带有区间不确定性的约束平差算法及应用

针对测量数据中带有区间约束先验信息和附加信息,基于Kuhn-Tucker条件,将测量平差问题转化为二次规划问题,该文提出了一种处理参数带有区间不确定性的新算法,给出了算法具体模型和解算步骤,并且通过模拟数值实验和病态测边网数据计算,分析了在处理病态问题时,最小二乘平差的局限性,通过与岭估计和奇异值分解法的结果相比较,说明了参数带有区间不确定性的平差算法的有效性。     

参数有界约束下的最小二乘平差算法

文中基于测量不确定度理论,建立参数有界约束下的平差模型及其解算方法。顾及变形监测网特点,将该平差模型及算法应用到沉降监测网实例中,即利用已知先验信息,建立相应约束模型,求得有界条件下的参数最优估值。通过与经典最小二乘平差法比较,结果证明模型的有效性,估计的参数值控制在给定范围内且不"失真",其沉降量更接近实际情况。     

An iterative solution of weighted total least-squares adjustment

Total least-squares (TLS) adjustment is used to estimate the parameters in the errors-in-variables (EIV) model. However, its exact solution is rather complicated, and the accuracies of estimated parameters are too difficult to analytically compute. Since the EIV model is essentially a non-linear model, it can be solved according to the theory of non-linear least-squares adjustment. In this contribution, we will propose an iterative method of weighted TLS (WTLS) adjustment to solve EIV model based on Newton–Gauss approach of non-linear weighted least-squares (WLS) adjustment. Then the WLS solution to linearly approximated EIV model is derived and its discrepancy is investigated by comparing with WTLS solution. In addition, a numerical method is developed to compute the unbiased variance component estimate and the covariance matrix of the WTLS estimates. Finally, the real and simulation experiments are implemented to demonstrate the performance and efficiency of the presented iterative method and its linearly approximated version as well as the numerical method. The results show that the proposed iterative method can obtain such good solution as WTLS solution of Schaffrin and Wieser (J Geod 82:415–421, 2008) and the presented numerical method can be reasonably applied to evaluate the accuracy of WTLS solution.     

加入边长的严密GPS网平差模型

本文根据空间坐标转换的推导过程,以GPS基线及空间测距边长为观测值,以当地高斯平面坐标、大地高、缩放系数、旋转角、测距常数和比例系数为平差参数,构造加入测距边长的严密GPS网平差模型。将测距边长观测值加入到平差模型中有效地利用了地面观测数据,增加了多余观测方程,提高了解算精度,还可以解得测距观测值的测距常数和测距比例系数,其中采用数值导数的方法,简化了GPS网平差的计算,通过对实测数据的处理和比较。表明了该模型是正确的,并且在精度方面也得到了改善。     

基于Matlab的控制网平差教学软件与应用

介绍了基于Matlab的控制网平差软件的功能和特点,并将该软件应用到《控制网平差程序设计》课程的教学过程以及实际工程的数据处理中,取得了良好的效果。     

基于MATLAB的水准网经典平差系统的开发和应用

一般情况下间接平差模型在平差前都给出参数的近似值,由于水准网观测值总能够由参数近似表示,在平差前可以不给出参数的近似值,直接进行平差,平差值为参数的估值。因此本文通过对间接平差模型的简化,基于MATLAB语言的丰富的数值计算功能和独特的GUI功能实现了任意网形的自由水准网、附合水准网经典平差系统的开发。用假设检验理论对平差结果从理论上进行可靠性分析,并用一个实例对系统的可靠性进行测试。试验结果表明,系统的平差结果是可靠的,系统可以对一等、二等、三等、四等以及等外任意网形的自由水准网、附合水准网进行经典平差,平差结果可靠。     

椭圆形地理实体定位中的平差问题

在地理实体中,有很多是椭圆或圆形的,大部分实体的中心无法到达或无法判定,必须对椭圆形实体边界进行测量,然后确定椭圆的中心位置(椭圆的定位)、长轴和短轴长度(椭圆形状)及长轴方向(椭圆的定向)。当测量其5个边界点,可惟一解出定位和定向参数,超过5个测点时,就产生平差问题。本文推导出一套椭圆定位和定向的直接计算公式,并提出平差模型,通过实例论证该模型的正确性和实用性。     

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.     

抗差卡尔曼滤波及其在动态水准网平差中的应用

介绍了标准卡尔曼滤波方程,总结了稳健M估计的基本方法,并根据等价权原理导出卡尔曼滤波的抗差估计方程,方程的形式与卡尔曼滤波方程相似,给出了卡尔曼滤波稳健估计的计算步骤.最后,以动态水准监测为例进行了模拟计算,证明了该方法的有效性.     

基于最小二乘平差的全极化SAR配准偏移量估计方法

全极化合成孔径雷达影像(PolSAR)相对单极化SAR影像有更加丰富的地表信息。为了提高SAR影像偏移量跟踪技术估算偏移量的精度,提出一种基于最小二乘平差法的全极化SAR数据偏移量估计方法。首先利用全极化SAR不同极化通道数据估算偏移量得到多个观测值,然后通过最小二乘平差法对多余观测值循环剔除粗差得到最优偏移量。文中选取美国科罗拉多州湖城(Lake city)区域的两景JPL无人机UAVSAR全极化SAR影像进行实验,结果表明,文中新方法具有良好的粗差探测和去除功能,相对于已有研究结果,在方位向和距离向的偏移量估算精度都有明显提高,达到15%~25%。新方法提高了偏移量跟踪估算偏移量的精度,这对利用偏移量跟踪技术监测滑坡、地震及冰川等有重要的意义。     

Best invariant covariance component estimators and its application to the generalize multivariate adjustment of heterogeneous deformation observations

Repeated measurements, like relevelling or periodically observed control networks, e.g., may be adjusted within the Simple Multivariate Gauss-Markov Model if the coefficient matrices are identical at each epoch and if the observations are homogeneous yielding proportional variance-covariance matrices between each two (not necessarily different) epochs. However, when processing data concerning recent crustal movements both conditions are violated, in general, such that the usual approach becomes inapplicable. Therefore, a procedure is proposed for this case which makes a joint adjustment possible within the Generalized Multivariate Regression Model of Heterogeneous Observations and which further coincides with the standard multivariate analysis in the special case.     

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。