A closed-form formula for GPS GDOP computation

Geometric dilution of precision (GDOP) is often used for selecting good satellites to meet the desired positioning precision. An efficient closed-form formula for GDOP has been developed when exactly four satellites are used. It has been proved that increasing the number of satellites for positioning will always reduce the GDOP. Since most GPS receivers today can receive signals from more than four satellites, it is desirable to compute GDOP efficiently for the general case. Previous studies have partially solved this problem with artificial neural network (ANN). Though ANN is a powerful function approximation technique, it needs costly training and the trained model may not be applicable to data deviating too much from the training data. Using Newton’s identities from the theory of symmetric polynomials, this paper presents a simple closed-form formula for computing GDOP with the inputs used in previous studies. These inputs include traces of the measurement matrix and its second and third powers, and the determinant of the matrix.     

基于伪卫星的改善GPS几何精度因子的研究

随着人们活动范围的日益扩大和周边环境的日益复杂,高精度GPS导航技术逐渐成为国内外研究的重点。GPS系统的定位精度在很大程度上取决于参与定位卫星的数目和几何布局,而几何精度因子(GDOP)正是衡量定位卫星几何布局优劣的量度。文章从几何精度因子着手,从理论上证明了伪卫星对GPS系统GDOP的改善,分析了伪卫星数量对GPS系统定位精度的影响。借助于仿真实验,结果表明,在GPS导航定位中,伪卫星能够显著增强卫星几何图形结构、提高测量精度、改善精度因子从而提高定位精度。     

几何精度因子对GRACE卫星几何轨道精度影响分析

分析了GDOP值与GRACE卫星几何轨道精度之间的关系,发现定轨精度较差的历元其GDOP值普遍较大甚至异常,进一步研究发现GDOP值异常现象是因剔除个别含有粗差的卫星而导致的,进而通过设置GDOP值阈值的方式剔除发生GDOP值异常的历元。实验结果表明,GDOP值阈值设置为50,将大于该阈值的历元剔除,能够有效抑制个别历元精度较差的情况,最终的RMS在地固系X,Y,Z3个方向分别为0.029m,0.043m,0.029m,实现了几何法厘米级精密定轨的目标。     

天文定位中几何精度衰减因子最小值分析

天文定位是一种重要的导航定位方法,被广泛应用于大地天文测量、天文航海等领域。该方法中观测恒星的选择会影响最终的定位精度,目前缺少针对同时测定经纬度天文定位算法中最优选星问题的研究。随着观测仪器自动化水平的提高,观测数据的获取变得更加高效,这就要求研究最优的选星方案以达到最高的定位精度。本文借鉴卫星导航中几何精度衰减因子GDOP的概念,研究了天顶距法中恒星的数量以及分布对定位精度的影响,最后通过仿真试验和实测数据验证得到结论:在天顶距观测误差的统计特性一定时,GDOP能够用来描述恒星的分布对定位结果影响的优劣,且观测的恒星方位角均匀分布时定位误差最小。考虑到不同高度的恒星天顶距大气折射改正残差不同,在实际测量中应尽量采用等天顶距且方位角均匀分布的恒星。     

A closed-form of Newton method for solving over-determined pseudo-distance equations

The Newton method has been widely used for solving nonlinear least-squares problem. In geodetic adjustment, one would prefer to use the Gauss–Newton method because of the parallel with linear least-squares problem. However, it is proved in theory as well as in practice that the Gauss–Newton method has slow convergence rate and low success rate. In this paper, the over-determined pseudo-distance equations are solved by nonlinear methods. At first, the convergence of decent methods is discussed after introducing the conditional equation of nonlinear least squares. Then, a compacted form of the Hessian matrix from the second partial derivates of the pseudo-distance equations is given, and a closed-form of Newton method is presented using the compacted Hessian matrix to save the computation and storage required by Newton method. At last, some numerical examples to investigate the convergence and success rate of the proposed method are designed and performed. The performance of the closed-form of Newton method is compared with the Gauss–Newton method as well as the regularization method. The results show that the closed-form of Newton method has good performances even for dealing with ill-posed problems while a great amount of computation is saved.     

一种单像外方位元素的稳健估计方法

获取影像外方位元素是摄影测量学一直要解决的问题,传统的单像空间后方交会利用测量控制点来计算外方位元素,但是很多情况下用于计算的数据是包含粗差的,粗差出现的概率约占1%~10%。本文设计了一种稳健的单像空间后方交会计算方法,把控制点坐标作为未知参数对待并线性化共线方程,最终达到了剔除粗差的目标,提高了计算结果的可靠性,可得到控制点及像点坐标的精度评价。     

Comment and reply regarding Changyou Zhang (1995) A general formula and its inverse formula for gravimetric transformation by use of convolution and deconvolution techniques.

The incorrectness in the derivations of error formula (52) in Zhang's paper is pointed out and the correction is given. Table 3 [list of error formulae of Eqs (5)–(8)] in Zhang's paper is also corrected. Received: 25 February 1998 / Accepted: 30 June 1998     

Assessment of PPP integer ambiguity resolution using GPS,GLONASS and BeiDou (IGSO,MEO) constellations

Although integer ambiguity resolution (IAR) can improve positioning accuracy considerably and shorten the convergence time of precise point positioning (PPP), it requires an initialization time of over 30 min. With the full operation of GLONASS globally and BDS in the Asia–Pacific region, it is necessary to assess the PPP–IAR performance by simultaneous fixing of GPS, GLONASS, and BDS ambiguities. This study proposed a GPS + GLONASS + BDS combined PPP–IAR strategy and processed PPP–IAR kinematically and statically using one week of data collected at 20 static stations. The undifferenced wide- and narrow-lane fractional cycle biases for GPS, GLONASS, and BDS were estimated using a regional network, and undifferenced PPP ambiguity resolution was performed to assess the contribution of multi-GNSSs. Generally, over 99% of a posteriori residuals of wide-lane ambiguities were within ±0.25 cycles for both GPS and BDS, while the value was 91.5% for GLONASS. Over 96% of narrow-lane residuals were within ±0.15 cycles for GPS, GLONASS, and BDS. For kinematic PPP with a 10-min observation time, only 16.2% of all cases could be fixed with GPS alone. However, adding GLONASS improved the percentage considerably to 75.9%, and it reached 90.0% when using GPS + GLONASS + BDS. Not all epochs could be fixed with a correct set of ambiguities; therefore, we defined the ratio of the number of epochs with correctly fixed ambiguities to the number of all fixed epochs as the correct fixing rate (CFR). Because partial ambiguity fixing was used, when more than five ambiguities were fixed correctly, we considered the epoch correctly fixed. For the small ratio criteria of 2.0, the CFR improved considerably from 51.7% for GPS alone, to 98.3% when using GPS + GLONASS + BDS combined solutions.     

A new implementation of narrowband interference detection,characterization, and mitigation technique for a software-defined multi-GNSS receiver

Due to the very low power of satellite signals when reaching the earth’s surface, global navigation satellite system receivers are vulnerable to various types of radio frequency interference, and, therefore, countermeasures are necessary. In the case of a narrowband interference (NBI), the adaptive notch filtering technique has been extensively investigated. However, the research on the topic has focused on the adaptation of the notch frequency, but not of the notch width. We present a fully adaptive solution to counter NBI. The technique is capable of detecting and characterizing any number of narrow interfered bands, and then optimizing the mitigation process based on such characterization, namely the estimates of both interference frequency and width. Its full adaptiveness makes it suitable to cope with the unpredictable and diverse nature of unintentional interfering events. In addition to a thorough performance evaluation of the proposed method, which shows its benefits in terms of signal quality improvement, an analysis of the impact of different NBI profiles on GPS L1 C/A and Galileo E1 is also conducted.     

摄影测量系统精度测试新方法

根据经纬仪测量系统点位真实精度的经验值和分别用工业摄影测量系统与经纬仪测量系统测量出的点位进行公共点转换得出的差值,来估计工业摄影测量系统测量的点位精度,从而提供一种检测工业摄影测量系统精度的新方法。分别使用INCA3与Nikon D2H相机试验,发现INCA3相机的精度大约是Nikon D2H精度的2倍。     

A general formula and its inverse formula for gravimetric transformations by use of convolution and deconvolution techniques

A general formula is developed and presented for transformations among geoidal undulation, gravity anomaly, gravity disturbance and other gravimetric quantities. Using a spectral form of the general formula, a criterion has been built in order to classify these transformations into forward and inverse transformations in this paper. Then, the two-dimensional convolution techniques are applied to the general formula to deal with the forward transformation while the two-dimensional deconvolution techniques are employed to treat the inverse transformation and evaluate the inverse general formula. Concepts of convolution and deconvolution are also reviewed in this paper. The stability and edge effect problems related to the deconvolution techniques are investigated using simulated data and numerical tests are done to quantify the stability of the deconvolution techniques for estimated gravity information. Finally, the marine gravity information for the Norwegian-Greenland Sea area has been derived from ERS-1 altimetry data using the deconvolution techniques.     

A formula for gravimetric terrain corrections using powers of topographic height

Journal of Geodesy - ?The application of Stokes' formula to create geoid undulations requires no masses outside the geoid. However, due to the existence of the topography, terrain...     

天文经纬度归心实用算式推证

文中分析天文经纬度归心公式中各变量的特点,推导基于2000国家大地坐标系统简单实用的归心计算公式,进一步给出由已确定变量推求归心元素测量精度的数学关系式。验证实用公式计算的归心改正数满足专用工程天文经纬度的计算精度需求。     

一种适用于对流层干延迟的新的几何映射函数

本文提出了一种新的对流层干延迟映射函数,此模型形式简洁,精度较高,是完全应用几何方法得出的,模型只与大气的有效高度有关,不包含任何气象因素,适用于动态定位及导航。文中通过实验在不同高度角、不同纬度与目前最常用的CFA2·2和Niell映射函数进行了比较,结果表明,在高度角大于6度时此函数与这两种模型精度相当,得到了非常理想的效果。     

提高对流层天顶总延迟解算精度的新方法探讨

对流层天顶总延迟的解算精度,直接影响长基线解算的精度和大气水汽含量的计算精度。文中提出克利金内插法解算天顶总延迟的新方法,并利用南极长城站和周边IGS跟踪站的GPS数据,通过高精度解算软件GAMIT/GLOBK,解算出长城站上空的对流层天顶总延迟,将其与利用内插方法解算的天顶总延迟进行了对比分析,得出:利用该内插方法获取的南极长城站在夏季的天顶总延迟的均方差可达0.2mm,这对今后GPS高精度定位和GPS气象学应用来说,具有重要意义。     

A method for computing the coefficients in the product-sum formula of associated Legendre functions

The product of two associated Legendre functions can be represented by a finite series in associated Legendre functions with unique coefficients. In this study a method is proposed to compute the coefficients in this product-sum formula. The method is of recursive nature and is based on the straightforward polynomial form of the associated Legendre function's factor. The method is verified through the computation of integrals of products of two associated Legendre functions over a given interval and the computation of integrals of products of two Legendre polynomials over [0,1]. These coefficients are basically constant and can be used in any future related applications. A table containing the coefficients up to degree 5 is given for ready reference.     

多源矢量空间数据中面状水域几何准确性及现势性评估方法

多源矢量空间数据的评估方法一直以来比较欠缺。目前常用的专家决策方法,主要依赖专家的人工参与,不仅主观性强、执行效率低,而且使用门槛高。本文提出了多源矢量空间数据中面状水域的几何准确性与现势性评估方法,可以"量化"描述不同数据几何准确性与现势性的差异,并将评估结果可视化表达。试验结果表明,该方法科学客观、可靠有效。     

一种提高北斗系统中低纬度无源定位精度的改进方法

本文提出一种提高北斗系统中低纬度无源定位精度的方法,利用星际间单差及高程约束来提高定位精度。与传统方法相比,新方法具有更高的精度及较好的稳定性,仿真结果表明,在中低纬度地区定位精度可达50~200M。     

A multi‐criteria decision‐making approach for geometric matching of areal objects

We propose a method for geometric areal object matching based on multi‐criteria decision making. To enable this method, we focused on determining the matched areal object pairs that have all relations, one‐to‐one relationships to many‐to‐many relationships, in different spatial data sets by fusing geometric criteria without user invention. First, we identified candidate corresponding areal object pairs with a graph‐based approach in training data. Second, three matching criteria (areal hausdorff distance, intersection ratio, and turning function distance) were calculated in candidate corresponding pairs and these criteria were normalized. Third, the shape similarity was calculated by weighted linear combination using the normalized matching criteria (similarities) with the criteria importance through intercriteria correlation method. Fourth, a threshold (0.738) of the shape similarity estimated in the plot of precision versus recall versus all possible thresholds of training data was applied, and the matched pairs were determined and identified. Finally, we visually validated the detection of similar areal feature pairs and conducted statistical evaluation using precision, recall, and F‐measure values from a confusion matrix. Their values were 0.905, 0.848, and 0.876, respectively. These results validate that the proposed classifier, which detects 87.6% of matched areal pairs, is highly accurate.