Combined Method of Datum Transformation Between Different Coordinate Systems

The similarity transformation model between different coordinate systems is not accurate enough to describe the discrepancy of them.Therefore,the coordinate transformation from the coordinate frame with poor accuracy to that with high accuracy cannot guarantee a high precision of transformation.In this paper,a combined method of similarity transformation and regressive approximating is presented.The local error accumulation and distortion are taken into consideration and the precision of coordinate system is improved by using the recommended method

Hawking effect and quantum nonthermal radiation of an arbitrarily accelerating charged black hole using a new tortoise coordinate transformation

Using a new tortoise coordinate transformation, this paper investigates the Hawking effect from an arbitrarily accelerating charged black hole by the improved Damour-Ruffini method. After the tortoise coordinate transformation, the Klein-Gordon equation can be written as the standard form at the event horizon. Then extending the outgoing wave from outside to inside of the horizon analytically, the surface gravity and Hawking temperature can be obtained automatically. It is found that the Hawking temperatures of different points on the surface are different. The quantum nonthermal radiation characteristics of a black hole near the event horizon is also discussed by studying the Hamilton-Jacobi equation in curved spacetime and the maximum overlap of the positive and negative energy levels near the event horizon is given. There is a dimensional problem in the standard tortoise coordinate and the present results may be more reasonable.

A complete solution of an improved universal 3D coordinate similarity transformation model

When linearizing three-dimensional(3 D)coordinate similarity transformation model with large rotations,we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions.To alleviate the problem,a series of conversions are contributed to the 3 D coordinate similarity transformation model in this paper.We deduced a complete solution for the 3 D coordinate similarity transformation at any rotation with the nonlinear adjustment methodology,which involves the errors of the common and the non-common points.Furthermore,as the large condition number of the normal matrix resulted in an intractable form,we introduced the bary-centralization technique and a surrogate process for deterministic element of the normal matrix,and proved its benefit for alleviating the condition number.The experimental results show that our approach can obtain the smaller condition number to stabilize the convergence of the interested parameters.Especially,our approach can be implemented for considering the errors of the common and the non-common points,thus the accuracy of the transformed coordinates improves.

Correlation of coordinate transformation parameters

Coordinate transformation parameters between two spatial Cartesian coordinate systems can be solved from the positions of non-colinear corresponding points. Based on the characteristics of translation, rotation and zoom components of the transformation, the complete solution is divided into three steps. Firstly, positional vectors are regulated with respect to the centroid of sets of points in order to separate the translation compo- nents. Secondly, the scale coefficient and rotation matrix are derived from the regulated positions independent- ly and correlations among transformation model parameters are analyzed. It is indicated that this method is applicable to other sets of non-position data to separate the respective attributions for transformation parameters.

Grid Model for High-accuracy Coordinate Transformation of China Geodetic Coordinate System 2000

After implementing CGCS2000,establishing grid models for high-accuracy coordinate transformation which are mainly used to transform border lines and coordinate grids of topographic maps becomes an important issue in mapping applications.Consequently,a grid model for high-accuracy coordinate transformation of CGCS2000 is proposed.Specifically,we firstly analyze a minimum curvature equation of coordinate transformation,which possesses the characteristics of both the global and local smoothness,achieving better consistency with the consecutive smoothness for the coordinate transformation of map’s linear feature.Then an iterative calculation method of grid nodes and an approach for establishing regional grid models based on collocation by two-step minimization are proposed.Meanwhile,a data structure of grid model is constructed.Finally we give the optimized grid interval and transformation accuracy in China corresponding to the proposed grid model.Using 48 433 points of 2000 National Geodetic Control Network of China,we take the proposed model into practice by constructing grid models for coordinate transformation from BJS54 and XAS80 to CGCS2000,and the external positional accuracies for both models are 0.26 m and 0.03 m respectively.

The Functional Gradient Description Method of Space Coordinate Transformation

The 3-dimension coordinate datum transformation is very important in geomatics.Generally,there are small angle coordinate transformation model (i.e.,Bursa model,et al) and large angle coordinate transformation model (i.e.,Rodrigo matrix model,et al).However,these papers only focus on the fixed and static situation regardless of the small or large angle.This paper proposes the conception of coordinate transformation gradient field,which can realize the space coordinate transformation from small angle to arbitrary angle,and from static to dynamical.Based on the equivalent characteristics of the unit quaternion rotation matrix and the Rodrigo matrix,through studying the mathematical relationship between the spatial coordinate transformation and the functional gradient,we derive a functional gradient expression of the arbitrary transformation formula in space.The study shows that the essence of spatial coordinate transformation is a kind of potential field mathematically.This potential field conception can unify all the space coordinate transformations.It is the theoretical foundation for the further study of time continuous space coordinate transformation,and this study gives a new solution for the attitude determination of motion carriers.

A VERTICAL COORDINATE TRANSFORMATION FOR 3-D NUMERICAL MODELLING OF OCEAN CIRCULATION

A so called sine-sigma vertical coordinate transformation is proposed. A vertical implicit scheme is de-rived by using cubic-spline representation of vertical current profiles. The derived 3-D nurmericalmodel has been applied to simulate the water leved field and the vertical structures of wind-induced cur-rents in an enclosed rectangular region, and the tides in the Bohai Sea. The model is believed to besatisfactory after comparing its results with an analytical soclution and observed data from tidal staions.

Evaluation of the Direct UTM Coordinates Transformation Method Based on the Standard 7-Parameters Transformation

GNSS(global navigation satellite system)observations produce the geodetic position including latitude,longitude,and altitude(or ellipsoidal height)concerning the global reference datum WGS84(Word Geodetic System 1984),which usually should be converted to another local datum to get the desired position meaning in a physical sense,coordinates of points in the local datum are usually calculated by the seven-parameter transformation method.This paper aims to validate the methods of position transformation between WGS84 and the Iraqi local datum Karbala 1979 using the UTM(universal transverse Mercator)projected coordinates directly.The proposed algorithm was tested for 10 ground control points in Erbil city and many selected points in other different cities over all Iraqi territory.The control points are measured by the CHCNAV i73 GNSS receiver.For the evaluation procedure,the RMSE(root mean square error)of the transformed coordinates is calculated with an average value of±10.715 m as an estimated uncertainty of the direct UTM coordinates transformation method over Erbil city territory,and more than±12 m over different places over Iraqi territory.

A Modified T/2 Fractionally Spaced Coordinate Transformation Blind Equalization Algorithm

When T/2 Fractionally Spaced blind Equalization Algorithm based Constant Modulus Algorithm (T/2-FSE- CMA) is employed for equalizing higher order Quadrature Amplitude Modulation signals (QAM), it has disadvantages of low convergence speed and large Mean Square Error (MSE). For overcoming these disadvantages, a Modified T/2 Fractionally Spaced blind Equalization algorithm based on Coordinate Transformation and CMA (T/2-FSE-MCTCMA) was proposed by analyzing the character of 16QAM signal constellations. In the proposed algorithm, real and imaginary parts of input signal of T/2 fractionally spaced blind equalizer are equalized, respectively, and output signals of equalizer are transformed to the same unit circle by coordinate transformation method, a new error function is defined after making coordinate transformation and used to adjust weight vector of T/2 fractionally spaced blind equalizer. The proposed algorithm can overcome large misjudgments of T/2 fractionally spaced blind equalization algorithm for equalizing multi-modulus higher order QAM. Simulation results with underwater acoustic channel models demonstrate that the proposed T/2-FSE-MCTCMA algorithm outperforms T/2 Fractionally Spaced blind Equalization algorithm bas-ed on Coordinate Transformation and CMA (T/2-FSE-CTCMA) and the T/2-FSE-CMA in convergence rate and MSE.

SARC Model for Three-Dimensional Coordinate Transformation

In this paper, a transformation model named SARC(static-filter adjustment with restricted condition) is presented, which is more practical and more rigorous in theory and fitting any angle of rotation parameter. The transformation procedure is divided into 4 steps: ① the original and object coordinates can be regarded as observations with errors; ② rigorous formula is firstly deduced in order to compute the first approximation of the transformation parameters by use of four common points and the transformation equation is linearized; ③ calculate the most probable values and variances of the seven transformation parameters by SARC model; ④ to demonstrate validity of SARC , an example is given.

Coordinate Transformation and Exact Solutions of Schrodinger Equation with Position-Dependent Effective Mass

Using the coordinate transformation method, we solve the one-dimensional Schrodinger equation with position-dependent mass. The explicit expressions for the potentials, energy eigenvalues, and eigenfunctions of the systems are given. The eigenfunctions can be expressed in terms of the Jacobi, Hermite, and generalized Laguerre polynomials. All potentials for these solvable systems have an extra term Vm, which is produced from the dependence of mass on the position, compared with those for the systems of constant mass. The properties of Vm for several mass functions are discussed.

A New Regularized Solution to Ill-Posed Problem in Coordinate Transformation

Coordinates transformation is generally required in GPS applications. If the transformation parameters are solved with the known coordinates in a small area using the Bursa model, the precision of transformed coordinates is generally very poor. Since the translation parameters and rotation parameters are highly correlated in this case, a very large condition number of the coefficient matrix A exists in the linear system of equations. Regularization is required to reduce the effects caused by the intrinsic ill-conditioning of the problem and noises in the data, and to stabilize the solution. Based on advanced regularized methods, we propose a new regularized solution to the ill-posed coordinate transformation problem. Simulation numerical experiments of coordinate transformation are given to shed light on the relationship among different regularization approaches. The results indicate that the proposed new method can obtain a more reasonable resolution with higher precision and/or robustness.

Uzbekistan's coordinate system transformation from CS42 to WGS84 using distortion grid model

Currently,a non-geocentric geodetic coordinate system introduced in 1942(CS42),based on the Krasovsky ellipsoid and the Baltic system of normal heights introduced in 1977,is used for geodetic works in the Republic of Uzbekistan.The development of the GNSS network proposes a task of transition to a new geocentric system based on the World Geodetic System 1984(WGS84)ellipsoid.Many software products adopt 3-or 7-parameter conversions,which can cause errors up to several meters and are not suitable for many applications.In this case,local transformations using a grid of differences between observation points with known coordinates in both datums would give the best accuracy.In this paper,we discuss various interpolation methods(Kriging,Minimum Curvature,Inverse Distance to a Power and Radial Basis Function)to solve the distortion modeling between CS42 and WGS84 systems for national datum improvement.The results show that the distortion models share a common tendency for all interpolation methods:the maximum horizontal displacements are concentrated along the West Tien Shan lineament,which is the boundary of the relief lowering.The discrepancies between the grid-based(calculated)and GPS-measured coordinates are evaluated.Statistical and spatial analysis has confirmed that for the co-ordinate transformation from CS42 to WGS84 and vice versa,grid-based transformation with Radial Basis Function interpolation has a high accuracy transformation.Analysis of the available data across the eastern part of the country shows that some positional distortions existed between the CS42 and WGS84 datums.For the best RBF method,the magnitude of these distortions is about 0.019-0.755 m with a standard deviation of 0.015 m.

Water Wave Focusing Using Coordinate Transformation

In this paper, wave focusing based on a coordinate transformation is proposed. It is known that the 2-dimensional wave equation which governs a shallow water problem in a potential theory can keep invariance under coordinate transformation. Once equivalent medium parameters are obtained so as to keep the invariance, wave rays can be arbitrarily designed. We show the design of equivalent medium for wave squeezing to focus waves on a specific domain. Numerical computations are carried out by a finite element based software COMSOL Multiphysics. Results show good agreement between predictions from the theory and computations. It can be applied for a wide range of frequency because the proposed method is able to be applied regardless of the frequency.

Error modeling of 3-RSR parallel robot based on D-H transformation matrix

By selecting any one limb of 3-RSR parallel robot as a research object, the paper establishes a position and orienta- tion relationship matrix between the moving platform and the base by means of Denavit-Hartenberg （D-H） transformation matrix. The error mapping model is derived from original error to the error of the platform by using matrix differential method. This model contains all geometric original errors of the robot. The nonlinear implicit function relation between po- sition and orientation error of the platform and the original geometric errors is simplified as a linear explicit function rela- tion. The results provide a basis for further studying error analysis and error compensation.

基于Contextual Transformer的自动驾驶单目3D目标检测

针对当前单目3D目标检测中存在的漏检和多尺度目标检测效果不佳的问题,提出了一种基于Contextual Transformer的自动驾驶单目3D目标检测算法(CM-RTM3D)。在ResNet-50网络中引入Contextual Transformer(CoT),构建ResNet-Transformer架构以提取特征。设计多尺度空间感知模块(MSP),通过尺度空间响应操作改善浅层特征的丢失情况,嵌入沿水平和竖直两个空间方向的坐标注意力机制(CA),使用softmax函数生成各尺度的重要性软权重。在偏移损失中采用Huber损失函数代替L1损失函数。实验结果表明:在KITTI自动驾驶数据集上,相较于RTM3D算法,该算法在简单、中等、困难三个难度级别下,AP3D分别提升了4.84、3.82、5.36个百分点,APBEV分别提升了4.75、6.26、3.56个百分点。

结合坐标Transformer的轻量级人体姿态估计算法

针对现有的大多数自底向上人体姿态估计算法存在模型规模大、计算成本高及对边缘设备不友好等问题,提出了一种基于YOLOv5s6-Pose的轻量级多人姿态估计网络模型YOLOv5s6-Pose-CT。该模型在颈部网络中引入空间和通道重建卷积,以减少空间和通道维度上的特征冗余。同时,提出了一种坐标Transformer嵌入于主干网络中,使模型专注于长距离依赖和拥有高效的局部特征提取能力。其次,通过使用无偏特征位置对齐来解决多尺度融合过程中出现的特征错位问题。最后,使用损失函数MPDIoU对边界框的回归损失重新定义。在COCO 2017数据集上的实验结果表明,本文优化的网络模型与主流的轻量级网络EfficientHRNet-H1模型相比,在保持相同精度的同时,参数量和计算量分别减少16.2%和66.1%。相比于基准模型YOLOv5s6-Pose,参数量减少11.2%,计算量降低5.8%,平均检测精度和平均召回率分别提升2.5%和2.6%。

引入轻量级Transformer的自适应窗口立体匹配算法

现有端到端的立体匹配算法为了减轻显存消耗和计算量而预设固定视差范围,在匹配精度和运行效率上难以平衡。提出一种基于轻量化Transformer的自适应窗口立体匹配算法。利用具有线性复杂度的坐标注意力层对低分辨率特征图进行位置编码,减轻计算量并增强相似特征的辨别力;设计轻量化Transformer特征描述模块,转换上下文相关的特征,并引入可分离多头自注意力层对Transformer进行轻量化改进,降低Transformer的延迟性;用可微匹配层对特征进行匹配,设计自适应窗口匹配细化模块进行亚像素级的匹配细化,在提高匹配精度的同时减少显存消耗;经视差回归后生成无视差范围的视差图。在KITTI2015、KITTI2012和SceneFlow数据集上的对比实验表明,该算法比基于标准Transformer的STTR在匹配效率上快了近4.7倍,具有更快的运行速度和更友好的存储性能;比基于3D卷积的PSMNet误匹配率降低了18%,运行时间快了5倍,实现了更好的速度和精度的平衡。

The Accuracy of GIS Tools for Transforming Assumed Total Station Surveys to Real World Coordinates

Most surveying works for mapping or GIS applications are performed with total station. Due to the remote nature of many of the sites surveyed, the surveys are often done in unprojected, local, assumed coordinate systems. However, without the survey data projected in real world coordinates, the range of possible analyses is limited and the value of existing imagery, elevation models, and hydrologic layers cannot be exploited. This requires a transformation from the local assumed to the real world coordinate systems. There are various built-in and add-in tools to perform transformations through GIS programs. This paper studies the effect of using Georeferencing tool, Spatial Adjustment tool (Affine and similarity) and CHaMP tool on the precision and relative accuracy of total station survey. This transformation requires real-world coordinates of at least two control points, which can be collected from different sources. This paper also studies the effect of using geodetic GPS, hand-held GPS, Google Earth (GE) and Bing Basemaps as sources for control points on the precision and relative accuracy of total station survey. These effects have been tested by using 111 points covered area of 60,000 m2and the results have shown that the CHaMP tool is the best for preserving the relative accuracy of the transformed points. The Georeferencing and spatial adjustment (similarity) tools give the same results and their accuracy are between 1/1000 and 1/300 depending on the source of control points. The results have also shown that the cornerstone to preserve the precision and relative accuracy of the transformed coordinates is the relative position of the control points despite their source.

基于CNN和Transformer混合网络模型的车道线检测

车道线检测技术在自动驾驶系统中发挥着重要作用,目前基于深度学习的车道线检测方法通常在主干网络提取特征之后分别获取车道线关键点的置信度以及这些点相对车道线起始点的偏移。但由于车道线是细长结构,现有的主干网络无法有效提取这种结构特征,偏移网络也难以回归车道线上关键点相对起始点的偏移。鉴于注意力机制在提取空间结构特征、表征长距离图像序列间依赖关系方面的优越性能,在基于点的车道线检测方法的基础上提出了一种基于卷积神经网络(convolutional neural network,CNN)和Transformer的混合网络(CNN-Transformer hybrid network,CTNet)模型,该模型通过特征金字塔和增强的坐标注意力机制提高特征的表征能力,使用基于视觉Transformer的偏移网络回归关键点的偏移量,因此,CTNet能够提取细长车道线特征、捕获长距离点间的偏移,有效提升车道线检测的精度。实验对比了CTNet和6种常用车道线检测算法在数据集TuSimple和CULane上的效果,在TuSimple上CTNet各项精度指标均优于现有方法,在CULane数据集的9种不同车道场景中,CTNet在6个场景中取得了最佳精度。