Estimation Method Research Articles

The Relationship between Smoking and Susceptibility to HIV Infection: A Two-Sample Mendelian Randomization Analysis

Smoking is prevalent among people living with the human immunodeficiency virus (HIV), and it increases morbidity and mortality in this population. However, due to ethical constraints, there is limited information on the effects of smoking on susceptibility to HIV infection. To investigate whether smoking is associated with an increased susceptibility to HIV infection, we conducted a two-sample Mendelian randomization (MR) study using summary statistics from genome-wide association studies of individuals of European ancestry who have ever smoked (n = 99,996) and have HIV (n = 412,130). The random-effects inverse-variance weighted estimation method was used as the study’s primary approach, with the MR-Egger regression and the weighted-median method as complementary approaches. Using 100 single-nucleotide polymorphisms of genome-wide significance as instrumental variables for smoking, we observed a significant association between smoking and HIV infection (odds ratio 5.790, 95% confidence interval [1.785, 18.787], and p = 0.003). Comparable results were obtained using the weighted-median method. Our findings implied that smoking is probably associated with increased susceptibility to HIV infection. Given the exploratory nature of this study, further research is needed to confirm this relationship.

Identifiability and Estimation for Potential-Outcome Means with Misclassified Outcomes

Potential outcomes play a fundamental and important role in many causal inference problems. If the potential-outcome means are identifiable, a series of causal effect measures, including the risk difference, the risk ratio, and the treatment benefit rate, among others, can also be identified. However, current identification and estimation methods for these means often implicitly assume that the collected data for analysis are measured precisely. In many fields such as medicine and economics, the collected variables may be subject to measurement errors, such as medical diagnostic results and individual wage data. Misclassification, as a non-classic measurement error, can lead to severely biased estimates in causal inference. In this paper, we leverage a combined sample to study the identifiability of potential-outcome means corresponding to different treatment levers under a plausible misclassification assumption for the outcome, allowing the misclassification probability to depend on not only the true outcome but also the covariates. Furthermore, we propose the multiply-robust and semiparametric efficient estimators for the means, consistent even under partial misspecification of the observed data law, based on the semiparametric theory framework. The simulation studies and real data analysis demonstrate the satisfactory performance of the proposed method.

Properties, estimation, and applications of the extended log-logistic distribution

This paper presents the exponentiated alpha-power log-logistic (EAPLL) distribution, which extends the log-logistic distribution. The EAPLL distribution emphasizes its suitability for survival data modeling by providing analytical simplicity and accommodating both monotone and non-monotone failure rates. We derive some of its mathematical properties and test eight estimation methods using an extensive simulation study. To determine the best estimation approach, we rank mean estimates, mean square errors, and average absolute biases on a partial and overall ranking. Furthermore, we use the EAPLL distribution to examine three real-life survival data sets, demonstrating its superior performance over competing log-logistic distributions. This study adds vital insights to survival analysis methodology and provides a solid framework for modeling various survival data scenarios.

Quantum-enhanced mean value estimation via adaptive measurement

Quantum-enhanced (i.e., higher performance by quantum effects than any classical methods) mean value estimation of observables is a fundamental task in various quantum technologies; in particular, it is an essential subroutine in quantum computing algorithms. Notably, the quantum estimation theory identifies the ultimate precision of such an estimator, which is referred to as the quantum Cramér-Rao (QCR) lower bound or equivalently the inverse of the quantum Fisher information. Because the estimation precision directly determines the performance of those quantum technological systems, it is highly demanded to develop a generic and practically implementable estimation method that achieves the QCR bound. Under imperfect conditions, however, such an ultimate and implementable estimator for quantum mean values has not been developed. In this paper, we propose a quantum-enhanced mean value estimation method in a depolarizing noisy environment that asymptotically achieves the QCR bound in the limit of a large number of qubits. To approach the QCR bound in a practical setting, the method adaptively optimizes the amplitude amplification and a specific measurement that can be implemented without any knowledge of state preparation. We provide a rigorous analysis for the statistical properties of the proposed adaptive estimator such as consistency and asymptotic normality. Furthermore, several numerical simulations are provided to demonstrate the effectiveness of the method, particularly showing that the estimator needs only a modest number of measurements to almost saturate the QCR bound.

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.

Neural networks for quantum state tomography with constrained measurements

Quantum state tomography (QST) aiming at reconstructing the density matrix of a quantum state plays an important role in various emerging quantum technologies. Recognizing the challenges posed by imperfect measurement data, we develop a unified neural network (NN)-based approach for QST under constrained measurement scenarios, including limited measurement copies, incomplete measurements, and noisy measurements. Through comprehensive comparison with other estimation methods, we demonstrate that our method improves the estimation accuracy in scenarios with limited measurement resources, showcasing notable robustness in noisy measurement settings. These findings highlight the capability of NNs to enhance QST with constrained measurements.

Harmonic voltage phasor reconstruction and harmonic state estimation based on the measurement data of a capacitive voltage transformer

AbstractHarmonic state estimation, which highly depends on accurate synchronised phasors, is a crucial basis for the location, traceability, and governance of harmonics in power systems. However, most existing synchronous phasor measurement units (PMUs) provide power frequency phasors rather than harmonic phasors. In addition, as the dominant voltage signal provider for PMUs in power systems, capacitive voltage transformers (CVTs) have complex frequency responses and cannot be directly used for harmonic measurement. Therefore, accurate harmonic state estimation is difficult to achieve in applications. A method for harmonic voltage phasor reconstruction and harmonic state estimation based on the measurement data of a CVT is proposed. First, the reasons for harmonic voltage measurement errors were analysed. Second, the scattering parameter method was used to measure the wideband voltage transfer characteristics of CVT. Third, a voltage reconstruction method was proposed to improve the measurement accuracy and expand the frequency range of synchronous phasor measurement. Fourth, this method was applied to harmonic state estimation, and the performance of harmonic state estimation before and after voltage reconstruction was quantitatively compared. Results showed that the proposed method can remarkably improve the accuracy of harmonic state estimation. Finally, some factors, such as state observability, complex error disturbances, CVT structure, and harmonic order, influencing the performance of the proposed method were investigated. Results further demonstrated that the method has high accuracy, strong anti‐interference, and adaptability, and can provide basic information for harmonic localisation and traceability.

Cost, Cost-effectiveness and Survival Impact Assessment for A Better Management of Colorectal Cancer Patients: A Single Centre Comprehensive Analysis.

The world healthcare systems are currently challenged by the accumulating burden of colorectal cancer (CRC), and cancer registries represent an important segment for prevention and developing management plans, being useful in providing data regarding incidence, mortality, survival, exposure to carcinogens, lifestyle. Retrospective data from CRC patients in Romania was used to assess survival impact, costs, and cost-effectiveness considering three crucial aspects: pharmacology, chemo-/radio-therapy, and hospitalization for care and management of these patients. 423 CRC patients from the Institutional Cancer Registry of the Prof. Dr. Ion Chiricuta Institute of Oncology in Cluj-Napoca, Romania were included in the cost analysis. For the assessment of cost efficiency of the primary treatment strategy, we collected data regarding direct medical costs associated with surgery, radiotherapy and medication, as well as the afferent day or continuous hospitalization, for each patient. For the cost-effectiveness analysis we used the method of estimation of incremental cost-effectiveness ratio. No compelling differences regarding survival time were observed in different therapeutic options per CRC stage. Substantial differences in cost effectiveness among therapeutic options in the same stage of several thousand Euros in stages I-III, while for stage IV, the ICER was more than 100,000 Euros per life saved. Systematic evaluation of costs, cost-effectiveness, and survival impact, helps healthcare systems can make informed decisions to improve the management of colorectal cancer patients, optimizing outcomes while minimizing financial burden.

Validity and Reliability of OpenPose-Based Motion Analysis in Measuring Knee Valgus during Drop Vertical Jump Test.

OpenPose-based motion analysis (OpenPose-MA), utilizing deep learning methods, has emerged as a compelling technique for estimating human motion. It addresses the drawbacks associated with conventional three-dimensional motion analysis (3D-MA) and human visual detection-based motion analysis (Human-MA), including costly equipment, time-consuming analysis, and restricted experimental settings. This study aims to assess the precision of OpenPose-MA in comparison to Human-MA, using 3D-MA as the reference standard. The study involved a cohort of 21 young and healthy adults. OpenPose-MA employed the OpenPose algorithm, a deep learning-based open-source two-dimensional (2D) pose estimation method. Human-MA was conducted by a skilled physiotherapist. The knee valgus angle during a drop vertical jump task was computed by OpenPose-MA and Human-MA using the same frontal-plane video image, with 3D-MA serving as the reference standard. Various metrics were utilized to assess the reproducibility, accuracy and similarity of the knee valgus angle between the different methods, including the intraclass correlation coefficient (ICC) (1, 3), mean absolute error (MAE), coefficient of multiple correlation (CMC) for waveform pattern similarity, and Pearson's correlation coefficients (OpenPose-MA vs. 3D-MA, Human-MA vs. 3D-MA). Unpaired t-tests were conducted to compare MAEs and CMCs between OpenPose-MA and Human-MA. The ICCs (1,3) for OpenPose-MA, Human-MA, and 3D-MA demonstrated excellent reproducibility in the DVJ trial. No significant difference between OpenPose-MA and Human-MA was observed in terms of the MAEs (OpenPose: 2.4° [95%CI: 1.9-3.0°], Human: 3.2° [95%CI: 2.1-4.4°]) or CMCs (OpenPose: 0.83 [range: 0.99-0.53], Human: 0.87 [range: 0.24-0.98]) of knee valgus angles. The Pearson's correlation coefficients of OpenPose-MA and Human-MA relative to that of 3D-MA were 0.97 and 0.98, respectively. This study demonstrated that OpenPose-MA achieved satisfactory reproducibility, accuracy and exhibited waveform similarity comparable to 3D-MA, similar to Human-MA. Both OpenPose-MA and Human-MA showed a strong correlation with 3D-MA in terms of knee valgus angle excursion.

Enhanced‐Resolution Learning‐Based Direction of Arrival Estimation by Programmable Metasurface

AbstractDue to its growing importance and wide range of applications, direction‐of‐arrival (DOA) estimation has become a major research topic, particularly in the field of communication systems. While traditional DOA estimation methods rely on antenna arrays and complex algorithms, recent progress achieved in the design and implementation of metasurfaces has proved their effectiveness as promising alternatives. This study presents a distinct approach for DOA estimation that combines the use of a programmable metasurface with deep learning. The programmable metasurface together with a radio‐frequency power detector placed at the focal point, acts as a parabolic reflector antenna with an adjustable pointing direction, which scans the azimuth plane in 5° increments to receive the power level of incoming signals. The collected data is then fed into a pre‐trained multilayer neural network to enable DOA estimation with a resolution of lower than 1° without requiring fine‐tuning of the scanning procedure. This approach ensures accurate and fast estimations, paving the way for advanced solutions in detection and localization for various applications.

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.

Estimating Unknown Parameters and Disturbance Term in Uncertain Regression Models by the Principle of Least Squares

In the field of statistics, uncertain regression analysis occupies an important position. It can thoroughly analyze data sets contained in complex uncertainties, aiming to quantify and reveal the intricate relationships between variables. It is worth noting that the traditional least squares method only takes into account the reduction in the deviations between predictions and observations, and fails to fully consider the inherent characteristics of the correlation uncertainty distributions under the uncertain regression framework. In light of this, this paper constructs a statistical invariant with symmetric uncertainty distribution based on the observations and the disturbance term. It also proposes the least squares estimation of unknown parameters and disturbance term in the uncertain regression model based on the least squares principle and, combined with the mathematical properties of the normal uncertainty distribution, gives a numerical algorithm for solving specific estimates. Finally, in order to verify the effectiveness of the least squares estimation method proposed in this paper, we also design two numerical examples and an empirical study of forecasting of electrical power output.

Exploring the causal associations between diet-derived circulating antioxidants and the risk of endometriosis: a Mendelian randomization study

BackgroundNumerous observational studies and randomized controlled trials have recently revealed the associations between circulating antioxidants and the risk of endometriosis, while the underlying causal relationship remains unclear. This study aimed to investigate the causal association between genetically determined circulating antioxidants and the risk of endometriosis using Mendelian randomization (MR).MethodsA two-sample MR analysis was conducted using publicly available summary data from genome-wide association studies (GWAS) to investigate the causal impact of genetically determined absolute circulating antioxidants (such as ascorbate, retinol, β-carotene, and lycopene) and their metabolites (including α-and γ-tocopherol, ascorbate, and retinol) on the risk of endometriosis. The study used inverse variance weighted (IVW) or Wald ratio analyses as the primary estimation method and also conducted sensitivity analyses to assess heterogeneity and pleiotropy.ResultsNo significant causality was observed for genetically determined circulating antioxidants and the risk of endometriosis. The pooled odds ratios (ORs) for absolute circulating antioxidants were 0.62 (95% CI: 0.32–1.18, retinol), 0.95 (95% CI: 0.79–1.15, β-carotene), 1.01 (95% CI: 0.95–1.08, lycopene), and 1.00 (95% CI: 0.99–1.02, ascorbate, expressed as a Wald ratio). The pooled ORs indicating the EM risk per unit increase in circulating antioxidant metabolites were 1.04 (95% CI: 0.82–1.33, γ-tocopherol), 0.91 (95% CI: 0.57–1.46, α-tocopherol), 1.03 (95% CI: 0.99–1.07, retinol), and 0.96 (95% CI: 0.87–1.06, ascorbate).ConclusionOur study demonstrated that increased levels of diet-derived circulating antioxidants were not significantly associated with a reduced risk of endometriosis.

Machine learning-based estimation of evapotranspiration under adaptation conditions: a case study in Heilongjiang Province, China.

The prediction of evapotranspiration (ET0) is crucial for agricultural ecosystems, irrigation management, and environmental climate regulation. Traditional methods for predicting ET0 require a variety of meteorological parameters. However, obtaining data for these multiple parameters can be challenging, leading to inaccuracies or inability to predict ET0 using traditional methods. This affects decision-making in critical applications such as agricultural irrigation scheduling and water management, consequently impacting the development of agricultural ecosystems. This issue is particularly pronounced in economically underdeveloped regions. Therefore, this paper proposes a machine learning-based evapotranspiration estimation method adapted to evapotranspiration conditions. Compared to traditional methods, our approach relies less on the variety of meteorological parameters and yields higher prediction accuracy. Additionally, we introduce a 'region of evapotranspiration adaptability' division method, which takes into account geographical differences in ET0 prediction. This effectively mitigates the negative impact of anomalies or missing data from individual meteorological stations, making our method more suitable for practical agricultural irrigation and ecosystem water resource management. We validated our approach using meteorological data from 25 stations in Heilongjiang, China. Our results indicate that non-adjacent geographical areas, despite different climatic conditions, can have similar impacts on ET0 prediction. In summary, our method facilitates accurate ET0 prediction, offering new insights for the development of agricultural irrigation and ecosystems, and further contributes to agricultural food supply.

Separable Synchronous Gradient‐Based Iterative Algorithms for the Nonlinear ExpARX System

ABSTRACTThis article is aimed to study the parameter identification of the ExpARX system. To overcome the computational complexity associated with a large number of feature parameters, a parameter separation scheme based on the different features of the identification model is introduced. In terms of the phenomenon that the coupling parameters lead to the inability of algorithms, a separable synchronous interactive estimation method is introduced to eliminate the coupling parameters and perform parameter estimation in accordance with the hierarchical principle. For the purpose of achieving high‐accuracy performance and reducing complexity, a separable synchronous gradient iterative algorithm is derived by means of gradient search. In order to improve the identification accuracy, a separable synchronous multi‐innovation gradient iterative algorithm is proposed by introducing the multi‐innovation identification theory. In order to improve the convergence speed, a separable synchronous multi‐innovation conjugate gradient iterative algorithm is proposed by introducing the conjugate gradient theory. Finally, a simulation example and a real‐life example of piezoelectric ceramics are used to verify the effectiveness of the proposed algorithm.

Methodological Recommendations for the Creation of Sensor Measurement Systems for Respiratory Rate Monitoring Based on Photoplethysmographic Signal Processing

A methodical apparatus for creating sensor measurement systems for monitoring human respiration rate is proposed. It includes a method for estimating respiratory rate based on statistical analysis of photoplethysmographic signals (human pulse wave), a method for selecting priority regions for estimating respiratory rate, and a criterion for determining the required bracelet tension during measurements. The application of the respiratory rate estimation method involves calculating the Correntropy spectral density of the pulse wave signal. A distinctive feature of the method is the use of an algorithm for selecting the priority empirical mode of the Hilbert-Huang decomposition, which is most closely related to the respiratory rate. Experimental verification of the method showed that the mean value of the absolute error for 58.8% of the sample of calculated respiratory rate values did not exceed 1 breath/min, and the 95% confidence interval for the mean absolute error of the entire sample was [0.72–2.2] breaths/min.

Six-Degree-of-Freedom Pose Estimation Method for Multi-Source Feature Points Based on Fully Convolutional Neural Network

An object’s six-degree-of-freedom (6DoF) pose information has great importance in various fields. Existing methods of pose estimation usually detect two-dimensional (2D)-three-dimensional (3D) feature point pairs, and directly estimates the pose information through Perspective-n-Point (PnP) algorithms. However, this approach ignores the spatial association between pixels, making it difficult to obtain high-precision results. In order to apply pose estimation based on deep learning methods to real-world scenarios, we hope to design a method that is robust enough in more complex scenarios. Therefore, we introduce a method for 3D object pose estimation from color images based on farthest point sampling (FPS) and object 3D bounding box. This method detects the 2D projection of 3D feature points through a convolutional neural network, matches it with the 3D model of the object, and then uses the PnP algorithm to restore the feature point pair to the object pose. Due to the global nature of the bounding box, this approach can be considered effective even in partially occluded or complex environments. In addition, we propose a heatmap suppression method based on weighted coordinates to further improve the prediction accuracy of feature points and the accuracy of the PnP algorithm in solving the pose position. Compared with other algorithms, this method has higher accuracy and better robustness. Our method yielded 93.8% of the ADD(-s) metrics on the Linemod dataset and 47.7% of the ADD(-s) metrics on the Occlusion Linemod dataset. These results show that our method is more effective than existing methods in pose estimation of large objects.

Changes in the spatiotemporal distribution of the timing and duration of the soil freeze–thaw status from 1979 to 2018 over the Tibetan Plateau

AbstractChanges in the soil freeze–thaw status will inevitably affect the thermal conditions and properties of the Tibetan Plateau (TP), thereby affecting its upper atmosphere, and further afield in East Asia and even globally. In this study, using the soil temperature simulated by the Community Land Model Version 5.0 (CLM5.0), the timing and duration of the soil freeze–thaw status were divided into freeze start‐date, freeze end‐date and freeze duration. Then, using linear trend estimation, correlation analysis and other methods, the changes in the spatiotemporal distribution of the timing and duration of the soil freeze–thaw status from 1979 to 2018 over the TP were analysed, and the relationships between them and surface temperature, altitude and latitude were analysed. The results obtained were as follows: (1) The soil temperature simulated by CLM5.0 can reasonably reproduce the seasonal changes in multilayer soil temperature, and correlated well with observations. Simulated by CLM5.0 of the time and duration of the soil freeze–thaw status also correlated well with observations. (2) The spatial distribution of the soil freeze–thaw status is characterized by a trend of delayed freezing, advanced thawing and shortened freeze duration from northwest to southeast over the TP. From 1979 to 2018, the freeze start‐date postponed by 7.3 days and became delayed at a rate of 1.9 days per decade, while the freeze end‐date advanced by 6.4 days at a rate of 1.7 days per decade, and the freeze duration shortened by 13.7 days at a rate of 3.6 days per decade. The timing and duration of the soil freeze–thaw status vary across different regions of the TP. The freeze start‐date in all areas of the TP has been delayed in the past 39 years. Except for the subcold zone and arid regions of the TP, the freeze end‐date has occurred earlier and the freeze duration has shortened, with the most significant changes in the subcold zone and humid regions, while the freeze end‐date has advanced at a rate of 3.6 days per decade and the freeze duration has shortened at a rate of 6.3 days per decade. (3) The timing and duration of the soil freeze–thaw status are significantly correlated with surface air temperature, elevation and latitude, exceeding the 99% confidence level. The correlation between the timing and duration of the soil freeze–thaw status and surface temperature is strongest, followed by altitude, and correlation with latitude is weaker. The correlation between surface air temperature and the timing and duration of the soil freeze–thaw status in the western TP is stronger than that in the eastern TP. The rate of change in the soil freeze–thaw status increases with altitude to 3000 m above sea level, while this rate decreases with elevation above 3000 m. The rate of change in the soil freeze–thaw status is greatest at 29°N, while the rate of delay in the freeze start‐date is minimal at 33°N and the rates of advancement in the freeze end‐date and shortening of the freeze duration are minimal at 35°N.

A Novel Method and System Implementation for Precise Estimation of Single-Axis Rotational Angles.

Accurately estimating single-axis rotational angle changes is crucial in many high-tech domains. However, traditional angle measurement techniques are often constrained by sensor limitations and environmental interferences, resulting in significant deficiencies in precision and stability. Moreover, current methodologies typically rely on fixed-axis rotation models, leading to substantial discrepancies between measured and actual angles due to axis misalignment. To address these issues, this paper proposes an innovative method for single-axis rotational angle estimation. It introduces a calibration technique for installation errors between inertial measurement units and the overall measurement system, effectively translating dynamic rotational inertial outputs to system enclosure outputs. Subsequently, the method employs triaxial accelerometers combined with zero-velocity detection technology to estimate the rotation axis position. Finally, it delves into analyzing the relationship between quaternion and axis-angle, aimed at reducing noise interference for precise rotational angle estimation. Based on this proposed methodology, a Low-Cost, a High Accuracy Measurement System (HAMS) integrating sensor fusion was designed and implemented. Experimental results demonstrate static measurement errors below ±0.15° and dynamic measurement errors below ±0.5° within a ±180° range.