A Steady-State Errors Correction Method for Eliminating Measurement Errors

This paper proposes a steady-state errors correction(SSEC)method for eliminating measurement errors.This method is based on the detections of error signal E(s)and output C(s)which generate an expected output R(s).In comparison with the conventional solutions which are based on detecting the expected output R(s)and output C(s)to obtain error signal E(s),the measurement errors are eliminated even the error might be at a significant level.Moreover,it is possible that the individual debugging by regulating the coefficient K for every member of the multiple objectives achieves the optimization of the open loop gain.Therefore,this simple method can be applied to the weak coupling and multiple objectives system,which is usually controlled by complex controller.The principle of eliminating measurement errors is derived analytically,and the advantages comparing with the conventional solutions are depicted.Based on the SSEC method analysis,an application of this method for an active power filter(APF)is investigated and the effectiveness and viability of the scheme are demonstrated through the simulation and experimental verifications.

Nonparametric Regression Estimation with Mixed Measurement Errors

We consider the estimation of nonparametric regression models with predictors being measured with a mixture of Berkson and classical errors. In practice, the Berkson error arises when the variable X of interest is unobservable and only a proxy of X can be measured while the inaccuracy related to the observation of the proxy causes an error of classical type. In this paper, we propose two nonparametric estimators of the regression function in the presence of either or both types of errors. We prove the asymptotic normality of our estimators and derive their rates of convergence. The finite-sample properties of the estimators are investigated through simulation studies.

WEIGHTED LASSO ESTIMATES FOR SPARSE LOGISTIC REGRESSION:NON-ASYMPTOTIC PROPERTIES WITH MEASUREMENT ERRORS

For high-dimensional models with a focus on classification performance,the?1-penalized logistic regression is becoming important and popular.However,the Lasso estimates could be problematic when penalties of different coefficients are all the same and not related to the data.We propose two types of weighted Lasso estimates,depending upon covariates determined by the Mc Diarmid inequality.Given sample size n and a dimension of covariates p,the finite sample behavior of our proposed method with a diverging number of predictors is illustrated by non-asymptotic oracle inequalities such as the?1-estimation error and the squared prediction error of the unknown parameters.We compare the performance of our method with that of former weighted estimates on simulated data,then apply it to do real data analysis.

A Combined Antenna Array Deployment with High Positioning Accuracy and Low Angular Measurement Error

In this paper,an antenna array composed of circular array and orthogonal linear array is proposed by using the design of long and short baseline“orthogonal linear array”and the circular array ambiguity resolution design of multi-group baseline clustering.The effectiveness of the antenna array in this paper is verified by sufficient simulation and experiment.After the system deviation correction work,it is found that in the L/S/C/X frequency bands,the ambiguity resolution probability is high,and the phase difference system error between each channel is basically the same.The angle measurement error is less than 0.5°,and the positioning error is less than 2.5 km.Notably,as the center frequency increases,calibration consistency improves,and the calibration frequency points become applicable over a wider frequency range.At a center frequency of 11.5 GHz,the calibration frequency point bandwidth extends to 1200 MHz.This combined antenna array deployment holds significant promise for a wide range of applications in contemporary wireless communication systems.

Online Capacitor Voltage Transformer Measurement Error State Evaluation Method Based on In-Phase Relationship and Abnormal Point Detection

The assessment of the measurement error status of online Capacitor Voltage Transformers (CVT) within the power grid is of profound significance to the equitable trade of electric energy and the secure operation of the power grid. This paper advances an online CVT error state evaluation method, anchored in the in-phase relationship and outlier detection. Initially, this method leverages the in-phase relationship to obviate the influence of primary side fluctuations in the grid on assessment accuracy. Subsequently, Principal Component Analysis (PCA) is employed to meticulously disentangle the error change information inherent in the CVT from the measured values and to compute statistics that delineate the error state. Finally, the Local Outlier Factor (LOF) is deployed to discern outliers in the statistics, with thresholds serving to appraise the CVT error state. Experimental results incontrovertibly demonstrate the efficacy of this method, showcasing its prowess in effecting online tracking of CVT error changes and conducting error state assessments. The discernible enhancements in reliability, accuracy, and sensitivity are manifest, with the assessment accuracy reaching an exemplary 0.01%.

Errors and Correction of Precipitation Measurements in China

In order to discover the range of various errors in Chinese precipitation measurements and seek a correction method, 30 precipitation evaluation stations were set up countrywide before 1993. All the stations are reference stations in China. To seek a correction method for wind-induced error, a precipitation correction instrument called the ＂horizontal precipitation gauge＂ was devised beforehand. Field intercomparison observations regarding 29,000 precipitation events have been conducted using one pit gauge, two elevated operational gauges and one horizontal gauge at the above 30 stations. The range of precipitation measurement errors in China is obtained by analysis of intercomparison measurement results. The distribution of random errors and systematic errors in precipitation measurements are studied in this paper. A correction method, especially for wind-induced errors, is developed. The results prove that a correlation of power function exists between the precipitation amount caught by the horizontal gauge and the absolute difference of observations implemented by the operational gauge and pit gauge. The correlation coefficient is 0.99. For operational observations, precipitation correction can be carried out only by parallel observation with a horizontal precipitation gauge. The precipitation accuracy after correction approaches that of the pit gauge. The correction method developed is simple and feasible.

Research of measurement errors caused by salt solution temperature drift in surface plasmon resonance sensors

Influence of temperature on measurement of surface plasmon resonance （SPR） sensor was investigated. Samples with various concentrations of NaCl were tested at different temperatures. It was shown that if the affection of temperature could be neglected, measurement precision of salt solution was 0.028 wt.-%. But measurement error of salinity caused by temperature was 0.53 wt.-% in average when the temperature drift was 1 ℃. To reduce the error, a double-cell SPR sensor with salt solution and distilled water flowing respectively and at the same temperature was implemented.

Objective Bayesian analysis for the accelerated degradation model usingWiener process with measurement errors

The Wiener process as a degradation model plays an important role in the degradation analysis.In this paper, we propose an objective Bayesian analysis for an acceleration degradation Wienermodel which is subjected to measurement errors. The Jeffreys prior and reference priors underdifferent group orderings are first derived, the propriety of the posteriors is then validated. It isshown that two of the reference priors can yield proper posteriors while the others cannot. A simulation study is carried out to investigate the frequentist performance of the approach comparedto the maximum likelihood method. Finally, the approach is applied to analyse a real data.

BLUP Estimation of Linear Mixed-effects Models with Measurement Errors and Its Applications to the Estimation of Small Areas

The linear mixed-effects model （LMM） is a very useful tool for analyzing cluster data. In practice, however, the exact values of the variables are often difficult to observe. In this paper, we consider the LMM with measurement errors in the covariates. The empirical BLUP estimator of the linear combination of the fixed and random effects and its approximate conditional MSE are derived. The application to the estimation of small area is provided. Simulation study shows good performance of the proposed estimators.

Measurement errors of ultrasonic velocity and attenuation due to nonparallelness of specimen faces

The measurement errors due to nonparallelness of specimen faces in the ultrasonic velocity and attenuation coefficient measured by the pulse reflection method in VHF range have been investigated theoretically, and the theoretical expressions for estimating these measurement errors are given. It has also been shown that, the attenuation coefficient error is depending on both the nonparallelness angle of specimen faces and the ultrasonic frequency, but the velocity error is only depending on the former. Furthermore, for pure silica glass specimen it is estimated that, in VHF range in order to insure that the attenuation coefficient and velocity errors due to nonparallelness of specimen faces are less than 10% and 0.01%, respectively, the nonparallelness angle of specimen faces must be less than 10 s and 40 s correspondingly.

STOCHASTIC APPROXIMATION UNDER CORRELATED MEASUREMENT ERRORS

In this paper the Kiefer-Wolfowitz (KW) procedure for searching the extremum of the regression function as well as the Robbins-Monro (RM) procedure for solving the regression equation are modified in order that they can be applied to the case when the measurement errors form an ARMA process. Simple conditions are given to guarantee their convergence to the extremum and the root of regression function respectively by using a new approach combining both the probabilistic method and the ordinary differential equation (ODE) method. The results given here are better than the well-known ones even if the measurement error is the martingale difference sequence.

Algorithms for automatic measurement of SIS-type hysteretic underdamped Josephson junction’s parameters by current-voltage characteristics

Some electrical parameters of the SIS-type hysteretic underdamped Josephson junction(JJ)can be measured by its current-voltage characteristics(IVCs).Currents and voltages at JJ are commensurate with the intrinsic noise level of measuring instruments.This leads to the need for multiple measurements with subsequent statistical processing.In this paper,the digital algorithms are proposed for the automatic measurement of the JJ parameters by IVC.These algorithms make it possible to implement multiple measurements and check these JJ parameters in an automatic mode with the required accuracy.The complete sufficient statistics are used to minimize the root-mean-square error of parameter measurement.A sequence of current pulses with slow rising and falling edges is used to drive JJ,and synchronous current and voltage readings at JJ are used to realize measurement algorithms.The algorithm performance is estimated through computer simulations.The significant advantage of the proposed algorithms is the independence from current source noise and intrinsic noise of current and voltage meters,as well as the simple implementation in automatic digital measuring systems.The proposed algorithms can be used to control JJ parameters during mass production of superconducting integrated circuits,which will improve the production efficiency and product quality.

Uncertainty analysis of forest carbon sink forecast with varying measurement errors:a data assimilation approach

Aims Accurate forecast of ecosystem states is critical for improving natural resourcemanagement and climate change mitigation.Assimilating observed data into models is an effective way to reduce uncertainties in ecological forecasting.However,influences ofmeasurement errors on parameter estimation and forecasted state changes have not been carefully examined.This study analyzed the parameter identifiability of a process-based ecosystem carbon cycle model,the sensitivity of parameter estimates and model forecasts to the magnitudes of measurement errors and the information contributions of the assimilated data to model forecasts with a data assimilation approach.Methods We applied a Markov Chain Monte Carlo method to assimilate eight biometric data sets into the Terrestrial ECOsystemmodel.The data were the observations of foliage biomass,wood biomass,fine root biomass,microbial biomass,litter fall,litter,soil carbon and soil respiration,collected at the Duke Forest free-air CO_(2)enrichment facilities from 1996 to 2005.Three levels ofmeasurement errorswere assigned to these data sets by halving and doubling their original standard deviations.Important Findings Results showed that only less than half of the 30 parameters could be constrained,though the observations were extensive and themodelwas relatively simple.Highermeasurement errors led to higher uncertainties in parameters estimates and forecasted carbon(C)pool sizes.The longterm predictions of the slow turnover pools were affected less by the measurement errors than those of fast turnover pools.Assimilated data contributed less information for the pools with long residence times in long-term forecasts.These results indicate the residence times of C pools played a key role in regulating propagation of errors from measurements to model forecasts in a data assimilation system.Improving the estimation of parameters of slowturnover C pools is the key to better forecast long-term ecosystem C dynamics.

Measurement errors on sediment concentration from traditional runoff collection tanks and its correction possibility

Runoff plots are widely used worldwide to monitor water and soil losses.Sediment concentration in runoff collection tank is measured by stirring-sampling procedure,but this method may produce high measurement error due to the uneven mixing of collected sediments with water and soil particle deposition.This study aimed to identify the relationship between actual and measured sediment concentrations,so as to estimate the systematic error of sediment concentration measurement from runoff collection tank by traditional stirring-sampling procedure and the possibility to eliminate it.Four major soils including black soil,silt loess,clay loess,and purple soil in China were used to determine the correlation between the measured and designed sediment concentrations in laboratory.Tested sediment concentration was 1,2,5,8,10,20,50,80,100,200,500,800,and 1000 kg/m^(3),and total sediment-laden water volume was 50 L and 100 L.Five samples were collected successively from collection tank for each treatment and their sediment concentrations were measured by conventional oven-drying method.The results showed that all the measured sediment concentration values were smaller than the designed ones,but both the measured and designed values were linearly correlated significantly with determination coefficients greater than 0.8,generally.In the whole tested concentration range,the systematical error was-0.19 to-319.95 kg/m^(3) and relative error was 0.30%-84.5% for the 4 tested soils and 2 total sediment-laden water volumes.These results indicated a necessity and possibility to correct conventional sediment concentration measurement value.The result is usable to assess and correct the measurement error of sediment concentrations from traditional runoff plot.

Generalized Profile LSE in Varying-Coefficient Partially Linear Models with Measurement Errors

This paper is concerned with the estimating problem of a semiparametric varying-coefficient partially linear errors-in-variables model Yi=Xτiβ＋Zτiα（Ui）＋εi , Wi=Xi＋ξi,i=1, · · · , n. Due to measurement errors, the usual profile least square estimator of the parametric component, local polynomial estimator of the nonparametric component and profile least squares based estimator of the error variance are biased and inconsistent. By taking the measurement errors into account we propose a generalized profile least squares estimator for the parametric component and show it is consistent and asymptotically normal. Correspondingly, the consistent estimation of the nonparametric component and error variance are proposed as well. These results may be used to make asymptotically valid statistical inferences. Some simulation studies are conducted to illustrate the finite sample performance of these proposed estimations.

Correction of measurement errors on sediment concentration sampled by stirring-sampling method from traditional runoff collection tanks

Stirring-sampling method is a widely adopted method to measure sediment concentrations in collection tanks of runoff plots,but with high systematic measurement errors.This research aimed to advance an approach for building correction equations to remove measurement errors in designed sediment concentration range.Experimental data of sediment measurement from the stirring-sampling method,with four representative soils,under the designed sediment concentrations(1,2,5,8,10,20,50,80,100,200,500,800,and 1000 kg/m^(3))were used to demonstrate the correction methodological process.Two correction methods(step-wise correction and universal correction)were suggested for the trial in this study based on the distribution of measurement errors.In the step-wise correction,the correction equations were made with a series of linear functions without intercept for the low concentration group(0-20 kg/m^(3)),a series of linear functions with intercept for the high(20-200 kg/m^(3))and extremely high(200-1000 kg/m^(3))concentration groups,consecutively.The correction equations were a series of power functions in the universal correction.For the step-wise correction,most of the relative errors of correction sediment concentrations were smaller than 15%and 10%under high and extremely high concentration groups,but the corrected accuracy was not good in the sediment concentration of 1,2,5 kg/m^(3)with the corrected relative errors of 0.20%-206.07%.For the universal correction,the corrected relative errors(0.19%-31.81%)of the four soils were low under the condition of extremely high sediment concentrations,but other corrected accuracies weren’t good with the corrected relative errors of 0.68%-1154.71%.The corrected accuracy of step-wise correction is higher than that of the universal correction,but the universal correction is more convenient.These results indicated that the correction equations could efficiently revise the measurement errors of the tested soils and that this method can be generalized to other soil types and was meaningful in monitoring soil erosion.

Effect of Measurement Error on the Multivariate CUSUM Control Chart for Compositional Data

Control charts(CCs)are one of the main tools in Statistical Process Control that have been widely adopted in manufacturing sectors as an effective strategy for malfunction detection throughout the previous decades.Measurement errors(M.E’s)are involved in the quality characteristic of interest,which can effect the CC’s performance.The authors explored the impact of a linearmodel with additive covariate M.E on the multivariate cumulative sum(CUSUM)CC for a specific kind of data known as compositional data(CoDa).The average run length(ARL)is used to assess the performance of the proposed chart.The results indicate that M.E’s significantly affects themultivariate CUSUM-CoDaCCs.The authors haveused theMarkov chainmethod to study the impact of different involved parameters using six different cases for the variance-covariance matrix(VCM)(i.e.,uncorrelated with equal variances,uncorrelated with unequal variances,positively correlated with equal variances,positively correlated with unequal variances,negatively correlatedwith equal variances and negatively correlated with unequal variances).The authors concluded that the error VCM has a negative impact on the performance of themultivariate CUSUM-CoDa CC,as the ARL increases with an increase in the value of the error VCM.The subgroup size m and powering operator b positively impact the proposed CC,as the ARL decreases with an increase in m or b.The number of variables p also has a negative impact on the performance of the proposed CC,as the values of ARL increase with an increase in p.For the implementation of the proposal,two illustrated examples have been reported formultivariate CUSUM-CoDaCCs inthe presence ofM.E’s.Onedealswith themanufacturingprocessof uncoated aspirin tablets,and the other is based on monitoring the machines involved in the muesli manufacturing process.

Positional Error Model of Line Segments with Modeling and Measuring Errors Using Brownian Bridge

Spatial linear features are often represented as a series of line segments joined by measured endpoints in surveying and geographic information science.There are not only the measuring errors of the endpoints but also the modeling errors between the line segments and the actual geographical features.This paper presents a Brownian bridge error model for line segments combining both the modeling and measuring errors.First,the Brownian bridge is used to establish the position distribution of the actual geographic feature represented by the line segment.Second,an error propagation model with the constraints of the measuring error distribution of the endpoints is proposed.Third,a comprehensive error band of the line segment is constructed,wherein both the modeling and measuring errors are contained.The proposed error model can be used to evaluate line segments’overall accuracy and trustability influenced by modeling and measuring errors,and provides a comprehensive quality indicator for the geospatial data.

Residual lifetime prediction model of nonlinear accelerated degradation data with measurement error

For the product degradation process with random effect (RE), measurement error (ME) and nonlinearity in step-stress accelerated degradation test (SSADT), the nonlinear Wiener based degradation model with RE and ME is built. An analytical approximation to the probability density function (PDF) of the product's lifetime is derived in a closed form. The process and data of SSADT are analyzed to obtain the relation model of the observed data under each accelerated stress. The likelihood function for the population-based observed data is constructed. The population-based model parameters and its random coefficient prior values are estimated. According to the newly observed data of the target product in SSADT, an analytical approximation to the PDF of its residual lifetime (RL) is derived in accordance with its individual degradation characteristics. The parameter updating method based on Bayesian inference is applied to obtain the posterior value of random coefficient of the RL model. A numerical example by simulation is analyzed to verify the accuracy and advantage of the proposed model.

UAV Velocity Measurement for Ground Moving Target

To satisfy the demand of measuring the velocity of ground moving target through unmanned aerial vehicle(UAV)electro-optical platform,two velocity measurement methods are proposed.Firstly,a velocity measurement method based on target localization is derived,using the position difference between two points with the advantages of easy deployment and realization.Then a mathematical model for measuring target velocity is built and described by 15 variables,i.e.UAV velocity,UAV attitude angular rate,camera direction angular rate and so on.Moreover,the causes of velocity measurement error are analyzed and a formula is derived for calculating the measurement error.Finally,the simulation results show that angular rate error has a strong influence on the velocity measurement accuracy,especially the UAV pitch angular rate error,roll angular rate error and the camera angular altitude rate error,thus indicating the direction for improving velocity measurement precision.