Parameter Estimation Method Research Articles

Assessing Transducer Parameters for Accurate Medium Sound Speed Estimation and Image Reconstruction.

The influence of the transducer lens on image reconstruction is often overlooked. Lenses usually exhibit a lower sound speed than soft biological tissues. In academic research, the exact lens sound speed and thickness are typically unknown. Here, we present a simple and nondestructive method to characterize the lens sound speed and thickness as well as the time to peak of the round-trip ultrasound waveform, another key parameter for optimal image reconstruction. We applied our method to three transducers with center frequencies of 2.5, 7.5, and 15 MHz. We estimated the three parameters with an element-by-element transmission sequence that records internal reflections within the lens. We validated the retrieved parameters using an autofocusing approach that estimates sound speed in water. We show that the combination of our parameters estimation method with two-layer ray tracing outperforms standard image reconstruction. For all transducers, we successfully improved the accuracy of medium sound speed estimation, spatial resolution, and contrast. The proposed method is simple and robust and provides an accurate estimation of the transducer lens parameters and the time to peak of the ultrasound waveform, which leads to improved ultrasound image quality.

New Bounded Probability Model: Properties, Estimation, and Applications

The article introduces a new unit distribution, an extension of Tiessier distribution, characterized by a versatile hazard function capable of adopting diverse shapes such as bathtub or N-shaped curves. An exploration of the fundamental properties of this distribution is undertaken, accompanied by the implementation of the maximum likelihood estimation technique and eleven alternative methods to approximate its parameters effectively. Through a simulation study, the article effectively demonstrates the precision of these parameter estimation methods, even when dealing with small sample sizes. Two datasets are employed to apply the novel distribution, subjecting it to a comprehensive evaluation against established models utilizing a range of model selection criteria and goodness of fit tests. Notably, the article illustrates that the performance of the new distribution surpasses that of existing models in effectively capturing data patterns. Beyond its empirical contributions, the article highlights the potential cross-disciplinary applications of the new distribution in many fields while concurrently advancing the realms of probability theory and statistical inferences.

Inferring Binary Properties from Gravitational-Wave Signals

This review provides a conceptual and technical survey of methods for parameter estimation of gravitational-wave signals in ground-based interferometers such as Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo. We introduce the framework of Bayesian inference and provide an overview of models for the generation and detection of gravitational waves from compact binary mergers, focusing on the essential features that are observable in the signals. Within the traditional likelihood-based paradigm, we describe various approaches for enhancing the efficiency and robustness of parameter inference. This includes techniques for accelerating likelihood evaluations, such as heterodyne/relative binning, reduced-order quadrature, multibanding, and interpolation. We also cover methods to simplify the analysis to improve convergence, via reparameterization, importance sampling, and marginalization. We end with a discussion of recent developments in the application of likelihood-free (simulation-based) inference methods to gravitational-wave data analysis.

Novel two-parameter quadratic exponential distribution: Properties, simulation, and applications

This research paper introduces a novel two-parameter quadratic exponential distribution (NTPQED), thoroughly examining its statistical properties and practical applications. The study delves into essential characteristics of the distribution, including its asymptotic behavior, moments, order statistics, and entropies. Additionally, we present fuzzy reliability, value at risk, mean excess function, limited expected value function, tail value at risk, and tail variance. A comprehensive simulation study evaluates fifteen parameter estimation methods. To illustrate the practical relevance of the proposed distribution, three sets of real-world data are analyzed. The performance of the proposed distribution model is rigorously assessed using various model selection criteria and goodness-of-fit test statistics. Empirical findings consistently demonstrate the proposed distribution's superiority over existing models, highlighting its potential for multiple applications.

Kalman tracking and parameter estimation of continuous gravitational waves with a pulsar timing array

Abstract Continuous nanohertz gravitational waves from individual supermassive black hole binaries may be detectable with pulsar timing arrays. A novel search strategy is developed, wherein intrinsic achromatic spin wandering is tracked simultaneously with the modulation induced by a single gravitational wave source in the pulse times of arrival. A two-step inference procedure is applied within a state-space framework, such that the modulation is tracked with a Kalman filter, which then provides a likelihood for nested sampling. The procedure estimates the static parameters in the problem, such as the sky position of the source, without fitting for ensemble-averaged statistics such as the power spectral density of the timing noise, and therefore complements traditional parameter estimation methods. It also returns the Bayes factor relating a model with a single gravitational wave source to one without, complementing traditional detection methods. It is shown via astrophysically representative software injections in Gaussian measurement noise that the procedure distinguishes a gravitational wave from pure noise down to a characteristic wave strain of h0 ≈ 2 × 10−15. Full posterior distributions of model parameters are recovered and tested for accuracy. There is a bias of ≈0.3 rad in the marginalised one-dimensional posterior for the orbital inclination ι, introduced by dropping the so-called ‘pulsar terms’. Smaller biases $\lesssim 10~{{\%}}$ are also observed in other static parameters.

Escalation of Human Resource Quality in National Health Resilience Through Estimating Multilevel Model Parameters with the Restricted Maximum Likelihood Approach to The 2019 UTBK Average

Multilevel modeling or Hierarchical Linear Modeling (HLM) is a statistical approach specifically used to analyze data with a two-level structure. This approach allows an understanding of the contribution of factors at both the individual and group levels to the response variable. One method commonly used in HLM is Restricted Maximum Likelihood (REML). REML is a parameter estimation method that is often applied in statistical models, especially linear models that incorporate random components. This allows more efficient parameter assessment compared to conventional estimation methods. In this research, multilevel model parameter estimation analysis was carried out using the limited maximum likelihood approach. The aim is to determine the multilevel linear regression model on the average UTBK score for health cluster study programs in 2019. This involves selecting the optimal node point based on the minimum Generalized Cross Validation (GCV) and identifying the factors that influence it. Predictor variables considered include interest and capacity of study programs at university level (Level-1), as well as the average UNBK and HDI scores at provincial level (Level-2). The findings of this research indicate that the most appropriate multilevel regression model is formed with three nodes with a minimum GCV value at Level-1 of 864.6593 and at Level-2 of 3.1816. At Level-1, the influencing factor is the interest variable and at Level-2 is the average provincial UNBK score in 2019 and the Human Development Index (HDI).

CT perfusion parameter estimation in stroke using neural network with transformer and physical model priors

ObjectivesCT perfusion (CTP) imaging is vital in treating acute ischemic stroke by identifying salvageable tissue and the infarcted core. CTP images allow quantitative estimation of CT perfusion parameters, which can provide information on the degree of tissue hypoperfusion and its salvage potential. Traditional methods for estimating perfusion parameters, such as singular value decomposition (SVD) and its variations, are known to be sensitive to noise and inaccuracies in the arterial input function. To our knowledge, there has been no implementation of deep learning methods for CT perfusion parameter estimation. Materials & methodsIn this work, we propose a deep learning method based on the Transformer model, named CTPerformer-Net, for CT perfusion parameter estimation. In addition, our method incorporates some physical priors. We integrate physical consistency prior, smoothness prior and the physical model prior through the design of the loss function. We also generate a simulation dataset based on physical model prior for training the network model. ResultsIn the simulation dataset, CTPerformer-Net exhibits a 23.4 % increase in correlation coefficients, a 95.2 % decrease in system error, and a 90.7 % reduction in random error when contrasted with block-circulant SVD. CTPerformer-Net successfully identifies hypoperfused and infarcted lesions in 103 real CTP images from the ISLES 2018 challenge dataset. It achieves a mean dice score of 0.36 for the infarct core segmentation, which is slightly higher than the commercially available software (dice coefficient: 0.34) used as a reference level by the challenge. ConclusionExperimental results on the simulation dataset demonstrate that CTPerformer-Net achieves better performance compared to block-circulant SVD. The real-world patient dataset confirms the validity of CTPerformer-Net.

Imperfect Measurement Devices Impact the Security of Tomography‐Based Source‐Independent Quantum Random Number Generator

AbstractSource‐independent quantum random number generators (SI‐QRNGs) can generate secure random numbers with untrusted and uncharacterized sources. Recently, a tomography‐based SI‐QRNG protocol has garnered significant attention for its higher randomness generation rate[Phys. Rev. A 99, 022328 (2019)], achieved through measurements utilizing three mutually unbiased bases. However, imperfect and inadequately characterized measurement devices would impact the security and performance of this protocol. In this work, considering the imperfect basis modulation, afterpulse effect and detection efficiency mismatch, it is demonstrated that the imperfect measurement devices would reduce the extractable randomness and lead to the incorrect estimation of the conditional min‐entropy. Additionally, the influences of the finite‐size effect and the performances of the protocol based on different parameter estimation methods are investigated and compared. To guarantee the security of generated random numbers, accurate conditional min‐entropy estimation methods that are compatible with imperfect factors are also developed. The work emphasizes the significance of considering the imperfections in measurement devices and establishing tighter bounds for parameter estimation, especially in high‐speed systems, thereby enhancing the robustness and performance of the protocol.

Hybrid Fuzzy Method for Performance Evaluation of City Construction

Evaluating the performance of city construction not only helps optimize city functions and improve city quality, but it also contributes to the development of sustainable cities. However, most of the scoring rules for evaluating the performance of city construction are overly cumbersome and demand very high data integrity. Moreover, the properties, change scale, and scope of different evaluation indicators of city construction often lead to uncertain and ambiguous results. In this study, a hybrid fuzzy method is proposed to conduct the performance evaluation of city construction in two phases. Firstly, a city performance index (CPI) was developed by combining the means and standard deviations of indicators of city construction to address the volatility of historical statistical data as well as different types of data. Considering the sampling errors in data analysis, the parameter estimation method was used to derive the 100% × (1 − α) confidence interval of the CPI. Buckley’s fuzzy approach was then adopted to extend the statistical estimators from the CPI into fuzzy estimators, after which a fuzzy CPI was proposed. To identify the specific improvement directions for city construction, the fuzzy axiom design (fuzzy AD) method was applied to explore the relationship between the targets set by city managers and actual performance. Finally, an example of six cities in China is provided to illustrate the effectiveness and practicality of the proposed method. The results show that the performance of Chongqing on several evaluation indicators is lower than that of other cities. The proposed method takes into account the issues of uniformity and diversity in the performance evaluation of city construction. It can enable a quantitative assessment of the city construction level in all cities and provide theoretical support and a decision-making basis for relevant government departments to optimize city construction planning and scientifically formulate city construction policies.

Markov Genealogy Processes

The COVID-19 pandemic has underscored the need for efficient and mathematically rigorous methods to analyze epidemiological time series and genetic data. This project introduces and evaluates various methods for estimating infectious disease parameters. We employed a dynamic Markov chain model incorporating random variables tracking infected and susceptible individuals, as well as their coalescent times. Our objective was to assess the accuracy of different techniques in predicting disease characteristics based on this model. Simulation studies of various existing parameter estimation methods revealed that prediction accuracy falls drastically when a recovery rate is introduced. In response to the limitations of existing methods, we initiated the development of a novel model which would incorporate lineages, allowing us to use phylogenetic trees to estimate parameters. This would lead to an improvement in parameter estimates, especially with a recovery rate, as phylogenetic trees contain more information than the types of data used in existing parameter estimation methods.

Parameter estimation methods for correlated observation mixed additive and multiplicative random error model

In the domain of geodetic adjustment, current methodologies addressing additive and multiplicative error models operate under the assumption of independence between additive and multiplicative random errors. However, limited research has been conducted on elucidating the correlation between the components of additive and multiplicative random errors. To extend a methodology of mixed error models with additive and multiplicative correlation observations, this paper derives three parameter adjustment methods: correlation observation least squares, correlation observation weighted least squares, and correlation observation bias-corrected weighted least squares, all based on the principles of least squares. Additionally, corresponding unit weight variance estimations are constructed. Finally, it is verified by two numerical simulation experiments and a real-world application example of a geodetic network that the correlated observation bcWLS studied in this paper proves to be the most efficient among the six methods for solving the correlated observation multiplication mixture error model.

State of Charge Estimation of Lithium-Ion Batteries Based on Fractional-Order Model with Mul-ti-Innovations Dual Cubature Kalman Filter Method

An accurate estimation of the lithium battery’s state of charge (SOC) is critical. The article proposes a dual fractional order multi-innovations cubature Kalman filter (DFOMICKF) algorithm for estimating lithium battery SOC. The algorithm adopts the idea of multiple time scales, where one of the FOMICKF is used to identify the circuit model parameters online in the macro time scale. Another FOMICKF is used to estimate the SOC in the micro time scale, and the circuit parameters updated online in real-time are passed into the estimation of the SOC filter to form an online joint estimation method of SOC and circuit parameters. Finally, multiple algorithms of DFOMICKF, FOMICKF, FOCKF, and CKF are compared and experimented under different working conditions to compare and analyze the estimated SOC errors. It is verified that the proposed algorithm can solve the problems of inaccuracy, poor convergence, and poor robustness of the traditional Kalman filtering algorithm for estimating SOC, which has good research value.

Twin experiments and detailed investigation of data assimilation system for columnar dendrite growth in thin film

Accurately predicting dendrite growth during alloy solidification is crucial for enhancing the quality of metallic products. Recently, data assimilation has emerged as a promising tool for integrating two cutting-edge methods for studying dendritic growth, viz. in situ X-ray observation experiments and phase-field (PF) simulations, to elucidate important parameter(s) of the simulation and produce a “digital twin” of a growing dendrite. This study was conducted to evaluate the performance of a data assimilation system, employing an ensemble Kalman filter, through systematic twin experiments focused on columnar dendrite growth in a thin film of a binary alloy. The results show that the data assimilation system effectively estimates multiple parameters and dendrite morphology simultaneously. Furthermore, two approaches—domain decomposition method and parameter estimation method from a part of the domain—to reduce computational costs are investigated. Both methods can effectively reduce the computational cost of data assimilation. Additionally, data assimilation using voxel observation data of varying resolutions, mimicking actual X-ray images, is performed. The study findings discourage the direct use of voxel data owing to incompatible PF simulations. PF relaxation computation is explored as a solution for generating observation data with smooth PF profiles. The results show that while relaxation computation enhances the estimation accuracy for high-resolution voxel data, its efficacy diminishes for low-resolution data. These detailed investigations of data assimilation provide valuable insights for utilizing actual in situ X-ray observation data in dendrite growth studies.

Estimation method of the Homodyned K-distribution based on the Improved Shuffled Frog Leaping Algorithm for ultrasound tissue characterization

Abstract Aiming at promoting the accuracy of the integral value of the probability distribution function (PDF) of Homodyned K-distribution (HK), a new maximum likelihood estimation method for HK distribution parameters is proposed by using the improved shuffled frog leaping algorithm (ADM-SFLA) and Newton-Raphson iterative algorithm (NR). To improve the accuracy of the global search of the traditional SFLA, two variation factors of Gauss and Cauchy are first used to find the global optimal solution in a convergence state. Secondly, to obtain the integral node with optimal segmentation, the ADM-SFLA is used to perform the non-equidistant adaptive segmentation of the integral interval. Then, the PDF of the HK distribution is calculated between each numerical integration cell based on Simpson integral formula. Subsequently, the integral value of the PDF for HK distribution is obtained by summing the integration values from each numerical integration cell. Finally, the optimal estimation of HK distribution parameters is obtained based on NR algorithm. The performance of the proposed method is evaluated and compared through simulated data as well as the envelope signals obtained from the ultrasonic simulation model with different scattering components. The results show that the ADM-SFLA based method can improve the estimation accuracy of HK distribution parameters effectively.

PesRec: A parametric estimation method for indoor semantic scene reconstruction from a single image

Reconstructing semantic indoor scenes is a challenging task in augmented and virtual reality. The quality of scene reconstruction is limited by the complexity and occlusion of indoor scenes. This is due to the difficulty in estimating the spatial structure of the scene and insufficient learning for object location inference. To address these challenges, we have developed PesRec, an end-to-end multi-task scene reconstruction network for parameterizing indoor semantic information. PesRec incorporates a newly designed spatial layout estimator and a 3D object detector to effectively learn scene parameter features from RGB images. We modify an object mesh generator to enhance the robustness of reconstructing indoor occluded objects through point cloud optimization in PesRec. Using the analyzed scene parameters and spatial structure, the proposed PesRec reconstructs an indoor scene by placing object meshes scaled to 3D detection boxes in an estimated layout cuboid. Extensive experiments on two benchmark datasets demonstrate that PesRec performs exceptionally well for object reconstruction with an average chamfer distance of 5.24 × 10-3 on the Pix3D dataset including 53.61 % mAP for 3D object detection and 79.7 % 3D IoU for the estimation of layout on the commonly-used SUN RGB-D datasets. The proposed computing network breaks through the limitations caused by complex indoor scenes and occlusions, showing optimization results that improve the quality of reconstruction in the fields of augmented reality and virtual reality.

Petrophysical parameter estimation using a rock-physics model and collaborative sparse representation

The estimation of petrophysical parameters is key in the identification of underground reservoirs. Current petrophysical parameter estimation methods are typically constrained by the choice of particular rock-physics models, necessitating the use of distinct models for various reservoirs. Furthermore, the inherent pronounced nonlinearity of these models presents significant challenges to the solution process in reservoir parameter inversion. Although linearized petrophysical inversion methods can simplify the solving process, they can introduce errors due to linearization. To address these limitations, we develop a petrophysical parameter estimation method driven by a rock-physics model and collaborative sparse representation (CSR). In this approach, the rock-physics model governs the fundamental pattern of the petrophysical parameters, with the CSR introducing perturbations to minimize model errors. Our method maximizes the use of well-log data and the rock-physics model, thereby reducing errors associated with linearized rock-physics (LRP) models and enhancing the method’s adaptability. We use the joint dictionary method to learn features and correlations among multiple parameters from the existing well-log data. This learned dictionary is then used as a CSR regularization constraint and applied to refine the LRP inversion objective function. Finally, the objective function is minimized using the block coordinate descent method to predict the petrophysical parameters. The effectiveness of this method in enhancing the adaptability and accuracy of petrophysical parameter estimation is confirmed through synthetic and field data tests.

Bayesian estimation of some reliability characteristics for Nakagami model using adaptive progressive censoring

The focus of this research is to clarify both conventional and Bayesian parametric estimation methods for the Nakagami distribution making use of adaptive progressive Type II censored data. From a classical estimation perspective, two estimation methods are considered: maximum likelihood and least squares estimations. Along with the model parameters, three reliability metrics are estimated using point and interval estimation. Bayes estimates with gamma and inverse gamma priors are investigated by employing the squared error loss function. The Bayes computations are created using the Markov Chain Monte Carlo technique. Moreover, the classical and Bayesian intervals are also taken into consideration. For evidence of the effectiveness of the given methodologies, a simulation study and three applications from the physics, chemistry, and engineering domains are explored. Lastly three optimality criteria are applied to the stated data sets to pick the best progressive censoring strategy.

Distributed control of spacecraft formation under [formula omitted] perturbation in the port-Hamiltonian framework

To control the relative position and relative velocity of spacecraft formation, a time-varying nonlinear relative motion model under J2 perturbation in an elliptical orbit is established in the port-Hamiltonian (PH) framework, and a distributed control law for spacecraft formation is developed using the consensus algorithm for parameter estimation and the passivity-based control (PBC) method based on the state-error interconnection and damping assignment (IDA) technique. First, the influence of J2 perturbation on the potential energy and orbit parameters in the model is considered when the relative motion model is built in the PH frame, and the expression of the relative motion acceleration under J2 perturbation is given. Second, to solve the problem that the state of the chief spacecraft cannot be directly obtained from the deputy spacecraft under distributed communication, a consensus-based parameter estimation method is introduced, the estimated parameter of the chief spacecraft is applied to the relative motion model in the PH frame, and a state error model with the estimated parameters derived from the consistency algorithm is established. Then, after the stability analysis is conducted on the desired PH system containing the estimated parameter values, the desired Hamiltonian energy function with the estimated parameters is designed according to the time-varying errors of the relative equilibrium states of the deputy spacecraft and the errors between deputy spacecraft, and the distributed control law of spacecraft formation is derived based on the state-error IDA-PBC method. Finally, the expected relative motion trajectory designed based on the TH equation is used to simulate a spacecraft formation under J2 perturbation, and the results indicate that the spacecraft can quickly converge to the expected formation under the influence of the control law.

On the empirical exploration of a new probability distribution in physical education and reliability

Probability-based methodologies have gained widespread recognition for their pivotal role in steering decision-making in contexts marked by uncertainty or vagueness. In order to guarantee that decisions made in these circumstances are both significant and impactful, various methodologies focused on probability have been devised and utilized. This study seeks to significantly enrich the existing literature by proposing a new probability model termed the weighted sine exponentiated Weibull distribution. Certain characteristics are obtained for the suggested model. Additionally, the parameter estimation method and simulation studies related to the suggested model are also provided. Two distinct data sets, acquired from the disciplines of physical education and reliability, were effectively implemented using the proposed model, resulting in a successful outcome. Through the utilization of the p-value and various tests, it becomes apparent that the weighted sine exponentiated Weibull model consistently surpasses its competitor distributions in terms of statistical significance. The proposed model’s practical illustration highlights its effectiveness and potential for extensive use in both physical education and reliability research and practice.

A fast method for intra-pulse parameters estimation of polyphase-coded radar signals based on FRFT

A fast method for intra-pulse parameters estimation of polyphase-coded radar signals based on FRFT