A fast and efficient integrity computation for non-precision approach performance assessment

The level of safety to be expected from global positioning system (GPS) must be known in order to use it to support safety critical operations such as air navigation. This is captured by the navigation performance parameter of integrity which includes the ability of the navigation system to deliver a warning to the user in the event of a significant failure and within a specified time-to-alert. Given the high percentile requirement associated with integrity, assessment of expected system performance both in the nominal case and during failure events, requires the application of analytical techniques. This paper identifies the weaknesses of the current methods for assessing the level of performance to be expected of GPS for non-precision approaches and proposes ways to address them including a novel application of a mathematical integration technique that greatly reduces the computational load associated with integrity performance calculations. Results based on computation times show that the new method reduces computational load by a factor of 500+ with a high accuracy and associated high level of confidence. It is shown that in some cases, the technique presented is able to improve GPS RAIM availability beyond the gains achieved by measurement weighting.     

Laser station coordinates and baselines from long-ARC and short-ARC analyses of starlette

Laser ranging to Starlette from April 1983 to April 1984 has been used to determine a coordinate set, UASC.ST1, of laser reference points for 18 tracking stations. The coordinates were derived by application of the least-squares data reduction procedure in a simultaneous solution along with geodynamic parameters for 49 near consecutive 5–6 day arcs. Comparisons with the University of Texas station coordinates,LSC 8112 andLSC 8402, and theRGO, Herstmonceux, coordinates,RGOSC.LG2, reveal consistency to near 30 cm in each coordinate. Furthermore, the translation vectors of the comparisons are not significantly different from zero indicating consistency in the implied origins of the systems. The period of analysis included seven occasions in which STARLETTE was tracked near simultaneously by three or four laser stations in North America. Using the short arcs as reference frameworks, station coordinates were determined by application of two contrasting methods, namely, a multi-arc simultaneous analysis and a weighted mean of the individual pass solutions. The former compared more favourably with baselines from the long-arc solution with anRMS error of near 16 cm. Comparison against theLSC 8402 coordinates confirmed that baselines accurate to within 15 cm can be achieved by satellite laser ranging to Starlette.     

An efficient solution for building polygonal objects

Polygonal object is a fundamental type of geometric data in vector GIS. The key step cleaning topological relationship after data collection of polygonal layer is to build polygonal objects from digital arcs. The raw digital arcs may intersect with each other. The algorithm for building polygonal objects after the raw arcs have been split at all intersections is presented. The build-up of polygonal objects in this paper is designed to be implemented by two steps. The first step is to extract all the polygons needed for build-up of polygonal objects from arcs. The second step is to organize polygonal objects from these polygons. For the first step, a tracing algorithm is proposed. The algorithm merely extracts the polygons needed for the build-up of polygonal objects, which is a subset of all the possible polygons that can be induced from the arcs. For the second step, an algorithm based on a specially designed order of polygons is advanced. All the topological relationships among the polygons are shown in a single scan. Experiments show that the two algorithms together offer a robust and efficient solution for building polygonal objects from intersected arcs.     

An efficient solution for building polygonal objects

Polygonal object is a fundamental type of geometric data in vector GIS. The key step of cleaning topological relationship after data collection of polygonal layer is to build polygonal objects from digital arcs. The raw digital arcs may intersect with each other. The algorithm for building polygonal objects after the raw arcs have been split at all intersections is presented. The build-up of polygonal objects in this paper is designed to be implemented by two steps. The first step is to extract all the polygons needed for build-up of polygonal objects from arcs. The second step is to organize polygonal objects from these polygons. For the first step, a tracing algorithm is proposed. The algorithm merely extracts the polygons needed for the build-up of polygonal objects, which is a subset of all the possible polygons that can be induced from the arcs. For the second step, an algorithm based on a specially designed order of polygons is advanced. All the topological relationships among the polygons are sho     

基于GPU的任意多边形相交面积计算方法

一直以来,任意多边形相交面积的高效计算都是地理信息系统中空间分析算法研究的重点。文中提出了一种基于GPU的栅格化多边形相交面积算法GPURAS,在此基础上,分别采用蒙特卡罗方法和遮挡查询技术进一步提出GPURASMC算法和GPURASQ算法,并证明了上述算法的正确性。实验对简单多边形、任意复杂多边形及大数据量多边形进行了测试对比,结果表明:GPURAS算法精度高,通用性较好但效率受CPU与GPU通信延迟的影响;GPURASMC算法效率较高但牺牲了部分精度;GPURASQ算法精度高、效率高但局限于特定运行环境。与基于CPU的传统算法相比,文中所提3种算法效率更高,在处理包含大量顶点的多边形时,效率提升尤为明显。     

TIN向规则格网DEM转换的快速算法

从TIN内插成规则格网可以获得高质量的DEM。在内插过程中,需要重点解决的问题就是如何快速查找待插点所在的三角形。本文介绍了一种基于建立空间索引实现TIN到DEM的快速转换算法,通过建立的索引,可以大大地提高检索的速度,提高内插的效率。最后本文通过实验验证了该算法的正确性与可行性。     

GPS-assisted GLONASS orbit determination

 Using 1 week of data from a network of GPS/GLONASS dual-tracking receivers, 15-cm accurate GLONASS orbit determination is demonstrated with an approach that combines GPS and GLONASS data. GPS data are used to define the reference frame, synchronize receiver clocks and determine troposphere delay for the GLONASS tracking network. GLONASS tracking data are then processed separately, with the GPS-defined parameters held fixed, to determine the GLONASS orbit. The quality of the GLONASS orbit determination is currently limited by the size and distribution of the tracking network, and by the unavailability of a sufficiently refined solar pressure model. Temporal variations in the differential clock bias of the dual-tracking receivers are found to have secondary impact on the orbit determination accuracy. Received: 5 January 2000 / Accepted: 15 February 2001     

An efficient solution of real-time data processing for multi-GNSS network

Global navigation satellite systems (GNSS) are acting as an indispensable tool for geodetic research and global monitoring of the Earth, and they have been rapidly developed over the past few years with abundant GNSS networks, modern constellations, and significant improvement in mathematic models of data processing. However, due to the increasing number of satellites and stations, the computational efficiency becomes a key issue and it could hamper the further development of GNSS applications. In this contribution, this problem is overcome from the aspects of both dense linear algebra algorithms and GNSS processing strategy. First, in order to fully explore the power of modern microprocessors, the square root information filter solution based on the blocked QR factorization employing as many matrix–matrix operations as possible is introduced. In addition, the algorithm complexity of GNSS data processing is further decreased by centralizing the carrier-phase observations and ambiguity parameters, as well as performing the real-time ambiguity resolution and elimination. Based on the QR factorization of the simulated matrix, we can conclude that compared to unblocked QR factorization, the blocked QR factorization can greatly improve processing efficiency with a magnitude of nearly two orders on a personal computer with four 3.30 GHz cores. Then, with 82 globally distributed stations, the processing efficiency is further validated in multi-GNSS (GPS/BDS/Galileo) satellite clock estimation. The results suggest that it will take about 31.38 s per epoch for the unblocked method. While, without any loss of accuracy, it only takes 0.50 and 0.31 s for our new algorithm per epoch for float and fixed clock solutions, respectively.     

Ellipsoidal geoid computation

Modern geoid computation uses a global gravity model, such as EGM96, as a third component in a remove–restore process. The classical approach uses only two: the reference ellipsoid and a geometrical model representing the topography. The rationale for all three components is reviewed, drawing attention to the much smaller precision now needed when transforming residual gravity anomalies. It is shown that all ellipsoidal effects needed for geoid computation with millimetric accuracy are automatically included provided that the free air anomaly and geoid are calculated correctly from the global model. Both must be consistent with an ellipsoidal Earth and with the treatment of observed gravity data. Further ellipsoidal corrections are then negligible. Precise formulae are developed for the geoid height and the free air anomaly using a global gravity model, given as spherical harmonic coefficients. Although only linear in the anomalous potential, these formulae are otherwise exact for an ellipsoidal reference Earth—they involve closed analytical functions of the eccentricity (and the Earths spin rate), rather than a truncated power series in e². They are evaluated using EGM96 and give ellipsoidal corrections to the conventional free air anomaly ranging from –0.84 to +1.14 mGal, both extremes occurring in Tibet. The geoid error corresponding to these differences is dominated by longer wavelengths, so extrema occur elsewhere, rising to +766 mm south of India and falling to –594 mm over New Guinea. At short wavelengths, the difference between ellipsoidal corrections based only on EGM96 and those derived from detailed local gravity data for the North Sea geoid GEONZ97 has a standard deviation of only 3.3 mm. However, the long-wavelength components missed by the local computation reach 300 mm and have a significant slope. In Australia, for example, such a slope would amount to a 600-mm rise from Perth to Cairns.     

城市海量三维场景的高效裁剪算法研究

针对目前三维GIS领域缺少城市海量三维场景的快速裁剪算法,方便城市三维数据的分发与应用,本文在对三维场景进行分区组织以及动态调度的基础上,提出了一种层-区-块-模型四层次由粗到精的快速真三维裁剪算法。数个城市的应用实践证明,该算法准确、高效,适用于城市海量三维场景的快速裁剪。     

一种高效的最小独立闭合环自动搜索算法

依据图论理论,在基于生成树、余树变换的闭合环搜索算法和基于深度优先的闭合环搜索算法的基础上,提出一种高效且稳定性好的控制网最小独立闭合环自动搜索算法.     

An application of a summation formula to numerical computation of integrals over the sphere

Summary This paper discusses a method to approximate an integral over the (unit) sphere by a linear combination of the values of the integrand at given points. The main concept of this method is the observation, that on the sphere for each sufficiently smooth function the integral can be expressed by a summation formula. A method is given for optimizing the accuracy of the computation for a given set of sample points for the function being integrated.     

Precise ERS-1 orbit calculation

This analysis was performed with the GEOSAT software developed at NDRE for high-precision analysis of satellite tracking and VLBI data for geodetic and geodynamic applications.For applications to ERS-1, a realistic surface force model is used together with the Jacchia 77 atmospheric model, semi-daily drag coefficients, a 1-cpr sinusoidal along-track acceleration, and the GSFC JGM-2 gravity model. ERS-1 orbits have been derived for 5.5-day arcs of laser tracking data between July 6 and August 12, 1992. Results from overlapping orbits and comparison with precise D-PAF orbits indicate an orbital accuracy of 10–15 cm in the radial direction, ~ 60 cm in the along-track direction and ~ 15 cm in the cross-track direction.     

Precision orbit computations for Starlette

The Starlette satellite, launched in February 1975 by the French Centre National d'Etudes Spatiales, was designed to minimize the effects of non-gravitational forces and to obtain the highest possible accuracy for laser range measurements. Analyses of the first four months of laser tracking data from nine stations. have confirmed the stability of the orbit and the precision to which the satellite's position can be established. Initial orbit computations using the GSFC GEM-7 gravity model produced rms fits of about 8 to 10 meters for arc lengths of 5 days. After tailoring a gravity model specifically to Starlette, the rms fits for the 5 day arcs were reduced significantly to the 1 to 2 meter level. An rms fit of 4.3 meters was obtained for a 90 day arc. Five day arcs overlapped by 2.5 days showed rms satellite position differences generally less than 2 meters. Prediction errors at the end of two months were less than 30 milliseconds.     

An improved sampling rule for mapping geopotential functions of a planet from a near polar orbit

One of the limiting factors in the determination of gravity field solutions is the spatial sampling. Especially during phases, when the satellite repeats its own track after a short time, the spatial resolution will be limited. The Nyquist rule-of-thumb for mapping geopotential functions of a planet, also referred to as the Colombo–Nyquist rule-of-thumb, provides a limit for the maximum achievable degree of a spherical harmonic development for repeat orbits. We show in this paper that this rule is too conservative, and solutions with better spatial resolutions are possible. A new rule is introduced which limits the maximum achievable order (not degree!) to be smaller than the number of revolutions if the difference between the number of revolutions and the number of nodal days is of odd parity and to be smaller than half the number of revolutions if the difference is of even parity. The dependence on the parity is reflected in the eigenvalue spectrum of the normal matrix and becomes especially important in the presence of noise. The rule is based on applying the Nyquist sampling theorem separately in North–South and East–West direction. This is only possible for satellites in highly inclined orbits like champ and grace. Tables for these two satellite missions are also provided which indicate the passed and (in case of grace) expected repeat cycles and possible degradations in the quality of the gravity field solutions.     

Reducing Influence of Gravity Model Error in Precise Orbit Determination of Low Earth Orbit Satellites

Based on the orbit integration and orbit fitting method, the influence of the characters of the gravity model, with different precisions, on the movement of low Earth orbit satellites was studied. The way and the effect of absorbing the influence of gravity model error on CHAMP and GRACE satellite orbits, using linear and periodical empirical acceleration models and the so-called "pseudo-stochastic pulses" model, were also analyzed.     

Reducing influence of gravity model error in precise orbit determination of low Earth orbit satellites

Based on the orbit integration and orbit fitting method, the influence of the characters of the gravity model, with different precisions, on the movement of low Earth orbit satellites was studied. The way and the effect of absorbing the influence of gravity model error on CHAMP and GRACE satellite orbits, using linear and periodical empirical acceleration models and the so-called “pseudo-stochastic pulses” model, were also analyzed.     

An efficient representation of quadtrees and bintrees for multiresolution terrain models

A space-filling curve in 2,3,or higher dimensions can be thought as a path of a continuously moving point.As its main goal is to preserve spatial proximity,this type of curves has been widely used in the design and implementation of spatial data structures and nearest neighbor-finding techniques.This paper is essentially focused on the efficient representation of Digital Ele-vation Models(DEM) that entirely fit into the main memory.We propose a new hierarchical quadtree-like data structure to be built over domains of unrestricted size,and a representation of a quadtree and a binary triangles tree by means of the Hilbert and the Sierpinski space-filling curves,respectively,taking into account the hierarchical nature and the clustering properties of this kind of curves.Some triangulation schemes are described for the space-filling-curves-based approaches to efficiently visualize multiresolu-tion surfaces.     

SIFT-FANN: An efficient framework for spatio-spectral fusion of satellite images

Image fusion techniques are widely used for remote sensing data. A special application is for using low resolution multi-spectral image with high resolution panchromatic image to obtain an image having both spectral and spatial information. Alignment of images to be fused is a step prior to image fusion. This is achieved by registering the images. This paper proposes the methods involving Fast Approximate Nearest Neighbor (FANN) for automatic registration of satellite image (reference image) prior to fusion of low spatial resolution multi-spectral QuickBird satellite image (sensed image) with high spatial resolution panchromatic QuickBird satellite image. In the registration steps, Scale Invariant Feature Transform (SIFT) is used to extract key points from both images. The keypoints are then matched using the automatic tuning algorithm, namely, FANN. This algorithm automatically selects the most appropriate indexing algorithm for the dataset. The indexed features are then matched using approximate nearest neighbor. Further, Random Sample Consensus (RanSAC) is used for further filtering to obtain only the inliers and co-register the images. The images are then fused using Intensity Hue Saturation (IHS) transform based technique to obtain a high spatial resolution multi-spectral image. The results show that the quality of fused images obtained using this algorithm is computationally efficient.