最小二乘配置中粗差的可发现性和可区分性问题

研究最小二乘配置中粗差与随机信号的区分性问题。从观测值残差和信号估值及其统计性质出发，根据高斯马尔可夫模型两个选假设理想，给出了最小二乘配置模型中观测粗差的可区分且可发现的表达式。     

总体最小二乘平差中粗差的可区分性

针对总体最小二乘中粗差的可区分性,在Partial-EIV模型加权总体最小二乘算法的基础上引入了两个备选假设下的可靠性理论,给出了分析总体最小二乘粗差可区分性的方法。通过直线拟合的算例分析,说明本文的方法是可行的,能够有效地分析总体最小二乘中粗差的可区分性,并发现采用总体最小二乘求解直线拟合时,存在粗差不可区分的情况,也就意味着粗差是不可定位的。对于其它计算模型也可能存在粗差不可区分的情况,须加以注意。     

控制网连接点坐标值粗差的可定位性研究

在原有测量控制网(称旧网)的基础上建立同级扩大网或低级加密网(称新网)时,新旧网之间的重合点(称连接点)坐标值粗差的检验是平差前的一个重要环节。本文将连接点坐标视为带协方差阵的观测值,采用数据探测法定位其粗差。借助于 Gauss-Markov模型下两个备选假设检验的理论,推导了连接点相关坐标观测值粗差可定位性基本公式,讨论了各类平面网中连接点坐标观测值粗差的可发现性和可区分性。     

控制网连接点坐标值粗差的可定位性研究

在原有测量控制网（称旧网）的基础上建立同级扩大网或低级加密网（称新网）时，新旧网之间的重合点（称连接点）坐标植粗差的检验是平差前的一个重要环节。本文将边接点坐标视为带协方差阵的观测值，采用数据探测法定位其粗差。借助于Ｇａｕｓｓ－Ｍａｒｋｏｖ模型下两个备选假设检验的理论，推导了连接点相关坐标观测值粗差可定位性基本公式，讨论了各类平面网中连接坐标观测值粗差的可发现性和可区分性。     

动态平差模型下形变与粗差的可区分性研究

从形变监测数据处理中常用的动态平差模型出发，推导出了研究形变与粗差可区分性的公式，给出在形变模型统计检验的同时统计检验粗差的方法与步骤，对垂直形变监测网的可区分性作了详细讨论和实例分析，得出几点结论．     

变形监测网的可区分性分析

本文首先借助于 Gauss-Markov 模型下两个多维备选假设检验的理论,将变形监测网单个备选假设下的灵敏度,在顾及模型误差的情况下,扩展成监测网的可区分性理论,提出了监测网的可区分性和区分可靠性概念;其次,对于监测网在三种典型变形模型(单点移动,错动和均匀应变)下变形与粗差的可区分性进行了讨论,获得了一些有益的结论。     

动态平差模型下形变与粗差的可区分性研究

从形变监测数据处理中常用的动态平差模型出发，推导了研究形变与粗差可区分性的公式，给出在形变模型统计检验的同时统计检验粗差的方法与步骤，对垂直形变监测网的可分性作了详细讨论和实例分析，得出几点结论。     

单频BDS定位的可靠性分析

针对BDS系统中存在的模型误差对模糊度解算造成估计偏差的问题,该文提出了以最小可探测偏差(MDB)为模型误差计算有偏估计成功率对模糊度解算的正确性进行评价,并分别以码观测和相位观测进行了仿真实验,得出了存在码观测MDB和相位观测MDB等情形时的有偏估计成功率大小的规律,并与不存在模型误差时的成功率进行对比分析。鉴于GNSS定位粗差包括伪距码观测粗差和相位周跳,推导了码观测和相位观测情况下的BDS系统单频定位可靠性指标MDB和最小可探测效应(MDE),并进行了中国大陆内某地点的BDS单频定位性能的仿真模拟,着重分析了载波相位MDB与周跳之间的关系。     

粗差探测与定位的一种新方法

本文阐述了模型误差的可发现性与可区分性的重要性以及判别方法，提出一种利用观测值改正数向量综合分析的方法探测粗差。在模型误差可区分时可以对粗差定位并估计粗差值。同ω检验法比较，综合分析法发现粗差的能力更强，定位更准确。     

粗差探测与定位的一种新方法

本文阐述了模型误差的可发现性与可区分性的重要性以及判别方法，提出一种利用观测使改正数向量综合分析的方法探测粗差。在模型误差可区分时可以对粗差定位并估计粗差值。同ω检验法比较，综合分析法发现粗差的能力更强，定位更准确。     

On separability for deformations and gross errors

According to the testing theory with two alternative hypotheses, the theory of detectability for a deformation monitoring network has been extended to the theory of separability for deformations and gross errors. With this theory it can be evaluated whether deformations and gross errors can be statistically distinguished each other, which is very important for deformation analysis. General formulas are established and the separability between deformations and gross errors for some typical deformation models is investigated. An example of separating gross errors from deformations is given.     

Simultaneous estimation of cross-validation errors in least squares collocation applied for statistical testing and evaluation of the noise variance components

The cross-validation technique is a popular method to assess and improve the quality of prediction by least squares collocation (LSC). We present a formula for direct estimation of the vector of cross-validation errors (CVEs) in LSC which is much faster than element-wise CVE computation. We show that a quadratic form of CVEs follows Chi-squared distribution. Furthermore, a posteriori noise variance factor is derived by the quadratic form of CVEs. In order to detect blunders in the observations, estimated standardized CVE is proposed as the test statistic which can be applied when noise variances are known or unknown. We use LSC together with the methods proposed in this research for interpolation of crustal subsidence in the northern coast of the Gulf of Mexico. The results show that after detection and removing outliers, the root mean square (RMS) of CVEs and estimated noise standard deviation are reduced about 51 and 59%, respectively. In addition, RMS of LSC prediction error at data points and RMS of estimated noise of observations are decreased by 39 and 67%, respectively. However, RMS of LSC prediction error on a regular grid of interpolation points covering the area is only reduced about 4% which is a consequence of sparse distribution of data points for this case study. The influence of gross errors on LSC prediction results is also investigated by lower cutoff CVEs. It is indicated that after elimination of outliers, RMS of this type of errors is also reduced by 19.5% for a 5 km radius of vicinity. We propose a method using standardized CVEs for classification of dataset into three groups with presumed different noise variances. The noise variance components for each of the groups are estimated using restricted maximum-likelihood method via Fisher scoring technique. Finally, LSC assessment measures were computed for the estimated heterogeneous noise variance model and compared with those of the homogeneous model. The advantage of the proposed method is the reduction in estimated noise levels for those groups with the fewer number of noisy data points.     

单个备选假设的可区分

根据单个备选假设的统计检验,详细导出了模型误差的可区分度公式,并论述了可区分度与可发现度及与Forstner法的关系。作为应用,可导出变形模型的可区分度及网的可区分标准,在监测网的设计中应用。     

一种基于多面函数的改进最小二乘配置方法

利用最小二乘配置对非平稳空间随机场进行推估时,趋势项数学模型的选择通常无法完整体现非平稳空间随机场的系统性,这将导致经验协方差函数估计出现偏差,最终推估结果可能错误。提出了一种基于多面函数的改进最小二乘配置方法来解决上述问题。该方法引入多面函数拟合区域内的趋势项,通过多次迭代计算得到稳定的待定系数值与协方差函数的参数值,最后综合趋势项与信号项得到最终估值。分别采用了模拟地震垂直形变数据和2009年意大利L’Aquila地震的合成孔径雷达干涉测量（Interferometric SAR,InSAR）与GPS同震位移数据来对该方法进行验证,并将其结果与常规方法进行比较。结果表明,改进方法在外部检核点估值的均方残差要小于多面函数法与常规的最小二乘配置法,且受采样点位的影响最小。     

Temporal optimisation of image acquisition for land cover classification with Random Forest and MODIS time-series

The analysis and classification of land cover is one of the principal applications in terrestrial remote sensing. Due to the seasonal variability of different vegetation types and land surface characteristics, the ability to discriminate land cover types changes over time. Multi-temporal classification can help to improve the classification accuracies, but different constraints, such as financial restrictions or atmospheric conditions, may impede their application. The optimisation of image acquisition timing and frequencies can help to increase the effectiveness of the classification process. For this purpose, the Feature Importance (FI) measure of the state-of-the art machine learning method Random Forest was used to determine the optimal image acquisition periods for a general (Grassland, Forest, Water, Settlement, Peatland) and Grassland specific (Improved Grassland, Semi-Improved Grassland) land cover classification in central Ireland based on a 9-year time-series of MODIS Terra 16 day composite data (MOD13Q1). Feature Importances for each acquisition period of the Enhanced Vegetation Index (EVI) and Normalised Difference Vegetation Index (NDVI) were calculated for both classification scenarios. In the general land cover classification, the months December and January showed the highest, and July and August the lowest separability for both VIs over the entire nine-year period. This temporal separability was reflected in the classification accuracies, where the optimal choice of image dates outperformed the worst image date by 13% using NDVI and 5% using EVI on a mono-temporal analysis. With the addition of the next best image periods to the data input the classification accuracies converged quickly to their limit at around 8–10 images. The binary classification schemes, using two classes only, showed a stronger seasonal dependency with a higher intra-annual, but lower inter-annual variation. Nonetheless anomalous weather conditions, such as the cold winter of 2009/2010 can alter the temporal separability pattern significantly. Due to the extensive use of the NDVI for land cover discrimination, the findings of this study should be transferrable to data from other optical sensors with a higher spatial resolution. However, the high impact of outliers from the general climatic pattern highlights the limitation of spatial transferability to locations with different climatic and land cover conditions. The use of high-temporal, moderate resolution data such as MODIS in conjunction with machine-learning techniques proved to be a good base for the prediction of image acquisition timing for optimal land cover classification results.     

Non-stationary covariance function modelling in 2D least-squares collocation

Standard least-squares collocation (LSC) assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the observed data. However, the assumption that the spatial dependence is constant throughout the region of interest may sometimes be violated. Assuming a stationary covariance structure can result in over-smoothing of, e.g., the gravity field in mountains and under-smoothing in great plains. We introduce the kernel convolution method from spatial statistics for non-stationary covariance structures, and demonstrate its advantage for dealing with non-stationarity in geodetic data. We then compared stationary and non- stationary covariance functions in 2D LSC to the empirical example of gravity anomaly interpolation near the Darling Fault, Western Australia, where the field is anisotropic and non-stationary. The results with non-stationary covariance functions are better than standard LSC in terms of formal errors and cross-validation against data not used in the interpolation, demonstrating that the use of non-stationary covariance functions can improve upon standard (stationary) LSC.     

Least-squares collocation with covariance-matching constraints

Most geostatistical methods for spatial random field (SRF) prediction using discrete data, including least-squares collocation (LSC) and the various forms of kriging, rely on the use of prior models describing the spatial correlation of the unknown field at hand over its domain. Based upon an optimal criterion of maximum local accuracy, LSC provides an unbiased field estimate that has the smallest mean squared prediction error, at every computation point, among any other linear prediction method that uses the same data. However, LSC field estimates do not reproduce the spatial variability which is implied by the adopted covariance (CV) functions of the corresponding unknown signals. This smoothing effect can be considered as a critical drawback in the sense that the spatio-statistical structure of the unknown SRF (e.g., the disturbing potential in the case of gravity field modeling) is not preserved during its optimal estimation process. If the objective for estimating a SRF from its observed functionals requires spatial variability to be represented in a pragmatic way then the results obtained through LSC may pose limitations for further inference and modeling in Earth-related physical processes, despite their local optimality in terms of minimum mean squared prediction error. The aim of this paper is to present an approach that enhances LSC-based field estimates by eliminating their inherent smoothing effect, while preserving most of their local prediction accuracy. Our methodology consists of correcting a posteriori the optimal result obtained from LSC in such a way that the new field estimate matches the spatial correlation structure implied by the signal CV function. Furthermore, an optimal criterion is imposed on the CV-matching field estimator that minimizes the loss in local prediction accuracy (in the mean squared sense) which occurs when we transform the LSC solution to fit the spatial correlation of the underlying SRF.     

Tuning a gravimetric quasigeoid to GPS-levelling by non-stationary least-squares collocation

This paper addresses implementation issues in order to apply non-stationary least-squares collocation (LSC) to a practical geodetic problem: fitting a gravimetric quasigeoid to discrete geometric quasigeoid heights at a local scale. This yields a surface that is useful for direct GPS heighting. Non-stationary covariance functions and a non-stationary model of the mean were applied to residual gravimetric quasigeoid determination by planar LSC in the Perth region of Western Australia. The non-stationary model of the mean did not change the LSC results significantly. However, elliptical kernels in non-stationary covariance functions were used successfully to create an iterative optimisation loop to decrease the difference between the gravimetric quasigeoid and geometric quasigeoid at 99 GPS-levelling points to a user-prescribed tolerance.     

最小二乘配置在钢结构建筑物沉降监测中的应用研究

根据最小二乘配置可以推估与观测值并无关系的未测点参数特点,文章给出一种钢结构建筑物沉降监测预报新方法,取得了较好的效果.研究结果表明,在建筑物变形监测数据处理中最小二乘配置是一种有效的分析方法.     

Land Use/Cover Mapping with Quad-polarization Radar and Derived Texture Measures near Wad Madani,Sudan

This study examines the relative utility of quad-polarization spaceborne radar and derived texture measures for classification of specific land cover categories at a site in east-central Sudan near the city of Wad Madani. Japanese Advanced Land Observing Satellite (ALOS) Phased Array type L-band Synthetic Aperture Radar (PALSAR) quad-polarization spaceborne radar data at 12.5 m spatial resolution were obtained for this study. Measures of variance texture were applied to the original PALSAR data over varied window sizes. Transformed divergence (TD) measures of separability were calculated in order to evaluate the best bands from the original and texture measures for classification. Results show that quad-polarization radar data and derived texture measures have high separability between different land cover classes, and therefore hold potential to attain high levels of classification accuracy. Specifically, when used individually the cross-polarization bands showed the highest separability, but when used in combination some mix of cross- and like-polarization bands had the highest separability.