Vertical Position Error Research Articles

Cooperative Localization under Ionospheric Scintillation Events

Ionospheric scintillation causes major impairments to Global Navigation Satellite System (GNSS) in low-latitude regions. In severe scenarios, this event can lead to complete loss of lock, thus making GNSS measurements unusable for navigation. In this paper, we derive a cooperative localization algorithm where a set of partially connected aircraft exchange messages with neighboring nodes on the network to improve their own position estimates. We consider the scintillation events as abrupt changes in the measurement variance, which are modeled by a discrete-valued Markov process at the nodes which have access to GNSS measurements. Simulation results show that Markovian modeling and cooperation via factor graph message passing reduce the average 3D root mean square localization error and yield an average vertical position error that meets civil aviation standards for approach and landing.

A high-precision positioning method for shield tunneling based on dual-axis hybrid inertial navigation system

During shield tunneling excavation, it is extremely important to obtain the accurate positions of the control points which determines the quality of the tunnel construction. The present process of measuring and checking the control points is labor-intensive and time-consuming. In this paper, we proposed a high-precision positioning method using a dual-axis hybrid inertial navigation system (HINS) mounted on a rail transport vehicle to measure the positions of control points automatically without other external sensors. Considering the movement constraints on the rails, an improved non-holonomic constraints (NHC) algorithm was introduced to promote navigation accuracy and a new calibration method of mounting angle errors was proposed. The semi-physics experiment and laboratory rail experiments were conducted whose results showed that the lateral position accuracy was increased by more than 94.23% and the vertical position error was reduced to the centimeter level averagely using the proposed algorithm compared to the normal INS algorithm.

Methodology for performing bathymetric measurements of shallow waterbodies using an UAV, and their processing based on the SVR algorithm

State-of-art methods of bathymetric measurements for shallow waterbodies use Global Navigation Satellite System (GNSS) receiver, bathymetric Light Detection and Ranging (LiDAR) sensor or satellite imagery. Currently, photogrammetric methods with the application of Unmanned Aerial Vehicles (UAV) are gathering great importance. This publication aims to present step-by-step methodology for carrying out the bathymetric measurements of shallow waterbodies with the use of UAV-Structure from Motion (SfM) and Support Vector Regression (SVR) algorithms. Proposed model is explained and verified on the basis of measurement campaign on Raduńskie Górne Lake located in Poland. The campaign included GNSS Real Time Kinematic (RTK) bathymetric measurements for robust training dataset and photogrammetric flight pass for SfM point cloud. The presented methodology will allow to perform bathymetric measurements with the accuracy provided for the International Hydrographic Organization (IHO) Special Order (horizontal position error ≤ 2 m (p = 0.95), vertical position error ≤ 0.25 m (p = 0.95)).

Method for determining of shallow water depths based on data recorded by UAV/USV vehicles and processed using the SVR algorithm

Bathymetric measurements in waters shallower than 1 m are necessary to monitor seafloor relief changes in the coastal zone. This is especially important for ensuring the safety of navigation, navigation efficiency, as well as during the design and monitoring of hydrotechnical structures. Therefore, the aim of this article is to present a method for determining of shallow water depths based on data recorded by Unmanned Aerial Vehicle (UAV) and Unmanned Surface Vehicle (USV), as well as processed using the Support Vector Regression (SVR) algorithm. Validation studies of this method was carried out on two selected waterbodies (inland and sea) using the DJI Phantom 4 Real Time Kinematic (RTK) UAV and the AutoDron USV. Then, the geospatial data recorded by a drone was applied to determine depths of shallow waterbodies using the SfM algorithm. Subsequently, the determined depths were compared with the depths measured by a Global Navigation Satellite System (GNSS) RTK receiver or a Single Beam Echo Sounder (SBES), in order to assess the accuracy of the proposed method. The research showed that it is able to determine shallow waterbody depths with the accuracy requirements specified for the International Hydrographic Organization (IHO) S-44 special order (depth error ≤ 0.25 m (p = 0.95)), but only to depths not exceeding 1 m. In the inland waterbody, the depth accuracy was 0.22–0.24 m (p = 0.95), while in the sea waterbody the measurement accuracy was higher, amounting to 0.16 m (p = 0.95). However, for the depth range up to 2 m, the results are radically different, because the vertical position error with a 95% confidence level exceeds the value of 0.3 m in the analysed waterbodies.

Accuracy and clinical validity of automated cephalometric analysis using convolutional neural networks.

This study aimed to assess the error range of cephalometric measurements based on the landmarks detected using cascaded CNNs and determine how horizontal and vertical positional errors of individual landmarks affect lateral cephalometric measurements. In total, 120 lateral cephalograms were obtained consecutively from patients (mean age, 32.5 ± 11.6) who visited the Asan Medical Center, Seoul, Korea, for orthodontic treatment between 2019 and 2021. An automated lateral cephalometric analysis model previously developed from a nationwide multi-centre database was used to digitize the lateral cephalograms. The horizontal and vertical landmark position error attributable to the AI model was defined as the distance between the landmark identified by the human and that identified by the AI model on the x- and y-axes. The differences between the cephalometric measurements based on the landmarks identified by the AI model vs those identified by the human examiner were assessed. The association between the lateral cephalometric measurements and the positioning errors in the landmarks comprising the cephalometric measurement was assessed. The mean difference in the angular and linear measurements based on AI vs human landmark localization was .99 ± 1.05°, and .80 ± .82 mm, respectively. Significant differences between the measurements derived from AI-based and human localization were observed for all cephalometric variables except SNA, pog-Nperp, facial angle, SN-GoGn, FMA, Bjork sum, U1-SN, U1-FH, IMPA, L1-NB (angular) and interincisal angle. The errors in landmark positions, especially those that define reference planes, may significantly affect cephalometric measurements. The possibility of errors generated by automated lateral cephalometric analysis systems should be considered when using such systems for orthodontic diagnoses.

Integration Data Model of the Bathymetric Monitoring System for Shallow Waterbodies Using UAV and USV Platforms

Changes in the seafloor relief are particularly noticeable in shallow waterbodies (at depths up to several metres), where they are of significance for human safety and environmental protection, as well as for which the highest measurement accuracy is required. The aim of this publication is to present the integration data model of the bathymetric monitoring system for shallow waterbodies using Unmanned Aerial Vehicles (UAV) and Unmanned Surface Vehicles (USV). As part of this model, three technology components will be created: a hydroacoustic and optoelectronic data integration component proposed by Dąbrowski et al., a radiometric depth determination component based on optoelectronic data using the Support Vector Regression (SVR) method, and a coastline extraction component proposed by Xu et al. Thanks to them, it will be possible to cover the entire area with measurements in the coastal zone, in particular between the shallow waterbody coastline and the min. isobath recorded by the echo sounder (the area is lacking actual measurement data). Multisensor data fusion obtained using Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS), Light Detection And Ranging (LiDAR), Real Time Kinematic (RTK), UAV, and USV will allow to meet the requirements provided for the International Hydrographic Organization (IHO) Special Order (horizontal position error ≤ 2 m (p = 0.95), vertical position error ≤ 0.25 m (p = 0.95)). To this end, bathymetric and photogrammetric measurements shall be carried out under appropriate conditions. The water transparency in the tested waterbody should be at least 2 m. Hydrographic surveys shall be performed in windless weather and the water level is 0 in the Douglas sea scale (no waves or sea currents). However, the mission with the use of an UAV should take place in appropriate meteorological conditions, i.e., no precipitation, windless weather (wind speed not exceeding 6–7 m/s), sunny day.

Research on Vertical Overlap of the Paired Approach Based on QAR

The paired approach can effectively improve the efficiency of closely spaced parallel runways. The calculation of vertical overlap probability and frequency is an indispensable step in evaluating the vertical collision risk of the paired approach. As the existence of vertical overlap is closely related to the vertical position error, this paper presents a method to calculate vertical overlap probability based on the position error caused by pilot control. Firstly, a fuzzy correlation model is established and combined with Quick Access Recorder (QAR) data. The correlation rules between QAR parameters and vertical position error are mined, and the relevance is calculated according to the rules. The results show that the correlation between the control column position and the vertical position error is the strongest. According to the flight dynamics principle, the Vertical Attitude Adjustment Model (VAAM) of an aircraft during the approach process is then established. The Pilot Operating Model (POM), which describes different actions taken by pilots when they encounter different position errors, is also created by employing the concepts of the Markov decision process. The VAAM can restore the process of changing the attitude of the aircraft by the pilot operating column and can simulate the position error of the aircraft in the approach process when combined with the POM. Based on the previous simulated result and considering the overlap condition of the Interval Management (IM) aircraft overlap, the vertical overlap process in the paired approach can then be simulated. We employ MATLAB to carry out numerous simulations. Changing the accuracy of pilot operation in the simulations show that the lower the accuracy, the greater the overlap probability and frequency. However, when the accuracy is between 61% and 73% (61%–73% is the range of operational accuracy based on QAR data analysis), the vertical overlap probability and frequency are maintained at about 5% and 20 flights per hour, respectively.

ZUPT-Aided INS Bypassing Stance Phase Detection by Using Foot-Instability-Based Adaptive Covariance

In this paper, we propose a Foot-Instability-Based Adaptive (FIBA) covariance to dynamically adjust the covariance matrix for the pseudo-zero-velocity measurements in the Zero velocity UPdaTe (ZUPT)-aided Inertial Navigation Systems (INS). The proposed ZUPT-aided INS using the FIBA covariance is implemented in an Extended Kalman Filter (EKF) framework, which utilizes a time-varying measurement covariance matrix that is updated in each iteration according to the FIBA covariance. The FIBA covariance is designed to have a very high value during the swing phases in a gait cycle, and the value significantly decreases during the stance phases. As a result, the proposed method eliminates a need to use a binary stance phase detector in implementation of the ZUPT-aided INS. Properties of EKF innovation sequences in the algorithm were studied, and two series of indoor pedestrian navigation experiments were conducted to demonstrate the navigation performance of the proposed system. In the first series of experiments, which included cases of walking and running, localization solutions produced by the system using the FIBA covariance demonstrated 36% and 64% improvements in navigation accuracy along the horizontal and vertical directions, respectively. In the second series of experiments, which included a pedestrian walking on different indoor terrains, such as flat planes, stairs, and ramps, the navigation accuracy of the system using the FIBA covariance reduced horizontal and vertical position errors by 12% and 45%, respectively, as compared to the conventional ZUPT-aided INS.

Path Planning Algorithm of Dijkstra-Based Intelligent Aircraft under Multiple Constraints

Aiming at the rapid planning of the optimal flight path of the intelligent aircraft, considering the error constraints and correction probability constraints, a model for intelligent aircraft path planning under multiple constraints is constructed, and a global search algorithm based on Dijkstra algorithm is proposed to solve the model. By calculating the residual error and restricts flight distance, the basic Dijkstra algorithm is improved to make it more adaptable to solve the path planning under multiple constraints. At the same time, simulation experiment is conducted with the optimal goal of the shortest track length and satisfying the error constraints. The experimental results show that the aircraft passed a total of 18 correction points when it reached the destination. The total track length was 144 287.932 m, the vertical position error was 17.254 units, and the horizontal position error was 6.420 units. The results meet the error requirements. The results show that the intelligent aircraft path planning model and Dijkstra-based global search algorithm with multiple constraints are reasonable in solving such problems.

An SBAS Integrity Model to Overbound Residuals of Higher-Order Ionospheric Effects in the Ionosphere-Free Linear Combination

The next generation of satellite-based augmentation systems (SBAS) will support aviation receivers that take advantage of the ionosphere-free dual-frequency combination. By combining signals of the L1 and L5 bands, about 99% of the ionospheric refraction effects on the GNSS (Global Navigation Satellite Systems) signals can be removed in the user receivers without additional SBAS corrections. Nevertheless, even if most of the negative impacts on GNSS signals are removed by the ionospheric-free combination, some residuals remain and have to be taken into account by overbounding models in the integrity computation conducted by safety-of-live (SoL) receivers in airplanes. Such models have to overbound residuals as well, which result from the most rare extreme ionospheric events, e.g., such as the famous “Halloween Storm”, and should thus include the tails of the error distribution. Their application shall lead to safe error bounds on the user position and allow the computation of protection levels for the horizontal and vertical position errors. Here, we propose and justify such an overbounding model for residual ionospheric delays that remain after the application of the ionospheric-free linear combination. The model takes into account second- and third-order ionospheric refraction effects, excess path due to ray bending, and increased ionospheric total electron content (TEC) along the signal path due to ray bending.

Simulation study of mitigation of plasma bubble effects on GBAS using a VHF radar

Plasma bubbles can affect ground-based augmentation system (GBAS) performance by posing large spatial ionospheric gradients between the aircraft and the airport, which makes it important to detect plasma bubbles effectively. In this study, we investigate the use of VHF radar to detect plasma bubbles and mitigate their potential impact on GBAS through a simulation. When the line-of-sight of a certain GPS satellite is determined to be passing through an area of plasma bubbles as detected by EAR, such GPS satellite shall be removed from the positioning calculation on board the aircraft. We set up different simulation scenarios by varying the satellite geometry, and airport coordinate. Results are described in the form of vertical protection level (VPL) and vertical position error (VPE), which we then analyse as a function of zonal and meridional distance. The results show that such a radar-based monitoring system can be used to mitigate the effects of plasma bubbles on GBAS to cover surrounding airports within a certain range, especially in the meridional direction.

Improvement of Differential GPS Performance Using Range Measurements Between Satellites

In global positioning system (GPS), inter-satellite link information enables communication between satellites, and inter-satellite range (ISR) represents the distance between satellites used for satellite maintenance. We propose a method to improve position accuracy using distance measurements between satellites, such as ISR. However, ISR information has not been made available to users until now. Therefore, we define distance measurements with inter-satellite ephemeris distance (ISED), which uses satellite coordinates calculated by GPS broadcast ephemeris rather than ISR, and propose a method to improve the position accuracy. ISED accuracy is solely determined by GPS broadcast ephemeris accuracy. GPS ephemeris has recently recorded greater accuracy; therefore, ISED can serve as an additional measurement for user navigation solution. When ISED serves as an additional measurement, the observation matrix is extended, resulting in a reduction in dilution of precision (DOP). Therefore, user accuracy is improved by applying ISED owing to the reduction in DOP. Additionally, the analysis results by applying real experimental data show that DOP, with an extended observation matrix, is more effective in the vertical than the horizontal part. Moreover, the differential GPS (DGPS) shows better performance than the standalone GPS when ISED is applied. The analysis results of applying real data to the method using the proposed ISED showed that vertical position errors were conspicuously decreased compared with horizontal position errors, and the performance was excellent for the DGPS. The proposed method is expected to be highly applicable in aircraft takeoff and landing, where the vertical sector is critical.

Compensation of Vertical Position Error Using a Force–Deflection Model in Friction Stir Spot Welding

Despite increasing need for friction stir spot welding (FSSW) for high-temperature softening materials, system deflection due to relatively high plunging force remains an obstacle. System deflection results in the vertical position error of a welding tool and insufficient plunge depth. In this study, we used adaptive control to maintain plunge depth, the plunging force was coaxially measured, and the position error was estimated using a force–deflection model. A linear relationship was confirmed between the force and deflection; this relationship is dependent on the stiffness of the welding system while independent of process parameters and base materials. The proposed model was evaluated during the FSSW of an Al 6061-T6 alloy sheet and a dissimilar metal combination of Al 6061-T6 alloy/dual phase (DP) 590 steel. Under varying process parameters, the adaptive control maintained a plunge depth with an error of less than 50 μm. Conventional position control has a maximum error of nearly 300 μm.

Quality assessment of GNSS observations from an Android N smartphone and positioning performance analysis using time-differenced filtering approach

The development of low-cost GNSS chips inspired the development of advanced positioning, navigation and timing devices. In ‘I/O of 2016’, Google announced that GNSS observations from devices running the Android version 7 operating system would be available to developers. Providing GNSS application developers the opportunity to develop advanced processing algorithms for accurate position estimation using pseudorange, Doppler and carrier phase observations. The quality of GNSS observations from Android smartphones and their accuracy in estimating position is assessed. The observed carrier-to-noise density ratio (C/N0), pseudorange noise, pseudorange rate error and phase rate error of GNSS observations are evaluated. The results demonstrate that the average (C/N0) value is approximately 10 dB-Hz lower than the representative values obtained from a geodetic-quality antenna and receiver. The station single-difference pseudorange residuals on all available signals vary from − 20 to 20 m, and the value of pseudorange rate varies within ± 10 m/s. In addition, the phase rate and Doppler reaches approximately ± 0.2 m/s. Different from the geodetic receivers, the signal noise ratio (SNR) obtained from smartphone varies more significantly, regardless of elevation angle. Therefore, the SNR-dependent weighting method is preferred during data processing. Furthermore, the results of the static data analysis show that the horizontal and vertical RMS position errors are less than 0.8 and 1.4 m, respectively, when Doppler and phase observations are incorporated into the positioning solution.

GPS, BDS and Galileo ionospheric correction models: An evaluation in range delay and position domain

The performance of GPS Klobuchar (GPSKlob), BDS Klobuchar (BDSKlob) and NeQuick Galileo (NeQuickG) ionospheric correction models are evaluated in the range delay and position domains over China. The post-processed Klobuchar-style (CODKlob) coefficients provided by the Center for Orbit Determination in Europe (CODE) and our own fitted NeQuick coefficients (NeQuickC) are also included for comparison. In the range delay domain, BDS total electrons contents (TEC) derived from 20 international GNSS Monitoring and Assessment System (iGMAS) stations and GPS TEC obtained from 35 Crust Movement Observation Network of China (CMONC) stations are used as references. Compared to BDS TEC during the short period (doy 010-020, 2015), GPSKlob, BDSKlob and NeQuickG can correct 58.4, 66.7 and 54.7% of the ionospheric delay. Compared to GPS TEC for the long period (doy 001-180, 2015), the three ionospheric models can mitigate the ionospheric delay by 64.8, 65.4 and 68.1%, respectively. For the two comparison cases, CODKlob shows the worst performance, which only reduces 57.9% of the ionospheric range errors. NeQuickC exhibits the best performance, which outperforms GPSKlob, BDSKlob and NeQuickG by 6.7, 2.1 and 6.9%, respectively. In the position domain, single-frequency stand point positioning (SPP) was conducted at the selected 35 CMONC sites using GPS C/A pseudorange with and without ionospheric corrections. The vertical position error of the uncorrected case drops significantly from 10.3 m to 4.8, 4.6, 4.4 and 4.2 m for GPSKlob, CODKlob, BDSKlob and NeQuickG, however, the horizontal position error (3.2) merely decreases to 3.1, 2.7, 2.4 and 2.3 m, respectively. NeQuickG outperforms GPSKlob and BDSKlob by 5.8 and 1.9% in vertical component, and by 25.0 and 3.2% in horizontal component.

Advanced receiver autonomous integrity monitoring using triple frequency data with a focus on treatment of biases

Most current Advanced Receiver Autonomous Integrity Monitoring (ARAIM) methods are designed to use dual-frequency ionosphere-free observations. These methods assume that receiver bias is absorbed in the common receiver clock offset and bound satellite biases by nominal values. However, most multi-constellation Global Navigation Satellite Systems (GNSS) can offer triple frequency data that can be used for civilian applications in the future, which can improve observation redundancy, solution precision and detection of faults. In this contribution, we explore the use of this type of observations from GPS, Galileo and BeiDou in ARAIM. Nevertheless, the use of triple frequency data introduces receiver differential biases that have to be taken into consideration. To demonstrate the significance of these additional biases we first present a method to quantify them at stations of known coordinates and using available products from the International GNSS service (IGS). To deal with the additional receiver biases, we use a between-satellite single difference (BSSD) observation model that eliminates their effect. A pilot test was performed to evaluate ARAIM availability for Localizer Performance with Vertical guidance down to 200feet (LPV-200) when using the triple-frequency observations. Real data were collected for one month at stations of known coordinates located in regions of different satellite coverage characteristics. The BSSD triple-frequency model was evaluated to give early indication about its feasibility, where the implementation phase still requires further comprehensive studies. The vertical position error was always found to be bounded by the protection level proven initial validity of the proposed integrity model.

Online monitoring of truing arc-shaped diamond wheel by acoustic emission signal

To realize the efficient and precision truing of arc-shaped diamond wheel, a novel on-machine precision form truing of arc-shaped diamond wheel is proposed utilizing rotary green silicon carbon rod, and online monitoring of the truing process by acoustic emission was studied. Through this truing method, any required radius of wheel arc profile could be formed by programmed truing paths; meanwhile, the vertical direction position error of the wheel center could be corrected after truing. In order to improve the truing efficiency, the acoustic emission signal was processed to monitor the truing process, and the AErms threshold of judging the finishing truing time was obtained.

Pilot Evaluation of Integrating GLONASS, Galileo and BeiDou with GPS in Araim

Abstract In this pilot study, availability of the Advanced Receiver Autonomous Integrity Monitoring (ARAIM) when integrating various combinations of satellite constellations including; Galileo, GLONASS and BeiDou with GPS is investigated. The Multiple Hypothesis Solution Separation method was applied using one month of real data. The data was collected at stations of known positions, located in regions that have different coverage levels by the tested constellations. While most previous studies used simulated data, the importance of using real data is twofold. It allows for the use of actual User Range Accuracy (URA) received within the satellite navigation message, which is a fundamental component for computation of the integrity protection level; and the computation of vertical position errors to validate the integrity approach. Results show that the vertical position error was always bounded by the protection level during the test period and the ARAIM availability can reach 100% of the time when using all constellations even though some constellations are yet incomplete.

Overview of the 2015 St. Patrick’s day storm and its consequences for RTK and PPP positioning in Norway

The 2015 St. Patrick’s day storm was the first storm of solar cycle 24 to reach a level of “Severe” on the NOAA geomagnetic storm scale. The Norwegian Mapping Authority is operating a national real-time kinematic (RTK) positioning network and has in recent years developed software and services and deployed instrumentation to monitor space weather disturbances. Here, we report on our observations during this event. Strong GNSS (Global Navigation Satellite System) disturbances, measured by the rate-of-TEC index (ROTI), were observed at all latitudes in Norway on March 17th and early on March 18th. Late on the 18th, strong disturbances were only observed in northern parts of Norway. We study the ionospheric disturbances in relation to the auroral electrojet currents, showing that the most intense disturbances of GNSS signals occur on the poleward side of poleward-moving current regions. This indicates a possible connection to ionospheric polar cap plasma patches and/or particle precipitation caused by magnetic reconnection in the magnetosphere tail. We also study the impact of the disturbances on the network RTK and Precise Point Positioning (PPP) techniques. The vertical position errors increase rapidly with increasing ROTI for both techniques, but PPP is more precise than RTK at all disturbance levels.

Balancing a retroreflector to minimize rotation errors using a pendulum and quadrature interferometer.

A corner-cube retroreflector has the property that the optical path length for a reflected laser beam is insensitive to rotations about a mathematical point called its optical center (OC). This property is exploited in ballistic absolute gravity meters in which a proof mass containing a corner-cube retroreflector is dropped in a vacuum, and its position is accurately determined with a laser interferometer. In order to avoid vertical position errors when the proof mass rotates during free fall, it is important to collocate its center of mass (COM) with the OC of the retroreflector. This is commonly done using a mechanical scale-based balancing procedure, which has limited accuracy due to the difficulty in finding the exact position of the COM and the OC. This paper describes a novel way to achieve the collocation by incorporating the proof mass into a pendulum and using a quadrature interferometer to interrogate its apparent translation in its twist mode. The mismatch between the COM and OC generates a signal in a quiet part of the spectrum where no mechanical resonance exists. This allows us to tune the position of the COM relative to the OC to an accuracy of about 1 μm in all three axes. This provides a way to directly demonstrate that a rotation of the proof mass by several degrees causes an apparent translation in the direction of the laser beam of less than 1 nm. This technique allows an order of magnitude improvement over traditional methods of balancing.