Position Of Point Research Articles

Preserving multi-dimensional information: A hypersphere method for parameter space analysis

BackgroundPhysiological modelling often involves models described by large numbers of variables and significant volumes of clinical data. Mathematical interpretation of such models frequently necessitates analysing data points in high-dimensional spaces. Existing algorithms for analysing high-dimensional points either lose important dimensionality or do not describe the full position of points. Hence, there is a need for an algorithm which preserves this information. MethodsThe most-distant uncovered point (MDUP) hypersphere method is a binary classification approach which defines a collection of equidistant N-dimensional points as the union of hyperspheres. The method iteratively generates hyperspheres at the most distant point in the interest region not yet contained within any hypersphere, until the entire region of interest is defined by the union of all generated hyperspheres. This method is tested on a 7-dimensional space with up to 35.8 million points representing feasible and infeasible spaces of model parameters for a clinically validated cardiovascular system model. ResultsFor different numbers of input points, the MDUP hypersphere method tends to generate large spheres away from the boundary of feasible and infeasible points, but generates the greatest number of relatively much smaller spheres around the boundary of the region of interest to fill this space. Runtime scales quadratically, in part because the current MDUP implementation is not parallelised. ConclusionsThe MDUP hypersphere method can define points in a space of any dimension using only a collection of centre points and associated radii, making the results easily interpretable. It can identify large continuous regions, and in many cases capture the general structure of a region in only a relative few hyperspheres. The MDUP method also shows promise for initialising optimisation algorithm starting conditions within pre-defined feasible regions of model parameter spaces, which could improve model identifiability and the quality of optimisation results.

Multipoint leak localization for pipelines via acoustic wave amplitude ratio

Pipeline leak localization is significant for maintaining the regular operation of pipelines. This paper proposes a multipoint leak localization method for pipelines via the acoustic wave amplitude ratio, which addresses the issue of the traditional time delay estimation method (TDE) not being able to locate multiple leaks simultaneously. Firstly, a multipoint leak localization method for pipelines is established without time delay estimation and acoustic velocity. This method merely needs to determine the amplitude of the leakage acoustic wave propagating to both ends of the pipeline to achieve leakage localization. Secondly, the improved empirical wavelet transform (IEWT) method denoises the leakage acoustic wave, which can obtain an accurate acoustic amplitude to reduce the localization error. Finally, the trouble that the mutation factor and crossover probability cannot be adaptively selected in the differential evolution (DE) algorithm is improved, and the improved differential evolution (IDE) algorithm is used to solve the objective function to obtain the position of each leakage point. Field experiments show that the multipoint leak localization method proposed in this paper has perfect accuracy, and the minimum localization error is 11 m.

Localization of overdamped bosonic modes and transport in strange metals

The strange metal phase of correlated electrons materials was described in a recent theory by a model of a Fermi surface coupled a two-dimensional quantum critical bosonic field with a spatially random Yukawa coupling. With the assumption of self-averaging randomness, similar to that in the Sachdev-Ye-Kitaev model, numerous observed properties of a strange metal were obtained for a wide range of intermediate temperatures, including the linear in temperature resistivity. The Harris criterion implies that spatial fluctuations in the local position of the critical point must dominate at lower temperatures. For an [Formula: see text]-component boson with [Formula: see text], we use multiple graphics processing units (GPUs) to compute the real frequency spectrum of the boson propagator in a self-consistent mean-field treatment of the boson self-interactions, but an exact treatment of multiple realizations of the spatial randomness from the random boson mass. We find that Landau damping from the fermions leads to the emergence of the physics of the random transverse-field Ising model at low temperatures, as has been proposed by Hoyos, Kotabage, and Vojta. This regime is controlled by localized overdamped eigenmodes of the bosonic scalar field, also has a resistivity which is nearly linear-in-temperature, and extends into a "quantum critical phase" away from the quantum critical point, as observed in several cuprates. For the [Formula: see text] Ising scalar, the mean-field treatment is not applicable, and so we use Hybrid Monte Carlo simulations running on multiple GPUs; we find a rounded transition and localization physics, with strange metal behavior in an extended region around the transition.

Indoor positioning fingerprint database construction based on CSA-DBSCAN and RCVAE-GAN

With the increasing size of buildings, in order to achieve high-precision indoor positioning services, it is a challenging task to build an offline fingerprint database with high quality, high density and less manpower and material consumption. Aiming to solve the problem of low-quality WiFi indoor positioning fingerprint inventory constructed by traditional methods, which affects positioning accuracy and incurs high costs, this paper proposes a method for indoor positioning fingerprint database construction based on Crow Search Algorithm Optimizes Density Clustering (CSA-DBSCAN) and Regressor Conditional VAE Generative Adversarial Network (RCVAE-GAN). Collecting only a tiny amount of sparse reference point position coordinates and RSS data makes it possible to construct a high-quality WiFi indoor positioning fingerprint database. Firstly, the method utilizes the density clustering method based on Crow Search Algorithm Optimization (CSA-DBSCAN) to process RSS data collected from the reference point. This helps minimize the impact of abnormal RSS data on creating the fingerprint database. Secondly, the RCVAE-GAN depth generation model was developed. The model consists of an encoder E, a generator G, a discriminator D, and a regressor R. After constructing the model, the data with abnormal RSS will be removed and input into the model for pre-training and joint training, resulting in a high-quality deep-generation model. Finally, a high-quality and high-density fingerprint database is constructed by combining the collected reference points with fingerprint data generated by the depth generation model. Experimental results show that the proposed method reduces the root mean square error (RMSE) deviation of the generated fingerprint data by 38% and 12% respectively, compared to the RBF interpolation method and the CVAE-GAN method in the same experimental scenario. The constructed fingerprint database is used for positioning, improving positioning accuracy by 70% and 65% respectively. The method described in this paper can construct a high-quality fingerprint database, effectively improving the efficiency of fingerprint database construction and reducing the costs associated with labor and time.

Performance Analysis of Multi-GNSS Real-Time PPP-AR Positioning Considering SSR Delay

For real-time (RT) precise point positioning (PPP), the state space representation (SSR) information is often delayed due to possible communication delays and specific broadcast intervals. In this case, the positioning results will diverge and re-converge due to the increase of SSR products extrapolation errors. In addition, RT orbit and clock offset accuracy, as well as their extrapolation errors, will vary in different systems and satellites. We propose a PPP with ambiguity resolution (PPP-AR) method that combines a time-differenced carrier phase (TDCP) model, in which the characteristics of the orbit and clock are considered. Under normal communication, the PPP-AR solution is obtained by fixing satellites with small SSR product errors. When the communication is abnormal, the TDCP model is utilized to extrapolate user coordinates by considering different extrapolation error characteristics of satellites. The experimental results show that GPS and Galileo SSR products have better accuracy than BDS, with signal-in-space user ranger errors (SISREs) of 2.7, 2.2, and 8.6 cm, respectively. Optimizing the PPP stochastic model based on SISREs can effectively reduce the convergence time. Under 5 min SSR delay, SISREs caused by clock and orbit extrapolation for GPS/Galileo/BDS are 3.5, 1.4, and 2.6 cm, respectively. After optimizing the TDCP stochastic model based on extrapolation errors, the horizontal and vertical positioning accuracies can be maintained at 0.7 cm and 5.0 cm. For multi-GNSS, the combination of the TDCP and PPP-AR can overcome the influence of short delay. After optimizing the stochastic model, the GPS/Galileo/BDS positioning accuracy can be maintained at about 2.4 cm under 3 min delay, showing an accuracy improvement rate of 59.3% compared with the traditional method using only PPP. Additionally, the rapid PPP convergence results can be obtained by inheriting previous filter state information when the communication recovers normally.

Yarn-level modeling and simulation of fancy weft-knitted fabric

Weft-knitted fabric is formed by interlocking loops, which results in an unstable and easily deformable structure. In particular, fancy weft-knitted fabric exhibits diverse structural variations and uneven distribution, leading to more prominent characteristics of instability and deformation. Achieving the desired pattern effect and dimensions often requires drawing multiple designs. In this work, to obtain the geometric model of fancy fabric, mesh-loop models with movement vectors are established based on the basic structure of four stitch types: plain stitch, tuck, float, and loop transfer. The cubic Catmull–Rom spline curves are used to fit the geometric centerline of the yarn. The movement vectors are used to represent the changes in the position of the key points of the standard loops in the fancy fabric, which are derived from the analysis of the pattern grid. A physical model is established based on the force analysis of the yarn, and the positions of yarn control points are determined by solving the Euler–Lagrange dynamic equations. Through iterative calculations, the deformation effects of the fabric are obtained, enabling the simulation of fancy weft-knitted fabric. The proposed algorithms were implemented using Visual C++. The reliability and accuracy of the simulation method are demonstrated by comparing the contours of the simulation results with the actual samples.

An intelligent recommendation system for personalised parametric garment patterns by integrating designer’s knowledge and 3D body measurements

Garment pattern-making is one of the most important parts of the apparel industry. However, traditional pattern-making is an experience-based work, very time-consuming and ignores the body shape difference. This paper proposes a parametric design method for garment pattern based on body dimensions acquired from a body scanner and body features (body feature points and three segmented body part shape classification) identified by designers according to their professional knowledge. By using this method, we construct a men’s shirt pattern recommendation system oriented to personalised fit. The system consists of two databases and three models. The two databases include a relational database (Database I) and a personalised basic pattern (PBP) database (Database II). The Database I is based on manual and three-dimensional (3D) measurements of human bodies by using designer’s knowledge. And Database I is a relational database, which is organised in terms of the relational model of the body part shape and its key body feature dimensions. After a deep analysis of measured data, the irrelevant measured dimensions to human body shape have been excluded by designers and extract representative human body feature dimensions. In addition, the relations between body shapes and previously identified body feature dimensions have been modelled. From the above relational model, we label key feature point positions on the corresponding 3D body model obtained from 3D body scanning and correct the whole 3D human upper body model into the semantically interpretable one. The 3D personalised basic pattern is drawn on the corrected model based on these key feature points. By using three-dimensional to two-dimensional (3D-to-2D) flattening technology, a 2D flatten graph of the 3D personalised basic pattern of the interpretable model is obtained and slightly adjusted to the form suitable for industrial production, i.e., PBP and the PBP database (Database II) is built. In addition, the three models include a basic pattern parametric model (Model I) (characterizing the relations between the basic pattern and its key influencing human dimensions (chest girth and back length)), a regression model (Model II) which enables to infer from basic pattern to PBP for three body parts based on the one-to-one correspondence of key points between the PBPs and the basic patterns and a personalised shirt pattern parametric model (Model III) (characterizing the structural relations between the personalised shirt pattern (PBPshirt) and PBP). The initial input items of the recommendation system are the body dimension constraint parameters, including chest girth, back length and the body feature dimensions used to determine each body part shape as well as three shirt style constraint parameters (slim, regular and loose). By using Model I, the corresponding basic pattern can be generated through the user’s chest girth and back length. Body feature dimensions determine the three body parts’ shapes. Then, Model II is used to generate the PBP for the corresponding body parts shape. Based on the shirt style chosen by the user, Mode III is used to generate the PBPshirt from the PBP. The output of the recommendation system is a fit-oriented PBPshirt. Moreover, if the PBPshirt is unsatisfactory after a virtual try-on, four adjustable parameters (front side-seam dart, back side-seam dart, waist dart and garment bodice length) are designed to adjust the PBPshirt generated by the proposed recommendation system.

Ionospheric corrections tailored to Galileo HAS: validation with single-epoch navigation

The Galileo high accuracy service (HAS) is a new capability of the European global navigation satellite system, currently providing satellite orbit and clock corrections and dispersive effects such as satellite instrumental biases for code and phase. In its full capability, Galileo HAS will also correct the ionospheric delay on a continental scale (initially over Europe). We analyze a real-time ionospheric correction system based on the fast precise point positioning (F-PPP), and its potential application to the Galileo HAS. The F-PPP ionospheric model is assessed through a 281-day campaign, confirming previously reported results, where the proof of concept was introduced. We introduce a novel real-time test that directly links the instantaneous position error with the error of the ionospheric corrections, a key point for a HAS. The test involved 15 GNSS receivers in Europe acting as user receivers at various latitudes, with distances to the nearest reference receivers ranging from tens to four hundred kilometers. In the position domain, the test results show that the 95th percentile of the instantaneous position error depends on the user-receiver distance, as expected, ranging in the horizontal and vertical components from 10 to 30 cm and from 20 to 50 cm, respectively. These figures not only meet Galileo HAS requirements but outperform them by achieving instantaneous positioning. Additionally, it is shown that formal errors of the ionospheric corrections, which are also transmitted, are typically at the decimeter level (1 sigma), protecting users against erroneous position by weighting its measurements in the navigation filter.

An adaptive robust strategy based on hypothesis testing for satellite clock bias short-term forecasting

The study of short-term forecasting of satellite clock bias (SCB) is important to promote the development of real-time precise point positioning, and the Kalman filter model has certain advantages over other models in the single forecast model. However, the filtering performance will be degraded by the model bias, and a fading factor is constructed to control the effect brought by the model bias. Considering that the fading factor may cause the covariance matrix to be abnormally inflated or even invalid when the observed information is unreliable, the chi-square test is introduced as a test indicator. At the current epoch moment, the fading factor or robust estimation is conditionally applied based on the result of the hypothesis test. An improved IGGIII weight function is used by the robust estimation, which simplifies the solution of the parametric robust solution. BeiDou satellite navigation system-3 satellite clock bias data with different clock types were selected for the analysis of fitting accuracy and forecasting accuracy, and the experimental results showed that the proposed algorithm can well eliminate the anomalous perturbation phenomenon caused by model deviation and improve the fitting accuracy. The comparison of forecast accuracy between the proposed strategy and GM(1,1), quadratic polynomial, and autoregressive integrated moving average (ARIMA) models at 3, 6, and 12 h intervals reveals that the proposed strategy consistently demonstrates optimal forecast accuracy.

Diagrams with composition fields of the pelitic fraction of bottom sediments in the estuarine parts of different modern river’s categories: another approach to verification

According to analytical data given in publications [Savenko, 2006; Bayon et al., 2015], compared the position of data points of pelitic fraction of bottom sediments in the estuarine parts of a number of large rivers (rivers of category 1 according to [Bayon et al., 2015]: Amazon, Congo, Mississippi, Niger, Yangtze, Mackenzie, Volga, Danube, Mekong, Amu Darya, Northern Dvina and Loire) and their suspended material on the (La/Yb)N – Eu/Eu* and (La/Yb)N – Th diagrams. The first samples were subjected to special processing. The samples of the latter were not processed before the study. It has been established that the data points of both sample’s groups in the above diagrams are localized in the field of fine-grained (pelitic) suspension of large rivers, demonstrating some scatter for specific rivers, but generally not going beyond its limits. This gives additional reason to believe that for decoding the categories of rivers that formed certain sedimentary sequences, not only specially prepared samples can be used, but also data obtained from bulk/unprocessed samples. At the example of a fine-grained suspension of Zambezi river (South Africa) some features of the use of (La/Yb)N – Eu/Eu* and (La/Yb)N – Th diagrams were considered.

An omnidirectional spatial monocular visual localization and tracking method for indoor unmanned aerial vehicles based on the two-axis rotary table

Aiming at the complexity and poor adaptability of the calibration process in the traditional unmanned aerial vehicles (UAV) indoor visual positioning, this paper proposes an omnidirectional spatial tracking and localization method for indoor UAV based on the two-axis rotary table. Firstly, the position of the UAV fuselage feature points in the camera coordinate system of the turntable camera is computed by the Pespective-n-Point algorithm utilizing known position information of a plurality of feature points with pixel coordinate information in the corresponding image. Pixel coordinate information is extracted by obtaining UAV body-specific feature points from rotary table camera shots. Then, UAV localization in omnidirectional space can be obtained by using the calibrated rotary axis parameters of the rotary table and the rotation angle of the rotary table and substituting them into Rodriguez’s formula to unify the UAV position information acquired by the rotary table camera at different positions into a unified coordinate system. Finally, the angle at which the rotary table should rotate is calculated from the obtained UAV pose and the spatial position of the camera optical center and the rotary axis of the rotary table. The calculated angle is fed back to the turntable as feedback information. The rotary table receiving the feedback information is rotated to a position where the UAV is located at the center of the camera image. Thereby the tracking and localization of the UAV is realized. The experimental results show that the spatial range of localization is greatly expanded with the localization accuracy reaching the level of binocular visual localization. The omnidirectional spatial tracking and localization of indoor UAV can be conveniently realized by this method.

Probing the critical point of MgSiO3 using deep potential simulation

The giant impact between proto-Earth and a Mars-sized planet called Theia resulted in the formation of the Earth–Moon system, and the silicate mantles of the initial bodies may have partly been vaporized. Here, we develop a machine learning potential for MgSiO3 based on the data from first-principles calculations to estimate its critical point. The variations in pressure along different isotherms yield the position of the critical point of MgSiO3 at 0.54 g cm−3 and 6750 ± 250 K, which agrees with the previous theoretical estimation. We also simulate the MgSiO3 melt under a spectrum of critical conditions to understand the changes in coordination environment with density and temperature. The fourfold Si–O coordination hardly changes with increasing density at 3000 K. However, with increasing temperature, the dominance of four-coordinated Si–O diminishes rapidly as density decreases. Regarding Mg–O coordination, the overall trend, which varies with temperature and density, remains largely consistent with Si–O but with a greater diversity in the types of coordination due to more bond breaking events. Our work opens a new avenue by employing machine learning methods to estimate the critical point of silicates.

Explicitly Perceiving and Preserving the Local Geometric Structures for 3D Point Cloud Attack

Deep learning models for point clouds have shown to be vulnerable to adversarial attacks, which have received increasing attention in various safety-critical applications such as autonomous driving, robotics, and surveillance. Existing 3D attack methods generally employ global distance losses to implicitly constrain the point-wise perturbations for optimization. However, these simple losses are quite difficult to accurately measure and restrict the proper 3D geometry as point clouds are highly structured. Although few recent works try to exploit additional shape-aware surface knowledge to globally constrain the point position, they still fail to preserve the detailed point-to-point geometric dependency in different local regions. To this end, in this paper, we propose a novel Multi-grained Geometry-aware Attack (MGA), which explicitly captures the local topology characteristics in different 3D regions for adversarial constraint. Specifically, we first develop multi-scale spectral local filter banks adapting to different 3D object shapes to explore potential geometric structures in local regions. Considering that objects may contain complex geometries, we then extend each filter bank into multi-layer ones to gradually capture the topology contexts of the same region in a coarse-to-fine manner. Hence, the focused local geometric structures will be highlighted in the coefficients calculated by the filtering process. At last, by restricting these coefficients between benign and adversarial samples, our MGA is able to properly measure and preserve the detailed geometry contexts in the whole 3D object with trivial perturbations. Extensive experiments demonstrate that our attack can achieve superior performance on various 3D classification models, with satisfying adversarial imperceptibility and strong resistance to different defense methods.

Point-to-Spike Residual Learning for Energy-Efficient 3D Point Cloud Classification

Spiking neural networks (SNNs) have revolutionized neural learning and are making remarkable strides in image analysis and robot control tasks with ultra-low power consumption advantages. Inspired by this success, we investigate the application of spiking neural networks to 3D point cloud processing. We present a point-to-spike residual learning network for point cloud classification, which operates on points with binary spikes rather than floating-point numbers. Specifically, we first design a spatial-aware kernel point spiking neuron to relate spiking generation to point position in 3D space. On this basis, we then design a 3D spiking residual block for effective feature learning based on spike sequences. By stacking the 3D spiking residual blocks, we build the point-to-spike residual classification network, which achieves low computation cost and low accuracy loss on two benchmark datasets, ModelNet40 and ScanObjectNN. Moreover, the classifier strikes a good balance between classification accuracy and biological characteristics, allowing us to explore the deployment of 3D processing to neuromorphic chips for developing energy-efficient 3D robotic perception systems.

Less Is More: Label Recommendation for Weakly Supervised Point Cloud Semantic Segmentation

Weak supervision has proven to be an effective strategy for reducing the burden of annotating semantic segmentation tasks in 3D space. However, unconstrained or heuristic weakly supervised annotation forms may lead to suboptimal label efficiency. To address this issue, we propose a novel label recommendation framework for weakly supervised point cloud semantic segmentation. Distinct from pre-training and active learning, the label recommendation framework consists of three stages: inductive bias learning, recommendations for points to be labeled, and point cloud semantic segmentation learning. In practice, we first introduce the point cloud upsampling task to induct inductive bias from structural information. During the recommendation stage, we present a cross-scene clustering strategy to generate centers of clustering as recommended points. Then we introduce a recommended point positions attention module LabelAttention to model the long-range dependency under sparse annotations. Additionally, we employ position encoding to enhance the spatial awareness of semantic features. Throughout the framework, the useful information obtained from inductive bias learning is propagated to subsequent semantic segmentation networks in the form of label positions. Experimental results demonstrate that our framework outperforms weakly supervised point cloud semantic segmentation methods and other methods for labeling efficiency on S3DIS and ScanNetV2, even at an extremely low label rate.

Point Deformable Network with Enhanced Normal Embedding for Point Cloud Analysis

Recently MLP-based methods have shown strong performance in point cloud analysis. Simple MLP architectures are able to learn geometric features in local point groups yet fail to model long-range dependencies directly. In this paper, we propose Point Deformable Network (PDNet), a concise MLP-based network that can capture long-range relations with strong representation ability. Specifically, we put forward Point Deformable Aggregation Module (PDAM) to improve representation capability in both long-range dependency and adaptive aggregation among points. For each query point, PDAM aggregates information from deformable reference points rather than points in limited local areas. The deformable reference points are generated data-dependent, and we initialize them according to the input point positions. Additional offsets and modulation scalars are learned on the whole point features, which shift the deformable reference points to the regions of interest. We also suggest estimating the normal vector for point clouds and applying Enhanced Normal Embedding (ENE) to the geometric extractors to improve the representation ability of single-point. Extensive experiments and ablation studies on various benchmarks demonstrate the effectiveness and superiority of our PDNet.

Numerical study of CO2 trans-critical process inside micromodel based porous structures under supercritical pressures

Understanding the flow, heat transfer, and trans-critical process of carbon dioxide in porous media is crucial for various applications, including CO2 sequestration, soil remediation and oil and gas recovery, due to its unique physical properties in the critical region. In this study, a porous media model on a microfluidic chip structure was simulated to emphasize the heat transfer and trans-critical process of CO2 under supercritical pressure in porous media. The study aims to observe the behaviors of CO2 during its transition from subcritical to supercritical temperature under supercritical pressure. The main objective is to observe the temperature distribution and pressure change of CO2 in a porous media model under the influence of bottom heating. At the same time, we observe the changes in the position of the critical temperature point of CO2 in porous media and analyze its heat exchange process in porous media. After the flow reaches a steady state, the temperature span near the grains is 1.6 K, and the pressure drop per unit length is 1480.3 Pa/mm. As the flow time progresses, the critical temperature line migrates from outlet region to inlet region, the range of sCO2 narrows from 81.7 % to 84.7 % in the porous media region. Finally, the influence of different working conditions on the trans-critical region is studied. It is hoped that this study will contribute to the understanding of the trans-critical process of CO2 in porous media.

A Symmetric Non-Stationary Loop Subdivision with Applications in Initial Point Interpolation

Loop subdivision is a significant surface scheme with wide applications in fields like computer graphics and wavelet. As a type of stationary scheme, Loop subdivision cannot adjust the limit surface directly. In this paper, we present a new way to solve this problem by proposing a symmetric non-stationary Loop subdivision based on a suitable iteration. This new scheme can be used to adjust the limit surfaces freely and thus can generate surfaces with different shapes. For this new scheme, we show that it is C2 convergent in the regular part of mesh and is at least tangent plane continuous at the limit positions of the extraordinary points. Additionally, we present a non-uniform generalization of this new symmetric non-stationary subdivision so as to locally control the shape of the limit surfaces. More interestingly, we present the limit positions of the initial points, both for the symmetric non-stationary Loop subdivision and its non-uniform generalization. Such limit positions can be used to interpolate the initial points with different valences, generalizing the existing result. Several numerical examples are given to illustrate the performance of the new schemes.

Calculation position of the focal point in self-focusing media

Using a laser beam in a self-focusing environment with different power more and less than the critical one, more accurate coordinates of the point with the maximum radiation intensity were obtained. The results of the calculations corresponded to the experimental data obtained by spatial filtering of the angular spectra of forced Raman scattering. The agreement of the results was satisfactory for all beam power levels.

Результаты сравнения длин линий на базисе пространственном эталонном СГУГиТ

The results of line lengths comparison on the spatial reference basis (SRB) of SGUGiT, carried out according to the program in all combinations measurements in the forward direction from point BI01 to point BI10 in spring and summer of 2021 and 2023 using total station Leica TM30, as well as, in the same seasons of 2023 done by laser tracker Leica AT403 are given. Based on the analysis of multiple measurements of each section of the basis (at least 30 ones), the standard deviation and uncertainty were calculated. Meanwhile, at the extreme points of the base section, meteorological parameters (temperature, pressure and relative humidity) were recorded by two independent instruments, which were then entered immediately when metering with a Leica TM 30 electronic total station. In the case of the Leica AT403 laser tracker, they were automatically taken into account in specialized software management and processing of Spatial Analyzer measurement data. Due to the research results, it was found out that the expanded uncertainty in measuring the lengths of the basic lines in the range from 12 to 192 m on the WPT using a Leica AT403 laser tracker and a Leica TM30 electronic total station, taking into account the accepted errors that affect the final result, is no more than 1,4 mm, and the maximum contribution to the mistake in determining line lengths is made by the standard uncertainty estimated by type B. In addition, seasonal fluctuations in the position of individual basis points are observed