Error Components Research Articles

Size of living space as a moderator for central and peripheral refractions in children

Undesirable living environment may impose risk on myopia development. Furthermore, peripheral refractive error was suggested to contribute to juvenile eye growth modulation. This study aimed to investigate the interaction between peripheral refractive error and living environment in relation to central refractive status in Hong Kong schoolchildren. Central and peripheral refractive errors, axial length (AL), and corneal radius of curvature (CR) were measured in 573 schoolchildren (age 9.5 ± 0.9 years). The AL/CR ratio was used to represent the central refractive status, accounting for non-cycloplegic refraction. The relative peripheral refractive errors (RPRE) up to ± 20° eccentricities were converted into power vectors: spherical-equivalent error (SER) and J0 astigmatic components and fitted with quadratic equations. The second-order coefficients of SER (aSER) and J0 astigmatism (aJ0) and home size reported by parental questionnaires were analyzed to indicate their relationships with AL/CR. Our results showed that children with higher AL/CR lived in smaller homes (p = 0.01) and had a more hyperopic (p < 0.001) but less astigmatic RPRE (p = 0.01). We further analyzed the relationship between AL/CR with RPRE for children living in small (< 300 ft2), moderate (300–600 ft2), and large home sizes (> 600 ft2). Regardless of the home size, a higher AL/CR remained moderately correlated with a more hyperopic aSER (all p < 0.001). However, a higher AL/CR was associated with a more positive aJ0 only in children living in large homes, and the relationships were not significant for small and moderate home sizes. Linear regression models further indicated that home size was a significant moderator contributing to the relationship between AL/CR and aJ0. In conclusion, our results were consistent with previous studies, showing that children with axial myopia usually lived in smaller homes and had more hyperopic defocus and more positive J0 astigmatism. However, the relationship between peripheral astigmatism and axial refraction was modulated by the home size of Hong Kong schoolchildren. While peripheral astigmatism is hypothesized as a visual cue for axial refractive development in children, extrinsic environmental factors, such as home size, might interfere with the relationship and dominate refractive development.

Non-pathologic components are associated with reduced visual acuity in myopes after spectacle correction.

To find the association between reduced best-corrected visual acuity and non-pathologic components after optical correction in individuals with low to high myopia. Myopic children under 16 years of age were reviewed using electronic medical records and the following data were extracted and recorded: participant's age, gender, uncorrected visual acuity (UCVA), manifest refraction, and best corrected visual acuity (BCVA). Spherical equivalent and cylinder were classified into low, moderate, and high categories based on the magnitude range. Similarly, astigmatism was defined into with-the-rule, against-the-rule, and oblique based on the location of the steepest meridian. Reduced BCVA was defined when the decimal visual acuity was less than 0.66 (equivalent to Snellen's acuity of 6/9 or 20/30). Logistic regression was performed to test the factors associated with reduced visual acuity after optical correction in the absence of myopic pathologic changes. Statistical significance was considered if P < 0.05. Overall 44.9% (N = 242/538) of myopes had reduced best-corrected visual acuity (BCVA) and none of the patients had pathologic myopic lesions. Using logistic regression, we found that high spherical refraction (OR 27.98, 95% CI 14.43-54.25, P < 0.001) and moderate spherical refraction (OR 5.52, 95% CI 2.56-11.91, P < 0.001) were significantly associated with reduced best corrected visual acuity despite any pathological lesions. Additionally, oblique and ATR astigmatism were associated with reduced visual acuity in myopic children with (OR 2.05, 95% CI 0.77-5.42) and (OR 1.59, 95% CI 0.82-3.08). Higher magnitude of refractive error components causes reduced visual acuity in the absence of pathologic changes.

Joint Uplink and Downlink Resource Allocation Toward Energy-Efficient Transmission for URLLC

Ultra-reliable and low-latency communications (URLLC) is firstly proposed in 5G networks, and expected to support applications with the most stringent quality-of-service (QoS). However, since the wireless channels vary dynamically, the transmit power for ensuring the QoS requirements of URLLC may be very high, which conflicts with the power limitation of a real system. To fufill the successful URLLC transmission with finite transmit power, we propose an energy-efficient packet delivery mechanism incorparated with frequency-hopping and proactive dropping in this paper. To reduce uplink outage probability, frequency-hopping provides more chances for transmission so that the failure hardly occurs. To avoid downlink outage from queue clearing, proactive dropping controls overall reliability by introducing an extra error component. With the proposed packet delivery mechanism, we jointly optimize bandwidth allocation and power control of uplink and downlink, antenna configuration, and subchannel assignment to minimize the average total power under the constraint of URLLC transmission requirements. Via theoretical analysis (e.g., the convexity with respect to bandwidth, the independence of bandwidth allocation, the convexity of antenna configuration with inactive constraints), the simplication of finding the global optimal solution for resource allocation is addressed. A three-step method is then proposed to find the optimal solution for resource allocation. Simulation results validate the analysis and show the performance gain by optimizing resource allocation with the proposed packet delivery mechanism.

Analysis of World Economic Growth Using Panel Data

In this paper, I consider panel data analysis of world economies to identify the relationship between GDP growth and the independent variables, and the nature of effect that may exist. Annual data for 161 countries from 1990 to 2020 sourced from the World Bank and UN are used. GDP is the independent variable while the independent variables are population, gross value added, total natural resources rent, and labor force. Firstly, a poolability test is performed to test for the joint significance of the fixed effects. The null hypothesis is rejected as there exist significant individual effects. Secondly, Huesman’s test is performed to test for consistency of fixed effect and random effect. The null hypothesis is rejected implying significant random effects exist. Thirdly, Bruesch-Pagan test for heteroscedasticity is performed, which shows the existence of heteroscedasticity. Finally, White’s covariance matrix estimator for random effect is performed which results to consistent and efficient parameter estimate in the presence of heteroscedasticity. The random effect model is statistically significant at the 5% level, with 68 % of the variation being explained by the model. All the explanatory variables are statistically significant at a 5 % level. They all have a positive effect on GDP with the labor force and population having the highest effect. The random effect is large and significant with a variance of 2.25±1.5 and 94.1 % share of the error component. Countries that have had consistent increases in either labor force or population growth or both, has over the period experienced consistent economic growth after controlling for the other variables and the random effect.

Results of study of quantization and discretization error of digital tachometers with encoder

The analysis of measuring channels of angular velocity with an encoder given by the authors made it possible for the first time to obtain an equation for estimating the quantization and sampling error for an exponential mathematical model describing the transient process of operation of electrical machines. The components of the mathematical model of this dynamic error are the sampling step and the derivative, which characterizes the rate of change of the measured value over time. It was found that the errors of quantization and sampling significantly depend on the value of the resolution z of the encoder. Moreover, an increase in z leads to a decrease in the sampling error, but the relative quantization error increases. To reconcile these components of errors, the laws of change in the distinguishing ability z of the encoder are adaptive to the dynamic properties of the change in angular velocity over time.&#x0D; Proved that to ensure the maximum speed of measuring the angular velocity during the transient process, it is advisable to implement the method of changing the distinguishing ability of the encoder on the internal timers of the microcontroller proposed adaptive to its dynamic properties, and the quantization of informative periods proportional to the measured angular velocity should be carried out in "adjoining intervals".

Revealing systematic errors in hole drilling measurements through a calibration bench: the case of zero-depth data

An accurate estimation of the measurement error in the hole drilling method is needed to choose an appropriate level of regularization and to perform a sensitivity analysis on the stress results. The latest release of ASTM E837 standard for the hole drilling method includes a procedure aimed at estimatingthe standard deviation of the random error component on strain measurements, proposed by Schajer. Nevertheless, strain measurements are also affected to some extent by systematic errors which are not included in the estimation and need to be compensated. For example, an error in the rosette gage factor orin the identification of the zero-depth datum systematically affects all strain measurements in a strongly correlated fashion. This paper describes a calibration bench, designed to superimpose a reference bending stress distribution on a given specimen while simultaneously performing a hole drilling measurement.Since the reference solution is known a priori and shares the measurement instrumentation, the hole geometry and the stepping process with the actual residual stress distribution, the bench provides the user with a direct validation of the obtained accuracy. In addition, strategies aimed at compensating systematicerrors can be tested on the reference solution and then applied on the residual stress evaluation. The imperfect hole geometry and drilling alignment are proven to cause a significant underestimation of stresses near the surface, as they lead to an incorrect identification of the zero-depth datum. It is shown that this effect can be corrected through the proposed calibration bench.

The Analysis of Social and Situational Systems as Components of Human Errors Resulting in Navigational Accidents

As in any industry exposed to risk, human and organizational factors are the main stakes of maritime safety. Understanding the causes and risks of maritime accidents is integral to the sustainability of shipping. The investigation of marine accidents is a crucial tool for their identification in areas related to operations and ships, including social and situational systems, their design, and technical systems. The authors conducted a cause–effect analysis of marine incidents. For this purpose, case-by-case analysis and an Ishikawa diagram were used, which is a tool that helps identify actual or potential causes of accidents. The study showed that by far the most significant cross-section of causes of accidents were elements of social and situational systems that affect the safety of the ship, crew, and environment. The least significant contribution came from the machinery area. Through the detailed descriptions, a picture emerges not so much of a lack of knowledge of the regulations as of a failure to comply with existing procedures or best practices. In the authors’ opinion, more emphasis is needed on preventive measures, including safety culture, training, competence assessment, and increased awareness of the need for sustainability.

Identification of magnetic field errors in synchrotrons based on deep Lie map networks

Magnetic field errors pose a limitation in the performance of synchrotrons, as they excite non-systematic resonances, reduce dynamic aperture and may result in beam loss. Their effect can be compensated assuming knowledge of their location and strength. Established identification procedures are based on orbit response matrices or resonance driving terms. While they sequentially build a field error model for subsequent accelerator sections, a method detecting field errors in parallel could save valuable beam time. We introduce deep Lie map networks, which enable construction of an accelerator model including multipole components for the magnetic field errors by linking charged particle dynamics with machine learning methodology in a data-driven approach. Based on simulated beam-position-monitor readings for the example case of SIS18 at GSI, we demonstrate inference of location and strengths of gradient and sextupole errors for all accelerator sections in parallel. The obtained refined accelerator model may support setup of corrector magnets in operation to allow more precise control over tunes, chromaticities and resonance compensation.

Analysis of the error of influencing factors on the result of measuring the moisture content of grain and grain products

The potential to utilize an ultrahigh-frequency method to regulate the humidity of grain and the products of their industrial processing, allowing one to use this method to regulate technological processes in the production environments of grain-processing industries by controlling the material under examination in free space and converting the measured parameters of the electromagnetic wave passed through the material into an electrical signal. The developed functional scheme of the experimental setup based on the ultrahigh-frequency method of dependence of attenuation and phase shift of electromagnetic wave on the volumetric density of wheat grain at different mass fraction of humidity is discussed, it is shown that with increasing volumetric density at a constant value of the mass fraction of moisture decreases the error of grain moisture measurement with increasing volumetric density, where the main component of the total error of the ultrahigh frequency method (amplitude and phase) is associated with the influence of interfering factors and depends mainly on the variable thickness and density of the controlled material. In order to reduce the components of measurement error brought on by various non-informative (interfering factors) parameters on the outcome of measuring the mass moisture ratio of grain and grain products, the method of moisture measurement in both discrete and inline manufacturing is investigated.

On Possibility of Complete Suppression of the Instrumental Error Component from Inaccuracy of a Diffraction Grating

On Possibility of Complete Suppression of the Instrumental Error Component from Inaccuracy of a Diffraction Grating

СРАВНИТЕЛЬНАЯ ОЦЕНКА МЕТОДОВ УСРЕДНЕНИЙ ДЛЯ ФИЛЬТРАЦИИ ИЗМЕРИТЕЛЬНЫХ СИГНАЛОВ

To improve the quality of manufactured products, it is necessary to improve all technologicalprocesses, which requires increasing the accuracy of the entire measuring path as a whole.For this it is necessary to carefully analyze systematic, random and fluctuating errors in the measurementchannel and take all measures to reduce them. Digital filtering or averaging of intermediatemeasurements (observations) according to certain rules is a radical means of improving theaccuracy of measurements performed. The aim of this work is to compare the quality of suppressionof near-real noise interference using the eight most well-known averaging methods. A model of the measurement path and a general block diagram for modeling the measurement process on acomputer under the influence of random interference are proposed for eight averaging algorithms.As a criterion for evaluating the quality of averaging methods, the ratios of absolute error variancesand mean square deviations before the computing device and after applying the specified averagingalgorithm are taken. Based on the simulation results, the following conclusions are made. 1. All averagingalgorithms provide suppression of random error components of complex interference to thelevel of 40–60 dB. Three algorithms are the best: arithmetic mean AR, a-truncated mean AU5 and atenderizedmean AB5, which provide for the suppression of 5 % of anomalous results. With an increasein the number of observations, the suppression coefficients increase proportionally. 2. Thesampling time must be a multiple of the duration of the 50 Hz AC mains period (20 ms). The optimalnumber of observations (measurements) is 100–128; with 128 measurements, the division operationis reduced to a simple shift, and the averaging result can be obtained in 1–2 μs. 3. When experimentallyapplying the AR averaging method for filtering a highly noisy measurement signal in a communicationline with a length of 800 m, a decrease in the spread of ADC output codes was observedfrom ± 3.5 % to ± 0.1 % after filtering (AR, 64 measurements in 40 ms).

Tackling Modeling and Kinematic Inconsistencies by Fixed Point Iteration-Based Adaptive Control

The Fixed Point Iteration-based Adaptive Control design methodology is an alternative to the Lyapunov function-based technology. It contains higher-order feedback terms than the standard resolved acceleration rate control. This design approach strictly separates the kinematic and dynamic issues. At first, a purely kinematic prescription is formulated for driving the components of the tracking error to zero. Then an available approximate dynamic model is used to calculate the approximated necessary control forces. Before exerting on the controlled system, these forces are adaptively deformed in order to precisely obtain the prescribed kinematic behavior. The necessary deformation is iteratively found by the use of a contractive map that results in a sequence that converges to the unique fixed point of this map. In the case of underactuated systems, when the relative order of the control task also increases, the highest-order time-derivative depends on the lower-order ones according to the dynamic model of the system. This makes it impossible to realize the arbitrarily constructed kinematic design. In the paper, a resolution to this discrepancy is proposed. The method is demonstrated using two non-linear paradigms, a three-degree-of-freedom robot arm, and a two-degree-of-freedom system, i.e., two coupled non-linear springs. The operation of the method was investigated via simulations made by the use of Julia language and simple sequential programs. It was found that the suggested solution could be considered as a new variant of the fixed point iteration-based model reference adaptive control that is applicable for underactuated systems even if the relative order of the task is increased.

Accurate extended time horizon drought prediction via wavelet-season-fuzzy models

Improved accurate prediction of the Palmer drought severity index (PDSI) is crucial for sustainable water supply demand, flood mitigation, management of hydraulic structures, sustainability of the ecosystem and, significant economic and social benefits. In this study, a novel predictive ASA-fuzzy model based on additive season algorithm (ASA) and fuzzy logic is proposed to enhance prediction accuracy with extended future lead times. For the first time, additive season algorithm (ASA) is introduced as an alternative data preprocessing algorithm in prediction of PDSI data obtained from measurement stations that exhibit distinct meteorological characteristics. The results showed that the newly proposed hybrid ASA-fuzzy approach can satisfactorily be utilized to predict monthly PDSI data up to 24-month time horizon. In comparison, for all stations’ data, the newly proposed ASA-fuzzy is found to be superior in accuracy to the stand-alone fuzzy and widely used W-fuzzy models for all lead time predictions based on the quantitative diagnostic measures, root mean squared error (RMSE) and the Nash–Sutcliffe coefficient of efficiency (CE). The remarkable performance of the introduced ASA-fuzzy model in this study clearly shows that the season algorithm can decompose the original data into trend cycle, seasonality and error components more effectively than wavelet technique. Therefore ASA-Fuzzy model has been advocated as a new prediction tool in predicting monthly PDSI data with superior accuracy when compared to conventional methods. In addition, when hybridized with a proper preprocessing algorithm, power of the fuzzy modeling approach in time-series forecasting is manifested.

Digital Banking through the Uncertain COVID Period: A Panel Data Study

This research investigates how the uncertainty caused by the COVID-19 pandemic has affected digital banking usage in India. The study is made by utilizing a panel of data consisting of 108 firm-month observations during covid period from 2020 to 2022, with data mainly collected to analyze the impact of COVID-19 uncertainty. Most of the determinants were collected from the RBI data website. The main emphasis of this study is on the utilization of digital banking services in the context of the pandemic, and the research assesses the factors that have influenced this trend, including the number of physical bank branches, the utilization of debit and credit cards at automated teller machines (ATMs) and points of sale (PoS), as well as the level of economic policy uncertainty (EPU). The analysis was conducted using panel regression analysis, a suitable method for handling the error components in the model that are either fixed or random. The findings indicate that the uncertainty caused by the pandemic has had a negative impact on the use of digital banking services. Additionally, the study highlights that the usage of debit and credit cards at PoS has significantly contributed to promoting the progress of digital banking services during the pandemic. Overall, this study provides valuable insights into how digital banking services have evolved during a period of significant uncertainty and disruption.

Stability of Lyophilized Homemade Control Serum After Reconstitution on SGOT and SGPT Levels Stored in Freezer at Temperature (-2° to -4°C) and -20°C for 8 Weeks

Improving health laboratory services is closely related to strengthening the quality of health laboratories. Serum control is part of the quality assurance of health laboratories. Lyophilized homemade serum is a type of homemade control serum. This research aims to determine the stability of lyophilized homemade control serum against Serum Glutamic Oxaloacetic Transaminase (SGOT) and Serum Glutamic Pyruvic Transaminase (SGPT) levels. This research used an experimental method with pooled sera as research material stored at -2°C to -4°C and -20°C for 8 weeks. Pooled sera were obtained from respondents who had no history of disease, were free from HIV, AIDS, and HBsAg. The research was conducted at the Reference Laboratory and Clinical Chemistry Laboratory Politeknik Kesehatan (Poltekkes) Kementerian Kesehatan, Surabaya. The results of the study were data analysis using linear regression test. The SGOT parameter at freezer temperature (-2 to -4°C) showed that the storage time had an effect of 90.97% with an error component of 9.03%. At freezer temperature (-20°C), the result of storage time has an effect of 78.71% with an error component of 21.29%. In the SGPT parameter with freezer temperature (-2 to -4°C), the result of storage time has an effect of 96.71% with an error component of 3.29%. At freezer temperature (-20°C), the result of storage time has an effect of 91.47% with an error component of 8.53%. The results of the SGOT and SGPT examinations did not exceed the limits of ±2SD and ±3SD The CV on the SGOT and SGPT examinations also did not exceed the CCV limits, which is to be stable.

A task-oriented calibration method for a 5-DOF hybrid machining robot based on the equivalent system

Calibration is a practical technique to improve robot accuracy. However, the pose error of the robot with fewer than six degrees of freedom (DOF) cannot be fully eliminated via calibration. The separation of compensable and uncompensable error components remains a controversial issue. This paper presents a novel task-oriented concept for calibration, which enables the uncompensable pose error to match the unconsidered pose error during the task. From the view of the equivalent system, the pose error is attributed to configuration-dependent motion errors of the actuated and virtual joints equivalently, where the virtual joint motion error is uncompensable and the virtual joint twist is determined according to the task. The calibration methodology of a 5-DOF hybrid machining robot is then described. Calibration results show that the maximum considered position/orientation errors can be reduced from 1.314 mm/0.101 deg to 0.118 mm/0.020 deg. Machining experiments also demonstrate the high-precision metal-cutting capacity after calibration.

Sensor of volume and angular position of the liquid mirror in tanks with axial symmetry at an indefinite orientation tanks in space

The issues of increasing the accuracy of volume sensors and the angular position of the liquid mirror in the fuel tanks of upper stages of spacecraft are covered. It is shown that the existing sensors of this type do not always meet the stringent requirements for their accuracy and reliability characteristics, especially under conditions of an indefi nite position of the liquid mirror. The principle of construction and design of a sensor for tanks with axial symmetry (spherical, cylindrical, lenticular, etc.) is proposed, which provides simultaneous measurement of the amount and angular position of the liquid mirror with high accuracy under the specifi ed conditions. This sensor consists of one linear and several ring sensing elements immersed in liquid and designed for the primary conversion of the immersion depth into an informative signal. The linear sensing element is installed along an axis passing through the center of the tank and the intake hole, and the ring elements are installed in a plane perpendicular to this axis, at a distance from each other determined by a given error. The operation of linear and ring elements can be based on a thermoresistive or capacitive principle. In the latter case, the sensitive elements may take the form of resonant circuits consisting of one linear and several ring capacitances, to which inductances are connected. Algorithms have been developed for converting the resonant frequencies of at least two sensitive elements into the desired parameters: the volume and angular position of the liquid in the tank. The estimation of the components of the total error of the sensor, due to various factors: the discreteness of the sensor design, the spread of the geometric dimensions of the tank and sensitive elements, as well as the own errors of the sensitive elements, was carried out. It is shown that the main factor limiting the accuracy of the sensors is the reduced errors of the sensitive elements: with the reduced error of these elements of 10 –3 , the similar errors of the sensor are no more than 2.2∙10 –2 in angle and 3.2∙10 –3 in volume. The proposed sensor can be used to measure the specifi ed parameters in objects characterized by an indefi nite position in space (spacecraft, sea vessels during rolling or heel).

Pyerrors: A python framework for error analysis of Monte Carlo data

We present the pyerrors python package for statistical error analysis of Monte Carlo data. Linear error propagation using automatic differentiation in an object oriented framework is combined with the Γ-method for a reliable estimation of autocorrelation times. Data from different sources can easily be combined, keeping the information on the origin of error components intact throughout the analysis. pyerrors can be smoothly integrated into the existing scientific python ecosystem which allows for efficient and compact analyses. Program summaryProgram Title: pyerrorsCPC Library link to program files:https://doi.org/10.17632/7ncw242ymh.1Developer's repository link:https://github.com/fjosw/pyerrorsLicensing provisions: MITProgramming language: pythonNature of problem: Data obtained from Markov chain Monte Carlo simulations exhibits autocorrelations. These become particularly severe when approaching the continuum limit of lattice discretized quantum field theories which becomes more and more relevant in modern day large scale simulations. In order to obtain reliable error estimates these autocorrelations have to be taken into account in complex data analysis workflows.Solution method: Linear error propagation in combination with automatic differentiation is implemented in a new python data type which keeps track of statistical errors across multiple sources of uncertainty. Operator overloading allows for a seamless integration into the scientific python ecosystem and into existing workflows. The Γ-method facilitates a controlled estimate of integrated autocorrelation times at any stage of the analysis and provides reliable error estimates without numerical overhead.

Co-simulation of human digital twins and wearable inertial sensors to analyse gait event estimation.

We propose a co-simulation framework comprising biomechanical human body models and wearable inertial sensor models to analyse gait events dynamically, depending on inertial sensor type, sensor positioning, and processing algorithms. A total of 960 inertial sensors were virtually attached to the lower extremities of a validated biomechanical model and shoe model. Walking of hemiparetic patients was simulated using motion capture data (kinematic simulation). Accelerations and angular velocities were synthesised according to the inertial sensor models. A comprehensive error analysis of detected gait events versus reference gait events of each simulated sensor position across all segments was performed. For gait event detection, we considered 1-, 2-, and 4-phase gait models. Results of hemiparetic patients showed superior gait event estimation performance for a sensor fusion of angular velocity and acceleration data with lower nMAEs (9%) across all sensor positions compared to error estimation with acceleration data only. Depending on algorithm choice and parameterisation, gait event detection performance increased up to 65%. Our results suggest that user personalisation of IMU placement should be pursued as a first priority for gait phase detection, while sensor position variation may be a secondary adaptation target. When comparing rotatory and translatory error components per body segment, larger interquartile ranges of rotatory errors were observed for all phase models i.e., repositioning the sensor around the body segment axis was more harmful than along the limb axis for gait phase detection. The proposed co-simulation framework is suitable for evaluating different sensor modalities, as well as gait event detection algorithms for different gait phase models. The results of our analysis open a new path for utilising biomechanical human digital twins in wearable system design and performance estimation before physical device prototypes are deployed.

An Optimization of Least-Square Harmonic Phasor Estimators in Presence of Multi-Interference and Harmonic Frequency Variance

The wide application of power electronic devices brings an increasing amount of undesired harmonic and interharmonic tones, and accurate harmonic phasor estimation under a complex signal input is an important task for smart grid applications. In this paper, an optimization of least-square dynamic harmonic phasor estimators, considering multi-interference and harmonic frequency variance, is proposed. A comprehensive error index (CEI) composed of the fundamental-leakage-led harmonic amplitude estimation error, harmonic mutual interference, out-of-band interference, and harmonic frequency deviation is employed. The largest CEI part of least-square algorithms using three different signal decomposition models is analyzed for the first time, and variables to reduce this error component are then introduced using singular value decomposition. With the CEI and defined variables, a minimum-error estimation of harmonic phasors under various interference and harmonic frequency change is discussed. Numerical tests are performed, and the test results show that after the proposed optimization is applied to least-square algorithms, the harmonic phasor estimation errors are considerably reduced, especially for low-order harmonics. We also show the possibility of choosing desired optimal phasor filter design by balancing the measurement accuracy and data latency. For example, when the window length is set to three nominal cycles, the proposed optimization can yield both good accuracy and fast measurement speed for estimating harmonic phasors under multi-interference and harmonic frequency variance.