Horizontal Position Error Research Articles

Enhanced Terrain-Referenced Navigation Through Adaptive Radar Altimeter Error Estimation with Monte Carlo Sampling

Abstract Terrain-referenced navigation serves as a reliable backup system for military aviation, but its performance is often compromised by inaccurate radar altimeter noise estimation. The wide beamwidth of radar altimeters causes complex error characteristics that vary with flight conditions and radar–terrain interactions. A mismatch between assumed and actual measurement error levels can lead to degraded navigation accuracy and potential filter divergence. This issue is exacerbated in mission scenarios such as low-altitude penetrations that require frequent rolling and pitching maneuvers. This study proposes a novel radar altimeter error modeling approach that uses Monte Carlo sampling to estimate measurement error levels on-the-fly. By incorporating a radar–terrain interaction measurement model, the method provides tighter error bounds to an extended Kalman filter, improving its response to state- and terrain-dependent error characteristics. Simulation across four distinct scenarios show that the proposed approach reduces the average divergence rate from 2.75 to 0.25%, and decreases horizontal position error by 32.3% in RMSE and 31.7% in CEP.

Performance of a fine-scale acoustic positioning system for monitoring temperate fish behavior in relation to offshore marine developments

Rapid global expansion of offshore wind farms, tidal, and wave technologies signifies a new era of renewable energy development. While a promising means to combat the impacts of climate change, such developments necessitate fine-scale monitoring of biological communities to determine impacts associated with construction, operation, and eventual decommission. Here, we evaluate the performance of a gridded, Innovasea Systems, Inc. fine-scale acoustic telemetry positioning system (FSPS, n = 20 acoustic receivers) for tracking behaviors of diverse, temperate fish assemblages in relation to a subsea cable route supporting the Ørsted offshore wind development in coastal New York. We examined array performance through positioning error derived from receiver reference transmitters and tracked animals (n = 260) comprising 17 species of teleost and elasmobranch. We evaluated the effects of environmental variables (temperature, tilt, noise, and depth), transmitter power, individual movement rates, and receiver loss on horizontal positioning error (HPE) and route mean squared error (RMSE). Across a 16-month deployment period, many positions were derived for Atlantic sturgeon (n = 2,612), black sea bass (n = 9,175), clearnose skate (n = 10,306), summer flounder (n = 13,304), and little skate (n = 15,186), suggesting that these species may serve as sentinel candidates for assessing behavioral changes following construction, operation, and decommission. We found that receivers placed at the boundary of the grid exhibited higher HPE and RMSE, however these errors did not significantly change despite large receiver losses (25%). Generalized Linear Models revealed that temperature, noise, tilt, and depth were often significant predictors of HPE and RMSE, however, a substantial amount of variance was not explained by the models (~ 70%). Average movement rates ranged from 1.1 m s−1 (common thresher shark) to 0.03 m s−1 (little skate and summer flounder) but had minimal effects on positioning error. Finally, we observed that higher transmitter powers (158 dB) may lead to higher and more variable HPE values. Overall, these findings provide new insight into the drivers of FSPS array performance and illustrate their broad utility for monitoring fish behavior associated with offshore marine developments.

Advancements and applications of GMS3: a surface and subsurface unified database system

Abstract GPR Mobile Mapping System 3D (GMS3) combines three-dimensional ground-penetrating radar (GPR) subsurface data with omnidirectional camera surface mobile mapping system (MMS) imagery to create a high-precision unified surface-subsurface database where underground features are easily localizable from the surface. In the context of Japan, the system is generally able to detect cavities as deep as 1.5 m (depending on soil water content) with a maximum horizontal positioning error of a few cm. The main application of GMS3 in Japan is road subsurface cavity investigations aimed at sinkhole prevention, detecting an average of 0.53 cavities per surveyed km in Japan’s national roads, and 4.76 cavities per km in municipal roads in the case of Matsuyama City. We also evaluate the feasibility of 3D mapping of buried pipes (necessary before undergrounding works) at the Johoku Campus of Ehime University. Since both services show increasing demand in Japan due to the country’s deteriorating infrastructure and its susceptibility to natural disasters, GMS3 is continuously being developed to stand out as a vital tool in subsurface surveying both in the Japanese and the international context.

S2CPL: A novel method of the harvest evaluation and subsoil 3D cutting-Point location for selective harvesting of green asparagus

Robotic selective harvesting is an ideal method for bionic manual harvest of green asparagus. However, the harvesting robot encounters difficulties in evaluating the suitable harvest due to the tilt and bending of the long stem, as well as determining the precise location of the subsoil cutting-point to prevent damage from bacteria on the cutting surface. This paper proposed the S2CPL model to address the challenges of the harvest evaluation and 3D localization of subsoil cutting-point for selective harvesting of green asparagus in field conditions. Firstly, an RGB-D sensor was used to acquire images and depth information of green asparaguses. Secondly, the improved YOLOv8 by introduced lightweight convolution and attention mechanisms in the feature fusion module to enhance the segmentation accuracy. Thirdly, a 3D morphology extraction method was proposed to calculate the length and diameter of green asparagus by utilizing the image mask fusion with depth information. Finally, harvest evaluation and subsoil 3D cutting-point location were achieved for robotic selective harvesting. In addition, the RGB-D sensor posture was optimized. The test results showed that the Intersection over Union (IoU) of green asparagus segmentation with S2CPL reaches 98.0 %, which outperforms YOLOv5 + uNet, YOLOv7 + uNet and YOLOv8-tiny by 5.60 %, 4.59 % and 1.34 % respectively. The average detection time per image was only 2.0 ms, and the GFLOPS was improved by 23.90 %, 88.49 % and 7.63 % compared with other models. The relative error of the length and diameter were less than 2.98 % and 2.15 %, respectively. The accuracy of location the subsoil cutting-point is more than 99.0 %, and the horizontal positioning error and depth positioning error of cutting-points were less than 6.0 mm and 7.4 mm. The proposed model is of strong robustness even dealing with partial occlusion and motion blur and is suitable with limited computing power to meet the needs of Robotic selective harvesting.

Digital Surgical Guides in Mandibular Genioplasty: Evaluating Precision Against Conventional Techniques.

Mandibular genioplasty, a central procedure in oral and maxillofacial surgery, has traditionally relied on surgeon experience with potential limitations in precision. The advent of digital methods, particularly computer-aided design/computer-aided manufacturing (CAD/CAM), offers a promising alternative. This study aims to evaluate the efficacy of digital surgical guides in improving the precision of mandibular genioplasty. A prospective analysis of 50 patients undergoing genioplasty was performed, 30 in the experimental group using digital surgical guides and 20 in the control group using traditional methods. Three-dimensional reconstructions were obtained using cone-beam computed tomography (CBCT) and digital scans. Osteotomy guides were 3D-printed based on group assignment. Postoperatively, accuracy was assessed by measuring distances between landmarks. The experimental group showed significantly reduced horizontal positioning errors in genioplasty advancement, with no significant differences in vertical errors. For genioplasty retraction, the experimental group showed fewer vertical positioning errors, while horizontal errors remained consistent. The use of digital surgical guides in mandibular genioplasty significantly improves surgical accuracy, resulting in improved outcomes and patient satisfaction. This study highlights the potential of digital methods in refining oral and maxillofacial surgical procedures. This journal requires that authors assign a level of evidence to each article. For a full description of these Evidence-Based Medicine ratings, please refer to the Table of Contents or the online Instructions to Authors www.springer.com/00266.

Application of Atmospheric Augmentation for PPP-RTK with Instantaneous Ambiguity Resolution in Kinematic Vehicle Positioning

The long convergence time and non-robust positioning accuracy are the main factors limiting the application of precision single-point positioning (PPP) in kinematic vehicle navigation. Therefore, a dual/triple-frequency multi-constellation PPP-RTK method with atmospheric augmentation is proposed to achieve cm-level reliable kinematic positioning. The performance was assessed using a set of static station and kinematic vehicle positioning experiments conducted in Wuhan. In the static experiments, instantaneous convergence within 1 s and centimeter-level positioning accuracy were achieved for PPP-RTK using dual-frequency observation. For the kinematic experiments, instantaneous convergence was also achieved for dual-frequency PPP-RTK in open areas, with RMS of 2.6 cm, 2.6 cm, and 7.5 cm in the north, east, and up directions, respectively, with accuracy similar to short-baseline real-time kinematic positioning (RTK). Horizontal positioning errors of less than 0.1 m and 3D positional errors of less than 0.2 m were 99.54% and 98.46%, respectively. Additionally, after the outage of GNSS and during satellite reduction in obstructed environments, faster reconvergence and greater accuracy stability were realized compared with PPP without atmospheric enhancement. Triple-frequency PPP-RTK was able to further enhance the robustness and accuracy of positioning, with RMS of 2.2 cm, 2.0 cm, and 7.3 cm, respectively. In summary, a performance similar to RTK was achieved based on dual-frequency PPP-RTK, demonstrating that PPP-RTK has the potential for lane-level navigation.

A hybrid information fusion method for SINS/GNSS integrated navigation system utilizing GRU-aided AKF during GNSS outages

Abstract To enhance the performance of integrated inertial navigation system (INS) and global navigation satellite system (GNSS) during GNSS outages, this paper proposed a fusion positioning method based on predictive observation information and adaptive filter parameter. Combined with an adaptive Kalman filter (AKF) and a Gated Recurrent Unit neural network (NN) that directly relates the inertial measurement unit (IMU) output sequence to the error estimation, the hybrid information fusion system can provide effective corrections to compensate for horizontal position errors under the constraints of complex and dynamic vehicle movement data during GNSS outages. Meanwhile, the designed adaptive parameter of the integrated navigation filter can adjust the credibility of the state prediction section when the GNSS is reconnected, ensuring the system can switch rapidly between the INS/GNSS and INS/NN integrated modes. The performance of the proposed information fusion method has been experimentally validated using IMU and GNSS data collected in a vehicle navigation test conducted on a stretch of expressway. The comparison results indicate that the proposed algorithm has error suppression capabilities under various experimental constraints and demonstrates a degree of extendibility and reusability.

A Robust Vector-Tracking Loop Based on KF and RTS Smoothing for Shipborne Navigation

High-precision navigation systems are crucial for unmanned autonomous vessels. However, commonly used Global Navigation Satellite System (GNSS) signals are often severely affected by environmental obstruction, leading to reduced positioning accuracy or even the inability to locate. To address the issues caused by signal obstruction in high-precision navigation systems, the research presented in this paper proposes a vector-tracking loop (VTL) structure based on the forward Kalman Filter (KF) and the backward Rauch Tung Striebel (RTS) smoothing algorithm. The introduction of loop filters in the signal-tracking loop improves the tracking accuracy of the carrier and code, thereby enhancing the stability and robustness of the navigation system. The traditional scalar-tracking loop (STL), traditional VTL, and Kalman Filter (KF)-based VTL were compared through shipborne motion experiments, and the proposed method demonstrated superior signal-tracking capability and navigation accuracy. In the experiment, there were three blocking areas along the experimental path. The experimental results show that, when there are signal blockages of 12 s, 18 s, and 40 s, compared to the traditional VTL method, the proposed method can reduce the horizontal position error by 93.9%, 95.8%, and 94.5%, respectively, as well as the horizontal velocity error by 71.1%, 95.8%, and 97.6%, respectively.

Real-Time 3D Tracking of Multi-Particle in the Wide-Field Illumination Based on Deep Learning.

In diverse realms of research, such as holographic optical tweezer mechanical measurements, colloidal particle motion state examinations, cell tracking, and drug delivery, the localization and analysis of particle motion command paramount significance. Algorithms ranging from conventional numerical methods to advanced deep-learning networks mark substantial strides in the sphere of particle orientation analysis. However, the need for datasets has hindered the application of deep learning in particle tracking. In this work, we elucidated an efficacious methodology pivoted toward generating synthetic datasets conducive to this domain that resonates with robustness and precision when applied to real-world data of tracking 3D particles. We developed a 3D real-time particle positioning network based on the CenterNet network. After conducting experiments, our network has achieved a horizontal positioning error of 0.0478 μm and a z-axis positioning error of 0.1990 μm. It shows the capability to handle real-time tracking of particles, diverse in dimensions, near the focal plane with high precision. In addition, we have rendered all datasets cultivated during this investigation accessible.

Unveiling Starlink LEO Satellite OFDM-Like Signal Structure Enabling Precise Positioning

This letter unveils the unknown structure of Starlink low Earth orbit (LEO) satellites' orthogonal frequency division multiplexing (OFDM)-like reference signals (RSs). The spectrum of Starlink's dowlink signals is presented, and the frame length is estimated. A blind receiver is proposed, which acquires via a sequential generalized likelihood ratio test multiple satellites, estimates their RSs and respective Doppler, and tracks their carrier and code phases. Experimental results are presented showing six tracked Starlink LEO satellites, three of which transmitted pure tones, while the other transmitted OFDM-like signals. The achieved horizontal positioning error with the six satellites was 6.5 m.

Error Compensation Method for Pedestrian Navigation System Based on Low-Cost Inertial Sensor Array.

In the pedestrian navigation system, researchers have reduced measurement errors and improved system navigation performance by fusing measurements from multiple low-cost inertial measurement unit (IMU) arrays. Unfortunately, the current data fusion methods for inertial sensor arrays ignore the system error compensation of individual IMUs and the correction of position information in the zero-velocity interval. Therefore, these methods cannot effectively reduce errors and improve accuracy. An error compensation method for pedestrian navigation systems based on a low-cost array of IMUs is proposed in this paper. The calibration method for multiple location-free IMUs is improved by using a sliding variance detector to segment the angular velocity magnitude into stationary and motion intervals, and each IMU is calibrated independently. Compensation is then applied to the velocity residuals in the zero-velocity interval after zero-velocity update (ZUPT). The experimental results show a significant improvement in the average noise performance of the calibrated IMU array, with a 3.01-fold increase in static noise performance. In the closed-loop walking experiment, the average horizontal position error of a single calibrated IMU is reduced by 27.52% compared to the uncalibrated IMU, while the calibrated IMU array shows a 2.98-fold reduction in average horizontal position error compared to a single calibrated IMU. After compensating for residual velocity, the average horizontal position error of a single IMU is reduced by 0.73 m, while that of the IMU array is reduced by 64.52%.

Analysis and Simulation of Lateral Collision Risk under Paired Approach

The paired approach can improve the efficiency of closely spaced parallel runways. Calculating the probability and frequency of horizontal overlap is an indispensable step when evaluating the horizontal collision risk of the paired approach. As the generation of horizontal overlap probability is closely related to horizontal position error, we propose a calculation method of horizontal overlap probability based on position error from the perspective of pilot operation. First, according to the principle of flight mechanics, the attitude adjustment model is established for the horizontal direction of the approach process, and the pilot’s operation model for various position errors is based on the concept of the stochastic process. This attitude adjustment model can replicates the process of the pilot operating the steering column to change the aircraft’s attitude. When combined with the pilot’s operation model, it is possible to simulate the position errors generated during the approach process. Building on this, the horizontal overlapping conditions of two aircraft are analyzed to simulate the horizontal overlap process in the paired approach. The duration and instances of overlap counted and the ratio between these results and the total running time give the overlap probability and frequency. Multiple simulations in MATLAB reveal that higher pilot operating accuracy shortens the time for the aircraft to align with the course, whereas lower accuracy leads to unstable horizontal position errors. Furthermore, the horizontal overlap in paired approaches primarily occurs at the beginning of the procedure, and enhancing the pilot’s operating accuracy does not significantly affect the probability and frequency of horizontal overlap.

A water track laser Doppler velocimeter for use in underwater navigation

Doppler velocity log (DVL) is usually employed to suppress the divergency of the Strapdown Inertial Navigation System (SINS) in underwater navigation, which is not concealable due to high transmittance for acoustic wave in the water. To conduct underwater navigation task with high concealment, a differential laser Doppler velocimeter (LDV) working at water track mode is integrated with SINS in this paper. The developed LDV measures the advance velocity of the underwater carrier with respect to the surrounding water in underwater navigation scenario with advantages of high concealment, high real-time performance, high update rate, light weight, and small dimension. A dynamic river test was conducted to validate the underwater navigation performance of SINS/LDV integrated system. The experimental results show that during the voyage of 4493s and 5271.8 m, the maximum horizontal positioning errors of the proposed SINS/LDV integrated underwater navigation system is 27.8 m and the relative position error is less than 0.6% with respect to total distance. Therefore, the water track LDV is practical to aid SINS in underwater navigation environment.

Assessment of the GNSS-RTK for Application in Precision Forest Operations

A smart thinning operation refers to an advanced method of selecting and cutting trees to be thinned based on digitally captured forest information. In smart thinning operations, workers use the coordinates of individual trees to navigate to the target trees for thinning. However, it is difficult to accurately locate individual trees in a forest stand covered with a canopy, necessitating a precise real-time positioning system that can be used in the forest. Therefore, this study aimed to evaluate the applicability of the global navigation satellite system real-time kinematic (GNSS-RTK) device in a forest stand through analysis of its positioning accuracy within the forest environment and evaluation of the operational range of the single-baseline RTK based on analysis of the positioning precision and radio signal strength index (RSSI) change with increasing distance from the base station. The results showed that the root mean square error (RMSE) of the horizontal positioning error was highly accurate, with an average of 0.26 m in Larix kaempferi stands and 0.48 m in Pinus koraiensis stands. The RSSI decreased to a minimum of −103.3 dBm within 1 km of distance from the base station; however, this had no significant impact on the horizontal positioning precision. The conclusion is that the GNSS-RTK is suitable for use in smart thinning operations.

Performance Analysis of Relative GPS Positioning for Low-Cost Receiver-Equipped Agricultural Rovers.

Global navigation satellite systems (GNSSs) became an integral part of all aspects of our lives, whether for positioning, navigation, or timing services. These systems are central to a range of applications including road, aviation, maritime, and location-based services, agriculture, and surveying. The Global Positioning System (GPS) Standard Position Service (SPS) provides position accuracy up to 10 m. However, some modern-day applications, such as precision agriculture (PA), smart farms, and Agriculture 4.0, have demanded navigation technologies able to provide more accurate positioning at a low cost, especially for vehicle guidance and variable rate technology purposes. The Society of Automotive Engineers (SAE), for instance, through its standard J2945 defines a maximum of 1.5 m of horizontal positioning error at 68% probability (1σ), aiming at terrestrial vehicle-to-vehicle (V2V) applications. GPS position accuracy may be improved by addressing the common-mode errors contained in its observables, and relative GNSS (RGNSS) is a well-known technique for overcoming this issue. This paper builds upon previous research conducted by the authors and investigates the sensitivity of the position estimation accuracy of low-cost receiver-equipped agricultural rovers as a function of two degradation factors that RGNSS is susceptible to: communication failures and baseline distances between GPS receivers. The extended Kalman filter (EKF) approach is used for position estimation, based on which we show that it is possible to achieve 1.5 m horizontal accuracy at 68% probability (1σ) for communication failures up to 3000 s and baseline separation of around 1500 km. Experimental data from the Brazilian Network for Continuous Monitoring of GNSS (RBMC) and a moving agricultural rover equipped with a low-cost GPS receiver are used to validate the analysis.

A Vision-Based Method for Simultaneous Instance Segmentation and Localization of Indoor Objects

Visual-based positioning technology plays a pivotal role in spatial artificial intelligence, facilitating precise perception and comprehension of the physical world for robotic platforms and augmented reality devices. In this study, we propose a binocular camera-based method for spatial localization of targets using CNN for instance segmentation while simultaneously providing target location information. The method encompasses image acquisition and correction, target recognition and segmentation, and stereo matching, among other components. Building upon this foundation, we introduce a pedestrian recognition segmentation network model with an attention mechanism. To accurately locate the target, we employ a multi-feature fusion feature point extraction and matching algorithm that combines edge information with semantic information. Finally, our proposed method is evaluated for dynamic pedestrian targets in indoor environments, achieving a horizontal positioning error of less than 0.25 m.

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)).

Real-time Detection System for Portable Transient Electromagnetic Unexploded Ordnance

Portable transient electromagnetic systems are not limited by terrain and can detect unexploded ordnance very flexibly. However, existing data processing methods are slow and cannot achieve real-time positioning of targets. In this paper, based on a laboratory-made portable transient electromagnetic detection system, the magnetic dipole model and tensor positioning algorithm are used to achieve fast and accurate target positioning. Using the magnetic gradient tensor algorithm for positioning reduces the calculation load, allowing it to run on embedded systems, and improving target positioning speed while ensuring the accuracy of measurements. Experimental results show that the vertical and horizontal positioning errors of the UXO are within 10 cm, and single-point positioning can be completed within 10 ms.

PPP-RTK with Rapid Convergence Based on SSR Corrections and Its Application in Transportation

Real-time Kinematic (RTK) positioning provides centimeter-level positioning accuracy within several seconds, but it has to rely on a nearby base station. Although Precise Point Positioning (PPP) supplies precise positions with one receiver, its convergence time takes several tens of minutes, which makes PPP not well suited for real-time kinematic applications where a rapid convergence is required. PPP-RTK integrates the benefits of PPP and RTK, which actually is PPP augmented by a ground GNSS network. The satellite orbit, clock offsets, signal biases, ionospheric and tropospheric corrections are determined based on this GNSS network, modeled as state space information and transmitted to PPP users. By applying these State Space Representation (SSR) corrections, a real-time kinematic PPP-RTK approach is developed and implemented, which can instantly resolve the ambiguities to integers and realize rapid convergence. In a static scenario, it realized an instant ambiguity resolution and a rapid convergence within 2 s in more than 90% of 120 hourly sessions. The PPP-RTK has been applied and evaluated in a kinematic scenario on the highway. The horizontal positioning errors are almost lower than 0.1 m except for the time of passing through bridges. After passing bridges, the PPP-RTK successfully resolved ambiguities within 2 s in 90.6% of the cases and achieved convergence in horizontal within 5 s in more than 90% of the cases. The PPP-RTK with a precision of 0.1 m and rapid convergence of several seconds benefits the precise navigation of automobile on the highway, which will support the development of autonomous driving in future.

Tightly coupled multi-frequency PPP-RTK/INS integration model and its application in an urban environment

ABSTRACT The Precise Point Positioning-Real Time Kinematic (PPP-RTK) technique, which provides centimeter-level positioning with instantaneous ambiguity resolution, is considered as a potential tool for intelligent vehicle applications. However, its performance is restricted under complex urban conditions owing to intermittent signal interruptions and poor satellite geometries. Thus, a tightly coupled Multi-Frequency (MF) PPP-RTK/INS (Inertial Navigation System) model was developed with the objective of providing a stable and reliable positioning for the urban vehicle. In this model, the augmentation of INS information, third-frequency observations, precise atmospheric corrections, the fixed Extra-Wide Lane (EWL), and Wide-Lane (WL) ambiguities can be used to enhance the positioning performance of PPP-RTK. We designed urban vehicle experiments under different scenarios to validate the proposed method. The results show that PPP-RTK can be significantly improved for urban vehicle positioning by fusing the MF and INS. In urban areas, the solution availability with a horizontal positioning error within 10 cm was 96.1% for MFPPP-RTK/INS with a fixing percentage of 90.9%. Compared with the dual-frequency PPP-RTK solutions, the fixing percentage and solution availability in the MFPPP-RTK/INS was improved by 9.5% and 8.8%, respectively. Moreover, MFPPP-RTK/INS provides continuous and stable positioning and fast ambiguity recovery in GNSS-challenged environments. The MFPPP-RTK/INS could achieve a fast ambiguity re-fixing within 1 s after continuously crossing obstacles, whereas PPP-RTK could achieve the same in 10 s.