Single-receiver single-channel multi-frequency GNSS integrity: outliers, slips, and ionospheric disturbances

In this contribution the integrity of single- receiver, single-channel, multi-frequency GNSS models is studied. The uniformly most powerful invariant test statistics for spikes and slips are derived and their detection capabilities are described by means of minimal detectable biases (MDBs). Analytical closed-form expressions of the phase-slip, code-outlier and ionospheric-disturbance MDBs are given, thus providing insight into the various factors that contribute to the detection capabilities of the various test statistics. This is also done for the phaseless and codeless cases, as well as for the case of a temporary loss-of-lock on all frequencies. The analytical analysis presented is supported by means of numerical results.     

均值漂移模式几种粗差探测法的MDB比较

针对均值漂移模式的几种粗差定位与定值方法,在显著水平和检验功效下,推出最小可探测偏差（minimal detectable bias,MDB）的计算公式。通过数值分析比较,得出观测值独立等精度时,几种方法的MDB的计算结果相同;独立不等精度时,数据探测法、拟准检定法和部分最小二乘法的MDB结果相同,而多维粗差同时定位与定值法略大于其他方法;相关观测情形下,拟准检定法和部分最小二乘法的MDB结果相同,数据探测法的MDB结果最小,多维粗差的同时定位和定值法的MDB结果最大。     

Short Note: Asymptotic theory for calculating deformations caused by dislocations buried in a spherical earth — gravity change

An asymptotic theory is presented for calculating co-seismic gravity changes, as a complement to a previous article by Sun [J Geod (2003) 77:381–387)], which presents the asymptotic theory for co-seismic geoid changes. Only the important formulas and results are summarized here; all the concepts and conventions are the same as for the companion paper. The theory is given by closed mathematical expressions so that it can be applied as easily as the flat-Earth theory. Moreover, since the asymptotic theory includes a sphericity effect, it is physically more reasonable than the flat-Earth theory.     

高斯投影的复变函数表示

借助复变函数理论讨论高斯投影的复变函数表示,与传统的高斯投影实数域表达式相比,本文导出的高斯投影正反解表达式形式紧凑,公式简单,特别是基于复变函数建立的尺度比和子午线收敛角公式能表示为闭合形式;当e=0时,高斯投影正反解公式均为简单准确的闭合表达式。最后,通过算例对导出的新公式进行验算。     

The Exact Distribution of the Multilook Magnitude

Gierull provides a statistical analysis of multilook synthetic aperture radar interferograms. Various expressions for the probability density function, cumulative distribution function, and the moments of associated statistics are derived. It appears, however, that most of these expressions are based on some approximation. In this letter, the corresponding expressions are derived in their exact form, including some elementary representations for certain expressions given by Gierull. A numerical comparison of the exact and approximate expressions is provided     

Influential Visual Design Parameters on TV Weather Maps

Abstract

Information transformation on television weather maps (TVWMs) is influenced by visual elements for a broad range of viewers. This research emphasizes the cartographic aspects of TVWMs through evaluating their visual variables. Currently defined visual variables including basic, dynamic and motion variables are investigated and some suggestions are made to improve their application on TVWMs. The rates of the represented visual information within different frames and the related standard deviation are proposed as measures to improve the performance of the ‘duration’ dynamic variable. The concept of ‘visual expressions’ is introduced, and their applications at the organisational level of map design are discussed. Such expressions (including background, boundary, spatial order, zoom and overview maps) are examined as tools for ‘user orientation’ in particular, and their role as dominant parameters in TVWMs’ cartographic communication is considered. Their incorporation in TVWMs of a number of global news channels is evaluated. Firstly, the concepts of visual design parameters are utilized as a foundation for an analytical evaluation, then an empirical evaluation is carried out based on a statistical investigation of a sample of TV viewers. The resulting ranking order and correlation coefficients for each of the elements shows a firm agreement, corroborating views on the importance and proficiency of the visual elements in communicating weather information. As a result, TVWMs of well-known global TV channels (BBC, Euronews, France24, PressTV) are ranked with respect to the effectiveness of their designs.     

Analytical dynamic orbit improvement for the evaluation of geodetic-geodynamic satellite data

Summary Given an analytical solution (solution of the equations of motion using analytical integration techniques) an integration of the variational equations is not necessary but simply a differentiation of the analytical solution. Based on a high-precision analytical solution explicit expressions for the coefficients of the observation equations to improve state variables and force model parameters have been derived.The definition of suitable unknowns for a pure dynamic orbital improvement can be based then on an analysis of the information content of the data at hand by using those expressions.Regarding the Fourier series structure of orbital perturbations as well as the special properties of crossover difference data, the proposed technique is particularly favourable for an evaluation of Remote Sensing Data such as altimeter, SST and gradiometer data from satellites in repeating orbits.After a general discussion of the observation equations for crossover data our present results using GEOSAT altimeter data are discussed as one example for applications. Some short remarks about further applications are given.     

常用等角投影及其解析变换的复变函数表示

借助复变函数理论讨论了常用等角投影及其解析变换的复变函数表示;给出了高斯投影、墨卡托投影和等角圆锥投影正反解的复变函数表示模型;在此基础上系统地推导出了高斯投影、墨卡托投影和等角圆锥投影间解析变换的复变函数表达式.这些复数变换公式是含参考椭球第一偏心率的符号形式,可解决不同参考椭球下的变换问题.与传统的实数变换公式相比,其结构更为简单、理论更为严密.     

单位四元数在航空摄影测量解算中的应用与实践

研究了单位四元数方法在航摄空中三角测量各个步骤中的应用,并对其算法稳定性和适用性作了评价。首先叙述了基于单位四元数构造旋转矩阵的方法,及基于单位四元数的相对定向模型的建立和解求方法;构建了基于单位四元数的光束法区域网平差模型。然后利用大量实际航空影像数据进行了相对定向和光束法区域网平差试验,并同传统的基于欧拉角构建旋转矩阵的方案进行了比较。试验结果表明,在相对定向试验中,若采取P-H算法,只需要最少控制点就能保证所有试验数据均可得到正确的解。而在光束法平差中,基于单位四元数的方法比传统方法的稳定性差,对摄影比例尺和控制点的数量较为敏感,导致部分试验数据无法正确收敛。     

Robust bayesian estimation

Classical least squares Bayesian estimation consists of minimizing the sum of the squared residuals of observations and the corrections to prior estimates of parameters.Many authors have produced more robust versions of this estimation by replacing the square by something else, such as the absolute value. In this article, three robust (M-LS, LS-M and M-M) estimators for three corresponding error models are described based on the principle of maximum likelihood type estimates (M-estimates). The influence functions of the three robust Bayesian estimators are given. The algorithm implementation problems are discussed and the expressions for the posterior variance-covariance are derived.     

GPS/BDS/Galileo三频精密单点定位模型及性能分析

在精细考虑伪距和载波相位硬件偏差时变特性的基础上,导出了更为严谨的非差非组合观测方程,并给出了非组合模式下两类GNSS偏差的数学表达形式.基于此,本文详细研究了3种常用的三频精密单点定位(PPP),即无电离层两两组合IF1213、单个无电离层组合IF123与非组合UC123函数模型的独立参数化方法,系统分析了3种PPP...     

Least squares collocation and statistical testing

The authors address the issue of statistical testing in least squares collocation (LSC) in two stages. The first stage concerns the extension and focusing of theLSC equations to the task of statistical testing. The second stage deals with statistical testing titself and is introduced in the second portion of the paper. The paper commences with an overview of the development ofLSC and its relationship to least squares adjustment (LSA). Expressions for the various random variables and their corresponding covariance matrices are derived and in some instances are gleaned from the literature for the following quantities: (i) corrections to the unknown parameters with a priori covariance information; (ii) estimated signal at both the observation and computation points; and (iii) the noise at the observation points. Some of the needed covariance matrices are either obscurely hidden in the literature or not available at all, but, nevertheless are given in the paper. Also given are expressions for the estimated variance factor which forms the basis of various statistical tests. The paper closes with an overview and enumeration of possible statistical tests for detection of outliers in the observations.     

整体大地测量的确定性参数模型

本文将整体大地测量各类观测方程中作为随机信号的重力场参数（ΔN，ξ，η）均表达为重力异常Δg的泛函，又引入Δg的B样条函数并以样条系数C_(11)作待定参数，提出一种整体大地测量的确定性参数模型，给出了相应系数矩阵的表达式和算法，最后对该模型的求解问题作了说明。     

抗差贝叶斯估计及应用

当未知参数具有先验期望和方差，且观测值与未知参数先验值均服从正态分布时，最小二乘贝叶斯估计将给出参数的最优解。然而当观测值和参数先验值的实际分布有悖于正态假设时，经典贝叶斯估计使估值偏高。本文基于常用的M估计原理，对三种类型的误差模式，导出了M－LS、LS－M和M－M三种抗差贝叶斯估计解式和影响函数；讨论了相应的计算方法；给出了参数验后方差表达式。     

ANGULAR CORRECTIONS FOR THE LAMBERT ORTHOMORPHIC CONICAL PROJECTION

Abstract

In E.S.R., viii, 56, 70, Brigadier K. M. Papworth has given expressions for the angular corrections, known as (t – t) corrections, in the Lambert NO.2 Projection, derived from empirical considerations based on actual detailed calculations. Apparently some difficulty has been experienced in offering a proof. In view of the widespread use of the Lambert Projection in World War II, it is hoped that the following proof will be found to be of more than academic interest.     

Generalized inverses of nonlinear mappings and the nonlinear geodetic datum problem

Motivated by the existing theory of the geometric characteristics of linear generalized inverses of linear mappings, an attempt is made to establish a corresponding mathematical theory for nonlinear generalized inverses of nonlinear mappings in finite- dimensional spaces. The theory relies on the concept of fiberings consisting of disjoint manifolds (fibers) in which the domain and range spaces of the mappings are partitioned. Fiberings replace the quotient spaces generated by some characteristic subspaces in the linear case. In addition to the simple generalized inverse, the minimum-distance and the x ₀-nearest generalized inverse are introduced and characterized, in analogy with the least-squares and the minimum-norm generalized inverses of the linear case. The theory is specialized to the geodetic mapping from network coordinates to observables and the nonlinear transformations (Baarda's S-transformations) between different solutions are defined with the help of transformation parameters obtained from the solution of nonlinear equations. In particular, the transformations from any solution to an x ₀-nearest solution (corresponding to Meissl's inner solution) are given for two- and three-dimensional networks for both the similarity and the rigid transformation case. Finally the nonlinear theory is specialized to the linear case with the help of the singular-value decomposition and algebraic expressions with specific geometric meaning are given for all possible types of generalized inverses. Received: 11 April 1996 / Accepted: 19 April 1997     

用主成分法求解秩亏自由网的研究

结合多数平差和主成分估计理论,导出误差方程中含多重共线性关系时求解未知数的公式,并证明主成分估计的解是最小二乘最小范效解。由此,将主成分估计推广到秩亏自由网平差中,导出求解未知多数及其协因数的公式,并据主成分估计演绎出用附有条件的参数平差法求解秩亏自由网的条件方程（基准在达式）。     

水准高差的日月潮汐改正

本文研究了日月潮汐对水准高差的影响 ,导出了水准高差的日月潮汐改正公式 ,从而验证了现行水准测量规范引用的公式 ,并发现其存在的个别错误 ,给出了计算潮汐改正需要的日月时角和赤纬的表达式     

GNSS receiver autonomous integrity monitoring (RAIM) performance analysis

The availability of GPS signals is a major concern for many existing and potential applications. Fortunately, with the development of Galileo by the European Commission (EC) and European Space Agency (ESA) and new funding for the restoration of the Russian GLONASS announced by the Russian Federation (Revnivykh et al., in European Navigation Conference 2005, Munich, Germany, July 19–22), the future for satellite-based positioning and navigation applications is extremely promising. With the complete cooperation from all these global navigation satellite systems (GNSS), greater levels of satellite visibility and therefore integrity can be expected. In this paper, a receiver autonomous integrity monitoring (RAIM) scheme along with reliability and separability measures are used to assess integrity performance levels of standalone GPS and integrated GPS/GLONASS, GPS/Galileo and GPS/GLONASS/Galileo systems where the clock offsets for each of the additional systems are estimated. It is shown, herein, that a minimum of three satellites must be visible in an additional system in order to provide a full integrity contribution when the system’s clock offset is to be estimated within the adjustment. A comparison of the integrity results obtained via system clock offsets estimated in the adjustment versus the case where the offsets are known and the measurements are corrected prior to the adjustment is also made for a high elevation mask scenario. Global simulation results for combined GPS/GLONASS/Galileo show that, theoretically, for the time of simulation and for any point on the globe, an outlier of 20 m can be detected with 80% probability at the 0.5% significance level and then separated from any other measurement with 90% probability. Corresponding values for the GPS only and combined GPS/GLONASS and GPS/Galileo systems, respectively, are approximately 435, 110 and 28 m, respectively, for the maximum MSBs and 312, 50 and 26 m, respectively, for the maximum MDBs. Temporal 24 h simulations for the GPS/GLONASS/Galileo scenario delivered agreeable results with the global snapshots for a 15° elevation mask. For the case where system clock offsets are estimated within the adjustment, it was shown that only the reliability measure was available for 100% of the time, with horizontal external reliability values of no more than about 12 m when a 30° masking angle was used. By assuming the clock offsets were determined and corrected for prior to the adjustment, the separability measure was markedly improved and was also available 100% of the time.     

GIS 中基本几何要素的置信区域问题研究

以概率论为工具解析地研究了误差椭圆的2个重要性质，在此基础上分别为点、线及多边形建立了由椭圆和线段组成的置信域，并给出了所建置信域与其置信水平的关系。最后通过算例讨论了置信域的可视化表示问题。