Coordinate Conversion Research Articles

Map construction algorithm based on dense point cloud

AbstractIn order to address the issue of the difficulty in constructing maps from sensor‐acquired point clouds, a map construction algorithm is proposed for the effective conversion from sparse point clouds to dense point clouds. First, it constructs a dense point cloud map in real‐time using colour and depth information of keyframes. Then, it generates an accurate point cloud map by voxel filtering and coordinate conversion. Finally, the point cloud map is converted into an octree map using OctoMap. This article uses the TUM dataset for simulation analysis to verify the effectiveness of the algorithm. The results demonstrate that the algorithm can construct dense point cloud maps with high positioning accuracy in sparse point cloud scenarios. The algorithm improves the positioning accuracy by more than 15% under the fr1_xyz, fr1_room, fr1_desk2, fr1_desk1, fr2_desk and fr3_str_tex_near sequences, compared to ORB‐SLAM2, ORB‐SLAM3 and GX ORB‐SLAM2 algorithm

A Crack Detection Method for Civil Engineering Bridges Based on Feature Extraction and Parametric Modeling of Point Cloud Data

Accurate detection and analysis of cracks is critical for ensuring the safety and reliability of concrete bridges. Point cloud data (PCD) obtained from 3D scanning provides a promising avenue for automated crack assessment. However, processing the massive and unstructured PCD poses significant challenges in feature extraction and crack modeling. This paper proposes a novel method for bridge crack analysis by combining PCD feature extraction with a hierarchical neural network and Rodriguez rotation. The method first extracts crack features from PCD using outlier removal, denoising, and 3D coordinate conversion. A crack analysis model is then constructed by integrating multi-scale feature extraction and Rodriguez rotation into a hierarchical neural network, enabling the capture of both local and global crack patterns. Experiments on a benchmark data set demonstrate the effectiveness of the proposed approach, achieving 92.83% feature extraction accuracy, 95.73% parameter analysis accuracy, 93.51% recognition accuracy, and 0.91 F1 score. The method also shows improved efficiency compared to existing techniques. These results highlight the potential of the proposed PCD-based approach for accurate and efficient crack analysis in concrete bridges.

Detection of rice panicle density for unmanned harvesters via RP-YOLO

Rice panicle density is one of the essential bases for the automatic speed regulation of unmanned harvesters, making density detection crucial for intelligent upgrades. Currently, existing methods for detecting rice panicle density do not meet actual harvesting scenarios and struggle to meet real-time requirements. To address this, we developed a real-time rice panicle density detection method for unmanned harvesters. This method includes a panicle detection model based on YOLOv5n (RP-YOLO) and a rice panicle density calculation based on coordinate transformations. RP-YOLO was optimized through various techniques, such as enhancing the target detection head, reconfiguring the backbone network and downsampling module, introducing an attention mechanism, and refining the loss function. Based on coordinate conversion, we converted the world coordinates of the detection frame vertex to image coordinates and calculated the panicle density. We established the RP-1668 dataset for japonica rice and trained and tested the model. Compared to the original YOLOv5n model, our modifications reduced floating-point operations per second (FLOPs) by 33.33 %, decreased model size by 31.90 %, increased detection speed by 12.63 %, and improved accuracy (AP0.5) by 3.82 % (AP0.5:0.95, 6.96 %). RP-YOLO achieved superior accuracy and detection speed compared to both conventional lightweight and non-lightweight models. In field applications, the error in density detection was less than 10 % compared to manual counting, and the results clearly reflected changes in rice panicle density. For a 1.4 m × 1.0 m rice field imaging area (with a resolution of 2560 × 1280), the method detects at 15 fps on an on-board industrial computer, providing reliable data support for adjusting the operating speed of driverless harvesters.

Experimental study on identifying anomaly azimuth based on acoustic vector array of borehole acoustic reflection imaging

Accurate anomaly azimuth identification is a major challenge in borehole acoustic reflection imaging. We propose an azimuth estimation method using an acoustic vector array to address this issue. This method was rigorously tested through a physical simulation experiment in a water-filled tank using a monopole acoustic source and an acoustic receiver station comprised of eight azimuthal elements. The proposed method involves the synthesis of multiazimuth acoustic pressure waveforms recorded by the receiver into multicomponent particle velocity waveforms. These waveforms are paired and subjected to coordinate conversion, yielding multiple groups of orthogonal component particle velocity waveforms. Each group underwent polarization analysis to obtain the direction of particle polarization on the horizontal plane and isolate the principal component particle velocity waveform. Using the particle polarization direction, the amplitude of the multiazimuth acoustic pressure waveform, and the type of echo mode, we accurately determined the azimuth of the anomaly, facilitating the creation of a spatial distribution image of the anomaly. Further validation of this method was conducted through a large-scale physical simulation experiment in a deep-water lake using a borehole acoustic reflection imaging instrument. The obtained experimental data were used to validate the effectiveness of this method. Finally, considering an actual logging environment, the feasibility of this method in a borehole environment was verified using numerical simulations and field data of acoustic detection of nearby wells. The present findings demonstrate that this novel method considerably enhances the accuracy and stability of the measurement of anomaly azimuth based on the particle polarization direction. In addition, this method effectively harnesses both acoustic pressure and particle velocity in borehole acoustic reflection imaging, exhibiting superior noise robustness, mitigating noise, and improving the signal-to-noise ratio of the echoes.

Spatial positioning method based on range-only measurement of multi-station radar

Aiming at the characteristics that affect the high ranging accuracy of shipborne radar, a multi station radar spatial positioning method based on ranging is proposed. This method is based on the ECEF (Earth Centered Earth Fixed) coordinate system, and adopts the method of intersecting the detection distances of multiple radars to the target, and directly calculates the spatial position of the target. This method only needs the geodetic coordinates of each radar station and the detection range of the target to calculate the geodetic coordinates of the target, which can effectively solve the coordinate conversion problem caused by the curvature of the earth, and does not involve higher-order equations and multi-value solutions, and it does not involve iterative initial value calculation. The positioning system can not only obtain high positioning accuracy, but also has a long operating distance, which can better solve the multi-radar range measurement intersection positioning problem.

3D positioning of Camellia oleifera fruit-grabbing points for robotic harvesting

Camellia oleifera is an oilseed crop with high economic value. The short optimum harvest period and high labour costs of C. oleifera harvesting have prompted research on intelligent robotic harvesting. This study focused on the determination of grabbing points for the robotic harvesting of C. oleifera fruits, providing a basis for the decision making of the fruit-picking robot. A relatively simple 2D convolutional neural network (CNN) and stereoscopic vision replaced the complex 3D CNN to realise the 3D positioning of the fruit. Apple datasets were used for the pretraining of the model and knowledge transfer, which shared a certain degree of similarity to C. oleifera fruit. In addition, a fully automatic coordinate conversion method has been proposed to transform the fruit position information in the image into its 3D position in the robot coordinate system. Results showed that the You Only Look Once (YOLO)v8x model trained using 1012 annotated samples achieved the highest performance for fruit detection, with mAP50 of 0.96 on the testing dataset. With knowledge transfer based on the apple datasets, YOLOv8x using few-shot learning realised a testing mAP50 of 0.95, reducing manual annotation. Moreover, the error in the 3D coordinate calculation was lower than 2.1 cm on the three axes. The proposed method provides the 3D coordinates of the grabbing point for the target fruit in the robot coordinate system, which can be transferred directly to the robot control system to execute fruit-picking actions. This dataset was published online to reproduce the results of this study.

Evolution of Industrial Robots from the Perspective of the Metaverse: Integration of Virtual and Physical Realities and Human–Robot Collaboration

During the transition from Industry 4.0 to Industry 5.0, industrial robotics technology faces the need for intelligent and highly integrated development. Metaverse technology creates immersive and interactive virtual environments, allowing technicians to perform simulations and experiments in the virtual world, and overcoming the limitations of traditional industrial operations. This paper explores the application and evolution of metaverse technology in the field of industrial robotics, focusing on the realization of virtual–real integration and human–machine collaboration. It proposes a design framework for a virtual–real interaction system based on the ROS and WEB technologies, supporting robot connectivity, posture display, coordinate axis conversion, and cross-platform multi-robot loading. This paper emphasizes the study of two key technologies for the system: virtual–real model communication and virtual–real model transformation. A general communication mechanism is designed and implemented based on the ROS, using the ROS topic subscription to achieve connection and real-time data communication between physical robots and virtual models, and utilizing URDF model transformation technology for model invocation and display. Compared with traditional simulation software, i.e., KUKA Sim PRO (version 1.1) and RobotStudio (version 6.08), the system improves model loading by 45.58% and 24.72%, and the drive response by 41.50% and 28.75%. This system not only supports virtual simulation and training but also enables the operation of physical industrial robots, provides persistent data storage, and supports action reproduction and offline data analysis and decision making.

A High-Precision Sub-Grid Parameterization Scheme for Clear-Sky Direct Solar Radiation in Complex Terrain—Part I: A High-Precision Fast Terrain Occlusion Algorithm

In atmospheric modeling, sub-grid parameterization is an important method for studying the topographic effects of solar radiation using high-resolution Digital Elevation Model (DEM) data. For reducing the amount of computation, some approximate methods that can lead to errors are used in existing sub-grid parameterization schemes for clear-sky direct solar radiation (SPS-CSDSR). The lack of a high-precision fast terrain occlusion algorithm (HPFTOA) remains one of the biggest constraints in this field. This study proposed an HPFTOA. It mainly uses two kinds of acceleration algorithms. One method is to use a dynamic, lossless, and fast occlusion search radius. Another way is to use the rectangular grid for calculations within the accuracy of DEM data to avoid coordinate projection conversions. The test results indicate that the HPFTOA can carry out large-scale computation based on DEM data with a resolution of 90 m. Because it rarely uses approximation algorithms and considers the curvature of the Earth, SPS-CSDSR can achieve unprecedented precision. The HPFTOA can also be used in the fields of mountain solar energy assessment, remote sensing, and telemetry, including terrain-obscuring the probe. As computer performance improves and algorithms and execution code are optimized, the application prospects will be very broad.

Calculation Model for the Exit Decision Sight Distance of Right-Turn Ramps on the Left at Interchange

Given the rapid construction of freeways in developing countries such as China, land use is constantly under strict constraints, leading to challenges in adopting conventional layouts for interchanges. Implementing right-turn ramps on the left (RTRL) at interchanges can minimize land occupancy; however, the traffic safety level in this type of diversion area design requires extra attention. This study examines the decision sight distance for right-turn exit ramps on the left side. Utilizing unmanned aerial vehicle (UAV) video and the YOLOv3 target detection algorithm, the original trajectory data of vehicles in the diversion area is extracted. Employing Kalman filtering and Frenet coordinate system conversion reveals microscopic vehicle lane-change patterns, velocities, and time headways. Furthermore, the driving simulation experiment assesses driver behaviors in RTRL, with subjective, task performance, and physiological measure indicators. Ultimately, the range of the decision sight distance is defined, and establishing a calculation model involves determining relevant parameters based on measured data and simulation outcomes. The results indicate potential insufficiencies in the decision sight distance when standardized values are applied to RTRL.

Research on the optimization methods of common points layout for survey and alignment of particle accelerators

As a fourth-generation synchrotron light source based on a diffraction-limited storage ring, Hefei Advanced Light Facility (HALF) puts forward higher requirements for the alignment accuracy of the main components. Aggregated common points result in a loss of accuracy during the coordinate transformation required by accelerator alignment. To address this challenge, we proposed two methods: “aggregated points centralization (APC)" and “uniformity-weighted algorithm (UWA)" according to different usage scenarios. APC combines uniformity with the K-means algorithm to enhance the accuracy of coordinate transformation while reducing the number of common points. UWA calculates the uniformity in different directions and assigns weights to common points, reducing the accuracy loss. Simulations demonstrate that these two methods have strong superiority and stability with significantly improved accuracy. Applications of these 2 methods in the magnet unit pre-alignment experiment and tunnel network measurement show promising results. APC in pre-alignment can reduce the cost of building common points by 26% while maintaining the coordinate conversion accuracy. In tunnel network measurement, accuracy can be increased by 28% using UWA. The methods proposed offer broad applicability in the field of particle accelerator alignment and guiding alignment solutions for HALF.

Automatic welding seam tracking and real-world coordinates identification with machine learning method

In the automatic welding process, the precision of the welding position significantly influences welding quality, relying heavily on the accurate identification of the welding seam. However, in complex and unstructured welding environments, such as those with strong arc lights, welding splashes, and thermal-induced deformations, various disturbances present a significant challenge to identify the welding seam. This paper introduces a cost-effective welding seam tracking model constructed using a laser line and a fixed viewpoint single RGB camera. The model's primary objective is to detect a chain of welding-seam points in both captured images and real-time camera feeds. The paper presents the techniques for camera calibration, laser detection, and the use of artificial intelligence to establish a real-world coordinate frame. The process begins with camera calibration using the OpenCV library to filter noise and undistort images. Subsequently, the thresholding technique is employed for color image segmentation, isolating the laser sensor light on the workpiece. An algorithm is then introduced to detect welding spots. Finally, the image coordinates are converted to world coordinates using two machine learning methods: Random Forest Regression and Gradient Boosting Regression. Experimental demonstrations were conducted at different positions on the object to assess algorithm precision. The results indicate average deviations of 0.83 mm, 0.74 mm, and 0.77 mm for X, Y, and Z coordinates, respectively, which fall below the expected standard deviation of 3 mm. Despite the overall consistency of the program, slight noise from environmental lighting may still exist. In conclusion, the proposed welding seam tracking method and coordinate conversion program have proven effective and cost-efficient, with potential for future improvements.

Accuracy compensation method with the combined dissimilar measurement devices for enhanced measurement quality: a digital aircraft assembly technology

PurposeThe pivotal aspect of aircraft assembly lies in precise measurement accuracy. While a solitary digital measuring tool suffices for analytical and small surfaces, it falls short for extensive synthetic surfaces like aircraft fuselage panels and wing spars. The purpose of this study is to develop a “combined measurement method” (CMM) that enhances measurement quality and expands the evaluative scope, addressing the limitations posed by singular digital devices in meeting measurement requirements across various aircraft components.Design/methodology/approachThe study illustrated the utilization of the CMM by combining a laser tracker and a portable arm-measuring machine. This innovative approach is tailored to address the intricate nature and substantial dimensions of aircraft fuselage panels. The portable arm-measuring machine performs precise scans of panel components, while common points recorded by the laser tracker undergo coordinate conversion to reconstruct the fuselage panel’s shape. The research outlines the CMM’s measurement procedure and scrutinizes the data processing technique. Ultimately, the investigation yields a deviation vector matrix and chromatogram deviation distribution, pivotal in achieving enhanced measurement precision for the novel CMM device.FindingsThe use of CMM noticeably enhances fuselage panel assembly accuracy, concurrently reducing assembly time and enhancing efficiency compared to conventional measurement systems.Practical implicationsThe research’s practical implication lies in revolutionizing aircraft assembly by mitigating accuracy issues through the innovative digital CMM for aircraft synthetic structure type product (aircraft fuselage panel). This ensures safer flights, reduces rework and enhances overall efficiency in the aerospace industry.Originality/valueIntroducing a new aircraft assembly accuracy compensation method through digital combined measurement, pioneering improved assembly precision. Also, it enhances aerospace assembly quality, safety and efficiency, offering innovative insights for optimized aviation manufacturing processes.

Lizard Body Temperature Acquisition and Lizard Recognition Using Artificial Intelligence.

The acquisition of the body temperature of animals kept in captivity in biology laboratories is crucial for several studies in the field of animal biology. Traditionally, the acquisition process was carried out manually, which does not guarantee much accuracy or consistency in the acquired data and was painful for the animal. The process was then switched to a semi-manual process using a thermal camera, but it still involved manually clicking on each part of the animal's body every 20 s of the video to obtain temperature values, making it a time-consuming, non-automatic, and difficult process. This project aims to automate this acquisition process through the automatic recognition of parts of a lizard's body, reading the temperature in these parts based on a video taken with two cameras simultaneously: an RGB camera and a thermal camera. The first camera detects the location of the lizard's various body parts using artificial intelligence techniques, and the second camera allows reading of the respective temperature of each part. Due to the lack of lizard datasets, either in the biology laboratory or online, a dataset had to be created from scratch, containing the identification of the lizard and six of its body parts. YOLOv5 was used to detect the lizard and its body parts in RGB images, achieving a precision of 90.00% and a recall of 98.80%. After initial calibration, the RGB and thermal camera images are properly localised, making it possible to know the lizard's position, even when the lizard is at the same temperature as its surrounding environment, through a coordinate conversion from the RGB image to the thermal image. The thermal image has a colour temperature scale with the respective maximum and minimum temperature values, which is used to read each pixel of the thermal image, thus allowing the correct temperature to be read in each part of the lizard.

Optimization of Human Posture Recognition based on Multi-view Skeleton Data Fusion

This research introduces a novel method for fusing multi-view skeleton data to address the limitations encountered by a single vision sensor in capturing motion data, such as skeletal jitter, self-pose occlusion, and the reduced accuracy of three-dimensional coordinate data for human skeletal joints due to environmental object occlusion. Our approach employs two Kinect vision sensors concurrently to capture motion data from distinct viewpoints extract skeletal data and subsequently harmonize the two sets of skeleton data into a unified world coordinate system through coordinate conversion. To optimize the fusion process, we assess the contribution of each joint based on human posture orientation and data smoothness, enabling us to fine-tune the weight ratio during data fusion and ultimately produce a dependable representation of human posture. We validate our methodology using the FMS public dataset for data fusion and model training. Experimental findings demonstrate a substantial enhancement in the smoothness of the skeleton data, leading to enhanced data accuracy and an effective improvement in human posture recognition following the application of this data fusion method.

Analysis of multi-UAV communication networking problem in constrained geographic environments based on improved simulated annealing optimization algorithm

This paper conducts an in-depth exploration of UAV communication networking and path planning within geographically constrained environments. The study begins with necessary data preprocessing, which includes the conversion of latitude and longitude coordinates and the organization of antenna parameters. Through the development of a model based on coordinate geometry, this research effectively identifies communication blind spots and establishes a comprehensive geometric envelope for signal coverage. To enhance network efficiency and path planning, the paper introduces a hybrid optimization algorithm that combines simulated annealing and genetic algorithms. Simulated annealing is used to optimize the selection of communication types between network nodes, while genetic algorithms refine the UAV fleet's flight routes based on these communication strategies. This dual-layered approach allows for fine-tuned adjustments in response to dynamic environmental constraints. The effectiveness of this method is demonstrated through simulations, which reveal a communication coverage rate of 73.7272%. These results confirm that the proposed hybrid optimization technique significantly improves both communication coverage and operational efficiency of UAV networks in complex environments. This provides substantial theoretical insights and practical contributions to the field of UAV network optimization, which is particularly valuable for applications in remote or urban areas where geographical constraints pose significant challenges.

Field cabbage detection and positioning system based on improved YOLOv8n

BackgroundPesticide efficacy directly affects crop yield and quality, making targeted spraying a more environmentally friendly and effective method of pesticide application. Common targeted cabbage spraying methods often involve object detection networks. However, complex natural and lighting conditions pose challenges in the accurate detection and positioning of cabbage.ResultsIn this study, a cabbage detection algorithm based on the YOLOv8n neural network (YOLOv8-cabbage) combined with a positioning system constructed using a Realsense depth camera is proposed. Initially, four of the currently available high-performance object detection models were compared, and YOLOv8n was selected as the transfer learning model for field cabbage detection. Data augmentation and expansion methods were applied to extensively train the model, a large kernel convolution method was proposed to improve the bottleneck section, the Swin transformer module was combined with the convolutional neural network (CNN) to expand the perceptual field of feature extraction and improve edge detection effectiveness, and a nonlocal attention mechanism was added to enhance feature extraction. Ablation experiments were conducted on the same dataset under the same experimental conditions, and the improved model increased the mean average precision (mAP) from 88.8% to 93.9%. Subsequently, depth maps and colour maps were aligned pixelwise to obtain the three-dimensional coordinates of the cabbages via coordinate system conversion. The positioning error of the three-dimensional coordinate cabbage identification and positioning system was (11.2 mm, 10.225 mm, 25.3 mm), which meets the usage requirements.ConclusionsWe have achieved accurate cabbage positioning. The object detection system proposed here can detect cabbage in real time in complex field environments, providing technical support for targeted spraying applications and positioning.

Robotic Arms for Telemedicine System Using Smart Sensors and Ultrasound Robots

Given the global population ages, the traditional medical system must change. Our telemedicine system combines the devices with sensors. Our telemedicine system is a new type of medical application. In this paper, we systematically integrate the force sensor, robot arm, optical radar device, and jelly mechanism to develop a telemedicine application system. We used a three-dimensional coordinate conversion formula to convert the coordinates of each axis of the robot arm into the coordinates of the smartphone so that the doctor can control the robot arm remotely using the smartphone. The force sensor embedded in the robot arm provides transparency to the doctor during operation, enabling them to monitor whether the force applied by the robotic arm on the human body is excessive. In addition, through the jelly mechanism installed on the robot arm, the doctor only needs to use a smartphone to control the jelly mechanism to achieve remote control needs. The experimental testing results sufficiently show the practicability of our scheme for telemedicine.

Consolidated Rotation Measure Catalog Update

We identified discrepancies between the rotation measure (RM) catalogs by Clegg et al. and Minter & Spangler and their corresponding rows in the Van Eck et al. consolidated catalog. The discrepancies, in the case of Minter & Spangler, are caused by the improper coordinate conversions between J2000 and B1950 Equatorial coordinate systems used between the catalogs. The discrepancies associated with Clegg et al. are due to differences in the number of significant figures reported between the original and consolidated catalogs, which result in overlapping points in the consolidated catalog. These errors affect studies that rely on the accuracy of the coordinate data. After proper unit conversions, we found that coordinate values differed by up to 1° between the Minter & Spangler and consolidated catalogs. Employing a combination of manual data extraction and automated coordinate conversion tools, we corrected and updated those RM coordinate values to align with the standardized format used in the Van Eck et al. consolidated catalog.

Refined Aircraft Positioning Based on Stochastic Hybrid Estimation with Adaptive Square-Root Unscented Particle Filtering

The positioning of civil aviation aircraft relative to a geographic reference point on Earth in a Cartesian frame is significant to detect the deviations from the desired path, especially for high-altitude airports or special airports based on performance-based navigation (PBN). To obtain these critical deviations during aircraft approach and landing, it is fundamental to estimate the continuous flight variables and discrete flight modes simultaneously with enough accuracy. With the coordinate conversion between the North, East, and Down (NED) frame and the geographic coordinate system based on World Geodetic System 1984 (WGS-84) considered, this study proposed a non-linear stochastic hybrid estimation algorithm with adaptive square-root unscented particle filtering (ASR-UPF) to estimate the true path. The probabilities of mode transition, represented by the normal cumulative density function of continuous states, determine whether to proceed with mode transitions. In addition, the adaptive update characterized by tracking variable noise and the importance sampling distributions based on the results of square-root unscented Kalman filtering (SR-UKF), as a comparative study of continuous system filtering, were used. The experiments illustrated the ASR-UPF is able to reduce the state estimation error more effectively, and more promptly track the error caused by incorrect mode estimation with adaptability compared to the SR-UKF. A further test with real flight data indicates that the proposed method gives the refined estimation of position and azimuth in NED frame.

Precise Positioning of Primary System of Geodetic Points by GNSS Technology in Railway Operating Conditions

This article deals with the analysis of the accuracy of the geodetic real-time GNSS measurement procedure used in railway operating conditions in the Czech Republic. The purpose was to determine to what extent the operating conditions affect the accuracy of the measurement result and whether an accuracy of standard deviation σx,y = 5 mm in the horizontal plane could be achieved. The use of geodetic GNSS equipment with an IMU unit was also tested. The accuracy obtained in operational conditions is compared with the accuracy obtained on a calibration base using the same measurement procedure. The consistency between the accuracy of the primary system (satellite-based) and the secondary system (terrestrially measured by the traverse method) is also discussed. The analysis includes the issue of residual inhomogeneities of the uniform transformation key when converted to the Czech national coordinate system S-JTSK. It is shown that a homogeneous accuracy in coordinate standard deviation better than σx,y = 5 mm can be achieved. The results indicate that the accuracy under operational conditions is two–three times worse than the accuracy achieved by the same procedure under ideal conditions on a calibration base. This is due to the non-ideal observing conditions, i.e., horizon occlusion by overlays, surrounding vegetation and multipath effects. It has been shown that the effect of multipath can be reduced by repeating short observations 3–4 h apart. Older GNSS instruments using an IMU unit in combination with an electronic compass (eCompass) are at risk of a systematic bias of up to several tens of millimeters, which can be detected by rotating the antenna by 180°. The current uniform transformation key used in the Czech Republic for the conversion of GNSS coordinates into the national system has residual geometric inhomogeneities (p = 0.90 to 10 mm/km, sporadically up to 20 mm/km), which metrologically deteriorate the results of the calculation of the terrestrially measured secondary system inserted into the GNSS measured primary system. Achieving homogeneous accuracy in coordinate standard deviation in a horizontal plane better than σx,y = 5 mm has been demonstrated in non-ideal railway operating conditions with increased risk of multipath. The innovative aspect of the approach used is that it simplifies and thus increases the efficiency of the measurement with respect to the availability of GPS, GLONASS, Galileo and BeiDou satellites, as well as reducing the effect of multipath on the noise by repeating the measurement procedure.