Drift Error Research Articles

Use of axle load spectra (ALS) for estimating calibration drift in weigh-in-motion (WIM) systems

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.

The advance of magnetic diagnostics system in support of EAST long-pulsed operation

In EAST long-pulsed discharge (hundreds of seconds), electric magnetic diagnosis (EMD) is very important, since EMD not only monitors tokamak security status but also provides accurate measurement accuracy for reconstruction of the plasma boundary. To avoid current measurement drift, a fiber optic current sensor, based on the Faraday effect, is developed and used for poloidal and plasma current feedback control for the first time, relative current measurement accuracy is within 0.5%. To ensure plasma boundary control accuracy, a detailed set of magnetic measurement calibration methods is developed before the plasma discharge. The maximum relative error is less than 1%, the corresponding control accuracy is within 1 cm. To minimize integrator drift error, a long-pulse integrator test is essential, the corresponding drift error needs to be subtracted in plasma control system. Besides, the saddle coil and Mirnov coil not only help to detect MHD issues, but are also utilized for plasma disruption prediction during the long-pulse discharge.

A novel uncertainty evaluation method based on the particle filter and beta distribution for data with unknown distribution.

Uncertainty evaluation for unknown distribution data is a key problem to be solved in uncertainty evaluation theory. To evaluate the measurement uncertainty of data with unknown distributions, a novel uncertainty evaluation method based on the particle filter (PF) and beta distribution is proposed in this paper. A beta distribution with wide adaptability was adopted as the distribution type of measurement results, the parameters of the beta distribution were taken as the parameters to be estimated, and a state-space model was established. The PF method, suitable for non-Gaussian data, was utilized to obtain the estimates of the parameters of the beta distribution according to the measurement results. Finally, the best estimates of the measurement results and their uncertainty were calculated using the beta distribution parameters. Simulation results show that the proposed method is adaptive to accurately evaluate the measurement uncertainties of data, especially for non-Gaussian distribution data or asymmetrically distributed data. Multiple evaluation results show that the method has good robustness. The experimental results for the drift errors of a laser interferometer show that the uncertainty result of the proposed method is consistent with the Monte Carlo method. This method is suitable for a variety of distribution types that can be characterized through beta distribution and can solve the optimal estimation and uncertainty evaluation of most measurement results with unknown distribution types.

Amplitude modulated feed-forward thermal drift compensation for linear and nonlinear current sensors

The linear and nonlinear temperature responses restrict the application of Hall current sensors operating in thermal power plants and industries. The rise in temperature of electron device-based measurement causes a significant error, leading to undesirable consequences for plant operation and relay coordination. This paper investigates four Hall current sensor types with linear and nonlinear temperature responses. The Hall current sensor, which receives the magnetic excitation from the permanent magnet, exhibits a linear temperature response, and the wire-wound design exhibits a nonlinear temperature response in the temperature range of 306–376 K. The solution scheme with amplitude modulation and thermal sensor integration with interdigitated electrode design having graphene and ZnO–KMnO4 compounds as the dielectric is also proposed. The use of amplitude modulation achieves input frequency immunity with a 0.03% K−1 improvement in the temperature response of the capacitive thermal sensor. Experimental observations confirm the validity of the thermal drift compensation scheme with a 20%–99% reduction of thermal drift error with a suitable choice of a thermal sensor.

An Efficient Online Loop Closure Detection System With Local Spatial Co-Occurrence Information

As a vital component in simultaneous localization and mapping techniques, appearance-based loop closure detection (LCD) plays important roles in bounding the long-term drift errors. In this paper, an online LCD system based on the mutual co-occurrence information among visual features is proposed. First, a feature tracker module is designed to generate distinctive visual words, exploiting tracked words tool to improve efficiency. Then an incrementally built vocabulary is organized by a hierarchical navigable small world graph, where the visual words are indexed. To merge a homologous word into the existing one, the vocabulary applies an improved high dimensional online clustering method, which regards individual cluster as a normal distribution form. At the query phase, a list of candidate frames is located due to the co-occurrence constraint. Ultimately, the loop closure is specified by passing the temporal and similarity check, which avoids the memory consumption of historic image data. Validation tests based on public datasets and experimental sequence demonstrate the merit of low running time and memory cost, while the high-precision performance is retained in the system.

IMU/UWB Fusion Method Using a Complementary Filter and a Kalman Filter for Hybrid Upper Limb Motion Estimation.

Motion capture systems have enormously benefited the research into human-computer interaction in the aerospace field. Given the high cost and susceptibility to lighting conditions of optical motion capture systems, as well as considering the drift in IMU sensors, this paper utilizes a fusion approach with low-cost wearable sensors for hybrid upper limb motion tracking. We propose a novel algorithm that combines the fourth-order Runge-Kutta (RK4) Madgwick complementary orientation filter and the Kalman filter for motion estimation through the data fusion of an inertial measurement unit (IMU) and an ultrawideband (UWB). The Madgwick RK4 orientation filter is used to compensate gyroscope drift through the optimal fusion of a magnetic, angular rate, and gravity (MARG) system, without requiring knowledge of noise distribution for implementation. Then, considering the error distribution provided by the UWB system, we employ a Kalman filter to estimate and fuse the UWB measurements to further reduce the drift error. Adopting the cube distribution of four anchors, the drift-free position obtained by the UWB localization Kalman filter is used to fuse the position calculated by IMU. The proposed algorithm has been tested by various movements and has demonstrated an average decrease in the RMSE of 1.2 cm from the IMU method to IMU/UWB fusion method. The experimental results represent the high feasibility and stability of our proposed algorithm for accurately tracking the movements of human upper limbs.

Wavelet-ARMA-Based Short-Term Drift Calibration of IMU Position on Human Lower Limbs

Position calibration in the inertial motion capture (Mocap) system is a crux to guarantee the correct calculation of human posture. Due to muscle movement and clothes slippage during motion, the position of inertial measurement units (IMUs) installed on the human body generates displacements. Aiming at the drift error caused by IMUs’ position shift in the short term, this paper proposes a wavelet-ARMA prediction model. Three different wavelet bases, Haar, Daubechies, and Coiflet, are selected to combine with the ARMA model to predict angle sequences, among which the Db4 wavelet-ARMA model with the best prediction performance, choosing the angle sequence predicted by the model and the measurement sequence to set up an error model, and using the Gauss-Newton (GN) and the dynamic weight particle swarm optimization (DWPSO) algorithms to realize IMUs’ position calibration. The experimental results show that the wavelet-ARMA model has better prediction performance than the ARMA, BP, and LSTM models with the value of the calibrated RMSE decreasing. The results confirm that the model proposed in this paper can accurately predict the changing trend of joint angle sequences on human lower limbs during gait motion and automatically calibrate the short-term drift error formed in the process of gait motion.

Neural inertial navigation system on pedestrian

The recent research shows that data-driven inertia navigation technology can significantly alleviate the drift error of micro-electro-mechanical system inertial measurement unit (MEMS-IMU) in pedestrian localization. However, most existing methods must rely on attitude information provided by external procedure (such as smartphone API), which violates the original intention of full autonomy of inertial navigation, and attitude information is also inaccurate. To address the problem, we propose a pedestrian indoor neural inertial navigation system that does not rely on external information and is only based on low-cost MEMS-IMU. First, a deep learning based neural inertial network was designed to estimate attitude. Then, in order to obtain position estimation with both global and local accuracy, an invariant extended Kalman filter (IEKF) framework was proposed, where 3D displacement and its uncertainty regressed by a deep residual network are utilized to update IEKF. Extensive experimental results on a public dataset and a self-collected dataset show that the proposed method provides accurate attitude estimation and outperforms state-of-the-art methods in position estimation, demonstrating the superiority of our method in reliability and accuracy.

Asynchronous Hyperbolic UWB Source-Localization and Self-Localization for Indoor Tracking and Navigation

Hyperbolic localization measures the time difference of arrivals (TDOAs) of signals to determine the location of a wireless source or receiver. Traditional methods depend on precise clock synchronization between nodes so that time measurements from independent devices can be meaningfully compared. Imperfect synchronization is often the dominant source of error. We propose two new message based TDOA equations for hyperbolic localization which require no synchronization and meet or exceed state-of-the-art accuracy. Our approaches leverage anchor nodes that observe each other’s packet arrival times and a novel reformulation of the TDOA equation to reduce the effect of clock drift error. Closed-form equations are derived for computing TDOA in both self-localization and source-localization modes of operation along with bounds on maximum clock drift error. Three experiments are performed including a clock drift simulation, a non-line-of-sight (NLOS) simulation, and an indoor validation experiment on custom ultra wideband (UWB) hardware all of which involved eight anchor nodes and one localizing node in a 128m3 capture volume. Our source-localization approach achieved unprecedented accuracy with lower cost equipment and trivial setup. Our self-localization matched state-of-the art accuracy but with infinite scalability and high privacy. These results could enable economical and infinite density indoor navigation and dramatically reduce the economic cost and increase the accuracy of implementing industrial and commercial tracking applications.

바이어스 추정을 위한 표본의 수가 자이로 센서의 드리프트 오차에 미치는 영향

바이어스 추정을 위한 표본의 수가 자이로 센서의 드리프트 오차에 미치는 영향

Retrospective frequency drift correction of rosette MRSI data using spectral registration.

Frequency drift correction is an important postprocessing step in MRS that yields improvements in spectral quality and metabolite quantification. Although routinely applied in single-voxel MRS, drift correction is much more challenging in MRSI due to the presence of phase-encoding gradients. Thus, separately acquired navigator scans are normally required for drift estimation. In this work, we demonstrate the use of self-navigating rosette MRSI trajectories combined with time-domain spectral registration to enable retrospective frequency drift corrections without the need for separately acquired navigator echoes. A rosette MRSI sequence was implemented to acquire data from the brains of 5 healthy volunteers. FIDs from the center of k-space ( FIDs) were isolated from each shot of the rosette acquisition, and time-domain spectral registration was used to estimate the frequency offset of each FID relative to a reference scan (the first FID in the series). The estimated frequency offsets were then used to apply corrections throughout -space. Improvements in spectral quality were assessed before and after drift correction. Spectral registration resulted in significant improvements in signal-to-noise ratio(12.9%) and spectral linewidths (18.5%). Metabolite quantification was performed using LCModel, and the average Cramer-Rao lower bounds uncertainty estimates were reduced by 5.0% for all metabolites, following field drift correction. This study demonstrated the use of self-navigating rosette MRSI trajectories to retrospectively correct frequency drift errors in in vivo MRSI data. This correction yields meaningful improvements in spectral quality.

Duty-Cycle Correction-Based Model Predictive Current Control for PMSM Drives Fed by a Three-Level Inverter With Low Switching Frequency

In this paper, a duty-cycle correction-based model predictive current control (DC-MPCC) is proposed for permanent magnet synchronous motor (PMSM) supplied by a neutral-point clamped three-level voltage source inverter (NPC-3LVSI). Unlike the conventional MPCC, which evaluates the impact of basic voltage vectors on the concerned state variables, the proposed DC-MPCC modifies the output voltage levels with optimized duty-cycle corrections. Firstly, the last three-phase voltage levels are assumed to be kept during the next control period. Then, the current tracking error and neutral-point potential are predicted. After that, the voltage levels are modified with zero, one, or two state changes, which formulate seven candidate solutions. Subsequently, the duty-cycle corrections of the modified voltage levels are computed based on the principle of minimizing current tracking error and neutral-point voltage drift. Finally, the optimal switch sequence is generated by evaluating and sorting a cost function with a penalty on switch actions. The proposed DC-MPCC features variable switching instants, relatively lower sampling frequency, and satisfactory performance under low switching frequency. Experimental tests carried out on a NPC-3LVSI fed PMSM drive, with 100 Hz fundamental frequency and 400 Hz switching frequency, accompanied by a video demonstration, validate the effectiveness of the proposed method.

TOM-Odometry: A Generalized Localization Framework Based on Topological Map and Odometry

The localization of autonomous vehicles mainly depends on GPS-based methods in large-scale outdoor scenarios. Unfortunately, GPS is vulnerable and not reliable in some regions, such as urban canyons. Odometry is taken as a complementary method for positioning in GPS-limited areas, but it suffers from accumulated errors, which limits its application. Topological map is a concise and low-cost representation of real world environment, which can be deemed as one of the information sources for localization. To realize accurate localization in the GPS-limited and large-scale scenes for autonomous vehicles, a generalized localization framework based on the topological map and odometry is proposed in this paper. The odometry trajectory can be automatically aligned with the correct paths of the map through matching without the initial global position. Under this framework, odometry is deemed as the kinematic model while topological map is regarded as a global sensor that is utilized to correct the drift errors of odometry. As an example, the integration of visual odometry and topological map is used to validate the effectiveness of the proposed method on KITTI benchmark. Experimental results demonstrate that the proposed method can effectively constrain the drift errors of odometry, and it achieves state-of-the-art localization performance compared with existing map-aided methods.

Doppler Positioning of Dynamic Targets with Unknown LEO Satellite Signals

A new concept of global navigation based on Doppler measurements from a large low Earth orbit (LEO) constellation is investigated that has potential to serve as a complement or backup to global navigation satellite systems (GNSSs) to provide navigation and positioning services in GNSS denial environments. In this work, we investigate the potential of LEO communication satellite opportunity signals in dynamic navigation, establish LEO satellite Doppler positioning equations, derive the main error sources affecting the Doppler positioning results of a dynamic target, and analyze the impact of each error source on positioning accuracy through a simulation. The results show that the orbit error and clock drift had a large impact on positioning accuracy. This navigation scheme would be more competitive if it could provide high-precision satellite orbits and accurate Doppler measurements. The obtained results show that the LEO satellite signals used as navigation opportunity signals are an attractive alternative in GNSS rejection environments for high dynamic targets.

Real Time Kinematic (RTK) heave as a replacement of Motion Reference Unit (MRU) heave in hydrographic surveying works

Heave is one of the major contributors to errors in water depth measurements. Motion Reference Unit (MRU) measures the heave signal with high-level accuracy as well as other ship motions. Unfortunately, MRU has been reported to have some of drawbacks such as; heave drift error, influence of ship motion dynamic, In addition to its very expensive price Real-Time Kinematic (RTK) GPS uses dual frequency receiver and carrier phase differential technique under kinematic solution and provides very accurate position in all three components in real time. In addition, RTK GPS also calculates the low frequency changes in water level such as tidal oscillation. This research is an attempt to investigate the possibility of using the RTK GPS data to deduce the heave signal from the GPS height (tides - heave) instead of heave from MRU to correct the water depth. Moreover, to examine to what extent, RTK heave can be used as a backup to satisfy the International Hydrographic Organization (IHO) survey order standards. A comparison between the extracted RTK heave and MRU heave signals revealed a good agreement with a strong direct correlation of 0.96. As shown in figure 1 RTK heave as a replacement for MRU heave in hydrographic surveying was statistically validated with the use of a lot of methods of analysis such as Test of the Normality, Paired Samples T Test, Wilcoxon Signed Ranks Test, Heave Signals Frequency Adjustment , Descriptive Statistics for the Two Heave Signals , Descriptive Statistics for Each Signal Individually , Correlation and Trend, Analysis Between the Two Signals, Scatter Diagram and Trend, Standard Deviation and Uncertainty for Soundings, Characteristics of the Difference between Two Signals , Comparing the Surfaces by TIN Model. The results of this analysis provided the possibility of using RTK heave as a replacement for MRU heave in hydrographic surveying. Therefore, RTK GPS is not only used to provide precise position or tidal oscillations but also based on this study, can be used to measure heave accurately to correct the depth satisfying IHO survey standards. Received: 28 January 2023 Accepted: 26 April 2023 Published: 22 May 2023

Accurate measurement and enhancement of fiber coil symmetry.

The pure Shupe effect is substantially reduced in a fiber optic gyroscope (FOG) with symmetrical windings. However, the effect of the temperature-induced nonuniformity of the stress in the coil depends on the mean temperature derivative (T-dot). Research on precision winding technology has discovered that the symmetry of optical fiber rings affects the temperature performance of fiber optic gyroscopes. Optical fiber rings with good symmetry also have good temperature performance. This paper first establishes a temperature drift model of optical fiber rings that includes the Shupe effect and T-dot effect and then uses finite element simulation to analyze the drift error of optical fiber rings in a variable temperature environment. Analysis shows that this drift is caused by the variation and uneven distribution of the fiber length and the refractive index in the positive and negative winding of the optical fiber ring, which results in a residual phase difference that is directly related to the symmetry of the optical fiber ring. Simulation and analysis show that balancing the residual phase difference of the optical fiber ring can be achieved by cutting the length of the optical fiber ring at both ends. This paper uses optical frequency domain reflectometry (OFDR) technology to precisely test the symmetry of the optical fiber ring, ensuring accurate adjustment of the lengths at both ends of the optical fiber ring. Experimental tests on two gyroscopes have shown that the optical fiber ring with a smaller drift error can be obtained after testing and adjusting its length. The experimental data indicates that the bias stability of two laboratory gyros are increased by 23.6% and 18.1%, and the bias range are reduced by 22.4% and 30.0%.

Arbitrary Spatial Trajectory Reconstruction Based on a Single Inertial Sensor

Compared with vision, infrared rays, and ultrasonic positioning technologies, the signal acquisition of portable inertial sensors is not affected by the external environment, such as light and occlusion. Therefore, motion tracking based on inertial signals is a promising complement. However, accurate trajectory reconstruction based on inertial sensors is a great challenge due to the intrinsic and measurement errors, especially the drift error that exacerbates the accumulative error in trajectory calculation. To address this challenge, we propose a new trajectory reconstruction method, Geometric Dynamic Segmental Reconstruction (GDSR), where we treat the movement trajectory as a combination of basic trajectories. To this end, we design a temporal and spatial interaction segmentation approach to decompose the trajectory into basic segments by combining the dynamic feature of IMU signals with the spatial morphological feature of motion. Accordingly, we design a geometrical model library with undetermined parameters to match these segments. For precise parameter prediction, we propose an extra-supervised learning method that integrates different prediction tasks into one framework, which can not only expand training samples but also enable different subtasks to compete with each other, thus improving the parameter prediction accuracy of each subtask, thereby accurately approximating the trajectory segments. To quantify the trajectory reconstruction accuracy, we propose the Fréchet Spline Sliding Error (FSSE) and Length Error Ratio (LER) to evaluate curve similarity. The range of FSSE is [0, 2], where 0 means that the two curves have the same shape. The range of LER is [1, +∞], where 1 means that the two curves have the same length. We test different IMUs in two experimental scenarios and one public available data set. In all the three tests, the FSSE of the GDSR method is less than 0.09, and the LER is less than 1.31, which is significantly better than all the comparison methods.

Accurate Cutting-Force Measurement with Smart Tool Holder in Lathe.

Cutting force in lathe work is closely related to tool wear and affects the turning quality. Direct measurement of the cutting force by measuring the strain of the tool holder is challenging because the tool holder design aims to be highly rigid in order to undertake large cutting forces. Accordingly, the most popular dynamometer designs modify the standard tool holder by decreasing the structural rigidity of the holder, which reduces the machining precision and is not widely accepted. In order to solve the issue of the low stiffness of the dynamometer reducing the machining precision, in this paper, the ultra-low strain on the tool holder was successfully detected by the highly sensitive semiconductor strain gauges (SCSG) adjacent to the blade cutting insert. However, the cutting process would generate much heat, which increases the force measuring area temperature of the tool holder by about 30 °C. As a result, the readout drifted significantly with the temperature changes due to the high temperature coefficient of SCSG. To solve this problem, the temperature on the tool holder was monitored and a BP neural network was proposed to compensate for temperature drift errors. Our methods improved the sensitivity (1.14 × 10-2 mV/N) and the average relative error of the BP neural network prediction (≤1.48%) while maintaining the original stiffness of the tool holder. The smart tool holder developed possesses high natural frequency (≥6 kHz), it is very suitable for dynamic cutting-force measurement. The cutting experiment data in the lathe work show comparable performance with the traditional dynamometers and the resolution of the smart tool holder is 2 N (0.25% of total range).

The Conjunctive Compensation Method Based on Inertial Navigation System and Fluxgate Magnetometer

Eliminating the magnetic interference of the carrier platform is an important technical link and plays a vital role in aeromagnetic survey. The traditional compensation method is based on the Tolles–Lawson (T-L) model and establishes the linear relationship between the aircraft interference magnetic field and the aircraft attitude. The compensation coefficients are solved by designing the calibration flight. At present, almost all aeromagnetic systems use the fluxgate magnetometer fixed to the aircraft to realize the attitude measurement of the flight platform. However, the fluxgate magnetometer has problems, such as non-orthogonal error, zero drift error, and linearity error limited by the production process, and the fluxgate magnetometer is also very susceptible to external magnetic interference as a magnetic sensor. These lead to the aircraft attitude calculated by the fluxgate magnetometer being inaccurate, thus reducing the compensation effect. In this article, we analyze the influence of the fluxgate magnetometer noise on compensation and propose a new conjunctive compensation method based on inertial navigation systems (INS) and fluxgate magnetometer information to improve the compensation effect. The flight experiment data show that the proposed method can significantly improve the quality of aeromagnetic data. Compared with the traditional compensation method only based on fluxgate magnetometer information, the improved ratio is increased by 30–60%, and it is a real-time compensation method. It shows that the proposed method has a remarkable compensation effect for aeromagnetic interference.

Laser 3D tightly coupled mapping method based on visual information

PurposeSimultaneous localization and map building (SLAM), as a state estimation problem, is a prerequisite for solving the problem of autonomous vehicle motion in unknown environments. Existing algorithms are based on laser or visual odometry; however, the lidar sensing range is small, the amount of data features is small, the camera is vulnerable to external conditions and the localization and map building cannot be performed stably and accurately using a single sensor. This paper aims to propose a laser three dimensions tightly coupled map building method that incorporates visual information, and uses laser point cloud information and image information to complement each other to improve the overall performance of the algorithm.Design/methodology/approachThe visual feature points are first matched at the front end of the method, and the mismatched point pairs are removed using the bidirectional random sample consensus (RANSAC) algorithm. The laser point cloud is then used to obtain its depth information, while the two types of feature points are fed into the pose estimation module for a tightly coupled local bundle adjustment solution using a heuristic simulated annealing algorithm. Finally, the visual bag-of-words model is fused in the laser point cloud information to establish a threshold to construct a loopback framework to further reduce the cumulative drift error of the system over time.FindingsExperiments on publicly available data sets show that the proposed method in this paper can match its real trajectory well. For various scenes, the map can be constructed by using the complementary laser and vision sensors, with high accuracy and robustness. At the same time, the method is verified in a real environment using an autonomous walking acquisition platform, and the system loaded with the method can run well for a long time and take into account the environmental adaptability of multiple scenes.Originality/valueA multi-sensor data tight coupling method is proposed to fuse laser and vision information for optimal solution of the positional attitude. A bidirectional RANSAC algorithm is used for the removal of visual mismatched point pairs. Further, oriented fast and rotated brief feature points are used to build a bag-of-words model and construct a real-time loopback framework to reduce error accumulation. According to the experimental validation results, the accuracy and robustness of the single-sensor SLAM algorithm can be improved.