Improved method for estimating the inter-frequency satellite clock bias of triple-frequency GPS

Considering the contribution of the hardware biases to the estimated clock errors, an improved method for estimating the satellite inter-frequency clock bias (IFCB) is presented, i.e., the difference in the satellite clock error as computed from ionospheric-free pseudorange and carrier phase observations using L1/L2 and P1/P2 versus L1/L5 and P1/P5. The IFCB is composed of a constant and a variable part. The constant part is the inter-frequency hardware bias (IFHB). It contains the satellite and receiver hardware delays and can be expressed as a function of the DCBs [DCB (P1 ? P2) and DCB (P1 ? P5)]. When a reference satellite is selected, the satellite IFHB can be computed but is biased by a reference satellite IFHB. This bias will not affect the utilization of IFCB in positioning since it can be absorbed by the receiver clock error. Triple-frequency observations of 30 IGS stations between June 1, 2013, and May 31, 2014, were processed to show the variations of the IFHB. The IFHB values show a long-term variation with time. When a linear and a fourth-order harmonic function are used to model the estimated IFCB, which contains contributions of the hardware delays and clock errors, the results show that 89 % of the IFCB can be corrected given the current five triple-frequency GPS satellites with the averaged fitting RMS of 1.35 cm. Five days of data are processed to test the estimated satellite clock errors using the strategy presented. The residuals of P1/P5 and L1/L5 have a STD of <0.27 m and 0.97 cm, respectively. In addition, most predicted satellite IFCBs reach an accuracy of centimeter level and its mean accuracy of 5 days is better than 7 cm.     

New developments on estimating satellite interfrequency bias for SVN49

In order to estimating satellite interfrequency bias T_gd for the anomalously behaving SVN49, a modified JPL GIM software suite is presented. This research assumed that the single-frequency user will not need to perform any modification in the receiver software and will not need any detailed knowledge of the satellite anomaly using the code observable. We performed a point positioning analysis and investigated the range residuals for SVN49. It was discovered that the new satellite bias estimate resulted in near zero mean residuals with the shape of P2-P1 and L1-L2 observables being consistent with shapes from other satellites. Also, computed is a 10-day average of the estimated satellite interfrequency bias T_gd, which turned out to be −19.13 ns.     

GPS仪器偏差的求解方法及其对电子总量的影响

指出了仪器偏差对计算电离层电子总量的影响，提出一种消除仪器偏差的方法，并依此方法计算了乌什和鼎新站2000年7月13日各个卫星交叉点沿天顶方向上的总量(VTEC)。分析表明，只有合理消除仪器偏差的影响，利用GPS观测资料计算的VTEC才更加可靠，才能更好地反映出电离层的实际变化情况。     

Partial integer decorrelation: optimum trade-off between variance reduction and bias amplification

Different techniques have been developed for determining carrier phase ambiguities, ranging from float approximations to the efficient solution of the integer least square problem by the LAMBDA method. The focus so far was on double-differenced measurements. Practical implementations of the LAMBDA method lead to a residual probability of wrong fixing of the order one percent. For safety critical applications, this probability had to be reduced by eight orders of magnitude, which could be achieved by linear multi-frequency code–carrier combinations. Scenarios with single or no differences include biases due to orbit errors, satellite clock offsets, as well as residual code and phase biases. For this case, a linear combination of Galileo E1 and E5 code and carrier phase measurements with a wavelength of 3.285 m and a noise level of a few centimeters is derived. This ionosphere-free combination preserves the orbit and clock errors, and suppresses the E1 code multipath by 12.6 dB. Since integer decorrelation transformations, as used in the LAMBDA method, inflate biases, the number of such transformations must be limited, and applied in a judicious order. With a Galileo type constellation, this leads to a vertical standard deviation of ca. 20 cm, while keeping the probability of wrong fixing extremely low for code biases of 10 cm, and phase biases of 0.1 cycle, combined in a worst case.     

GLONASS频间码偏差实时估计方法及其在RTK定位中的应用

GLONASS伪距频间偏差难以利用经验模型消除。在RTK定位解算中,尤其是需顾及大气延迟的中长距离异质基线,IFCB会降低模糊度收敛速度,甚至导致模糊度固定错误。本文基于双差HMW组合和消电离层组合,提出一种站间IFCB实时估计算法,实时获取各频段的非组合站间单差IFCB。试验结果表明,站间IFCB长期稳定,可达数个纳秒;在GPS/GLONASS观测值先验误差比值为3：5的条件下,未改正的IFCB可能导致基线GPS/GLONASS组合RTK定位性能比单GPS差。将本文提出算法应用于RTK定位,能够有效消除IFCB的影响,RTK模糊度浮点解精度、定位收敛速度和固定率都有明显改善,部分基线的RTK定位首次固定时间从9.2 s提高到2.1 s,固定解比率从84.5%提高到97.9%。     

子午线长度正反算公式及相应系数值

给出两种高精度的子午线长度直接正反算公式,以及公式中相应于四种椭球的系数值.     

引力和垂线偏差的非奇异公式

基于$\frac{{{{\bar{P}}}_{nm}}\left( \cos \theta \right)}{\sin \theta }\left( m>0 \right)$的非奇异递推公式,给出了基于球坐标的引力矢量和垂线偏差非奇异计算公式;针对极点λ可任意取值引起的地方指北坐标系方向的不确定性问题,证明了引力矢量在转换到地心直角坐标系后不随λ的变化而变化,即与λ的取值无关。最终的数值计算结果表明,直角坐标系下的非奇异计算公式与本文提出的球坐标下的非奇异计算公式所得计算结果绝对值差异小于10-16m/s2,证明了该非奇异公式的正确性。最后总结了所有引力位球函数一阶导、二阶导非奇异性计算的一般思路。     

方差分量估计迭代算法收敛性分析与改进

本文首先对方差分量估计中的收敛性问题进行分析,指出方差分量的收敛性和估计方程的摄动性有关。提出了改进收敛性的思想,在此基础上提出了一种改进收敛的方法,用算例证明了所提出方法的有效性。     

A general framework for error analysis in measurement-based GIS Part 4: Error analysis in length and area measurements

This is the final of a series of four papers on the development of a general framework for error analysis in measurement-based geographic information systems (MBGIS). In this paper, we discuss the error analysis problems in length and area measurements under measurement error (ME) of the defining points. In line with the basic ME model constructed in Part 1 of this series, we formulate the ME models for length and area measurements. For length measurement and perimeter measurement, the approximate laws of error propagation are derived. For area measurement, the exact laws of error propagation are obtained under various conditions. An important result is that area measurement is distributed as a linear combination of independent non-central chi-square variables when the joint ME vectors of vertices coordinates are normal. In addition, we also give a necessary and sufficient condition under which the area measurement estimator is unbiased. As a comparison, the approximate law of error propagation in area measurement is also considered and its approximation is substantiated by numerical experiments.This project was supported by the earmarked grant CUHK 4362/00H of the Hong Kong Research grant Council.     

弦线法解算大地测量主题精密公式

本文通过引入测站切面空间直角坐标系,导出用椭球面上弦线解算长距离大地测量主题正、反算精密公式。理论严密,公式封闭简单,宜于电算。为了便于实用,本文还扩展了相应的归算公式。     

菲涅耳积分计算公式及其应用

菲涅耳积分是物理光学、微波技术与天线等多学科共用的特殊函数,其形式为上限可变而又不能积出的两个定积分,通常将其按变量u的不同区间分别用正或负幂级数计算。本文在原有公式的基础上研究出了简单、精密且变量复盖实数域的计算公式及其计算机程序。内容包括:(1)最佳分区点u₁的选择;(2) u≤u_t时菲涅耳积分的变比级数表达式;(3) u>u₁时菲涅耳积分的三角函数表达式;(4)程序流程图;(5)抽样运行数据及检验结果。     

Influence of the GLONASS inter-frequency bias on differential code bias estimation and ionospheric modeling

GPS Solutions - Due to the application of frequency division multiple access, the signals of GLONASS satellites suffer from code and carrier phase inter-frequency biases (IFBs). In this study, the...     

非线性函数相关信号的滤波与推估

滤波与推估是把参数作为正态随机量,观测方程常常是非线性的.从极大验后非线性滤波与推估的基本公式[1]出发,推导函数非线性相关信号的滤波与推估信号的计算公式.证明函数相关信号的滤波与推估公式是具有非线性函数关系的滤波与推估信号公式的一个特例.     

Helmert型方差-协方差分量估计的通用公式

本文在概括函数模型和它的通用公式的基础上,导出了一个适用于所有平差方法的方差-协方差分量估计的通用公式,并由此给出方差分量估计的通用公式和简化的通用公式。     

GPS水准拟合模型的选取与精度估计

GPS水准拟合中,多项式曲面模型法使用率较高,但通常要人工选取已知点和检核点,带有一定的人为因素。本文在分析检核点作用的基础上,提出了一种尽量减少人工干预选取模型系数的方法,并将该法作为探测测区高程异常是否呈单一曲面的基础,给出了一般测区选取GPS水准拟合模型的步骤。此外,就用户所关心的转换正常高精度估计问题,讨论了其可能达到的精度。     

完整后牛顿近似下原时与坐标时的转换

IAU2000通过了新的时空参考系和时间尺度决议，建议时空坐标理论必须在完整的后牛顿近似下来考虑。基于IAU2000决议，文中研究了在完整后牛顿近似下相对论参考系的基本概念、太阳系质心天球参考系(BCRS)和地球质心天球参考系(GCRS)的定义及其转换公式；推导了原时与坐标时之间的理论关系和严格转换公式。得到的理论公式可为进一步确定或定义相对论框架下的其它时间尺度(例如地球时和太阳系动力学时)提供了严格的理论基础和依据。     

实际测距精度公式的建立与应用

给出检定厂方给定的标称精度公式和评定实际测距精度公式的方法,并可用来检验控制网平差中是否存在测边系统误差.     

完整后牛顿近似下原时与坐标时的转换

IAU2000通过了新的时空参考系和时间尺度决议,建议时空坐标理论必须在完整的后牛顿近似下来考虑.基于IAU2000决议,文中研究了在完整后牛顿近似下相对论参考系的基本概念、太阳系质心天球参考系(BCRS)和地球质心天球参考系(GCRS)的定义及其转换公式;推导了原时与坐标时之间的理论关系和严格转换公式.得到的理论公式可为进一步确定或定义相对论框架下的其它时间尺度(例如地球时和太阳系动力学时)提供了严格的理论基础和依据.     

An alternative method for non-negative estimation of variance components

A typical problem of estimation principles of variance and covariance components is that they do not produce positive variances in general. This caveat is due, in particular, to a variety of reasons: (1) a badly chosen set of initial variance components, namely initial value problem (IVP), (2) low redundancy in functional model, (3) an improper stochastic model, and (4) data’s possibility of containing outliers. Accordingly, a lot of effort has been made in order to design non-negative estimates of variance components. However, the desires on non-negative and unbiased estimation can seldom be met simultaneously. Likewise, in order to search for a practical non-negative estimator, one has to give up the condition on unbiasedness, which implies that the estimator will be biased. On the other hand, unlike the variance components, the covariance components can be negative, so the methods for obtaining non-negative estimates of variance components are not applicable. This study presents an alternative method to non-negative estimation of variance components such that non-negativity of the variance components is automatically supported. The idea is based upon the use of the functions whose range is the set of all positive real numbers, namely positive-valued functions (PVFs), for unknown variance components in stochastic model instead of using variance components themselves. Using the PVF could eliminate the effect of IVP on the estimation process. This concept is reparameterized on the restricted maximum likelihood with no effect on the unbiasedness of the scheme. The numerical results show the successful estimation of non-negativity estimation of variance components (as positive values) as well as covariance components (as negative or positive values).