Height Coordinates Research Articles

Group-selection system as alternative management of Scots pine (Pinus sylvestris L.) forests facing climate change

AbstractThe Scots pine (Pinus sylvestris L.) is economically and ecologically the most important forest tree species in Poland with its aerial share estimated at 59% and share in growing stock at 68%. Pine forests have been managed according to even-aged silviculture for decades, resulting in a simplified structure and increased vulnerability to climatic stress. Structurally simple forests also show low resilience and adaptability to the observed global changes. The growing awareness of the risks associated with global change is drawing particular attention to the need for alternative management of pine forests that meets the expectations of the public and foresters themselves. In 1992, an experiment with uneven-aged silviculture for pine forest was established in the Gubin Forest District (western Poland). Based on data collected from 49 permanent circular plots (size of 500 m2 each) covering approximately 30 ha of Scots pine forest, the effect of such silviculture on stand structure was analyzed. Dbh, total tree height, tree status, and tree coordinates (x, y) were measured on each plot. Measurements and observations were taken twice, in 1992 and 2019. Structural indices describing different aspects (size structure, vertical structure, spatial structure) were calculated. The dynamics of the stand structure were then analyzed over 27 years, during which the forest was managed under alternative management strategies. The results showed that group-selection cuttings promote strong differentiation of stand structure. The positive effect of such silviculture can be observed in each aspect of the stand structure. Together with other research findings, the results confirm the effectiveness of this alternative silviculture to diversify simplified pine forests to be better adapted to novel environmental conditions.

Research on position Model of Surface-to-air Missile Defense against Cruise Missile Based on Rule GA

Abstract The deployment of weapon systems prior to the engagement of anti-cruise missiles constitutes the primary research challenge in surface-to-air missile operations. Initially, it is essential to analyze operational requirements and scientifically delineate the guided radar detection area, kill zone, and interception zone based on physical realities. A model should be established to ascertain the fundamental conditions for site deployment, taking into account factors such as position height, shielding angle, and geographic coordinates. In relation to low-altitude approaches by adversarial forces, key considerations include the depth and breadth of firepower from the weapon system in the attack direction, firepower density in that direction, and lethality probability. An Operational Effectiveness model should be developed based on coverage area of firepower, effective interceptions per unit time, and lethality probabilities of weapon systems to evaluate each location’s effectiveness. Finally, leveraging land selection principles and external information coordination mechanisms will facilitate establishing a genetic algorithm-based strategy for deploying surface-to-air missile systems. The validity of this algorithm has been demonstrated through practical examples.

Influence of tool wear on geometric surface modeling for TC4 titanium alloy milling

Addressing the insufficient accuracy of milling surface roughness prediction model, the formation causes of different roughness were analyzed, and a surface roughness prediction model which takes tool wear into account was established based on an improved Z-MAP algorithm. Combining tool geometry and tool wear morphology, a mathematical model of surface profile was built; And the motion trajectory equations of the milling cutter teeth were established via machining kinematics. The servo rectangular encirclement and Newton iterative method were adopted to improve the Z-MAP algorithm. Combining the Z-MAP algorithm with the insert motion trajectory equations, the values at different height coordinates of the workpiece grid nodes were obtained, allowing numerical simulation of workpiece surface geometry and analysis of the effect of cutting trajectory overlap on the machined surface morphology. TC4 titanium alloy milling experiment was conducted to validate the simulation model. The simulated surface roughness Sa exhibited significant deviation from experimental values before tool wear, with a maximum error of 53.08 %. Nevertheless, the simulated values of Sa were closer to experimental values after tool wear, with a maximum error of 15.45 % and a minimum of only 3.07 %. Additionally, the predicted results for the bearing length ratio Rmr(c) were consistent with experimental values. The mathematical model for surface roughness taking tool wear into account effectively predicted the shape profile and surface roughness of the machined surface, providing theoretical guidance and technical support for practical production.

Near-infrared Spectrum Characteristics of Micro-Nano Material Based Diffraction Optical Devices

Diffractive optics devices are optical devices in which the amplitude or phase of the incident light is spatially modulated periodically by a micro-nanomaterial based structure. The study of diffractive optics devices in the field of micro and nano can change the spectroscopic behavior of micro and nano diffractive optics devices by varying the microstructure of the structure and the optical wave properties, which can effectively and reasonably modulate the optical wave signal. To study the effect of different parameter structures on the performance of micro-nano diffraction optical devices, in this paper, two three-dimensional array structures of diffractive optical devices are proposed, which are a vertex-intersecting regular tetrahedron structure and a base-intersecting regular frustum structure. Using the Finite-Difference Time-Domain method, the spectroscopic images of the diffractive optics of the constructed micro-nano diffractive devices are studied in the near-infrared band by varying the height of the constructed structures, the type of structures, the wavelength of the incident light waves, and the polarization direction of the light waves in different 3D height coordinates. The effects of different parameter changes on the performance of the micro-nano diffractive optics devices were analyzed by image comparison. The results show that the best diffraction effect is achieved at a structure height of 0.9 μm for both models with different structure types. The study of both structures at this structure height reveals that the location of diffraction occurrence and the intensity of diffraction can be tuned by varying the structure and the relevant parameters such as the polarization of the light wave. This paper has some theoretical applications for the study of high-performance diffractive optics.

Spline Model: A Hydrostatic/Non-Hydrostatic Dynamic Core with Space-Time Second-Order Precision and Its Exact Tests

We present a new explicit quasi-Lagrangian integration scheme with the three-dimensional cubic spline function transform (transform = fitting + interpolation, referred to as the “spline format”) on a spherical quasi-uniform longitude–latitude grid. It is a consistent longitude–latitude grid, and to verify the feasibility, accuracy, convergence, and stability of the spline format interpolation scheme for the upstream point on the longitude–latitude grid, which may map a quasi-uniform longitude–latitude grid, a set of ideal, exact test schemes is adopted, which are recognized and proven to be effective internationally. The equilibrium flow test, cross-polar flow test, and Rossby–Haurwitz wave test are used to illustrate the spline scheme uniformity to the linear scheme and to overcome the over-dense grid in the polar region and the non-singularity of the poles. The cross-polar flow test demonstrates that the geostrophic wind crosses the polar area correctly, including the South Pole and North Pole. A non-hydrostatic, fully compressible dynamic core is used to complete the density flow test, demonstrating the existence of a time-varying reference atmosphere and that the spline format can simulate highly nonlinear fine-scale transient flows. It can be compared for the two results of the density flow test between the solution with the spline format and the benchmark reference solution with the linear format. Based on the findings, the non-hydrostatic dynamic core with the spline format is recommended for adoption. When simulated for the flow over an ideal mountain, through the “topographic gravity wave test”, the bicubic surface terrain and terrain-following height coordinates, time-split integration, and vector discrete decomposition can be derived successfully. These may serve as the foundations for a global, unified spline-format numerical model in the future.

INVESTIGATION OF THE ACCURACY OF DETERMINING THE COORDINATES OF SPHERES USING THE FARO FOCUS S 120 LASER SCANNER

Goal. The purpose of the work is research and analysis of the accuracy of determining the coordinates of spheres during geodetic work on laser scanning.
 Methods. The study of the accuracy of measurements of the laser scanner was carried out by the method of direct measurements. During the research, the reference value of the displacement of the sphere was measured using a laser interferometer. The measurements were performed to determine the measurement errors of various measured values of the laser scanner: horizontal angle, vertical angle and distance. Processing of scans and determination of sphere coordinates was carried out in the FARO Scene Lt software complex. Processing of measurement results was carried out by methods of mathematical statistics using MS Excel.
 Scientific novelty. A study of the sensitivity of the laser scanner for determining minor displacements of reference targets, using spheres as an example, was carried out. Work with sensitivity studies in determining the coordinates of reference targets, as a component of the error in determining their coordinates, we did not find.
 Practical significance. The conducted studies will allow determining the optimal ranges of location of reference targets during scanning to ensure the highest accuracy of determining their coordinates. However, it has been experimentally proven that this method cannot be used to determine the full accuracy characteristics of a laser scanner in determining the coordinates of reference targets, since the influence of some systematic errors, such as the eccentricity of the component parts of the laser scanner, is excluded in the measurements.
 The results. According to the research results, it is possible to draw a conclusion about the most appropriate location of reference targets in the form of spheres to achieve the highest accuracy of determining their coordinates. As can be seen from the research, it is desirable to place the spheres at a distance of approximately 5 m from the NLS. At shorter distances (about 2 m), the accuracy of determining the coordinates of the spheres begins to be affected by the growing errors of measuring distances by the scanner, at large distances (from 10 m), the errors of measuring the height coordinates of the spheres increase. The results presented in the paper require further research. These studies should be performed for other types of reference targets and with the use of other models of laser scanners, which is the goal of further research by the authors.

A point cloud hole spiral-filling method based on 2D and 3D data fusion

Due to unfavorable factors, such as environmental noise, reflection, and occlusion of a scanned object, a point cloud obtained by structured light measurement equipment contains holes, which limits further application of the three-dimensional data. This study proposes a point cloud hole spiral-filling method based on the fusion of two- and three-dimensional data. The pixel coordinates corresponding to the point cloud are calculated according to the scanning system parameters. Based on a matrix-like distribution pattern of a camera’s pixel coordinates, the missing pixel coordinates are used to locate the hole boundary points, and the pixel coordinates of the filled points are obtained. In addition, the pixel coordinates of the hole boundary points are used as a sampling layer, which can be used to separate the outermost pixel coordinates of the filled points. Similarly, the pixel coordinates of the filling points are helically stratified. The pixel coordinates of the filling points and their neighboring points, as well as the height coordinates of the neighboring points, are used for surface interpolation to estimate the height coordinates of the filling points. The hole filling is realized after the correction of coordinates using the four-connected domain. The experimental results demonstrate that the proposed spiral hole filling algorithm can accurately identify the hole boundary and can estimate the filling points completely while preserving the details of the repair area.

Learning Region Similarities via Graph-Based Deep Metric Learning

Region similarity learning plays an essential role in applications such as business site selection, region recommendation, and urban planning. Earlier studies mainly represent regions as bags of points of interest (POIs) for region similarity comparisons, which cannot fully exploit the spatial features of the regions. Recently, researchers propose to use deep neural networks to exploit spatial features such as POI geo-coordinates and categories, which have produced more accurate and robust region similarity learning results. However, many useful features such as the height and size of a POI, and the distance and relative importance between the POIs, are still overlooked in these methods. To take advantage of such features, we propose to represent regions as graphs, where nodes are POIs with rich features such as height, size, and hexagonal coordinates, while edges are the relationships between POIs formulated by their road network distances. To capture POIs' importance, we weigh them by their height and size. Since there is limited availability of ground-truth region similarity data, we propose a contrastive learning-based multi-relational graph neural network (C-MPGCN) for region similarity learning based on the graph representations. To generate data for model training, we propose a soft graph edit distance (SGED) based algorithm to generate triples of similar and dissimilar graphs of a given graph (representing a given region) based on the POI weights. Experimental results show that C-MPGCN outperforms the state-of-the-art methods for region similarity learning consistently with an improvement of at least 8.6% and 9.4% in terms of MRR and HR@1, respectively.

BDS Dual-Frequency Carrier Phase Multipath Hemispherical Map Model and Its Application in Real-Time Deformation Monitoring.

The BDS multipath delay error is highly related to the surrounding monitoring environment, which cannot be eliminated or mitigated by applying the double difference observation model. In the actual monitoring environment, due to the complexity of the BDS constellation, it is difficult for existing algorithms to consider GEO, IGSO, MEO and other different orbital types of satellites for real-time and efficient multipath error reduction. Therefore, we propose a novel BDS dual-frequency multipath error reduction method for real deformation monitoring for BDS considering various satellite orbit types. This method extracts the single error residual of each satellite based on the assumption of "zero mean" and divides the appropriate grid density of GEO and IGSO/MEO, respectively, to construct a dual-frequency multipath hemispherical map model suitable for BDS satellites with different orbital types. This method can realize the multipath error elimination of the observed values of different orbits and different frequencies. The results of simulation experiments and real deformation monitoring data demonstrate that this method can effectively eliminate low-frequency multipath delay errors in the observation domain and coordinate domain. After multipath correction, the precision of the horizontal coordinates and height coordinates are 1.7 mm and 4.6 mm. The precision of the horizontal coordinate and height coordinate is increased by 50% and 60%, respectively. The fixed rate of ambiguity increased by 5-7%.

A precise forest spatial structure investigation using the SLAM+AR technology

IntroductionForest spatial structures are the foundations of the structure and function of forest ecosystems. Quantitative descriptions and analyses of forest spatial structure have recently become common tools for digitalized forest management. Therefore, the accuracy and intelligence of acquiring forest spatial structure information are of great significance.MethodsIn this study, we developed a forest measurement system using a mobile phone. Through this system, the following tree measurements can be achieved: (1) point cloud of tree and chest diameter circle to measure tree diameter at breast height (DBH) and position coordinates of tree by using simultaneous localization and mapping (SLAM) technology, (2) virtual boundary creation of the sample plot, and the auxiliary measurement function of tree with the augmented reality (AR) interactive module, and (3) position coordinates and single-tree volume factor to calculate the spatial structural parameters of the forest (e.g., Mingling degree, Dominance index, Uniform angle index, and Crowdedness index).The system was tested in three 32 x 32 martificial forest plots.ResultsThe average DBH estimations showed BIAS of -0.47 to 0.45 cm and RMSEs of 0.57 to 0.95 cm. Its accuracy level met the requirements of forestry sample surveys. The tree position estimates for the three plots had relatively small RMSEs with 0.17 to 0.22 m on the x-axis and 0.16 to 0.26 m on the y-axis. The spatial structural parameters were as follows: the mingling degree of plot 1 was 0.32, and the overall mixing degree of tree species was low. The trees in plots 2 and 3 were all single species, and the mixing degree of both plots was 0. The dominance index of the three plots was 0.56, 0.51, and 0.51, indicating that the competitive advantage of the whole orest species was not obvious. The uniform angle index of the three plots was 0.55, 0.59, and 0.61, indicating that the positions of trees in the three plots were randomly distributed. The crowdedness index of plot 1 was 1.03, indicating that the degree of aggregation of the trees was low and showed a random distribution trend. The crowdedness index of the other plots were 1.36 and 1.40, indicating that the trees in the plots show a trend of uniform distribution, and the uniformity of plot 3 is higher than that of plot 2, but the overall uniformity is relatively weak.DiscussionThe findings of this study provide support for the optimization of forest structures and improve our conceptual understanding of forest community succession and restoration, in addition to the informatization and precision of forest spatial structure surveys.

Height coincidences in products of the projective line

We consider hypersurfaces in $${\mathbb {P}}_1^n$$ that contain a generic sequence of small dynamical height with respect to a split map and project onto $$n-1$$ coordinates. We show that these hypersurfaces satisfy strong coincidence relations between their points with zero height coordinates. More precisely, it holds that in a Zariski-open dense subset of such a hypersurface $$n-1$$ coordinates have height zero if and only if all coordinates have height zero. This is a key step in the resolution of the dynamical Bogomolov conjecture for split maps.

Accurate 3D to 2D Object Distance Estimation from the Mapped Point Cloud Data.

Distance estimation is one of the oldest and most challenging tasks in computer vision using only a monocular camera. This can be challenging owing to the presence of occlusions, noise, and variations in the lighting, texture, and shape of objects. Additionally, the motion of the camera and objects in the scene can affect the accuracy of the distance estimation. Various techniques have been proposed to overcome these challenges, including stereo matching, structured light, depth from focus, depth from defocus, depth from motion, and time of flight. The addition of information from a high-resolution 3D view of the surroundings simplifies the distance calculation. This paper describes a novel distance estimation method that operates with converted point cloud data. The proposed method is a reliable map-based bird's eye view (BEV) that calculates the distance to the detected objects. Using the help of the Euler-region proposal network (E-RPN) model, a LiDAR-to-image-based method for metric distance estimation with 3D bounding box projections onto the image was proposed. We demonstrate that despite the general difficulty of the BEV representation in understanding features related to the height coordinate, it is possible to extract all parameters characterizing the bounding boxes of the objects, including their height and elevation. Finally, we applied the triangulation method to calculate the accurate distance to the objects and statistically proved that our methodology is one of the best in terms of accuracy and robustness.

A method for identifying and repairing holes on the surface of unorganized point cloud

During scanning, reflection and occlusion of objects, produce holes in the acquired point clouds, causing problems to functions such as map building and target detection. In this paper, a new method for identifying and repairing such holes is proposed. First, the density and the 2D projection points of the point cloud are calculated. Based on the Euclidean distance, the hole boundary points of the original point cloud are obtained. Following, a novel preprocessing segmentation algorithm is used to obtain the boundary points of holes. Next, even if the boundary points are not fully identified, the total 2D repairing points are obtained by the proposed algorithm. Finally, a new hole repairing model, based on fuzzy inference system, is proposed, integrating geometry and curvature information of boundary points, while it can fast and accurately estimate the height coordinates of the repairing points. The experimental results show that the proposed algorithm is efficient.

Establishing a citywide street tree inventory with street view images and computer vision techniques

Trees in urban areas have diverse ecological, social, and health benefits. The establishment of up-to-date and accurate street-tree inventories that list the species and locations of individual street trees is critical to urban tree management and tree-planting campaigns. However, street-tree inventories are incomplete or lacking altogether in most cities. This is partly because conventional field assessment is laborious or expensive. In this study, we developed and validated a novel and cost-effective method to establish a city-wide tree inventory based on computer vision and freely available street view images (SVIs). Tree information such as species, height, crown diameter, and geographical coordinates at the individual tree level can be assessed. Based on an object detection model, we adopted a species-based loss function to address the challenges of long-tailed class distribution of species, which is caused by imbalance among sample size of different tree species and can lead to poor performance of the model. Compared with other research in urban tree species recognition, the modified model shows a higher accuracy. In order to calculate quantitative features of street trees, we employed a deep learning algorithm, which is pretrained on stereo dataset and validated on Google Street View images, to estimate the depth of each pixel in SVIs. Furthermore, as a demonstration, we established the citywide tree inventory and conducted tree diversity analysis for Jinan, China. Compared with new developed area, the old town has more street trees and more diverse tree species which can improve biodiversity and walkability. We also found that plane trees, which can cause allergic reactions, are dominant in northern new developed urban area.

Forest Road Wearing Course Damage Assessment Possibilities with Different Types of Laser Scanning Methods including New iPhone LiDAR Scanning Apps

Forests make up 34.1% of the Czech Republic total area and forest roads account for nearly the same length (47,465 km) as all other roads administered by the state and its regions (55,738 km). Forest roads are not as intensively used as other roads. On the other hand, as logging trucks carry the maximum permitted load on roads and forests create a specific microclimate, forest roads are subject to rapid wear. A road wearing course is generally designed for 20 years of service and for a maximum damage level of 25% before they are supposed to be reconstructed. To ensure this life cycle is adhered to, more efficient, faster, and more flexible surface damage detection adaptable for forest environment is needed. As smartphones and their optical devices, i.e., new iPhones with LiDAR sensors, become more advanced, the option arises to perform laser scanning on road surfaces using smartphones applications. This work aimed to test this technology and its precision applicability to assessing damage to a forest wearing course and compare it with another hand-held personal laser scanner (PLShh), represented in this study by GeoSLAM ZEB Horizon scanner, and more precise terrestrial laser scanning (TLS) technology, represented in this study by Faro Focus 3D laser scanner, which have started to replace tacheometric wearing course damage surveying thanks to their greater precision. So, this study involved a comparison of three alternative laser scanning methods focused especially on these, which are implemented in new iPhones for tacheometric surveying. First, a Faro Focus 3D laser scanner was used for the TLS method. Second, the PLShh method was tested on a GeoSLAM ZEB Horizon scanner. Third, another PLShh method using an iPhone 13 Pro with applications 3D Scanner and Polycam was evaluated. If we are comparing positional height accuracy of PLShh to tacheometric surveying on reference cross position height coordinates, ZEB Horizon achieved devXY and devZ RMSE 0.108 m; 0.025 m; iPhone 13 Pro with 3D Scanner app devXY and devZ RMSE 0.185 m; 0.021 m, and with Polycam app devXY and devZ RMSE 0.31 m; 0.045. TLS achieved the best results with devXY RMSE 0.049 and devZ RMSE 0.0077. The results confirm that only the TLS scanner achieves precision values in height differences applicable for an assessment of forest road wearing course damage measurement comparable with tacheometric surveying. Surprisingly, comparing the PLShh scanners to the TLS technology, they achieved interesting results, comparing their transverse profiles and 3D objects as digital surface models (DSM) of the road to TLS in height position. In transverse profiles, ZEB Horizon achieved devZ RMSE 0.032 m; iPhone 13 Pro with 3D Scanner app devZ RMSE 0.017 m, and with Polycam app devZ RMSE 0.041 m compared to the TLS method measured using a Faro Focus 3D static laser scanner. Comparing forest road DSM to Faro Focus 3D, ZEB Horizon achieved devZ RMSE 0.028 m; iPhone 13 Pro with 3D Scanner app devZ RMSE 0.018 m and with Polycam devZ RMSE 0.041 m. These results in height differences show that the height accuracy of PLShh achieves precision, which is applicable to determining the current shape of forest road wearing course compared to the required roof shape gradient. However, further testing provided the insight that such a kind of PLShh measurement is still only possible to use for the identification of a transverse profile shape, as in length measurement the length error increases. All PLShh are able to capture the current shape of forest road cross profile, but still they cannot be used for any design or calculation of material measurement needed for wearing course repair.

Spatial variability of the productive capacity of teak (Tectona grandis Linn F.) plantations in the eastern Amazonia

Application of geostatistics in mapping the productive capacity of forest stands is an important tool to guide decision making regarding precision silviculture. In this study, we investigated the productive capacity of teak clonal plantations and its spatial dependence, making the site mapping possible. We also investigated the influence of soil chemical attributes on productive potential. We used dominant height, age and geographic coordinates data from plots during five evaluations in clonal teak plantations of different ages. We performed the classification of the forest sites by the guide-curve method. The principal components analysis was used to group the forest stands according to soil chemical attributes (available P and exchangeable K, Na and Mg). The spatial variability analysis of productive capacity was carried out through geoestatistics. The results show that the productive capacity has spatial dependence. The exponential model has provided the best estimates of dominant height, revealing that 69.2% of the mapped area was from medium and 30.8% from high productive capacity. The multivariate analysis showed that soil fertility has influenced the productive capacity, discerning the most productive sites, in agreement with the soil quality. The geostatistical technique was efficient to estimate the productive capacity in unsampled areas, revealing sites with different productive potentials and their response to edaphic factors. This may assist in the efficient management of planting, when establishing silvicultural actions in specific locations, which are identified in the planted area maps, reducing the management costs.

Three-dimensional measurement for specular reflection surface based on deep learning and phase measuring profilometry

ObjectivePhase measuring profilometry (PMP) is a non-contact 3D measurement method. However，it is still a very challenging task when it is applied to an object with a specular reflection surface. In this paper, a 3D measurement method for specular reflection surface based on a deep learning framework is proposed to reduce the measurement error caused by highlights. MethodsFirstly, a dual-channel U-Net network (DC-UNet) is used to identify the highlight areas in the fringe image. Secondly, the dilated residual networks (DRN) combined with the features of the neighborhood of the highlight pixels are used to correct the highlight pixels, and the predicted fringe image without highlight can be obtained. Thirdly, the predicted fringe image is blended with the original image, regarded as the final result of the highlight removal. Fourthly, phase unwrapping is implemented using the fringe image of highlight removal, and the 3D coordinates values can be obtained by combining the calibrated parameters with the phase values unwrapped. ResultsSimulated results show that the absolute maximum deviation, absolute mean error and standard deviation of reconstructed 3D height coordinates are reduced by 98.27 %, 68.70 %, and 91.11 %, respectively. The real experiment results show that the maximum error of the absolute phase is reduced by more than 87.00 %, and the mean error of the absolute phase is reduced by more than 92.72 %. Finally, more than 99.14 % of the pixels with intensity saturated caused by highlights can be corrected by the proposed method.

Analysis of Transformation Methods of Hydroacoustic and Optoelectronic Data Based on the Tombolo Measurement Campaign in Sopot

Measurements in the coastal zone are carried out using various methods, including Global Navigation Satellite Systems (GNSS), hydroacoustic and optoelectronic methods. Therefore, it is necessary to develop coordinate transformation models that will enable the conversion of data from the land and marine parts to one coordinate system. The article presents selected issues related to the integration of geodetic and hydrographic data. The aim of this publication is to present the various transformation methods and their effects that relate to the data from the tombolo measurement campaign in Sopot conducted in 2018. Data obtained using GNSS Real Time Kinematic (RTK) measurements, Terrestrial Laser Scanning (TLS), the Unmanned Aerial Vehicle (UAV) and the Unmanned Surface Vehicle (USV) were transformed. On the basis of the coordinate transformation methods used, it can be concluded that the adjustment calculus method obtained the best results for the plane coordinates, while the method of P.S. Dąbrowski et al. obtained the best results for the height coordinates. The standard deviation for the difference of the modelled coordinates acquired by the method of P.S. Dąbrowski et al. with respect to the reference coordinates amounted to: 0.022 m (Northing), 0.040 m (Easting) and 0.019 m (height), respectively, while the adjustment calculus method allowed to obtain the following values: 0.009 m (Northing), 0.005 m (Easting) and 0.359 m (height). It can be assumed that a combination of these two seven-parameter transformation methods would provide the best results. In the future, a new seven-parameter transformation method should be developed based on the synthesis of these two existing methods.

Modeling and Analysis of Micro Surface Topography from Ball-End Milling in a Trochoidal Milling Mode.

The trochoidal milling mode is widely used in high-speed machining, and due to good adaptability and flexible posture adjustment, ball-end milling cutters are conducive to complex surface machining with this mode. However, the processes of material removal and formation of machined micro surfaces are very difficult to describe as the profile of cutter teeth is complex and the trajectory direction changes continuously during the trochoidal milling process. A modeling method for the generation of micro surface topography of ball-end milling in the trochoidal milling mode is put forward. In this method, the locus equation of each cutter tooth is established based on the principle of homogeneous coordinate transformation, after which a Z-MAP algorithm is designed to simulate the micro surface topography. The Z-MAP algorithm can quickly obtain the part grid nodes potentially swept by the cutter tooth within a unit time step through the establishment of servo rectangular encirclement and instantaneous sweeping quadrilateral of the element of cutter teeth; the part grid nodes actually swept are further determined through an angle summation method, and the height coordinate is calculated with the method of linear interpolation according to Taylor’s formula of multivariate functions. Experiments showed that the micro surface topography resulting from ball-end milling in the trochoidal milling mode had high consistency with the simulation, which indicates that the proposed method can predict micro surface topography in practical manufacturing. In addition, a comparison of micro surface topography between trochoidal milling and ordinary straight-linear milling was conducted, and the results showed that the former was overall superior to the latter in resulting characteristics. Based on this conclusion, the influences of cutting parameters of ball-end trochoidal milling on surface characteristics, particularly amplitude and function, were analyzed according to the simulated micro surface topography data.

Using A Sliding Window Phase Matching Method for Imaging of GNSS Radio Occultation Signals

Global Navigation Satellite System Radio Occultation (GNSS-RO) is a technique used to sound the atmosphere and derive vertical profiles of refractivity. Signals from GNSS satellites are received in a low-Earth orbit, and they are then processed to produce bending angle profiles, from which meteorological parameters can be retrieved. Generating two-dimensional images in the form of spectrograms from GNSS-RO signals is commonly done to, for instance, investigate reflections or estimate signal quality in the lower troposphere. This is typically implemented using, e.g., the Short-Time Fourier Transform (STFT) to produce a time-frequency representation that is subsequently transformed to bending angle (BA) and impact height (IH) coordinates by non-linear mapping. In this paper, we propose an alternative method based on a straightforward extension of the Phase Matching (PM) operator to produce two-dimensional spectral images in the BA-IH domain by applying a sliding window. This Sliding Window Phase Matching (SWPM) method generates the spectral amplitude on an arbitrary grid in BA and IH, e.g., along the coordinate axes. To illustrate, we show both SWPM and STFT methods applied to operational MetOp-A data. For SWPM we use a constant window in the BA-dimension, whereas for STFT we use a conventional constant time window. We show that the SWPM method produces the same result as STFT when the same window length is used for both methods. The sample points in impact parameter and bending angle are those generated by and the main advantage is that SWPM offers the user a convenient way to freely sample the BA-IH space. The cost for this is processing time that is somewhat longer than implementations based on the Fast Fourier Transform, such as the STFT method.