有界不确定性平差模型的迭代算法

针对现有的有界不确定性平差模型算法较为复杂且没有顾及权重的问题,该文提出了一种无需奇异值分解的迭代算法及其一种加权方法。直接采用了迭代算法求解有界不确定性平差模型的min-max准则,推导出了未知参数估值,算法概念简单,易于实现,收敛速度更快。基于该文提出的迭代算法,当系数矩阵和观测向量各自均不等权时,采用了一种加权方法,并推导了其解算过程。算例结果表明:该文提出的迭代算法是可行的,并且解算效率更高;加权后的迭代算法是有效的。     

An integrated bundle adjustment approach to range camera geometric self-calibration

This paper describes a new method for integrated range camera system self-calibration in which both traditional camera calibration parameters and rangefinder systematic error parameters are estimated simultaneously in a free-network bundle adjustment of observations to signalised targets. Its mathematical basis is collinearity and range observation equations augmented with correction models for systematic error sources identified in the data. The self-calibration results from datasets captured with two different range cameras, a SwissRanger SR3000 and a SwissRanger SR4000, are presented and analysed in detail. The method’s effectiveness is demonstrated in terms of systematic error removal and independent accuracy assessment. Up to a 54% reduction in the residual RMS was achieved by inclusion of the proposed error models in the self-calibration adjustment. An improvement of at least 74% in the RMS of object point co-ordinate differences, over that achieved without calibration or provided by the manufacturer’s software (in the case of the SR3000), was realised in an independent accuracy assessment. In addition, the effects of several influencing variables, including the range stochastic error model, the network geometry and the range measurements themselves, on key correlation mechanisms are analysed in detail.     

半参数回归与模型精化

就一般情况给出了半参数平差的算法，并结合一种特定的情况，讨论了正规化矩阵半正定时的计算方法，给出了相应的公式，最后构造了一个模拟的平差问题，对半参数法和最小二乘法的计算结果进行了比较，计算表明，半参数法能够发现并识别模型误差或观测值中的系统误差。     

基于附加参数模型的自检校光束法区域网平差算法运行结果对比

像点偏移是影响光束法区域网平差结果精度的主要因素之一。克服平差过程中像点偏移的影响,以提高区域网平差精度,一直受到业界高度重视。当前,克服像点偏移的常规做法是借助特定的参数模型对其进行描述,构建基于附加参数模型的自检校光束法区域网平差模型,在区域网平差的同时求解引入的参数,进而实现对系统误差的补偿。Bauer模型、Ebner模型、Brown模型、光学畸变模型是现有算法中描述像点偏移的常用模型。为了对上述4种模型的系统误差进行验证,本文首先在经典的光束法区域网平差模型基础上分别设计了与4种模型相对应的自检校光束法区域网平差模型,并予以编程实现;然后通过实例对上述4种模型的算法运行结果进行了验证、比较及分析。试验结果表明,Ebner模型和Brown模型的引入可有效提高光束法区域网平差的精度;Bauer模型的引入对小型区域网平差精度的提升更加有效;光学畸变模型的引入对区域网平差结果的精度提升作用相对较小。     

利用半参数模型精化GPS绝对定位中残余的系统偏差

为了减弱GPS单点定位中残余的系统偏差对参数估值精度的影响,在误差方程中引入一非参数分量来表示测量中残余的系统误差,即利用半参数模型来精化GPS绝对定位的函数模型。最后利用实测GPS数据检验了此算法的有效性,计算结果表明在一定程度上该算法不仅能够提高参数估值的精度,而且还能提取出平差模型中残余的系统偏差。但因为半参数模型在测量数据处理中的应用才刚刚起步,还有许多问题值得在理论与实践上进行深入的探讨与研究。     

3维最小二乘表面匹配泛型数学模型及在机载LiDAR条带平差中的应用

以3维表面间共轭点欧氏距离之和最小为理论基础,提出一种泛型3维表面匹配数学模型,并推导其最小二乘平差理论模型,利用该模型进行机载LiDAR点云条带平差。针对真实机载LiDAR点云数据进行条带平差对比实验,结果表明本文所提出的表面匹配模型,不仅能准确估计出相邻重叠3维表面间的正形变换参数,较好地解决机载LiDAR点云条带间配准问题,而且能同时适用于多种同名点对应准则,是一种泛型的配准模型。     

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.     

Principle, software and experiment of GPS-supported aerotriangulation

1 IntroductionAs is now well known, the high accurate point de-termination with airborne remOe sensing data hasalways ben one of the most fundaxnental prObletns..in aerial photOgrammtry. According to the princi-ple of the geOmtry reversal in photOgramrntry,the interior and exterior orientation elements ofaerial phOtOgraphs must first be known in order toreconstnJct the measuring stereo geometric medels.For the past 60 years, however, the interior orienta-tion parameters of carnera were main…     

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。     

三原则整体最小二乘用于平面自由网平差计算

文中在平面网平差中应用整体最小二乘理念.在最小二乘模型中,为了消除观测方程系数误差和未知参数系统误差,加入系数改正数和参数改正数,并提出三原则整体最小二乘模型.研究平差两大步骤,用最小二乘多次改用"参考点组"而选出w个稳定点;用最小二乘多次改用"近似坐标"而消除系数误差和参数系统误差.三原则整体最小二乘适用于平面自由网...     

A unified approach to post-mission processing of intertial data

The outpout of inertial survey systems is available to the user in two basic forms: as Kalman filtered information at updates or as integrated velocity and position information at regular time intervals. In case of the second data type, the post-mission processing starts with the approximation of the velocity error curve. This approximation is either based on a system error model as in Kalman filtering or uses curve fitting techniques. From there on, smoothing or adjustment procedures are used as further steps in the post-mission treatment of both data types. A unified treatment of the various post-mission approaches starts with the formulation of appropriate error models of the system outputs. It is then possible to present all existing methods as intermediate steps of a rigorous adjustment procedure. This unified approach gives insight into the limitations of individual methods and provides a means to detect inconsistencies in post-mission processing strategies. An analysis of existing approaches is made and a new method, spectral decomposition, is treated in detail. Compared to the existing procedures, it has advantages with respect to a rigorous covariance propagation and blunder detection.     

利用已有像控点的多期航空影像光束法区域网联合平差

为了充分利用已有航空影像与控制成果,节约作业成本,缩短作业周期,提出一种利用已有像控点联合多期航空影像进行整体平差加密的数学模型,并采用我国南方某地区的数据资料进行了试验证明。结果表明,联合平差能将已有像控点的控制作用通过多期影像间的同名点传递到最新航空影像上,联合平差加密点的平面精度与常规光束法区域网平差加密精度基本一致,而高程精度则取决于多期影像间同名点的观测值个数,同名点观测值越多,加密点高程精度越高,因此只要多期影像间存在足够多的同名点观测值,则联合平差的加密精度完全能够满足摄影测量地形图测绘的生产需要。     

海洋重力测量网自检校平差

海洋重力测量是在测量平台不断动态状态下进行的一种动态测量,由于受海浪起伏,风,流等扰动因素的干扰,海洋重力观测值将受到水平加速度,垂直加速度,交叉耦合以及Ｅｏｅｔｖｏｅｓ效应等于交错面干扰加速度的影响。最扣一个时期为了提高海洋重力测量成果的质量,世界各国海洋重力测量工作者曾就海洋重力观测网平差问题进行了大量的研究工作。     

地图数字化中基于点位坐标的统一平差模型

探讨了地图数字化过程中采用平差方法来建立坐标计算的统一模型。将测得的角度、边长等数据化为方向、距离观测值列立误差方程，通过调用统一的平差迭代计算程序来计算未知点坐标及精度。详细给出了基于平差的11种常用坐标计算方法，并通过实例进行了说明。     

基于有理函数模型的星载SAR影像几何校正

主要研究了面向星载合成孔径雷达SAR(Synthetic Aperture Radar)影像几何处理的有理函数模型RFM(Rational Function Model)的建模、求解和应用方法。首先采用与地形无关的方式,利用严密的距离-多普勒模型(Range Doppler,RD)构建虚拟控制点格网来进行RFM建模,实现了一种RFM模型参数的快速无偏解算新方法,能够取得相对于RD模型很高的拟合精度,在几何定位功能上实现了对RD模型的有效替代,同时大大提高了计算效率。然后在此基础上利用RFM模型实现了星载SAR影像的快速几何校正,为了提高几何校正结果的绝对定位精度,引入少量地面控制点对RFM模型进行了像方改正处理,以消除SAR影像几何定位的系统误差,并利用ENVISAT ASAR数据的实验结果验证了本文方法的有效性。     

Error modelling,calibration and analysis of an AM–CW terrestrial laser scanner system

A rigorous method for terrestrial laser scanner self-calibration using a network of signalised points is presented. Exterior orientation, object point co-ordinates and additional parameters are estimated simultaneously by free network adjustment. Spherical co-ordinate observation equations are augmented with a set of additional parameters that model systematic errors in range, horizontal direction and elevation angle. The error models include both physically interpretable and empirically identified components. Though the focus is on one particular make and model of AM–CW scanner system, the Faro 880, the mathematical models are formulated in a general framework so their application to other instruments only requires selection of an appropriate set of additional parameters. Results from controlled testing show that significant improvement is achieved by using the proposed model in terms of both reducing the magnitude of observational residuals as well as the three-dimensional positioning accuracy of signalised points. Ten self-calibration datasets captured over the course of 13 months are used to examine short- and long-term additional parameter stability via standard hypothesis testing techniques. Detailed investigations into correlation mechanisms between model parameters accompany the self-calibration solution analyses. Other contributions include an observation model for incorporation of integrated inclinometer observations into the self-calibration solution and an effective a priori outlier removal method. The benefit of the former is demonstrated to be reduced correlation between exterior orientation and additional parameters, even if inclinometer precision is low. The latter is arrived at by detailed analysis of the influence of incidence angle on range.     

联合平差中大地网定向和尺度系统误差的影响和分离

本文从地面大地网的定向、尺度系统误差的定义及对坐标的影响关系出发,分析了这些系统误差与地面网、卫星网之问转换参数的关系,推导了系统误差对转换参数的影响公式。在此基础上,提出了转换参数的区域性问题,并提出了分离区域性定向误差与尺度比参数的联合平差模型。     

Solution of the weighted symmetric similarity transformations based on quaternions

A new method through Gauss–Helmert model of adjustment is presented for the solution of the similarity transformations, either 3D or 2D, in the frame of errors-in-variables (EIV) model. EIV model assumes that all the variables in the mathematical model are contaminated by random errors. Total least squares estimation technique may be used to solve the EIV model. Accounting for the heteroscedastic uncertainty both in the target and the source coordinates, that is the more common and general case in practice, leads to a more realistic estimation of the transformation parameters. The presented algorithm can handle the heteroscedastic transformation problems, i.e., positions of the both target and the source points may have full covariance matrices. Therefore, there is no limitation such as the isotropic or the homogenous accuracy for the reference point coordinates. The developed algorithm takes the advantage of the quaternion definition which uniquely represents a 3D rotation matrix. The transformation parameters: scale, translations, and the quaternion (so that the rotation matrix) along with their covariances, are iteratively estimated with rapid convergence. Moreover, prior least squares (LS) estimation of the unknown transformation parameters is not required to start the iterations. We also show that the developed method can also be used to estimate the 2D similarity transformation parameters by simply treating the problem as a 3D transformation problem with zero (0) values assigned for the z-components of both target and source points. The efficiency of the new algorithm is presented with the numerical examples and comparisons with the results of the previous studies which use the same data set. Simulation experiments for the evaluation and comparison of the proposed and the conventional weighted LS (WLS) method is also presented.     

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。