance improvement of shunt active power filter based on non-linear least-square approach

Nowadays, the shunt active power filters (SAPFs) have become a popular solution for power quality issues. A crucial issue in controlling the SAPFs which is highly correlated with their accuracy, flexibility and dynamic behavior, is generating the reference compensating current (RCC). The synchronous reference frame (SRF) approach is widely used for generating the RCC due to its simplicity and computation efficiency. However, the SRF approach needs precise information of the voltage phase which becomes a challenge under adverse grid conditions. A typical solution to answer this need is the application of advanced phase locked loops (PLLs). The PLLs are closed-loop control systems that often have a response time more than two cycles of the nominal frequency. Besides, a special care should be paid in designing their control parameters to ensure their stable operation in all circumstances. This paper proposes an improved open loop strategy which is unconditionally stable and flexible. The proposed method which is based on non-linear least square (NLS) approach can extract the fundamental voltage and estimates its phase within only half cycle, even in the presence of odd harmonics and dc offset. The performance of the proposed method is verified under MATLAB/Simulink environment and validated experimentally and compared with advanced PLLs.

Vastly accelerated linear least-squares fitting with numerical optimization for dual-input delay-compensated quantitative liver perfusion mapping.

To propose an efficient algorithm to perform dual input compartment modeling for generating perfusion maps in the liver. We implemented whole field-of-view linear least squares (LLS) to fit a delay-compensated dual-input single-compartment model to very high temporal resolution (four frames per second) contrast-enhanced 3D liver data, to calculate kinetic parameter maps. Using simulated data and experimental data in healthy subjects and patients, whole-field LLS was compared with the conventional voxel-wise nonlinear least-squares (NLLS) approach in terms of accuracy, performance, and computation time. Simulations showed good agreement between LLS and NLLS for a range of kinetic parameters. The whole-field LLS method allowed generating liver perfusion maps approximately 160-fold faster than voxel-wise NLLS, while obtaining similar perfusion parameters. Delay-compensated dual-input liver perfusion analysis using whole-field LLS allows generating perfusion maps with a considerable speedup compared with conventional voxel-wise NLLS fitting. Magn Reson Med 79:2415-2421, 2018. © 2017 International Society for Magnetic Resonance in Medicine.