最小二乘配置法在GPS高程异常推估中的应用

简述了最小二乘配置法的基本原理,并在水准联测点不多的情况下,直接采用平方根函数作为各随机参数间的协方差函数用于推估GPS高程异常值。由于最小二乘配置法的函数模型中同时考虑了非随机变量和随机变量,使得高程异常值的推估精度更高。实例分析也证明了此模型在精度上优于传统的平面拟合模型和协方差推估模型。残差分析表明此方法更适合于同时存在内插和外推高程异常值的情况。     

The effects of spatial autoregressive dependencies on inference in ordinary least squares: a geometric approach

There is a common belief that the presence of residual spatial autocorrelation in ordinary least squares (OLS) regression leads to inflated significance levels in beta coefficients and, in particular, inflated levels relative to the more efficient spatial error model (SEM). However, our simulations show that this is not always the case. Hence, the purpose of this paper is to examine this question from a geometric viewpoint. The key idea is to characterize the OLS test statistic in terms of angle cosines and examine the geometric implications of this characterization. Our first result is to show that if the explanatory variables in the regression exhibit no spatial autocorrelation, then the distribution of test statistics for individual beta coefficients in OLS is independent of any spatial autocorrelation in the error term. Hence, inferences about betas exhibit all the optimality properties of the classic uncorrelated error case. However, a second more important series of results show that if spatial autocorrelation is present in both the dependent and explanatory variables, then the conventional wisdom is correct. In particular, even when an explanatory variable is statistically independent of the dependent variable, such joint spatial dependencies tend to produce “spurious correlation” that results in over-rejection of the null hypothesis. The underlying geometric nature of this problem is clarified by illustrative examples. The paper concludes with a brief discussion of some possible remedies for this problem.     

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.     

地图投影的最小二乘二元多项式拟合的误差估计

探讨了在地图投影的最小二乘二元多项式拟合中参考点的分布对拟合误差的影响,提出了一种基于矩阵的秩亏的方法来判断参考点是否在指定次数的二元多项式空间的代数曲线上,并导出在极小范数最小二乘意义下的拟合多项式的误差估计式,公式表明拟合误差和参考点的最小二乘误差无关。     

A procedure for testing the assumption of homoscedasticity in least squares residuals: a case study of GPS carrier-phase observations

Due to increased demands on the quality of the results of Global Positioning System (GPS) evaluations, various authors have studied improvements of the stochastic model of GPS carrier-phase observations. These improvements are based on the reasonable assumption that the commonly used stochastic model with independent and homoscedastic (i.e. equal variance) errors is unrealistic. However, this has not been proved rigorously so far. A statistical test procedure based on uncorrelated least–squares residuals, which allows verification of the hypothesis of a heterogeneous variance, is provided. The statistical test procedure is of interest in its own right, and is independent of the practical problem considered. The presented technique is applied to GPS carrier-phase observations. Results show that the variances of the investigated observations are far from homogeneous. It is indicated that the error variances of the presented data increase with decreasing GPS satellite elevation. These results confirm the assumption that the commonly used stochastic model of GPS observations is inadequate and has to be improved.     

两等级网不使用导数的联合非线性最小二乘估计

针对不同等级测量控制网的联合平差，介绍一种不使用导数的解析方法，该方法一方面克服了传统平差中由于起算数据误差对低级网的精度影响，而使加密的精度逐次降低的缺点；另一方面，完全避免了导数的计算，大大减少了计算工作量。     

Optimal multi-step collocation: application to the space-wise approach for GOCE data analysis

Collocation is widely used in physical geodesy. Its application requires to solve systems with a dimension equal to the number of observations, causing numerical problems when many observations are available. To overcome this drawback, tailored step-wise techniques are usually applied. An example of these step-wise techniques is the space-wise approach to the GOCE mission data processing. The original idea of this approach was to implement a two-step procedure, which consists of first predicting gridded values at satellite altitude by collocation and then deriving the geo-potential spherical harmonic coefficients by numerical integration. The idea was generalized to a multi-step iterative procedure by introducing a time-wise Wiener filter to reduce the highly correlated observation noise. Recent studies have shown how to optimize the original two-step procedure, while the theoretical optimization of the full multi-step procedure is investigated in this work. An iterative operator is derived so that the final estimated spherical harmonic coefficients are optimal with respect to the Wiener–Kolmogorov principle, as if they were estimated by a direct collocation. The logical scheme used to derive this optimal operator can be applied not only in the case of the space-wise approach but, in general, for any case of step-wise collocation. Several numerical tests based on simulated realistic GOCE data are performed. The results show that adding a pre-processing time-wise filter to the two-step procedure of data gridding and spherical harmonic analysis is useful, in the sense that the accuracy of the estimated geo-potential coefficients is improved. This happens because, in its practical implementation, the gridding is made by collocation over local patches of data, while the observation noise has a time-correlation so long that it cannot be treated inside the patch size. Therefore, the multi-step operator, which is in theory equivalent to the two-step operator and to the direct collocation, is in practice superior thanks to the time-wise filter that reduces the noise correlation before the gridding. The criteria for the choice of this filter are investigated numerically.     

A detailed study of the duality relation for the least squares adjustment in euclidean spaces

The Euclidean spaces with their inner products are used to describe methods of least squares adjustment as orthogonal projections on finite-dimensional subspaces. A unified Euclidean space approach to the least squares adjustment methods “observation equations” and “condition equations” is suggested. Hence not only the two adjustment solutions are treated from the view-point of Euclidean space theory in a unified frame but also the existing duality relation between the methods of “observation equations” and “condition equations” is discussed in full detail. Another purpose of this paper is to contribute to the development of some familiarity with Euclidean and Hilbert space concepts. We are convinced that Euclidean and Hilbert space techniques in least squares adjustment are elegant and powerful geodetic methods.     

坐标转换四参数解算的整体最小二乘新方法

在平面四参数坐标转换模型中,观测向量和误差方程系数矩阵中部分元素都存在误差。提出一种使用整体最小二乘迭代法求解坐标转换四参数的新方法,只改正系数矩阵中含误差的元素,同时使系数矩阵中不同位置的相同元素具有相同改正数,理论上更严谨。设计了平面四参数模型坐标转换实验数据,通过与经典最小二乘、整体最小二乘、混合整体最小二乘3种方法结果对比,验证了新方法的可行性且解算结果更优。     

Induced earthquakes and house prices: the role of spatiotemporal and global effects

Journal of Geographical Systems - This paper contributes to the existing literature on the explanation of housing prices. First, our proposed methodology accounts for cross-sectional dependence,...     

Analysis of housing price by means of STAR models with neighbourhood effects: a Bayesian approach

In this paper, we extend the Bayesian methodology introduced by Beamonte et al. (Stat Modelling 8:285–311, 2008) for the estimation and comparison of spatio-temporal autoregressive models (STAR) with neighbourhood effects, providing a more general treatment that uses larger and denser nets for the number of spatial and temporal influential neighbours and continuous distributions for their smoothing weights. This new treatment also reduces the computational time and the RAM necessities of the estimation algorithm in Beamonte et al. (Stat Modelling 8:285–311, 2008). The procedure is illustrated by an application to the Zaragoza (Spain) real estate market, improving the goodness of fit and the outsampling behaviour of the model thanks to a more flexible estimation of the neighbourhood parameters.     

The Basic Formal Ontology as a Reference Framework for Modeling the Evolution of Administrative Units

In information systems, ontologies promise advantages such as enhanced interoperability, knowledge sharing, and integration of data sources. In this article, we show that the upper ontology Basic Formal Ontology can facilitate the modeling of an evolution of administrative units. This is demonstrated by creating a spatiotemporal ontology for the administrative units of Switzerland. The ontology tackles the problem that the geometric data is typically captured by taking snapshots at regular intervals while the thematic data is continually updated. The ontology presented merges time‐stamped geometries with a formally described history of administrative units, allowing for complex spatiotemporal queries neither standard approach would support. The resulting populated knowledge base was evaluated against a set of spatiotemporal test queries. The evaluation showed that this knowledge base supports a wide range of queries on the evolution of the administrative units of Switzerland between 1960 and 2010.     

Evaluation of multisource data for glacier terrain mapping: a neural net approach

Spectrally similar nature of land covers in a glacierized terrain hampers their automated mapping from multispectral satellite data, which may be overcome by using multisource data. In the present study, an artificial neural network (ANN)-based information extraction approach was applied for mapping the Kolahoi glacier and adjoining areas, using Landsat TM (Thematic Mapper) data and several ancillary layers such as image transformations and topographic attributes. Results reveal that ANN (highest overall accuracy (OA): 83.74%) outperforms maximum likelihood classifier (highest OA: 66.90%) and the incorporation of ancillary data into the classification process significantly enhances the mapping accuracy (>9%), particularly the addition of Near Infrared Red/Short Wave Infrared (NIR/SWIR) data to the spectral data. A nine-band combination dataset (spectral data, slope, Red/NIR and decorrelation stretch) was found to be the best multisource dataset. Results of the Z-tests (at 95% confidence level) also corroborate and statistically validate the above findings.     

ParSymG: a parallel clustering approach for unsupervised classification of remotely sensed imagery

ABSTRACT

Symmetry is a common feature in the real world. It may be used to improve a classification by using the point symmetry-based distance as a measure of clustering. However, it is time consuming to calculate the point symmetry-based distance. Although an efficient parallel point symmetry-based K-means algorithm (ParSym) has been propsed to overcome this limitation, ParSym may get stuck in sub-optimal solutions due to the K-means technique it used. In this study, we proposed a novel parallel point symmetry-based genetic clustering (ParSymG) algorithm for unsupervised classification. The genetic algorithm was introduced to overcome the sub-optimization problem caused by inappropriate selection of initial centroids in ParSym. A message passing interface (MPI) was used to implement the distributed master–slave paradigm. To make the algorithm more time-efficient, a three-phase speedup strategy was adopted for population initialization, image partition, and kd-tree structure-based nearest neighbor searching. The advantages of ParSymG over existing ParSym and parallel K-means (PKM) alogithms were demonstrated through case studies using three different types of remotely sensed images. Results in speedup and time gain proved the excellent scalability of the ParSymG algorithm.     

Spatial prediction of rainfall-induced shallow landslides using hybrid integration approach of Least-Squares Support Vector Machines and differential evolution optimization: a case study in Central Vietnam

This study represents a hybrid intelligence approach based on the differential evolution optimization and Least-Squares Support Vector Machines for shallow landslide prediction, named as DE–LSSVM_SLP. The LSSVM is used to establish a landslide prediction model whereas the DE is adopted to search the optimal tuning parameters of the LSSVM model. In this research, a GIS database with 129 historical landslide records in the Quy Hop area (Central Vietnam) has been collected to establish the hybrid model. The receiver operating characteristic (ROC) curve and area under the curve (AUC) were used to assess the performance of the newly constructed model. Experimental results show that the proposed model has high performances with approximately 82% of AUCs on both training and validating datasets. The model’s results were compared with those obtained from other methods, Support Vector Machines, Multilayer Perceptron Neural Networks, and J48 Decision Trees. The result comparison demonstrates that the DE–LSSVM_SLP deems best suited for the dataset at hand; therefore, the proposed model can be a promising tool for spatial prediction of rainfall-induced shallow landslides for the study area.     

高轨无缝面阵扫描判断方法：栅格法和几何相交法

极轨海洋卫星的时间分辨率低,不能及时感知快速变化的海洋现象及海洋突发事件,因此,发展静止轨道海洋成像辐射计势在必行。静止轨道卫星可以长时间观测指定海域,但是视场小,需要通过二维指向镜等方式扩大卫星的观测区域。本文意在通过提出漏扫判断方法,给出合理的扫描方式,保证高轨面阵扫描无地理信息遗漏。首先,本文在分析二维指向镜成像原理的基础上,给出了指向镜子图像成像特性以及不同方向、大小的电机转角所引入的像面旋转。其次,画出了子图像的边界包络图,直观地给出了扫描角度变化与图像覆盖程度的关系。最后,提出了两种无缝拼接的判断方法:栅格法和几何相交法,栅格法能够判断出图像覆盖次数,几何法速度快、准确度高。实验结果表明应用本文的两种方法得到了不同扫描角度间隔下地球边缘有无漏扫的情况,找到基于本文光学系统、可覆盖全球且无缝拼接图像的最大俯仰、方位转角间隔,为电机转角步距的设置提供理论依据,保证不漏扫的同时提高载荷的时间分辨率。     

Near real-time characterisation of urban environments: a holistic approach for monitoring dengue fever risk areas

Despite frequent use of digital devices in everyday life, cost-effective measurement of public health issues in urban areas is still challenging. This study was, therefore, planned to extract land-use types using object-based and spatial metric approaches to explore the dengue incidence in relation to the surrounding environment in near real-time using Google and Advanced Land Observation Satellite images. The characterised image showed useful classification of an urban area with 77% accuracy and 0.68 kappa. Geospatial analysis on public health data indicated that most of the dengue cases were found in densely populated areas surrounded by dense vegetation. People living in independent houses having sparsely vegetated surroundings were found to be less vulnerable. Disease incidence was more prevalent in people of 5–24 years of age (67%); while in terms of occupation, mostly students, the unemployed, labourers and farmers (88%) were affected. In general, males were affected slightly more (10%) than females. Proximity analyses indicated that most of the dengue cases were around institutions (40%), religious places (18%) and markets (15%). Thus, usage of Digital Earth scalable tools for monitoring health issues would open new ways for maintaining a healthy and sustainable society in the years ahead.     

A novel approach to leveraging social media for rapid flood mapping: a case study of the 2015 South Carolina floods

Rapid flood mapping is critical for local authorities and emergency responders to identify areas in need of immediate attention. However, traditional data collection practices such as remote sensing and field surveying often fail to offer timely information during or right after a flooding event. Social media such as Twitter have emerged as a new data source for disaster management and flood mapping. Using the 2015 South Carolina floods as the study case, this paper introduces a novel approach to mapping the flood in near real time by leveraging Twitter data in geospatial processes. Specifically, in this study, we first analyzed the spatiotemporal patterns of flood-related tweets using quantitative methods to better understand how Twitter activity is related to flood phenomena. Then, a kernel-based flood mapping model was developed to map the flooding possibility for the study area based on the water height points derived from tweets and stream gauges. The identified patterns of Twitter activity were used to assign the weights of flood model parameters. The feasibility and accuracy of the model was evaluated by comparing the model output with official inundation maps. Results show that the proposed approach could provide a consistent and comparable estimation of the flood situation in near real time, which is essential for improving the situational awareness during a flooding event to support decision-making.