GPS data processing with equivalent observation equations

A unified GPS data processing method based on equivalent observation equations is proposed. The theoretic background of this method is given in detail. By selecting the unknowns to be eliminated as vector of zeros, i.e. the satellite clock errors, all clock errors, the clock and ambiguity parameters or user-defined unknowns, the equivalent observation equations can be formed. These equations are equivalent to the zero-, single-, double-, triple- or user-defined differenced equations. The advantages of the method are that the various GPS data processing methods are unified to a unique one, whereas the observation vector remains the original one and the weight matrix keeps the un-correlated diagonal form. Using this equivalent method one may selectively reduce the number of unknowns without having to deal with the correlations. Several special cases of single, double and triple difference are discussed in detail to illustrate the theory. Electronic Publication     

单历元非差GPS定位函数模型

依据GPS测量原理，导出非差模糊度和双差模糊度，分析一省的组成与特性。原始非差GPS定位函数模型中，设计矩阵秩亏，非差模糊度不具备整数特性，故提出参数重整，将非差模糊度转换为双差模糊度，推出基于参数重整的单历元非差GPS定位函数模型。     

利用Allan方差分析GPS非差随机模型特性

非差GPS定位中,通常采用以观测值服从高斯白噪声条件的估计准则进行参数求解。研究表明卫星端误差、传播路径误差、测站环境误差等会破坏观测值的白噪声特性,并且未模型化误差同样具有不利影响。这不仅破坏了估计准则的假设条件,而且部分非白噪声有可能被状态参数吸收,影响估计的准确性。本文将观测值白噪声、有色噪声和未模型化误差一同纳入GPS非差随机模型,以验后残差来表征GPS数据的随机特性,进行Allan方差分析,研究噪声成分及其参数。结果表明,GPS非差噪声组合主要为WN+GM,相位白噪声为2.392mm,GM过程噪声为4.450mm/s,相关时间为52.074s,伪距白噪声为0.936m,GM过程噪声为0.833m/s,相关时间为14.737s,相位的GM过程噪声与卫星相关性较大,而其余噪声则与测站相关性较大,大量分析结果表明GPS非差随机模型并不服从高斯白噪声假设,有待精化。     

Comparing Fire Severity Models from Post-Fire and Pre/Post-Fire Differenced Imagery

Wildland fires are common in rangelands worldwide. The potential for high-severity fires to affect long-term changes in rangelands is considerable, and for this reason assessing fire severity shortly after the fire is critical. Such assessments are typically carried out following Burned Area Emergency Response teams or similar protocols. These data can then be used by land managers to plan remediation and future land uses. To complement these procedures and explore fire severity modeling of sagebrush steppe rangelands, we compared models developed using (1) post-fire imagery only with (2) differenced imagery (pre-fire minus post-fire imagery). All models were developed from Classification Tree Analysis (CTA) techniques using Satellite Pour l'Observation de la Terre 5 (SPOT 5) imagery and Shuttle Radar Topography Mission (SRTM) elevation data. The results indicate that both techniques produced similar fire severity models (model agreement = 98.5%) and that little improvement in overall accuracy was gained by using differenced imagery (0.5%). We suggest the use of CTA models developed using only the post-fire imagery. The analyses and techniques described in this paper provide land managers with tools to better justify their recommendations and decisions following wildland fires in sagebrush steppe ecosystems and provide remote sensing scientists with information that will potentially improve future modeling efforts.     

三维网平差的方差分量估计

本文将方差分量估计理论运用于三维网平差中,推导出了含定向角未知数及消去定向角未知数的方差分量估计公式,并进行了模拟和实例计算,从而建立了合理的三维网平差随机模型。     

IAU2000决议对卫星轨道的影响

研究了IAU2000对GPS卫星轨道确定的影响。以2006年DOY186的GPS数据为例,分析了GPS卫星在IAU2000决议模型以及原有模型下,惯性参考系统以及地固坐标系中轨道的差别。结果显示,采用不同模型,卫星轨道在惯性参考系中的差值存在周期性,其中X、Z方向的幅度达到了2.5 m,Y方向的幅度约为1 m;在地固系中,轨道差别也存在周期,幅度约为4 mm。并对卫星轨道的差值进行了统计,得出了在惯性系下,不同模型引起轨道差值的3D RMS为m级。     

GPS天线相位模型变化对高精度GPS测量解算的影响研究

GPS天线存在相位中心偏差,在高精度测量中必须对其进行补偿改正。本文针对GPS天线的两种改正模型:相对改正模型和绝对改正模型,在讨论了它们所具有的相同改正办法的基础上,分析了它们在测定方法上存在区别,最后通过一个算例分别研究了这两种模型对GPS测量解算精度的影响,得出了一些有意义的结论。     

A comparative study of algorithms for reducing the fill-in during Cholesky factorization

In this paper several ordering algorithms for the unknowns in geodetic least squares systems are compared. The comparison is restricted to the case of the well known Cholesky factorization of the normal matrixA into a lower triangular factorL. p ]The algorithms which were investigated are: minimum degree, minimum deficiency, nested dissection, reverse Cuthill-McKee, King's-, Snay's-, and Levy's-banker's and Gibbs-King. p ]Also some strategies are presented to reduce the time needed to compute the ordering using a priori information about the way the unknowns are connected to each other. p ]The algorithms are applied to normal matrices of the least squares adjustment of 2D geodetic terrestrial networks, photogrammetric bundle-block adjustments, and a photogrammetric adjustment using independent models. p ]The results show that ordering the unknowns yields a considerable decrease of the cpu time for computing the Cholesky factor, and that in general the minimum degree and Snay's banker's ordering perform best. Furtheron they show that a priori information about the connection structure of the unknowns speeds up the computation of the ordering substantially.Supported by the Netherlands Organization for Scientific Research (NWO)     

GNSS非差非组合数据处理与PPP-RTK高精度定位

本文首先回顾了GNSS差分和组合数据处理的起源、特点和应用,并阐述了其在多频多模背景下的局限。然后,引出了非差非组合数据处理的诸多优势,介绍了构建满秩非差非组合函数模型的消秩亏方法。基于该方法,本文系统构建了系列非差非组合PPP-RTK模型,包括伪距加相位和仅用相位两大类。两类模型均考虑不同的大气约束而衍生出电离层加权、浮点和固定3种变体,且所有模型均顾及码分多址和频分多址两类系统。最后,本文测试分析了非差非组合PPP-RTK在无人船、无人机和农机应用中的动态定位性能。试验结果表明,3个场景下的模糊度首次固定时间均在10 s以内,模糊度固定成功率在96%以上,水平定位精度优于2 cm,高程定位精度优于5 cm。在Galileo+GPS+BDS三系统农机定位中,仅用相位PPP-RTK与伪距加相位PPP-RTK定位性能相当。与Galileo+GPS双系统定位相比,三系统PPP-RTK将模糊度首次固定时间从几百秒缩短至几秒,模糊度固定成功率从85%左右提升至99%以上,定位精度提升了30%左右。     

区域可持续发展评价系统研制

区域可持续发展是指区域自然环境容量可以不断满足人类生活质量保障的社会发展状态,要实现这种可持续发展,就必须评价区域的可持续性,EIS／RSD是在windows NT环境下开发的一个以遥感专题信息作为重要信息来源,具有综合分析和空间制图显示能力的区域可持续发展评价息系统,该文阐述了EIS／RSD的系统目标,技术路线,概念模型,系统功能,使用方法和结果表达方式。     

北斗伪距码偏差对基线解算的影响分析

北斗二代系统伪距码中存在与高度角相关的系统性偏差,该偏差会影响高精度的数据处理。基于Melbourne-Wübbena（MW）组合,分别利用现有的伪距码偏差改正模型和实测基线的双差宽巷模糊度残差,分析了伪距码偏差对基线解算的影响。理论分析表明,随着基线长度的增加,伪距码偏差对MW组合确定双差宽巷模糊度的影响越来越大,对300 km基线的影响可达0.36周。实际算例表明,无论基线长短,地球同步轨道（geostationary earth orbit,GEO）卫星的双差宽巷模糊度残差中始终存在偏差;而对于倾斜地球同步轨道（inclined geostationary orbit,IGSO）和中轨（medium earth orbit,MEO）卫星而言,当基线小于300 km时,双差基本可以消除伪距码偏差,其双差宽巷模糊度固定率基本和GPS一致,但当基线超过300 km时,部分卫星的双差宽巷模糊度残差就会存在明显偏差,其双差宽巷模糊度固定率也较低,此时需考虑伪距码偏差的影响。     

Least-squares prediction in linear models with integer unknowns

The prediction of spatially and/or temporal varying variates based on observations of these variates at some locations in space and/or instances in time, is an important topic in the various spatial and Earth sciences disciplines. This topic has been extensively studied, albeit under different names. The underlying model used is often of the trend-signal-noise type. This model is quite general and it encompasses many of the conceivable measurements. However, the methods of prediction based on these models have only been developed for the case the trend parameters are real-valued. In the present contribution we generalize the theory of least-squares prediction by permitting some or all of the trend parameters to be integer valued. We derive the solution for least-squares prediction in linear models with integer unknowns and show how it compares to the solution of ordinary least-squares prediction. We also study the probabilistic properties of the associated estimation and prediction errors. The probability density functions of these errors are derived and it is shown how they are driven by the probability mass functions of the integer estimators. Finally, we show how these multimodal distributions can be used for constructing confidence regions and for cross-validation purposes aimed at testing the validity of the underlying model. Dedicated to the memory of Dr. Tech.hc. Torben Krarup (1919–2005).     

Fast GNSS ambiguity resolution as an ill-posed problem

A linear observational equation system for real-time GNSS carrier phase ambiguity resolution (AR) is often severely ill-posed in the case of poor satellite geometry. An ill-posed system may result in unreliable or unsuccessful AR if no care is taken to mitigate this situation. In this paper, the GNSS AR model as an ill-posed problem is solved by regularizing its baseline and ambiguity parameters, respectively, with the threefold contributions: (i) The regularization parameter is reliably determined in context of minimizing mean square error of regularized solution where the covariance matrix of initial values of unknowns is used as an approximate smoothness term instead of the quadratic matrix of the true values of unknowns; (ii) The different models for computing initial values of unknowns are systematically discussed in order to address the potential schemes in real world applications; (iii) The superior performance of the regularized AR are demonstrated through the numerically random simulations as well as the real GPS experiments. The results show that the proposed regularization strategies can effectively mitigate the model’s ill-condition and improve the success AR probability of the observational system with a severely ill-posed problem.     

Network-based geometry-free three carrier ambiguity resolution and phase bias calibration

Continuously operating reference stations (CORS) are increasingly used to deliver real-time and near-real-time precise positioning services on a regional basis. A CORS network-based data processing system uses either or both of the two types of measurements: (1) ambiguity-resolved double-differenced (DD) phase measurements, and (2) phase bias calibrated zero-differenced (ZD) phase measurements. This paper describes generalized, network-based geometry-free models for three carrier ambiguity resolution (TCAR) and phase bias estimation with DD and ZD code and phase measurements. First, the geometry-free TCAR models are constructed with two Extra-Widelane (EWL)/Widelane (WL) virtual observables to allow for rapid ambiguity resolution (AR) for DD phase measurements without distance constraints. With an ambiguity-resolved WL phase measurement and the ionospheric estimate derived from the two EWL observables, an additional geometry-free equation is formed for the third virtual observable linearly independent of the previous two. AR with the third geometry-free model requires a longer period of observations for averaging than the first two, but is also distance-independent. A more general formulation of the geometry-free model for a baseline or network is also introduced, where all the DD ambiguities can be more rigorously resolved using the LAMBDA method. Second, the geometry-free models for calibration of three carrier phase biases of ZD phase measurements are similarly defined for selected virtual observables. A network adjustment procedure is then used to improve the ZD phase biases with known DD integer constraints. Numerical results from experiments with 24-h dual-frequency GPS data from three US CORS stations baseline lengths of 21, 56 and 74 km confirm the theoretical predictions concerning AR reliability of the network-based geometry-free algorithms.

在高海拔地区Saastamoinen与Hopfield模型推算水汽含量差异的研究

详细分析了在高海拔地区利用Saastamoinen和Hopfield两种模型推算水汽含量时产生差异的原因，并通过对高程不同的测站上实测数据的分析和研究，给出了Hopfield模型的修正项。     

逐历元GNSS-R测高单差和双差算法

GNSS-R测高是一种高效监测水面高度及其变化的新技术。与传统水面测量技术,如验潮站、卫星测高等相比,其主要优点包括可实现更高时空分辨率的观测、测高结果不受板块垂直运动的影响等。本文提出了一种基于单差观测值组合的cGNSS-R逐历元测高算法,可提高水面高度测量的时空分辨率,并给出了基于双差观测值逐历元cGNSS-R测高算法。利用武汉东湖清河桥上cGNSS-R试验中GPS反射信号观测数据,给出了高精度高时空分辨率的湖面到反射天线相位中心垂直距离,验证了本文算法的准确性,精度可达±2~±4 cm。与水面高实际观测比较结果表明,cGNSS-R单差、双差算法可有效削弱钟差以及电离层和对流层误差对反演水面高度的影响。     

Evaluating and comparing Sentinel 2A and Landsat-8 Operational Land Imager (OLI) spectral indices for estimating fire severity in a Mediterranean pine ecosystem of Greece

The main purpose of this study is to explore the relationship between three field-based fire severity indices (Composite Burn Index-CBI, Geometrically structure CBI, weighted CBI) and spectral indices derived from Sentinel 2A and Landsat-8 OLI imagery on a recent large fire in Thasos, Greece. We employed remotely sensed indices previously used from the remote sensing fire community (Normalized Difference Vegetation Index (NDVI), Normalized Burn Ratio (NBR), differenced NDVI, differenced NBR, relative differenced NBR, Relativized Burn Ratio) and seven Sentinel 2A-specific indices considering the availability of spectral information recorded in the red-edge spectral region. The statistical correlation indicated a slightly stronger relationship between the differenced NBR and the GeoCBI for both Sentinel 2A (r = 0.872) and Landsat-8 OLI (r = 0.845) imagery. Predictive local thresholds of dNBR values showed slightly higher classification accuracy for Sentinel 2A (73.33%) than Landsat-8 OLI (71.11%), suggesting the adequacy of Sentinel 2A for forest fire severity assessment and mapping in Mediterranean pine ecosystems. The evaluation of the classification thresholds calculated in this study over other fires with similar pre-fire conditions could contribute in the operational mapping and reconstruction of the historical patterns of fire severity over the Eastern Mediterranean region.     

整周模糊度去相关的两种实现方法

整周模糊度搜索一直是GPS快速精确定位的关键问题。短时间的观测会导致观测方程和整周模糊度方差、协方差矩阵的高相关性，因而急剧增大整周模糊度的搜索空间，对整周模糊度未知数方差、协方差矩阵进行去相关性处理，可以有效地压缩搜索空间。本文对整周模糊度去相关的迭代法和联合变换法从原理上进行了阐述，并结合实际算倒进行了分析和比较。     

地球重力场平差模型误差的控制

针对模型误差，给出了函数模型优选的标准；提出了衡量模型误差大小的精确度指标及实用估计方法；给出了估计函数模型拟合精度的标准差公式。     

GOCE地球重力场模型在青藏地区的评价及分析

2009年GOCE卫星升空以后,卫星重力梯度数据参与解算的GOCE系列重力场模型已有多家研究机构相继公布。本文分别采用青藏地区的GPS/水准和重力异常实测数据对GOCE重力场模型进行了外部测试,并在重力异常验证过程中引入了一种新的滤波方法,验证结果表明在青藏地区GOCE重力场模型相比其它系列模型的优势在于中波段。同时,探讨了GOCE重力场模型与其他系列模型在青藏地区主要差异值的空间分布以及首次利用统计分析方法找出模型之间主要差异值的阶次分布,得出如下结论：模型之间的较大差异值在空间水平方向上主要分布在喜马拉雅山脉、天山等地形起伏较大的区域,在垂直方向上主要集中在岩石圈。