A new method for indentifying the model error of adjustment system

Some theory problems affecting parameter estimation are discussed in this paper. Influence and transformation between errors of stochastic and functional models is pointed out as well. For choosing the best adjustment model, a formula, which is different from the literatures existing methods, for estimating and identifying the model error, is proposed. On the basis of the proposed formula, an effective approach of selecting the best model of adjustment system is given. Project supported by the Open Research Fund Program of the Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University (No. 905276031-04-10).     

测量平差模型误差对平差结果的影响

测量平差模型不仅包括函数模型还包括随机模型,因此要研究测量平差模型误差对平差结果的影响就要研究函数模型误差和随机模型误差二者同时的影响。本文以间接平差模型为例,随机模型误差、函数模型误差和随机模型误差三个层次研究了测量平差模型误差对平差结果影响的公式,论证了不同平差模型误差情况下的平差结果,并推导和论证了同时考虑函数模型误差和随机模型误差对平差结果影响的公式。     

A New Method for Identifying the Model Error of Adjustment System

IntroductionAdjust ment process deals with the problemsfor esti mating parameters and assessing precisionbased on observations with errors . The researchon adjust ment system involves building mathmodel , determining the opti mization rule andstudying adjust ment arithmetic . Math model ofadjust ment system(also called adjust ment mod-el)is composed of functional and stochastic mod-els . The former describes the relationship be-tween observations and the expectation of pa-rameters . The latte…     

模型误差平差补偿方法比较

在高精度数据处理中,模型误差是不可忽视的。针对模型误差,简单介绍了模型误差补偿的四种方法。通过某一实例四种方法的补偿比较发现在此例中最小二乘方法补偿效果最好,并分析解释了半参数法在此例中不适合的原因。     

污染模型下的最优估计

在目前的抗差估计理论研究中,抗差估计的建立与模型误差没有关系,主要是依据抗差准则设计相应的权函数,但权函数的选择带有主观性,因而抗差估计是经验的。本文就合适于测量数据处理的污染误差模型,提出了未知参数向量和方差的最小均方误差的抗差估计,探讨了最小均方误差估计的计算问题。     

一种新的摄影测量误差分析方法

针对摄影测量误差分析中存在的问题,提出了一种新的误差分析方法,把计算机仿真技术用于摄影测 量误差分析中,对框幅式影像建立了误差仿真分析系统,并对卫星影像和航空影像进行了误差影响分析,得到了 许多有价值的结论。     

病态不确定性平差模型的岭估计算法

测量数据在获取的过程中,常存在不确定性,它们会影响参数估计结果,不确定性平差模型的解算方法可以有效提高参数估计的有效性和可靠性。当观测方程的系数矩阵存在接近零的奇异值,采用岭估计可有效抑制观测方程病态性对参数估值结果的影响。当不确定性平差模型出现病态,其受系数矩阵误差和观测值误差的影响更为严重,本文将岭估计法应用于病态不确定性平差模型,推导了迭代算法,以提高解的稳定性,并用算例验证,结果表明了新方法的有效性和可行性。     

平差系统的模型误差及其识别方法研究

论述了模型误差影响参数估值的一些理论问题,指出了随机模型误差和函数模型误差之间的相互作用和转化。为讨论平差系统最优模型的选取,给出了与现有文献将模型误差纳入平差系统的思路不同的一个估计和识别模型误差的理论基础公式,由此导出了相应的实用公式,给出了平差系统模型的优选方法。     

Rank-defect adjustment model for survey-line systematic errors in marine survey net

In this paper, the structure of systematic and random errors in marine survey net are discussed in detail and the adjustment method for observations of marine survey net is studied, in which the rank-defect characteristic is discovered first up to now. On the basis of the survey-line systematic error model, the formulae of the rank-defect adjustment model are deduced according to modern adjustment theory. An example of calculations with really observed data is carried out to demonstrate the efficiency of this adjustment model. Moreover, it is proved that the semi-systematic error correction method used at present in marine gravimetry in China is a special case of the adjustment model presented in this paper.     

Rank-Defect Adjustment Model for Survey-Line Systematic Errors in Marine Survey Net

In this paper,the structure of systematic and random errors in marine survey net are discussed in detail and the adjustment method for observations of marine survey net is studied,in which the rank-defect haracteristic is discovered first up to now.On the basis of the survey-line systematic error model,the formulae of the rank-defect adjustment model are deduced according to modern adjustment theory.An examle of calculations with really observed data is carried out to demonstrate the efficiency of this adjustment model.Moreover,it is proved that the semi-systematic error correction method used at present in marine gravimetry in China is a special case of the adjustment model presented in this paper.     

概括平差模型的通用解法

鉴于概括平差模型的参数系数矩阵可能为非列满秩的情况,本文从概括平差模型实质出发提出一种以解方程组为基础的通用解法,该方法显著的特点是无论系数矩阵是否为列满秩均可求解。最后用具体实例计算与分析,结果表明,该方法不仅思路简单、通用性强,而且也为进一步认识概括平差模型的实质提供了新思路。     

等价条件平差模型的方差-协方差分量最小二乘估计方法

提出等价条件闭合差的方差-协方差分量最小二乘估计方法,简称LSV-ECM法。首先,利用等价条件平差模型建立了基于等价条件闭合差二次型的方差-协方差分量估计方程,由矩阵半拉直算子将其变换为线性Gauss-Markov形式,进而通过最小二乘准则导出了具有模型通用性、形式简洁性且满足无偏性和最优性的方差-协方差分量估计公式。其次,证明了LSV-ECM方法与残差型VCE方法的等价性,并在此基础上通过计算复杂度定量分析了所提方法的计算高效性。最后,通过边角网平差和中国区域GNSS站坐标时序建模及其结果分析,验证了所提新方法的正确性和计算高效性。     

附加傅里叶补偿项的卫星遥感影像RFM平差方法

卫星光学遥感影像的几何畸变是制约其定位精度的重要原因。采用一般系统误差补偿模型难以从根本上消除影像复杂畸变。本文在有理函数模型RFM平差方案基础上,根据傅里叶级数的逼近特性,提出用二元傅里叶多项式代替一般多项式作为系统误差补偿项,以适用符合连续条件的任意形式畸变。仿真和实际数据平差试验结果表明,本文方法能够有效补偿由于影像内外方位元素误差造成的像方定位系统误差及不同大小的畸变。在控制点充足的条件下,附加3阶傅里叶补偿项的RFM平差定位精度显著优于附加一般多项式补偿项的常规方法,其中SPOT-5异轨立体像对平差后平面和高程定位精度可分别达到3.34 m和2.48 m,QuickBird同轨立体像对平差后平面和高程定位精度分别达到0.77 m和0.54 m,均达到了子像素精度水平。二元傅里叶多项式可作为一种通用的影像系统误差补偿模型,拓展应用于航空和近景影像的畸变校正。     

海底控制点定位的半参数平差模型法

针对圆走航确定海底控制点三维绝对坐标存在垂直解精确度差的问题,本文提出了基于半参数平差模型处理测距系统误差的方法,首先分析了声速变化对测距误差的影响,其次在圆走航观测方程的基础上建立了水下控制点三维坐标解算的半参数平差模型,分别给出了观测时长为测距误差长周期项整数倍与非整数倍时的解算方法。仿真试验表明,当内波存在且观测时长不足测距误差长周期项的整数倍时,该方法相比于差分法和最小二乘法可明显提高水下控制点垂直解的精确度。     

回归模型误差补偿半参数法中正则矩阵任意时的参数估计

用试验观测数据建立的回归拟合模型不可避免地存在模型误差,将模型误差视为非参数分量列入回归模型的半参数模型是一种重要的回归模型.本文利用补偿最小二乘原理,导出了顾及预测点的半参数回归模型参数及模型误差的估计量,并对估计量进行精度评定,给出了估计量及精度评定的相应公式.在理论分析的基础上,得出了只要正则矩阵R的选取使法方程...     

基于RPC的TerraSAR-X影像立体定向平差模型

针对新型高分辨率雷达卫星TerraSAR-X立体像对,本文提出采用基于RPC的平差模型,通过少量的地面控制点来拟合因传感器不稳定、平台星历数据不精确及测距误差引起的影像几何畸变,从而达到精确定向目的.为验证RPC平差模型的适用性,通过在立体成像区域均匀市设人工角反射器点的方法验证其模型精度,并评估了其三维定向平差后的精...     

联合平差中的方差分量估计问题的探讨

天文大地网与GPS空间网联合平差从大的方面分为空间网与地面网两部分。空间网主要是GPS点的三维地心坐标及协方差阵 ;而地面网又涉及到多类观测值 ,主要包括方向观测、导线边、天文方位角三类观测值 ,且各类观测值又分为不同等级的观测。空间网与地面网之间、地面网不同类观测之间及同一类不同观测等级之间的权比不正确将直接影响平差结果 ,因此 ,各类观测值的最佳权匹配就成为联合平差的一个关键。本文就Helmert方差分量简化算法及Baumker简化公式用于联合平差中方差分量估计问题进行讨论 ,并用我国天文大地网 1万点的地面观测数据进行实算、比较、分析 ,以确定联合平差中方差分量估计的方法     

加权混合估计中权值的确定方法

综合了大地测量中各种异方差多源观测模型和联合平差方法,说明了混合估计方法可以用于测量数据融合,平衡附加信息和样本信息对参数估计的影响。通过求取权值使参数估计的协方差阵的迹最小的方法,给出了一个权的最优选择方法。本文扩展了已有的加权混合估计方法,使得新方法中的权不受验前单位权方差的限制,能有效应用于大地测量数据处理。     

A Bayesian method for linear, inequality-constrained adjustment and its application to GPS positioning

One of the typical approaches to linear, inequality-constrained adjustment (LICA) is to solve a least-squares (LS) problem subject to the linear inequality constraints. The main disadvantage of this approach is that the statistical properties of the estimate are not easily determined and thus no general conclusions about the superiority of the estimate can be made. A new approach to solving the LICA problem is proposed. The linear inequality constraints are converted into prior information on the parameters with a uniform distribution, and consequently the LICA problem is reformulated into a Bayesian estimation problem. It is shown that the LS estimate of the LICA problem is identical to the Bayesian estimate based on the mode of the posterior distribution. Finally, the Bayesian method is applied to GPS positioning. Results for four field tests show that, when height information is used, the GPS phase ambiguity resolution can be improved significantly and the new approach is feasible.     

A method of error adjustment for marine gravity with application to Mean Dynamic Topography in the northern North Atlantic

International compilations of marine gravity, such as the International Gravity Bureau (BGI) contain tens of millions of point data. Lemoine et al. (The Development of the Joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96, NASA/TP-1998-206861) chose not to include any marine gravity in the construction of the global gravity model EGM96. Instead they used synthetic anomalies derived from altimetry, so that no independent information about Mean Dynamic Topography (MDT) can be deduced. Software has been developed not only to identify and correct those aspects of marine gravity data that are unreliable, but to do so in a way that can be applied to very large, ocean-wide data sets. First, we select only straight-line parts of ship-tracks and fit each one with a high-degree series of Chebyshev polynomials, whose misfit standard deviation is σ _line and measures the random error associated with point gravity data. Then, network adjustment determines how the gravity datum is offset for each survey. A free least squares adjustment minimises the gravity anomaly mismatch at line-crossing points, using σ _line to weight the estimate for each line. For a long, well crossed survey, the instrumental drift rate is also adjusted. For some 42,000 cross-over points in the northern Atlantic Ocean, network adjustment reduces the unweighted standard deviation of the cross-over errors from 4.03 to 1.58 mGal; when quality weighted, the statistic reduces from 1.32 to 0.39 mGal. The geodetic MDT is calculated combining the adjusted gravity anomalies and satellite altimetry, and a priori global ocean model through a new algorithm called the Iterative Combination Method. This paper reports a first demonstration that geodetic oceanography can characterise the details of basin wide ocean circulation with a resolution better than global ocean circulation models. The result matches regional models of ocean circulation from hydrography measurements (Geophys Res Lett 29:1896, 2002; J Geophys Res 108:3251, 2003).