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Accelerated failure time models are appealing due to their intuitive interpretation. However, when covariates are subject to measurement errors, naive estimation becomes severely biased. To address this issue, the regression calibration (RC) approach is a widely applicable and effective method. Traditionally, the RC method requires a good predictor for the true covariate, which can be obtained through parametric distribution assumptions or validation datasets. Consequently, the performance of the estimator depends on the plausibility of these assumptions. In this work, we propose a novel method that utilizes error augmentation to duplicate covariates, facilitating nonparametric estimation. Our approach does not require a validation set or parametric distribution assumptions for the true covariate. Through simulation studies, we demonstrate that our approach is more robust and less impacted by heavy censoring rates compared to conventional analyses. Additionally, an analysis of a subset of a real dataset suggests that the conventional RC method may have a tendency to overcorrect the attenuation effect of measurement error. [ABSTRACT FROM AUTHOR]

Background: In the winter of 2022/2023, excess death estimates for Germany indicated a 10% elevation, which has led to questions about the significance of this increase in mortality. Given the inherent errors in demographic forecasting, the reliability of estimating a 10% deviation is questionable. This research addresses this issue by analyzing the error distribution in forecasts of weekly deaths. By deriving empirical prediction intervals, we provide a more accurate probabilistic study of weekly expected and excess deaths compared to the use of conventional parametric intervals. Methods: Using weekly death data from the Short-term Mortality Database (STMF) for 23 countries, we propose empirical prediction intervals based on the distribution of past out-of-sample forecasting errors for the study of weekly expected and excess deaths. Instead of relying on the suitability of parametric assumptions or the magnitude of errors over the fitting period, empirical prediction intervals reflect the intuitive notion that a forecast is only as precise as similar forecasts in the past turned out to be. We compare the probabilistic calibration of empirical skew-normal prediction intervals with conventional parametric prediction intervals from a negative-binomial GAM in an out-of-sample setting. Further, we use the empirical prediction intervals to quantify the probability of detecting 10% excess deaths in a given week, given pre-pandemic mortality trends. Results: The cross-country analysis shows that the empirical skew-normal prediction intervals are overall better calibrated than the conventional parametric prediction intervals. Further, the choice of prediction interval significantly affects the severity of an excess death estimate. The empirical prediction intervals reveal that the likelihood of exceeding a 10% threshold of excess deaths varies by season. Across the 23 countries studied, finding at least 10% weekly excess deaths in a single week during summer or winter is not very unusual under non-pandemic conditions. These results contrast sharply with those derived using a standard negative-binomial GAM. Conclusion: Our results highlight the importance of well-calibrated prediction intervals that account for the naturally occurring seasonal uncertainty in mortality forecasting. Empirical prediction intervals provide a better performing solution for estimating forecast uncertainty in the analyses of excess deaths compared to conventional parametric intervals. [ABSTRACT FROM AUTHOR]

Measurements are of paramount importance in industry and other areas of importance to society. They are used to determine the characteristics of processes and products, to control and regulate processes, to decide on the acceptable quality of products, etc. To ensure the quality of measurements, we have to calibrate measuring devices regularly. In our laboratory - the holder of the national length standard, we mainly calibrate high-precision standards from accredited laboratories. As the demands on the accuracy of measurements are constantly increasing, we are also forced to continuously improve the accuracy of our calibration procedures. This article presents the development of methods for calibrating the diameter of ring gauges, which represent an important standard for calibrating measuring instruments for measuring internal dimensions. The main objective of this development is to reduce the measurement uncertainty based on a scientific investigation of all influencing parameters. The presented study focuses in particular on the control and reduction of the influence of geometric anomalies of the calibrated rings on the measurement uncertainty during calibration. [ABSTRACT FROM AUTHOR]

We study the goodness-of-fit tests for checking the normality of the model errors under the additive distortion measurement error settings. Neither the response variable nor the covariates can be directly observed but are distorted in additive fashions by an observed confounding variable. The proposed test statistics is based on logarithmic transformed variables with residuals and a particular choice of the kth power covariance-based estimator. The proposed test statistics has three advantages. Firstly, the asymptotic null distribution of the test statistics are obtained with known asymptotic variance. Secondly, the test statistic tests are irrelevant to the model. Thirdly, the proposed test statistics automatically eliminate the additive distortion effects involved in the response and covariates. The simulation studies show the proposed test statistics can be used to check normality when the sample size is very large. A real example is analysed to illustrate its practical usage. [ABSTRACT FROM AUTHOR]

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This paper presents new method for traceability assurance of measurements performed using hybrid measuring systems built using one system that is based on tactile point measurement method (for example: coordinate measuring machine, articulated arm coordinate measuring machine, laser tracker system) and the second one that is based on optical field measurement method (for example: structured light scanners, digital image correlation systems). Within works described in this paper a series of tests aimed at determining task-specific errors for measurements performed using such composed systems were run. Measurement tasks for which such errors were determined include length measurements and measurements of form deviations (roundness, flatness, etc). Measurements were performed using material standards representing various shapes, dimensions and geometric relations. Measurements were run in different orientations and positions of the standards. Types of standards along with orientations and positions used were chosen basing on the guidelines of the ISO 10360 standard, parts 2, 5, 7, 8, 9, 10, 12, VDI/VDE 2634 and longtime experience of authors of this paper. At the end, results of performed measurements were checked for consistency with results of material standards calibration and values of task- specific maximum permissible errors were established. Guidelines for using developed method in other hybrid systems were also presented in the paper. [ABSTRACT FROM AUTHOR]

The calibration method is used in stratified random sampling in the presence of measurement error to achieve optimum strata weights for better precision. In this study we attempt to analyze the behaviour of calibration estimators with different types of distance measures in the presence of measurement error for the estimation of population mean under stratified random sampling. The proposed estimators are compared with the estimators in the absence of measurement error. A simulation study has been carried out to evaluate the proposed estimators. [ABSTRACT FROM AUTHOR]

We consider a parametric hypothesis test of the multiplicative distortion model with both a parametric global trend and a nonparametric local trend. In the model, neither the response variable nor the covariates can be directly observed, but are measured with multiplicative distortion measurement errors. Four calibration procedures with several estimation methods are used to construct the test statistics, namely, conditional mean calibration based test statistic, conditional absolute mean calibration based test statistic, conditional variance calibration based test statistic, and conditional absolute logarithmic calibration based test statistic. Asymptotic properties for these test statistics are established under the null hypothesis and alternative hypothesis. Monte Carlo simulation experiments are carried out to examine the performance of the proposed test statistics. A real example is analyzed to illustrate their practical usages. [ABSTRACT FROM AUTHOR]

In this article, we study a goodness of fit test for a multiplicative distortion model under a uniformly distributed but unobserved random variable. The unobservable variable is distorted in a multiplicative fashion by an observed confounding variable. The proposed k-th power test statistic is based on logarithmic transformed observations and a correlation coefficient-based estimator without distortion measurement errors. The proper choice of k is discussed through the empirical coverage probabilities. The asymptotic null distribution of the test statistics are obtained with known asymptotic variances. Next, we proposed the conditional mean calibrated test statistic when a variable is distorted in a multiplicative fashion. We conduct Monte Carlo simulation experiments to examine the performance of the proposed test statistics. [ABSTRACT FROM AUTHOR]

In survey research, it is commonly assumed that all the observations are measured accurately. However, in practice, this assumption is not achieved due to many reasons, so it causes measurement errors to be inevitably present in the sample estimation. This article addresses the problem of estimation of finite population mean under stratified random sampling in the presence of measurement errors. A calibration estimator is proposed for the sensitive variable by utilizing suitable calibration techniques, which can be applied to obtain the optimal strata weight. The calibration estimator not only incorporates the auxiliary information but also the ranks of the auxiliary variable. Expressions for bias and mean square error are derived up to first order of approximation. Simulation studies and real-life datasets are used to assess the performances of the proposed estimator by comparing them with the contemporary estimators in the presence and absence of measurement errors. The theoretical and empirical studies demonstrate that the proposed calibration estimator consistently outperforms classical mean, usual ratio, conventional difference, Khail randomized response estimators. [ABSTRACT FROM AUTHOR]

The digital transformation of metrology is one of the most active activities in the field of metrology at present, where the digital calibration certificate (DCC) being developed is the topic receiving the most concern in the current digital transformation. In practical industrial applications, the issue of storage carrier for the DCC plays a crucial role in its promotion and implementation. To address this issue, a DCC meta-model called DCC-Lite schema has been designed along with a corresponding processing method. This solution involves compressing and segmenting the DCC to make it suitable for storage using RFID tags. These RFID tags are affixed to the instruments and accompany them throughout their usage. Additionally, the DCC-RFID processing system has been developed to validate the effectiveness of the DCC meta-model and its corresponding processing method within a wireless temperature acquisition system. Experimental results demonstrate that the system successfully reads and writes the DCC stored within the RFID tag group. Furthermore, it enables automated parsing of the DCC calibration data by the machine and real-time compensation of measurement data to reduce measurement errors. [ABSTRACT FROM AUTHOR]

Zonal calibration algorithm is the most widely used method to extend the measurement range of five-hole probes. However, large measurement error will be aroused near the boundary between two neighboring zones and this is acknowledged as the inner boundary measurement problem of zonal calibration algorithm. To tackle this problem, a two-dimensional uniform flow model is developed in this paper to describe the relationship between pressure from holes and flow angles. Based on this model, a method to adjust the boundary between two neighboring zones automatically with respect to inlet flow conditions is developed. With this novel method, the data extrapolation of zonal calibration algorithm at measurement stations near the boundary between two neighboring zones is avoided, and the corresponding large measurement error is eliminated. According to the experimental data, maximum measurement error of total pressure and flow angle can reach 7.5% and 3.2°, and will be reduced to 0.89% and 0.12° by the novel method. Resultantly, the inner boundary measurement problem of zonal calibration algorithm is solved. Influences of several key parameters on the measurement accuracy of the novel method are investigated too, and criteria to adjust the boundary between two neighboring zones are given. Conclusions of this paper can be used to further improve the accuracy of five-hole probes in measuring large angle flows. [ABSTRACT FROM AUTHOR]

The present work deals with examining the effect of measurement errors on the design based statistical properties of the estimators of the population mean when the survey is encountered with some non-response. The technique of sub-sampling of non-respondents have been equipped with calibration techniques to handle the presence of non-response. Two kind of distance measures have been proposed and studied in detail to improve the calibration weights. The data on study as well as auxiliary variable has been assumed to be contaminated with correlated measurement errors. The specific properties of the estimators are derived under simple random sampling without replacement design. The proposed hybrid estimators are supported with numerical illustration incorporating simulation using specific population to show the applicability of proposed techniques practically. It is observed that the absolute relative bias of the estimators increase slightly with increase in error variance. Similarly, the precision of the estimators degrade with increase in error dispersion. Overall the proposed hybrid estimator with the chi-square type distance measure is observed to be remarkably efficient in comparison to the logarithmic type distance measure in presence of non-response and measurement errors. [ABSTRACT FROM AUTHOR]

This paper presents the design and validation of a high-precision angular vibration calibration system based on a laser vibrometer, aimed at meeting the high-precision requirements for measuring small angular vibrations. The system primarily consists of a self-driving angular vibration platform and a laser vibrometer. The platform is isolated from ground interference via an air-floating platform and uses a split-type motor to control the platform, generating specific angular vibrations. Detailed simulations of the platform's modal characteristics and the stability of the spring plates were conducted using the finite element analysis software ANSYS 11. Moreover, fundamental frequency testing and measurement accuracy testing were conducted on the system. Experimental results demonstrate that the system has a fundamental frequency of 2.69 Hz and a maximum measurement error of 0.00172″, confirming the system's effectiveness in dynamic characteristics, stability, and measurement accuracy. This research provides essential technical support for high-precision angular vibration control in spacecraft. [ABSTRACT FROM AUTHOR]

The Cohort Study of Mobile Phone Use and Health (COSMOS) has repeatedly collected self-reported and operator-recorded data on mobile phone use. Assessing health effects using self-reported information is prone to measurement error, but operator data were available prospectively for only part of the study population and did not cover past mobile phone use. To optimize the available data and reduce bias, we evaluated different statistical approaches for constructing mobile phone exposure histories within COSMOS. We evaluated and compared the performance of 4 regression calibration (RC) methods (simple, direct, inverse, and generalized additive model for location, shape, and scale), complete-case analysis, and multiple imputation in a simulation study with a binary health outcome. We used self-reported and operator-recorded mobile phone call data collected at baseline (2007-2012) from participants in Denmark, Finland, the Netherlands, Sweden, and the United Kingdom. Parameter estimates obtained using simple, direct, and inverse RC methods were associated with less bias and lower mean squared error than those obtained with complete-case analysis or multiple imputation. We showed that RC methods resulted in more accurate estimation of the relationship between mobile phone use and health outcomes by combining self-reported data with objective operator-recorded data available for a subset of participants. [ABSTRACT FROM AUTHOR]

Accurate on-orbit wavelength calibration of the spaceborne hyperspectral payload is the key to the quantitative analysis and application of observational data. Due to the high spectral resolution of general spaceborne hyperspectral greenhouse gas (GHG) detection instruments, the common Fraunhofer lines in the solar atmosphere can be used as a reference for on-orbit wavelength calibration. Based on the performances of a GHG detection instrument under development, this study simulated the instrument's solar-viewing measurement spectra and analyzed the main sources of errors in the on-orbit wavelength calibration method of the instrument using the solar Fraunhofer lines, including the Doppler shift correction error, the instrumental measurement error, and the peak-seek algorithm error. The calibration accuracy was independently calculated for 65 Fraunhofer lines within the spectral range of the instrument. The results show that the wavelength calibration accuracy is mainly affected by the asymmetry of the Fraunhofer lines and the random error associated with instrument measurement, and it can cause calibration errors of more than 1/10 of the spectral resolution at maximum. A total of 49 Fraunhofer lines that meet the requirements for calibration accuracy were screened based on the design parameters of the instrument. Due to the uncertainty of simulation, the results in this study have inherent limitations, but provide valuable insights for quantitatively analyzing the errors of the on-orbit wavelength calibration method using the Fraunhofer lines, evaluating the influence of instrumental parameters on the calibration accuracy, and enhancing the accuracy of on-orbit wavelength calibration for similar GHG detection payloads. [ABSTRACT FROM AUTHOR]

To study the symmetry and asymmetry of the model error under multiplicative distortion measurement errors setting, we propose a correlation coefficient-based measure between the distribution function and the root of density function. The unknown distribution function and density function are estimated from four kinds of residuals: the conditional mean calibration-based residuals, the conditional absolute mean calibration-based residuals, the conditional variance calibration-based residuals, and the conditional absolute logarithmic calibration-based residuals. We study the asymptotic results of the estimators of correlation coefficient-based measure under four calibrations. Next, we consider statistical inference of the correlation coefficient-based measure by using the empirical likelihood method. The empirical likelihood statistics are shown to be an asymptotically standard chi-squared distribution. Simulation studies demonstrate the performance of the proposed estimators and test statistics. A real example is analyzed to illustrate its practical usage. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

While interest in using wearable sensors to measure infant leg movement is increasing, attention should be paid to the characteristics of the sensors. Specifically, offset error in the measurement of gravitational acceleration (g) is common among commercially available sensors. In this brief report, we demonstrate how we measured the offset and other errors in three different off-the-shelf wearable sensors available to professionals and how they affected a threshold-based movement detection algorithm for the quantification of infant leg movement. We describe how to calibrate and correct for these offsets and how conducting this improves the reproducibility of results across sensors. [ABSTRACT FROM AUTHOR]

The data collected at Weigh-in-Motion (WIM) stations have many applications. Primarily, the data are used for pavement design, bridge design, freight studies, transportation planning, and enforcement. The WIM data are also used in mechanistic-empirical pavement design guide (Pavement-ME) for predicting performance. Highway agencies and the state department of transportation (DOTs) are the main users of WIM data. With a number of important applications, all WIM users desire to collect accurate loading data. This paper addresses three core issues related to WIM systems accuracy and calibration procedures, i.e., how to; (1) perform successful calibration of a WIM system by quantifying the effect of sample size (truck runs), speed, temperature, and truck type on measurement errors, (2) model gross vehicle weight (GVW) WIM errors as a function of individual axle errors [(single axle (SA) and two tandem axles (TA), (drive and trailer)], and (3) estimate WIM measurement errors using the long-term pavement performance (LTPP) and the ASTM protocols. The research objectives were accomplished by synthesizing and analyzing the WIM error data available in the LTPP database for bending plate (BP) and quartz piezo (QP) sensors. Successful WIM equipment calibration can eliminate systematic weights, speed, and axle spacing errors. The ASTM and the LTPP accuracy estimation methods agree; however, the methods should be compared when the sample size is small (10 or fewer truck runs). The representative pre- and post-calibration data can be collected accurately using one test truck with 12 or more runs at multiple speed points for QP and BP sensors. The developed models showed that the GVW errors could be accurately predicted using SA and two TA. The results also show that if GVW errors are within ASTM Type I tolerance, the SA and TA errors will likely be within acceptable limits. Therefore, calibrating a WIM site using GVW errors should continue. The suggested changes in current WIM procedures can significantly reduce time and resources for successful equipment calibration. [ABSTRACT FROM AUTHOR]

The global Pavement-mechanistic-empirical (ME) transfer functions have been calibrated using the long-term pavement performance (LTPP) pavement sections at the national level. These functions may need calibration for local conditions for reliable performance predictions. Several calibration studies have been conducted for local conditions, but limited research is available on the impact of calibration on pavement design. This study calibrates and validates the Pavement-ME transfer functions using version 2.6 for Michigan. A total of 256 flexible and 113 rigid sections have been selected based on the performance and availability of Pavement-ME inputs. The authors obtained the Pavement-ME inputs using construction records, plans, job mix formula (JMF), and material testing results. In contrast, the performance data was obtained from the Michigan Department of Transportation (MDOT) pavement management system (PMS) database. The calibrated models were then used for pavement design to estimate the impact of calibration and for comparison with AASHTO93 designs. The paper identifies the controlling distresses for pavement design. A total of 44 new flexible and rigid sections were designed based on the newly calibrated coefficients. The results show a significant improvement in performance prediction after local calibration. A comparison between AASHTO93 and Pavement-ME designs showed a reduction in hot-mix asphalt (HMA) and plain cement concrete (PCC) slab thicknesses for the latter approach. On average, the surface thicknesses using locally calibrated coefficients were thinner by 0.22 in. (0.56 cm) and 0.44 in. (1.12 cm) for flexible and rigid pavements, respectively. Critical design distresses for flexible pavements include bottom-up and thermal cracking. Conversely, transverse cracking and international roughness index (IRI) control the designs for rigid sections. Evaluating the impact of locally calibrated models on pavement designs is essential to obtaining practical and cost-effective design thickness. Practical Applications: This study provides a framework for the local calibration. Several factors affect the local calibration process, including the field performance data. The recorded performance data may have irregularities due to measurement errors, limitations in distress identification, and conversion to the Pavement-ME units. Therefore, the authors recommend analyzing the raw performance data and filtering it (if required) for practicality. Pavement design is one of the most crucial calibration process steps and is often not considered in practice. It is worth mentioning that pavements were designed based on calibrated models, and based on MDOT feedback, the calibration improved the designs. The authors recommend that the calibration results should not be based only on statistical parameters (SEE, bias, etc.) but also on practical engineering judgments. By understanding which distress types are most relevant to their region, agencies can develop mitigation and maintenance strategies leading to longer pavement service lives. For example, MDOT can mitigate the occurrence of thermal cracking, a critical distress, by using modified and improved binders. [ABSTRACT FROM AUTHOR]

Based on the polynomial theory, the error propagation characteristics of the widely used N-step discrete Fourier transform (N-DFT) phase-shift algorithm were analyzed via theoretical analysis, under the effect of Gamma distortion and phase detuning. The results showed that the N-DFT algorithm could not simultaneously suppress both types of error. A robust linear phase-shift (RLPS) algorithm was designed, the performance of the RLPS and 8-DFT algorithms in terms of spectral response, detuning robustness, and G S / N was briefly analysis by Manuel Servin method. The Simulation analysis and comparison of the results show that the RLPS algorithm could suppress both types of error simultaneously, which exhibited better stability and accuracy than N-DFT and exponential algorithms, particularly in gradient measurement stability, peak-to-valley (PV) and root-mean-square (RMS) error suppression. Moreover, a physical experiment apparatus was built to test unidirectionally inclined plane mirror and concave mirror using the RLPS, N-DFT, and exponential algorithms. The results showed that the RLPS algorithm could significantly improve the measurement stability and accuracy in the presence of detuning and without screen Gamma calibration. [ABSTRACT FROM AUTHOR]

The usage of liquefied hydrogen (LH 2) is growing fast as the EU aims to be climate-neutral by 2050. Therefore, reliable and consistent measurements of LH 2 amounts (as determined by flow meters) will become increasingly important for custody transfers. Reliability and consistency of measurements is established from calibration. Due to the lack of facilities being able to calibrate flow meters directly with LH 2 as calibration fluid, the question arises whether the measurement error of the calibration performed on a different fluid and different process conditions are representative for the errors when measuring LH 2. An on-site calibration of two turbine meters measuring LH 2 flow was performed. A Coriolis mass flow meter calibrated on water was used as a reference in conjunction with a dedicated flow meter model, which was validated by a directly SI-traceable calibration on liquefied natural gas. LH 2 flow rates were within 1000 kg/h and 3000 kg/h, which are relevant to hydrogen transport by LH 2 trailers. The analysis of the measurement data reveal errors on totalized mass ranging from 2.0 % to 2.9 % with a total calibration uncertainty of 1.3 % (k = 2), where the main uncertainty source was identified as the on-site density estimate necessary to convert the volume flow measurements into mass flow measurements. The results indicate the need for reliable and accurate temperature measurements (the latter allowing for an accurate density estimate), so that volume based and mass based amount measurements can be compared with smaller uncertainties. • Reliable measurements of liquefied hydrogen amounts will be crucial for custody transfer. • Direct calibration of flow meters on liquefied hydrogen is currently not possible. • Novel results of liquefied hydrogen flow measurement of an on-site calibration are presented. • The analysis reveals errors between 2.0 % and 2.9 % with an uncertainty of 1.3 % (coverage factor = 2). • The main uncertainty source was identified as the on-site density estimate. [ABSTRACT FROM AUTHOR]

This paper presents a cost-effective and efficient closed-loop calibration method to enhance the absolute positioning accuracy of industrial robots. The method utilizes an economical and highly accurate set of simple measurement devices, including a device mounted on the robot's end effector and a spherical constraint device positioned within the robot's workspace. A novel local area measurement method is employed for the spherical constraint device, effectively converting position errors into the errors in the sphere center position of the constraint device. Furthermore, the error model considers both kinematic parameter deviations of the robot itself as well as those of the measurement device, along with non-kinematic errors caused by link self-weight. The closed-loop calibration model relies on position constraints, enabling identification and compensation of all error parameters using Levenberg Marquardt method after substituting measured data. The effectiveness of this proposed method is demonstrated through simulation and experimentation. In simulations, average position error reduces from 8.249 mm to 0.8384 mm, while absolute mean difference in sphere center positions obtained using our measurement equipment decreases from 1.206 mm to 0.1027 mm. Significant reductions in both position error and difference in sphere center position are indicated after calibration. This proves that the absolute mean value of the sphere center position difference can be used as the basis for judging the size of the robot's end position error. Experimental results show that absolute mean difference in sphere center position decreases from 0.4319 mm to 0.02869 mm, leading to substantial improvement in overall positioning accuracy. • Calibration model incorporates both kinematic and non-kinematic deviation. • Local area measurement data effectively reflects the robot's end position error. • Closed-loop calibration method exhibits robustness in the presence of noise. [ABSTRACT FROM AUTHOR]

The automatic control of excavator operation trajectories is a pivotal technology for autonomous excavators, with the essential prerequisite being the real-time measurement of manipulator poses. Given the complexity of the operating environment, traditional sensor-based measurement methods face limitations, whereas visual measurement emerges as a promising technique. Accurately measuring excavator manipulator poses involves a crucial aspect: mapping the relationship between image information and poses. First, to address the significant errors in pose prediction encountered with machine learning techniques like artificial neural networks, this work introduces a mathematical model for mapping this relationship, referred to as the pose mapping mathematical model, which includes calibrating model parameters. Second, to address the sensitivity of initial values in the calibration process, we propose a residual-guided initialization algorithm. This algorithm aims to ensure that initial values closely approximate the ground truth values, thus preventing matrix singularity at the source and avoiding parameter estimation divergence. Third, to tackle challenges such as unstable lighting conditions and discrepancies between the dataset and the mathematical model, we introduce the random sample consensus-driven Levenberg–Marquardt parameter optimization algorithm to enhance parameter estimation accuracy. Experiments with static and dynamic online measurement demonstrate that our method reduces pose measurement errors compared to existing methods. This research lays a solid foundation for developing visual measurement techniques for excavators and automated manipulator control based on visual measurements, also serving as a valuable reference for research on mechanical arms. [ABSTRACT FROM AUTHOR]

Three-axis magnetic flux gate sensors are widely used in Chinese geomagnetic observatories, but due to their directional errors, it is necessary to study error correction methods to improve measurement accuracy. Firstly, the mechanism of directional errors produced by three-axis magnetic flux gate sensors is analyzed, followed by the development of measurement tools for conducting directional error measurement experiments on the high-precision three-axis magnetic flux gate sensors of the Chinese FGM-01 series. Experimental results show that correcting the Z-axis and D-axis directional errors is essential. The observation data after error correction, whether in terms of the standard deviation of its all-day baseline values or the relative difference magnitude with the reference instrument, significantly decrease, demonstrating the clear correction effect and proving the effectiveness of this correction method. [ABSTRACT FROM AUTHOR]

Summary: Where the response variable in a big dataset is consistent with the variable of interest for small area estimation, the big data by itself can provide the estimates for small areas. These estimates are often subject to the coverage and measurement error bias inherited from the big data. However, if a probability survey of the same variable of interest is available, the survey data can be used as a training dataset to develop an algorithm to impute for the data missed by the big data and adjust for measurement errors. In this paper, we outline a methodology for such imputations based on an k‐nearest neighbours (kNN) algorithm calibrated to an asymptotically design‐unbiased estimate of the national total, and illustrate the use of a training dataset to estimate the imputation bias and the "fixed‐k asymptotic" bootstrap to estimate the variance of the small area hybrid estimator. We illustrate the methodology of this paper using a public‐use dataset and use it to compare the accuracy and precision of our hybrid estimator with the Fay–Harriot (FH) estimator. Finally, we also examine numerically the accuracy and precision of the FH estimator when the auxiliary variables used in the linking models are subject to undercoverage errors. [ABSTRACT FROM AUTHOR]

The redshifted 21 cm line signal is a powerful probe of the cosmic dawn and the epoch of reionization. The global spectrum can potentially be detected with a single antenna and spectrometer. However, this measurement requires an extremely accurate calibration of the instrument to facilitate the separation of the 21 cm signal from the much brighter foregrounds and possible variations in the instrument response. Understanding how the measurement errors propagate in a realistic instrument system and affect system calibration is the focus of this work. We simulate a 21 cm global spectrum observation based on the noise wave calibration scheme. We focus on how measurement errors in reflection coefficients affect the noise temperature and how typical errors impact the recovery of the 21 cm signal, especially in the frequency domain. Results show that for our example set up, a typical vector network analyzer (VNA) measurement error in the magnitude of the reflection coefficients of the antenna, receiver, and open cable, which are 0.001, 0.001, and 0.002 (linear), respectively, would result in a 200 mK deviation on the detected signal, and a typical measurement error of 0.48 ° , 0.78 ° , or 0.15 ° in the respective phases would cause a 40 mK deviation. The VNA measurement error can greatly affect the result of a 21 cm global spectrum experiment using this calibration technique, and such a feature could be mistaken for or be combined with the 21 cm signal. [ABSTRACT FROM AUTHOR]

The operating environment greatly influences the accuracy of power metering devices, resulting in variations and inconsistencies in measurement results across different working situations. A calibration model for power metering devices is proposed in this study, considering a range of environmental circumstances. The first step involves investigating the environmental conditions that impact the accuracy of power metering devices. The mutual information approach is utilized to identify environmental disturbances affecting device accuracy. A machine learning-driven symmetry attention Long Short-Term Memory (LSTM) network addresses measurement errors, capitalizing on the network's symmetry data knowledge. Ultimately, the efficacy of the suggested approach is substantiated through the utilization of performance indicators, namely, Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE). The results show that the proposed method can effectively reduce the errors of the power measurement device in all quarters, and the error reduction effect is over 10% in the spring, which is better than other models, demonstrating exemplary performance in correcting the calibration errors of the power measurement device. [ABSTRACT FROM AUTHOR]

Commercial mobile robots are usually equipped with multiple depth sensors that can measure the point cloud information around the robot's environment. The installation process of these sensors contains assembly error and sensor measurement error, so it is necessary to calibrate each sensor to align the point cloud. In order to obtain the sensor calibration results of commercial robots under normal working conditions, this study proposes a fixture free multi depth sensor joint calibration method that can be deployed on low‐cost embedded computing units, which efficiently aligns the point clouds of each sensor. During the calibration process, the robot is placed in the center of three upright thin plates perpendicular to the ground. 2D LIDAR depicts high‐precision contours of the upright thin plates. In the calibration process of each depth sensor, the roll angle and pitch angle of the sensor point cloud are first calibrated to make it perpendicular to the ground, and then the yaw angle and position of the point cloud are calibrated to fit the high‐precision contour of the upright thin plate. The results show that this method can be deployed on low‐cost embedded computing units, with real‐time and accurate calibration results. The convergence of calibration results can be achieved through up to 5 iterations, and the average running time is less than 120 ms. This research achievement provides a reference for multi‐sensor calibration of commercial robots. [ABSTRACT FROM AUTHOR]

The research in this paper is related to the accuracy of the tilt compensation function of the GNSS/IMU receivers, which were examined in an open sky environment. The purpose of the paper is to point out to geodesists the conditions and limitations of using GNSS/IMU technology in precise measurements to not jeopardize the coordinate's accuracy. The environment in which the measurement is made affects the quality of the GNSS signal and can limit the visibility of the satellite, leading to larger errors in the measurement. In this experiment, the current performance of the GNSS/IMU receivers was checked. Seven GNSS/IMU receivers were used for the realization of the experiment. For six receivers the compensation angle was α = 30°, while for one receiver, the compensation angle was α = 45°. The standard uncertainty of GNSS coordinates of the antenna phase center has values less than 9 mm. The standard uncertainty of the IMU component has values less than 31 mm. The measurement uncertainty of the position of the used GNSS receivers is in the range of 18.1 mm to 31.7 mm. The limit values for the differences along the coordinate axes x and y were determined, and their values are from 26 mm to 44 mm. In the conducted experiment, it was confirmed that three GNSS/IMU receivers have a "Satisfactory" result. The results show that GNSS/IMU measurements with a slope greater than 30° significantly affect the accuracy and reliability of GNSS/IMU technology. A slope greater than 45° has a deviation along the coordinate axes of 121.3 mm. The conducted research is particularly important for geodetic works that require high positioning performance. The testing method of the GNSS/IMU receiver presented in this paper can help its users to make correct conclusions regarding the coordinate accuracy of the measured point of interest. [ABSTRACT FROM AUTHOR]

To improve the measuring accuracy of circular encoders in special applications, self-calibration of the circular encoder is necessary. The commonly used self-calibration method, namely the Equal Division Average (EDA) method, requires a large number of reading heads and cannot be used when the structural space is limited. In this paper, a self-calibration method for a circular encoder based on two reading heads with adjustable positions (TRAP) is proposed. This TRAP method uses two reading heads to simulate multiple reading heads, which can be used to achieve self-calibration of circular encoders in limited space. This paper investigates the principle of simulating multiple reading heads with two reading heads, designs and builds an experimental system, and obtains and analyzes experimental data. The experimental results show that the peak-valley value of the angle measurement error is reduced from 252.41″ to 18.82″ after self-calibration with the TRAP method, and the repeatability of multiple self-calibration experimental results is less than 0.75″. The TRAP method breaks through the limitation of the number of reading heads that can be installed during the self-calibration of the circular encoder and can effectively suppress the angle measurement error of the circular encoder. [ABSTRACT FROM AUTHOR]

Laser trackers are instruments used to measure the three-dimensional coordinates of objects with high precision. It is necessary to study calibration methods to identify geometric errors of laser trackers so as to compensate for errors and improve measurement accuracy. Among the offsets, tilts, and eccentricity errors in the system, the transit tilt and offset errors play important roles and have an essential effect on the measurement accuracy, which need to be calibrated and compensated for. Current methods for detecting geometric errors between the transit and standing axes are complex and time-consuming. In this paper, a fast and novel calibration method is proposed, which can be easily operated with high precision. Two test rods are coaxially mounted on the ends of the transit axis to extend the hidden transit axis. Then, a telecentric measurement system is used to record the projection images of the test rods and identify the position of the transit axis. The transit offset and tilt errors were thus obtained by comparing the central axis positions of the two test rods before and after the standing axis rotated 180 degrees. Moreover, a numerical analysis method was proposed based on the least square circle fitting method to calibrate the installation eccentricity errors of the test rods. Experimental results verify that the measurement accuracy of the laser tracker can be improved after error compensation using the calibrated transit offset and tilt errors. The measurement error of the laser tracker can be reduced from 161 µm to about 73 µm after compensation at a distance of 5 m, while the error can be decreased from 143 µm to about 108 µm at a distance of 10 m. [ABSTRACT FROM AUTHOR]

The road agencies collect and submit weigh-in-motion (WIM) data to the Federal Highway Administration as part of their traffic monitoring program. Therefore, the WIM data should be precise and accurate. One way to evaluate WIM measurement errors is by using the test truck data collected immediately before and after equipment calibration. The limitation of this approach is that the data represent a snapshot in time and may not represent a long-term WIM site performance. This paper presents an approach for estimating WIM system accuracy based on axle load spectra attributes (normalized axle load spectra (NALS) shape factors). This alternative approach allows for characterizing temporal changes in WIM data consistency. The WIM error data collected before and after calibration were related to Class 9 NALS shape factors in the proposed methodology. This paper aims to determine WIM system errors based on axle loading without physically performing WIM equipment performance validation using test trucks. The presented methodology can be used to estimate systematic errors (drift) in the WIM system at any point in time after the equipment calibration. This approach can help highway agencies select optimum timings for routine maintenance and calibration of WIM equipment without compromising its accuracy. The results show that the WIM accuracy for the single axle (SA) and tandem axle (TA) can be estimated with SA and TA NALS shape factors with an acceptable degree of error for bending plate to quartz piezo sensors. Examples are included to demonstrate the application and significance of the developed models. [ABSTRACT FROM AUTHOR]

High-precision temperature control of large-area blackbodies has a pivotal role in temperature calibration and thermal imaging correction. Meanwhile, it is necessary to correct the temperature difference between the radiating (surface of use) and back surfaces (where the temperature sensor is installed) of the blackbody during the testing phase. Moreover, large-area blackbodies are usually composed of multiple temperature control channels, and manual correction in this scenario is error-prone and inefficient. At present, there is no method that can achieve temperature-automated calibration for a large-area blackbody radiation source. Therefore, this article is dedicated to achieving temperature-automated calibration for a large-area blackbody radiation source. First, utilizing two calibrated infrared thermometers, the optimal temperature measurement location was determined using a focusing algorithm. Then, a three-axis movement system was used to obtain the true temperature at the same measurement location on a large-area blackbody surface from different channels. This temperature was subtracted from the blackbody's back surface. The temperature difference was calculated employing a weighted algorithm to derive the parameters for calibration. Finally, regarding experimental verification, the consistency error of the temperature measurement point was reduced by 85.4%, the temperature uniformity of the surface source was improved by 40.4%, and the average temperature measurement deviation decreased by 43.8%. In addition, this system demonstrated the characteristics of strong environmental adaptability that was able to perform temperature calibration under the working conditions of a blackbody surface temperature from 100 K to 573 K, which decreased the calibration time by 9.82 times. [ABSTRACT FROM AUTHOR]

Industrial robots are important components in the production and manufacturing industry. As a core component of the industrial robot, the industrial robot reducer plays a crucial role in the performance of the entire industrial robot. The error analysis and accuracy traceability of the industrial robot reducer testing instrument are of great significance in improving the quality of the precision reducer. Therefore, it is essential to calibrate the dynamic torsional moment measurement error of the instrument. The features of the dynamic torsional moment measurement error are analyzed in this paper. Based on these features, a new dynamic torsional moment measurement error calibration method is proposed based on the Bisquare curve fitting–improved Bayes particle swarm optimization–nonlinear echo state network (BCF–IBPSO–NESN) algorithm. The proposed method focuses on calibrating the dynamic torsional moment measurement error of the industrial robot reducers in real time. The experimental results show that the dynamic torsional moment measurement error of the input side torsional moment measurement module and the output side torsional moment measurement module can be reduced to ±0.05 Nm and ±1 Nm, respectively. The contribution of this paper is that the method calibrates the dynamic torsional moment measurement error. It supplies a guideline for calibrating the dynamic torsional moment measurement error of the instrument under any load. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a parametric hypothesis test of the multiplicative distortion model under the exponentially distributed but unobserved random variable. The unobservable variable is distorted in a multiplicative fashion by an observed confounding variable. Firstly, some new test statistics are proposed to checking the exponential distribution assumption without distortion effects. Next, we proposed several test statistics when the variable is distorted in the multiplicative fashion. For the latter, the proposed test statistics automatically eliminate the distortion effects involved in the unobserved variable. The proposed test statistics with or without distortions are all asymptotical free, and the asymptotic null distribution of the test statistics are obtained with known asymptotic variances. We conduct Monte Carlo simulation experiments to examine the performance of the proposed test statistics. These methods are applied to analyze four real datasets for illustrations. [ABSTRACT FROM AUTHOR]

Control rod calibration experiment results for the Oregon State TRIGA® Reactor (OSTR) immediately following LEU conversion in 2008, and MCNP® 5 predicted rod worths from the 2008 LEU Conversion Safety Analysis Report (CSAR) are discussed. The reactivity worth of the four OSTR control rods is measured using the rod-pull method. Reactor power and period measurements in this method rely on the fission chamber power detector on the north side of the reflector. It is proposed that the location of the fission chamber and the neutron flux distribution in the core may result in an inaccurate reactor period measurement due to the asymmetry of the neutron flux distribution in the OSTR core. The asymmetry of the flux is believed to be more pronounced during super-criticality, resulting in errors in the time-of-power-rise measurements. As a result, control rod calibration experiments may under-predict or over-predict the reactivity worth of certain control rods. A time-independent Monte–Carlo method for the quantification of these effects is presented. Thermal flux maps at the core axial mid-plane are obtained from the model to inform discrepancies between predicted and observed results. [ABSTRACT FROM AUTHOR]

Measurements collected from ground monitoring stations have gained popularity as a valuable data source for calibrating numerical models and correcting model errors through data assimilation. Both model calibration and assimilation are driven by the penalty quantified by simulation-minus-observations. However, the penal forces are challenged by the existence of a spatial scale disparity between model simulations and observations. The Chemical Transport Models (CTMs) allow the division of the atmosphere into grid cells, yet their spatial resolution may not align with the limited range of in-situ measurements, particularly for short-lived air pollutants. Within a broad grid pattern, air pollutant concentrations can exhibit significant heterogeneity due to their rapid generation and dissipation. Ground observations with traditional methods (including nearest search and grid mean) are less representative when compared to model simulations. This study develops a new land-use-based representative (LUBR) observational operator to generate spatially representative gridded observation for model calibration and evaluation. It incorporates high-resolution urban-rural land use data to address intra-grid variability. The LUBR operator is validated to consistently provide insights that align with satellite OMI measurements. It is an effective solution to accurately quantify these spatial scale mismatches and further resolve them via assimilation. Model calibrations with 2015-2017 NO2 measurement in China demonstrates biases and errors differed substantially when the LUBR and other operator are used, respectively. The results highlight the importance of considering fine-scale urban-rural differences when comparing models and observations, especially for short-lived pollutants like NO2. [ABSTRACT FROM AUTHOR]

The article examines the moment and compositional approaches to solving the measurement problem of calibration. The use of the moment approach in solving a standard example problem of thermometer calibration is considered. In this work, this problem is solved under the compositional approach, yielding more accurate and better results as compared to the moment approach. This fact is consistent with the accuracy assessment of solutions to measurement problems performed back in 2001 using the compositional approach (more rigorous than the moment approach): in the problem of measuring instrument calibration, the moment approach fails to fully take into account the inadequacy of functional models, overestimates the accuracy, and fails to obtain nonlinear models of optimal complexity. In order to solve the measurement problem under the compositional approach, the present work used the MMI-calibration 3.0 program, which provides a means to factor in the inadequacy errors of mathematical models of calibration functions and to obtain tolerance intervals for a given confidence level. Among polynomials up to and including degree nine, a three-parameter model of optimal complexity was obtained, with an average modulus of inadequacy error of 0.002745℃ and a tolerance interval of [−0.00828; 0.00761] at a confidence level of 0.95. Under the compositional approach, the average modulus of inadequacy error and kappa test used to find the optimal complexity model were compared. The compositional approach is shown to be rigorous in describing the solution of the calibration problem without simplifications and to avoid overestimation of accuracy; therefore, it can serve as an exemplary approach provided the MMI-calibration 3.0 program is applied. The combined use of the criteria of minimum average modulus of inadequacy error and maximum kappa test constitutes a necessary and sufficient condition for identifying a model of optimal complexity in the class of polynomials of degree n. [ABSTRACT FROM AUTHOR]

Division of time polarimeter (DoTP) is one of the popular imaging instruments in several applications because of its simple configuration and accurate performance. However, calibration of the optical axis of the used polarizer is also the premise of an accurate polarimeter. In this paper, a novel on-line and accurate method is proposed to calibrate the transmission angle of the polarizer using a Wollaston prism. The Wollaston prism splits the incident light into two light beams with orthogonal polarization directions, which are vertical and parallel with the beams plane, respectively. Then these two beams pass through the candidate polarizer. The detected light intensity can be adjusted by rotating the polarizer, whose position is marked by a digital encoder. The angle of optical axis of the polarizer relative to the line of points of two light beams can be solved by a series of light intensities. Finally, the optical axis of the polarizer is calibrated on-line, and the state of polarization of incident light can be measured accurately. Numerical simulation and experiments have validated the feasibility of the proposed on-line calibration method. The experimental results show that the calibration accuracy is about 0.0106° with a maximum polarization measurement error of 3.7 × 10–4. In general, the proposed calibration method is very fast, on-line, accurate, and would be a good reference for polarization imaging and polarization calibration. [ABSTRACT FROM AUTHOR]

This paper considers linear regression models when neither the response variable nor the covariates can be directly observed, but are measured with multiplicative distortion measurement errors. We propose new identifiability conditions for the distortion functions via the varying coefficient models, then moment‐based estimators of parameters in the model are proposed by using the estimated varying coefficient functions. This method does not require the independence condition between the confounding variables and the unobserved response and variables. We establish the connections among the varying coefficient based estimators, the conditional mean calibration and the conditional absolute mean calibration. We study the asymptotic results of these proposed estimators, and discuss their asymptotic efficiencies. Lastly, we make some comparisons among the proposed estimators through the simulation. These methods are applied to analyze a real dataset for an illustration. [ABSTRACT FROM AUTHOR]

Rationale: Stable isotope analysis of O2 is a valuable tool to identify O2‐consuming processes in the environment; however, reference materials for O2 isotope analysis are lacking. Consequently, a one‐point calibration with O2 from ambient air is often applied, which can lead to substantial measurement uncertainties. Our goals were to develop a simple multipoint isotope‐ratio calibration approach and to determine measurement errors of δ18O and δ17O values of O2 associated with a one‐point calibration. Methods: We produced O2 photosynthetically with extracted spinach thylakoids from source waters with δ18O values of −56‰ to +95‰ and δ17O values of −30‰ to +46‰. Photosynthesis was chosen because this process does not cause isotopic fractionation, so that the O isotopic composition of the produced O2 will be identical to that of the source water. The δ18O and δ17O values of the produced O2 were measured by gas chromatography coupled with isotope‐ratio mass spectrometry (GC/IRMS), applying a common one‐point calibration. Results: Linear regressions between δ18O or δ17O values of the produced O2 and those of the corresponding source waters resulted in slopes of 0.99 ± 0.01 and 0.92 ± 0.10, respectively. In the tested δ range, a one‐point calibration thus introduced maximum errors of 0.8‰ and 3.3‰ for δ18O and δ17O, respectively. Triple oxygen isotopic measurements of O2 during consumption by Fe2+ resulted in a δ18O–δ17O relationship (λ) of 0.49 ± 0.01 without δ scale correction, slightly lower than expected for mass‐dependent O isotopic fractionation. Conclusions: No significant bias is introduced on the δ18O scale when applying a one‐point calibration with O2 from ambient air during O2 isotope analysis. Both O2 formation and consumption experiments, however, indicate a δ17O scale compression. Consequently, δ17O values cannot be measured accurately by GC/IRMS with a one‐point calibration without determining the δ17O scale correction factor, e.g. with the O2 formation experiments described here. [ABSTRACT FROM AUTHOR]

This paper starts with an overview of the main principles used for pressure measurements, focusing on their usage in industrial applications' domains. Then, the importance of calibration procedures, namely, static and dynamic calibration of pressure sensors, is analyzed. Regarding calibration, it is important to note that there are several applications where the pressure signals to be measured can have large variations in short periods of time. In industrial applications, particularly in continuous production processes, generally, dynamic pressure measurements are less common; however, they are still required in several cases, such as control loops that are very sensitive to pressure variations, even if the frequencies of those variations are in the range of a few tens of hertz, or even lower. The last part of the paper presents the hardware and software of a flexible and low-cost static and dynamic pressure calibrator that also presents the capability to generate arbitrary waveform pressure signals for calibration and testing purposes. The proposed calibrator also includes the following advantages: remote pressure sensing capabilities that can be used to minimize calibration errors, such as those associated with capillary effects and pressure leakages; portability; and low cost. The paper ends with some experimental results obtained with the proposed calibrator. [ABSTRACT FROM AUTHOR]

We consider partial linear regression models when all the variables are measured with additive distortion measurement errors. To eliminate the effect caused by the distortion, we propose the conditional mean calibration to obtain calibrated variables. A profile least squares estimator for the parameter is obtained, associated with its normal approximation based and empirical likelihood based confidence intervals. For the hypothesis testing on parameters, a restricted estimator under the null hypothesis and a test statistic are proposed. A smoothly clipped absolute deviation penalty is employed to select the relevant variables. The resulting penalized estimators are shown to be asymptotically normal and have the oracle property. Lastly, a score-type test statistic is then proposed for checking the validity of partial linear models. Simulation studies demonstrate the performance of our proposed procedure and a real example is analyzed as illustrate its practical usage. [ABSTRACT FROM AUTHOR]

We consider the average derivation estimation when neither the response variable nor the covariates can be directly observed, but are measured with multiplicative distortion measurement errors. Three calibration procedures with several estimation methods are used to estimate the average derivation, namely, conditional mean calibration, conditional absolute mean calibration and conditional variance calibration. The asymptotic properties for the estimators are established. Monte Carlo simulation experiments are conducted to examine the performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

Robust and effective fruit detection and localization is essential for robotic harvesting systems. While extensive research efforts have been devoted to improving fruit detection, less emphasis has been placed on the fruit localization aspect, which is a crucial yet challenging task due to limited depth accuracy from existing sensor measurements in the natural orchard environment with variable lighting conditions and foliage/branch occlusions. In this paper, we present the system design and calibration of an Active LAser-Camera Scanner (ALACS), a novel perception module for robust and high-precision fruit localization. The hardware of the ALACS mainly consists of a red line laser, an RGB camera, and a linear motion slide, which are seamlessly integrated into an active scanning scheme where a dynamic-targeting laser-triangulation principle is employed. A high-fidelity extrinsic model is developed to pair the laser illumination and the RGB camera, enabling precise depth computation when the target is captured by both sensors. A random sample consensus-based robust calibration scheme is then designed to calibrate the model parameters based on collected data. Comprehensive evaluations are conducted to validate the system model and calibration scheme. The results show that the proposed calibration method can detect and remove data outliers to achieve robust parameter computation, and the calibrated ALACS system is able to achieve high-precision localization with the maximum depth measurement error being less than 4 mm at distance ranging from 0.6 to 1.2 m. [ABSTRACT FROM AUTHOR]

A bias current in the power system will cause saturation of the measuring current transformer (CT), leading to an increase in measurement error. Therefore, in this paper, we first conducted measurements of the direct current component in a 10 kV distribution system. Subsequently, a reverse extraction method for the CT distorted current under direct current bias conditions based on Random Forest Classification (RFC) and Long Short-Term Memory (LSTM) was proposed. This method involves two stages for the reverse extraction of CT distorted currents under direct current bias conditions. In the offline stage, data samples were generated by changing the operating environment of the CT. The RFC classification algorithm was used to divide the saturation levels of the CT, and for each sub-class, Particle Swarm Optimization–Long Short-Term Memory Network (PSO-LSTM) models were trained to establish the mapping relationship between the secondary distorted current and the primary current fundamental component. In the online stage, the saturated data segments were extracted from the secondary current waveform using wavelet transform, and these segments were input into the offline model for current reverse extraction. The simulation results show that the proposed method exhibited strong robustness under various CT conditions, and achieved high reconstruction accuracy for the primary current. [ABSTRACT FROM AUTHOR]