Single GPS receiver time-relative positioning with loop misclosure corrections

Time-relative positioning makes use of observations taken at two different epochs and stations with a single global positioning system (GPS) receiver to determine the position of the unknown station with respect to the known station. The limitation of this method is the degradation over time of the positioning accuracy due to the temporal variation of GPS errors (ionospheric delay, satellite clock corrections, satellite ephemerides, and tropospheric delay). The impact of these errors is significantly reduced by adding to the one-way move from the known to the unknown station, a back move to the known station. A loop misclosure is computed from the coordinates obtained at the known station at the beginning and at the end of the loop, and is used to correct the coordinates of the unknown station. The field tests, presented in this paper, show that using the loop misclosure corrections, time-relative positioning accuracy can be improved by about 60% when using single frequency data, and by about 40% with dual frequency data. For a 4-min processing interval (an 8-min loop) and a 95% probability level, errors remain under 20 cm for the horizontal components and 36 cm for the vertical component with single frequency data; and under 11 cm for the horizontal components and 29 cm for the vertical component with dual frequency data.     

A catalog of station coordinates for GEOS-C orbit determination

Center-of-mass coordinates for 57 tracking sites participating in the GEOS-C mission are given in a unified system having a common origin and scale. The positions were obtained either directly from analyses of satellite observations or from survey ties to colocated sites with coordinates previously determined by various investigators from optical, laser of doppler data. The uncertainty of the positions in nearly all cases is 5 m in each coordinate. Data reductions show that station coordinates of this quality introduce a rapidly changing error into the altitude of a satellite unless global tracking constrains the orbit.     

一种伪距单点定位的数学模型研究及程序实现

对伪距单点定位的数学模型进行了详细分析,列出详细步骤和误差方程式,包括中间涉及到的坐标转换以及一些重要技术细节,并通过编程实现计算测站点各历元单点定位的空间直角坐标XYZ以及综合各历元数据计算得到的坐标．利用若干工程实测获得的原始数据,并转换为RINEX格式,采用GPS卫星的伪距观测值和导航N文件计算得到测站点坐标,与接收机自带的程序计算的近似坐标进行坐标比较和精度分析,结果显示坐标较差在米级左右,而单点定位的精度为米级．证明该数学模型是可行的,且易于通过编程实现．      

总体最小二乘方法在空间后方交会中的应用

在空间后方交会的解算过程中,利用共线条件方程式列出误差方程后,针对地面控制点以及像点坐标均存在误差这一特点,引入总体最小二乘(total least squares,TLS)的方法,对系数矩阵A以及观测向量b同时进行改正,计算像片的6个外方位元素,建立更加合理的计算模型,可获得精度更高、更稳定的解。     

Error study for the determination of the center of mass of the earth from Pageos observations

The least squares adjustment for the station coordinates of the worldwide satellite triangulation net gives, in addition to the station positions, the positions of the satellites observed in a simultaneous event from two or more stations. Through successive events short arcs can be fitted and the coordinates of the center of mass of the earth can be determined. It is shown that the center of mass will be obtained with an accuracy consistent with the accuracy of the station positions, if well distributed Pageos arcs of about one quarter of a revolution are taken and if three events per arc are given.     

病态加权总体最小二乘的广义岭估计解法

针对加权情形下的变量误差(EIV)模型,采用广义岭估计法处理总体最小二乘平差的病态性问题.结合最优化准则和协方差传播率推导了未知参数的改正数求解公式;根据参数估计值的均方误差最小化原理,通过求偏导数列出广义岭估计中岭参数的迭代解式,并讨论了广义岭参数的含义和作用,给出了确定岭参数的L-曲线法.通过算例比较分析了加权最小...     

正规化矩阵正定时半参数估计量的统计性质

利用补偿最小二乘原理构造加权惩罚平方和,得到半参数模型中正规化矩阵正定时参数和半参数的估计量.从偶然误差的统计特征出发,详细讨论这种平差方法得到的参数估值的一些统计性质,并对半参数平差与最小二乘法的参数估计值进行比较.理论分析表明,通过选取合适的平滑参数,半参数平差方法优于最小二乘法.另外从数理统计的角度对平滑参数的选取进行分析,得到平滑参数的取值范围,也给出了平滑参数对模型精度的影响.     

"嫦娥"卫星绕月飞行轨道的激光测定法

依据地月激光测距的成功实践和对卫星激光定轨的基础研究,提出了用地面对嫦娥卫星作激光测距的方法,高精度地测定嫦娥卫星绕月飞行时的实时在轨位置,论述了多站激光定轨和单站激光定轨的解算数模。     

基于相对电离层延迟模型的单频GPS精密单点定位算法研究

分析了单频GPS精密单点定位的特点,提出了先在卫星间求差,再在相邻历元间求差的单频GPS动态定位数学模型,实现了定位坐标的非线性参数估计求解方法。为了降低电离层延迟残差对单频PPP的影响,研究建立了一种相对电离层延迟模型,并基于神经网络理论,实现了相应的算法,通过计算实例进行了精度分析。     

随机模型对解算西安流动SLR站坐标的影响

合理的参数估计及精度评定不仅需要可靠的函数模型,而且需要正确的随机模型。从权函数和粗差编辑两方面,研究了不同随机模型对西安流动卫星激光测距（satellite laser ranging,SLR）站坐标解算的影响,采用全球Lageos-1卫星观测数据计算了西安流动SLR站坐标。计算结果表明:①西安流动SLR站的观测精度和坐标解算精度均达到厘米级。②随机模型直接影响SLR站坐标的解算结果及可靠性;对于相同的计算弧段,抗差方差分量估计得到的站坐标精度最高、结果最稳定,残差加权均方差最小,观测资料利用率也最高;对于相同的计算方案,采用的SLR数据越多,坐标估计精度越高。     

ΔVLBI用于“嫦娥一号”地月转移轨道段定轨及EOP解算

推导了基于相对论时空理论的"嫦娥一号"地月转移轨道段差分VLBI(ΔVLBI)的数学模型,在此基础上利用"嫦娥一号"实测的VLBI时延观测量和模拟的河外射电源时延观测量组成了ΔVLBI时延观测量,在参数最优先验精度下解算了不同弧段长度的"嫦娥一号"轨道及地球定向参数(EOP)等未知参数,并根据各参数的解算精度及外符合程度确定了最优观测弧段长度,并分析了该条件下的参数解算精度。     

分离系统差的地面网与卫星网之间转换的数学模型及其解算方法

本文分析了地面网所含系统差之后,指出只需要两个参数就可描述地面网的定向系统差。若分别考虑地面水平网的尺度参数K_L和高程网的尺度参数K_H,则地面网与卫星网间转换的数学模型中参数的个数为10个。若假定K_L=K_H,则参数需要9个。导出了含有9个和10个未知参数的模型。提出采用部分参数带权的相关平差法解决九参数和十参数模型的法方程式系数阵秩亏问题。最后,利用我国实际数据检核了这些模型。计算表明,这种方法能有效地将坐标系的定向参数和地面网的定向系统差参数分开。揭示了我国地面水平网的尺度参数与高程网的尺度参数不一致,并给出了它们的参考值。     

基于车载移动测量的GNSS定位方法

针对车载移动测量需要高频高精度的动态差分定位解算的问题,文中介绍利用GPS、北斗、GLONASS三个卫星导航系统进行载波相位动态差分的解算方法。首先利用双频观测值组成双差宽巷观测方程,利用M-W组合求出较高精度的宽巷模糊度浮点解,然后对宽巷模糊度进行搜索固定;接着对载波双差的基础模糊度进行搜索固定;最后将固定的模糊度代入载波相位双差观测方程,利用最小二乘求解测站坐标。文中使用该方法对车载GNSS实测数据进行解算,最终可得到厘米级别的定位结果。     

基于Moore-Penrose广义逆及立体矩阵的可分离非线性最小二乘解算方法

针对测绘领域中函数模型为非线性函数的线性组合的特殊结构,本文提出了基于Moore-Penrose广义逆和立体矩阵的可分离非线性最小二乘解算方法。该方法首先利用变量投影算法消除可分离非线性模型中的线性参数,将包含两类参数的原非线性优化问题转化为仅含有非线性参数的最小二乘问题。然后,基于Moore-Penrose广义逆矩阵的微分和立体矩阵理论计算最小二乘目标函数的一阶导数,进而采用非线性优化的LM方法求解非线性参数的最优估值。最后,根据最小二乘方法求解线性参数的最优估值。通过指数函数模型拟合和机载LiDAR全波形参数求解试验与传统参数不分离优化方法进行对比,结果表明,基于Moore-Penrose广义逆和立体矩阵的可分离非线性最小二乘解算方法对待求参数初值依赖性低,同时避免了迭代过程中线性参数导致的病态问题,算法稳定性好,为测绘领域中可分离非线性最小二乘问题的解算提供了一种思路,也拓展了可分离非线性最小二乘方法的应用。     

Rational function optimization using genetic algorithms

In the absence of either satellite ephemeris information or camera model, rational functions are introduced by many investigators as mathematical model for image to ground coordinate system transformation. The dependency of this method on many ground control points (GCPs), numerical complexity, particularly terms selection, can be regarded as the most known disadvantages of rational functions. This paper presents a mathematical solution to overcome these problems. Genetic algorithms are used as an intelligent method for optimum rational function terms selection. The results from an experimental test carried out over a test field in Iran are presented as utilizing an IKONOS Geo image. Different numbers of GCPs are fed through a variety of genetic algorithms (GAs) with different control parameter settings. Some initial constraints are introduced to make the process stable and fast. The residual errors at independent check points proved that sub-pixel accuracies can be achieved even when only seven and five GCPs are used. GAs could select rational function terms in such a way that numerical problems are avoided without the need to normalize image and ground coordinates.     

基于总体最小二乘的直线拟合方法探究

在直线拟合问题中,经典的最小二乘拟合方法在自变量选取不同时,拟合的参数值和中误差存在较大差别,故本文利用模拟数据对经典最小二乘和总体最小二乘拟合结果进行对比分析,得出结论认为:经典最小二乘自变量选取不同结算参数的原因是在进行拟合计算时忽略了自变量的误差,使拟合结果只能在一个方向上保持最佳;利用总体最小二乘参数拟合的方法进行直线拟合时拟合结果不受自变量变化的影响,并能够提高拟合精度。     

非线性二维转换模型的稳健总体最小二乘算法

针对应用线性最小二乘估计准则求解非线性平面转换模型参数时,通过定义间接参数将模型线性化的方法不能直接求解转换模型参数的问题,该文在非线性平面转换模型的基础上,建立线性模型,实现平面坐标的转换。为解决控制点已知坐标与观测坐标中均含有误差对转换参数求解的影响,对应用稳健总体最小二乘求解线性模型参数的算法进行讨论。最后,通过算例比较稳健总体最小二乘算法与最小二乘算法在抗差性方面的优势。结果表明,稳健总体最小二乘算法更适用于应用线性模型求解未知控制点的转换坐标。     

一种CORS基准站整周模糊度解算方法

利用CORS基准站坐标精确已知,根据各种双频线性组合观测方程,探讨了一种长基线整周模糊度快速解算方法,详细介绍了其解算原理,逐步推导了计算公式。最后通过CORS站实例,数据计算分析结果显示,其方法可快速、准确地确定整周模糊度值。     

静止卫星标称投影解析方法及其在FY2-C中的应用

通过对静止卫星在三轴椭球参数条件下地心坐标的标称投影公式推导过程,建立了经纬度到单位平面位置的可逆映射方程,其正反算公式精度可达10<'-20>;并对大地坐标的经纬度进行了类似的推导,但标识线垂直地表而不过地心的坐标定义导致正算公式中存在角度正切的四次方项,因此反算需要采用数值解法.两组解析表达式为查照表的建立提供了直接的数学依据,相对于迭代数值计算方法而言,解析方法更便于分析投影过程的误差和畸变.围绕FY2-C卫星地面系统工程中查照表的重建,兼顾卫星图像陆地位置与主要大陆轮廓数据的投影吻合,需要对单位平面的投影进行放大和平移,并提供多组可选择的放大因子,使得经纬度到图像点映射与查照表对应值整体误差较小.建议根据实际应用的坐标系统、卫星位置参数、地球参数选择不同的匹配参数.这种方法可以应用于图像点地理位置精度要求很高但计算不是特别频繁的数据处理算法中,如相对定标和定位,但在其他算法中除了精度以外查照表还是有作用的.     

Time-Relative Positioning with a Single Civil GPS Receiver

Time-relative positioning is a recent method for processing GPS phase observations. The operational method undertaken in this paper consists of the following steps: first, recording phase observations at a station of known coordinates; second, moving the GPS receiver to an unknown station (which can be located up to a few hundred meters away, dependint on what type of transportation – e. g., walking, motorcycle – is available) while continuously observing carrier phases; and, third, recording phase observations at a second station of unknown coordinates with a single GPS receiver. To obtain the position of the unknown station relative to the first (known) station, the processing method uses combined observations taken at two different epochs and two different stations with the same receiver. For this reason, the errors that vary between two epochs must be taken into account in an appropriate way, especially errors in satellite clock corrections and ephemerides, and errors related to tropospheric and ionospheric delays. Ionospheric modeling using IONEX files (the ionospheric maps calculated by the International GPS Service) was also tested to correct L1 phase observations. This method has been used to calculate short vectors with an accuracy of a few centimeters (for a processing interval of 30 s) using a single civil GPS receiver. ? 2001 John Wiley & Sons, Inc.