Another approach to reliability measures for systems with correlated observations

An approach to internal reliability analysis is presented which, compared to existing approaches, offers further insight into the system responses to observation gross errors. The proposed reliability measures are defined on the diagonal and non-diagonal elements of the modified reliability matrix being an oblique projector. It maps the observations into the least squares residuals, both expressed as multiples of the a priori standard deviations of the observations. The system responses to a single gross error, such as the local, the quasi-global or the global response, are discussed and their consistency with non-correlation case is proved. Also, the reliability criteria interpretable in terms of those responses are proposed. They enable one to evaluate the observation systems with correlated and uncorrelated observations with respect to internal reliability. An attempt is also made to relate the global responses to reliability numbers that are the basis for determining the magnitude of the minimal detectable bias. Some differences of the new reliability measures in relation to existing measures are indicated. A numerical example is provided, showing the reliability analysis for a simulated horizontal network (distances, angles and GPS vectors), with given covariance matrix for GPS-vector components. In addition, a reliability analysis is presented for a simple leveling network being a study case for other authors referred to in this paper.     

Terrestrial laser scanner self-calibration: Correlation sources and their mitigation

Instrument calibration is recognised as an important process to assure the quality of data captured with a terrestrial laser scanner. While the self-calibration approach can provide optimal estimates of systematic error parameters without the need for specialised equipment or facilities, its success is somewhat hindered by high correlations between model variables. This paper presents the findings of a detailed study into the sources of correlation in terrestrial laser scanner self-calibration for a basic additional parameter set. Several pertinent outcomes, resulting from experiments conducted with simulated data, and 12 real calibration datasets captured with a Faro 880 terrestrial laser scanner, are presented. First, it is demonstrated that panoramic-type scanner self-calibration from only two instrument locations is possible so long as the scans have orthogonal orientation in the horizontal plane. Second, the importance of including scanner tilt angle observations in the adjustment for parameter de-correlation is demonstrated. Third, a new network measure featuring an asymmetric distribution of object points that does not rely upon a priori observation of the instrument position is proposed. It is shown to be an effective means to reduce the correlation between the rangefinder offset and the scanner position parameters. Fourth, the roles of several other influencing variables on parameter correlation are revealed. The paper concludes with a set of recommended design measures to reduce parameter correlation in terrestrial laser scanner self-calibration.     

Measuring differential access to facilities between population groups using spatial Lorenz curves and related indices

Access to certain types of facilities can promote health and well‐being. When population and facilities are not uniformly distributed across the landscape, inequities in accessibility may occur. Current research into GIS‐based accessibility measures has focused primarily on spatial inequities between different geographic locations but not directly on differences in accessibility between subgroups of the population. The research presented here develops a new method for measuring differential accessibility to facilities between various segments of the population. The method extends concepts and techniques in spatial point pattern analysis that account for the spatial structure of demand and its relationship to supply. In this approach, the traditional Lorenz curve and its associated indices, the Gini coefficient and the dissimilarity index, which are used to measure inequality, are recast in spatial terms for measuring differences in accessibility between population subgroups. An analysis of spatial accessibility to grocery stores in Akron, OH illustrates the value of the spatial Lorenz curve and its associated indices compared to other methods.     

基于QR分解的Ⅱ类病态性诊断

为了对现代测绘数据处理中参数估计系统的Ⅱ类病态性[1]进行诊断,利用观测结构分析方法解决了观测有效性的分析问题.通过对观测矩阵的QR分解,将观测结构的分析过渡到对R矩阵的分析,提出了相对体积法,方法几何意义明确.算例表明,该方法能够准确度量参数估计系统的Ⅱ类病态性程度,是一种对Ⅱ类病态性进行定量诊断的新方法.     

Comparison of vegetation indices for practicable homology

Vegetation indices are widely used to assess quantitatively the biophysical characteristics of vegetation from remote sensing measurements. Different indices have their own advantages in retrieving vegetation information. It is very difficult to precisely attribute any vegetation index to any particular vegetation biophysical parameter. This study examines the correlations among different vegetation indices derived from a set of mustard, gram and wheat fields at three different phenological growth stages. The results are presented as correlation matrices along with correlation scatter plots. Homologous (equi-magnitude) vegetation information is represented by NDVI, PVI and AtRVI for wheat crop with leaf area index less than 1.     

Robust Kalman filtering based on Mahalanobis distance as outlier judging criterion

A robust Kalman filter scheme is proposed to resist the influence of the outliers in the observations. Two kinds of observation error are studied, i.e., the outliers in the actual observations and the heavy-tailed distribution of the observation noise. Either of the two kinds of errors can seriously degrade the performance of the standard Kalman filter. In the proposed method, a judging index is defined as the square of the Mahalanobis distance from the observation to its prediction. By assuming that the observation is Gaussian distributed with the mean and covariance being the observation prediction and its associate covariance, the judging index should be Chi-square distributed with the dimension of the observation vector as the degree of freedom. Hypothesis test is performed to the actual observation by treating the above Gaussian distribution as the null hypothesis and the judging index as the test statistic. If the null hypothesis should be rejected, it is concluded that outliers exist in the observations. In the presence of outliers scaling factors can be introduced to rescale the covariance of the observation noise or of the innovation vector, both resulting in a decreased filter gain. And the scaling factors can be solved using the Newton’s iterative method or in an analytical manner. The harmful influence of either of the two kinds of errors can be effectively resisted in the proposed method, so robustness can be achieved. Moreover, as the number of iterations needed in the iterative method may be rather large, the analytically calculated scaling factor should be preferred.     

Effects of granulometric and mineralogical composition on spectral reflectance of soils in a Sahelian area

During the Hapex-Sahel international investigation, portable radiometers (Barringer and Cimel) were used to study, in the optical domain, the relationship between soil mineralogical and granulometric compositions and radiometric indices: redness index, colour index and texture index. The results show that the granulometric distribution and the mineralogical composition have both important influence on these indices.In this Sahelian area, for soils having more than 1% of hematite, the redness index presents a high correlation with hematite content. For soils with less than 1% of hematite, the redness index depends on the size of the particles and their distribution at the surface.For eolian sandy and ferricrust soils, the colour and texture indices present good correlations, respectively, with iron oxide and kaolinite content. No such correlation is observed for ferruginous soils because of the complex interactions existing between iron oxides, kaolinite and the size of particles.     

鲁棒多特征谱聚类的高光谱影像波段选择

传统谱聚类的高光谱影像波段选择模型中,采用的波段相似矩阵受到噪声或异常值的影响且仅能表征波段的单一相似特征,导致波段子集的选取结果受到限制.本文从波段选择的目的 出发,提出鲁棒多特征谱聚类方法,整合多个特征的波段相似矩阵来形成综合相似矩阵以解决上述问题.该方法假设4种相似性度量包括光谱信息散度、光谱角度距离、波段相关性...     

A new metric for measuring structure-preserving capability of despeckling of SAR images

In this paper, a new metric called despeckling structure loss (DSL) is proposed for performance assessment of despeckling algorithms with a focus on the preservation of structural features such as edges and textures. The ratio image of a synthetic aperture radar (SAR) image to its despeckled result can clearly indicate the loss of structural features caused by the despeckling process. By taking into account characteristics of the best and worst structure preservation in despeckling, the DSL metric examines the presence of structural features in ratio images by using local correlations between the ratio image and the noise-free reference image at edge points. The DSL is shown to be a monotonic function of structure loss bounded between the best and worst cases, leading an objective and quantitative measure of the structure-preserving capability of despeckling algorithms. Experimental evaluations of the proposed metric have been carried out on simulated SAR images including one generated by SAR raw signal simulator. Despeckled results using five typical algorithms clearly demonstrate the efficiency of the DSL metric. In comparison, the commonly used despeckling metrics including the signal-to-mean-square error ratio, the edge correlation index, the Pratt’s figure of merit, the structural similarity and the equivalent number of looks of ratio images, fail to keep a consistency with the structure loss shown in despeckled results as well as ratio images.     

一种相关观测的Partial EIV模型求解方法

Partial errors-in-variables(Partial-EIV)模型作为EIV模型的扩展形式,其构造方式更有规律,解算方法更为简便,能有效应用于实际情况。针对已有Partial EIV模型方法未考虑观测向量和系数矩阵存在相关性这一情况,通过提取观测向量和系数矩阵组成的增广矩阵中非重复出现的随机元素,构建更具一般适用性的Partial EIV模型,在该模型的基础上,将特殊假定条件扩展到不限定观测数据相关性的一般情况,详细推导了观测向量和系数矩阵元素相关且不等精度情况下的加权总体最小二乘方法,通过算例试验,并与目前已有的解决EIV模型相关观测情况下的方法进行了比较分析,研究表明本文方法可以提高计算效率,更具一般性,特别是对于观测向量和系数矩阵中存在常数元素和重复元素的情况。     

基于变量投影的结构总体最小二乘算法

测绘领域诸多实际应用中系数矩阵和观测向量具有结构特征,即系数矩阵和观测向量中包含固定量(甚至固定列)和随机量,并且不同位置的随机量线性相关。针对这个问题,从变量误差(errors-in-variables,EIV)函数模型出发,首先,将系数矩阵和观测向量构成的增广矩阵表示为仿射函数形式,并采用变量投影法对函数模型进行重构;然后,利用拉格朗日法推导出了一种结构总体最小二乘(structured total least squares,STLS)估计算法。算例分析结果表明,该算法与已有能够解决系数矩阵和观测向量存在结构特征的加权或结构总体最小二乘算法估计结果一致,说明了该算法的有效性,同时阐明了该算法与已有相关算法的关系。     

基于矩阵相似度的InSAR图像配准方法研究

图像配准是干涉合成孔径雷达成像的关键技术之一,相关系数是InSAR图像配准的重要指标。本文在分析研究常见相似性度量的基础上,研究了相关系数与矩阵相似度度量之间的关系,研究发现,矩阵相似度度量可涵盖多种图像配准数值指标,且其表达形式精炼,几何意义明确,便于把握图像配准的机理。此外,本文提出了一种加权矩阵相似度度量,并通过仿真数据进行了验证。     

On agricultural drought monitoring in Australia using Himawari-8 geostationary thermal infrared observations

Monitoring agricultural drought effectively and timely is important to support drought management and food security. Effective drought monitoring requires a suite of drought indices to capture the evolution process of drought. Thermal infrared signals respond rapidly to vegetation water stress, thus being regarded useful for drought monitoring at the early stage. Several temperature-based drought indices have been developed considering the role of land surface temperature (LST) in surface energy and water balance. Here, we compared the recently proposed Temperature Rise Index (TRI) with several agricultural drought indices that also use thermal infrared observations, including Temperature Condition Index (TCI), Vegetation Health Index (VHI) and satellite-derived evapotranspiration ratio anomaly (Δf_RET) for a better understanding of these thermal infrared drought indices. To do so, we developed a new method for calculating TRI directly from the top-of-atmosphere brightness temperatures in the two split-window channels (centered around ∼11 and 12 μm) rather than from LST. TRI calculated using the Himawari-8 brightness temperatures (TRI_BT) and LST retrievals (TRI_LST), along with the other LST-based indices, were calculated for the growing season (July–October) of 2015−2019 over the Australian wheatbelt. An evaluation was conducted by spatiotemporally comparing the indices with the drought indices used by the Australian Bureau of Meteorology in the official drought reports: the Precipitation Condition Index (PCI) and the Soil Moisture Condition Index (SMCI). All the LST-based drought indices captured the wet conditions in 2016 and dry conditions in 2019 clearly. Ranking of Pearson correlations of the LST-based indices with regards to PCI and SMCI produced very similar results. TRI_BT and TRI_LST showed the best agreement with PCI and SMCI (r > 0.4). TCI and VHI presented lower consistency with PCI and SMCI compared with TRI_BT and TRI_LST. Δf_RET had weaker correlations than the other LST-based indices in this case study, possibly because of outliers affecting the scaling procedure. The capability of drought early warning for TRI was demonstrated by comparing with the monthly time series of the greenness index Vegetation Condition Index (VCI) in a case study of 2018 considering the relatively slow response of the greenness index to drought. TRI_BT and TRI_LST had a lead of one month in showing the changing dryness conditions compared with VCI. In addition, the LST-based indices were correlated with annual wheat yield. Compared to wheat yields, all LST-based indices had a peak correlation in September. TRI_BT and TRI_LST had strong peak and average correlations with wheat yield (r ≥ 0.8). We conclude that TRI has promise for agricultural drought early warning, and TRI_BT appears to be a good candidate for efficient operational drought early warning given the readily accessible inputs and simple calculation approach.     

On the degree correlation of urban road networks

Recent advances in network science and the development of volunteered geographic information (VGI) have created new research opportunities in the topological analysis of road networks. The degree correlation of road networks is rarely studied. This study applied four measures, including the average degree of nearest neighbor, correlation profile, Newman's assortativity coefficient, and Litvak–Hofstad's assortativity coefficient, to measure the degree correlations of road networks represented as dual graphs of strokes, axial lines, and named roads. After investigating 100 road networks worldwide obtained from OpenStreetMap, it has been found that road networks are mostly disassortative or uncorrelated in stroke and named road representations, but assortative when represented as axial lines. Inconsistency in different measures persists regardless of method of representation; therefore, qualitative dichotomy or trichotomy is insufficient to describe the actual connection pattern in road networks. A taxonomy of road network assortativity is proposed. Two of the proposed disassortative types are associated with the absence of a grid pattern and are less robust than the typical disassortative type.     

A priori fully populated covariance matrices in least-squares adjustment—case study: GPS relative positioning

In this contribution, using the example of the Mátern covariance matrices, we study systematically the effect of apriori fully populated variance covariance matrices (VCM) in the Gauss–Markov model, by varying both the smoothness and the correlation length of the covariance function. Based on simulations where we consider a GPS relative positioning scenario with double differences, the true VCM is exactly known. Thus, an accurate study of parameters deviations with respect to the correlation structure is possible. By means of the mean-square error difference of the estimates obtained with the correct and the assumed VCM, the loss of efficiency when the correlation structure is missspecified is considered. The bias of the variance of unit weight is moreover analysed. By acting independently on the correlation length, the smoothness, the batch length, the noise level, or the design matrix, simulations allow to draw conclusions on the influence of these different factors on the least-squares results. Thanks to an adapted version of the Kermarrec–Schön model, fully populated VCM for GPS phase observations are computed where different correlation factors are resumed in a global covariance model with an elevation dependent weighting. Based on the data of the EPN network, two studies for different baseline lengths validate the conclusions of the simulations on the influence of the Mátern covariance parameters. A precise insight into the impact of apriori correlation structures when the VCM is entirely unknown highlights that both the correlation length and the smoothness defined in the Mátern model are important to get a lower loss of efficiency as well as a better estimation of the variance of unit weight. Consecutively, correlations, if present, should not be neglected for accurate test statistics. Therefore, a proposal is made to determine a mean value of the correlation structure based on a rough estimation of the Mátern parameters via maximum likelihood estimation for some chosen time series of observations. Variations around these mean values show to have little impact on the least-squares results. At the estimates level, the effect of varying the parameters of the fully populated VCM around these approximated values was confirmed to be nearly negligible (i.e. a mm level for strong correlations and a submm level otherwise).     

Orthogonality defect and reduced search-space size for solving integer least-squares problems

In the context of ambiguity resolution (AR) of global navigation satellite systems (GNSS), decorrelation among entries of an ambiguity vector, integer ambiguity search, and ambiguity validations are three standard procedures for solving integer least-squares problems. This paper contributes to AR issues from three aspects. Firstly, the orthogonality defect is introduced as a new measure of the performance of ambiguity decorrelation methods and compared with the decorrelation number and with the condition number, which are currently used as the judging criterion to measure the correlation of ambiguity variance–covariance matrix. Numerically, the orthogonality defect demonstrates slightly better performance as a measure of the correlation between decorrelation impact and computational efficiency than the condition number measure. Secondly, the paper examines the relationship of the decorrelation number, the condition number, the orthogonality defect, and the size of the ambiguity search space with the ambiguity search candidates and search nodes. The size of the ambiguity search space can be properly estimated if the ambiguity matrix is decorrelated well, which is shown to be a significant parameter in the ambiguity search progress. Thirdly, a new ambiguity resolution scheme is proposed to improve ambiguity search efficiency through the control of the size of the ambiguity search space. The new AR scheme combines the LAMBDA search and validation procedures together, which results in a much smaller size of the search space and higher computational efficiency while retaining the same AR validation outcomes. In fact, the new scheme can deal with the case there are only one candidate, while the existing search methods require at least two candidates. If there are more than one candidate, the new scheme turns to the usual ratio-test procedure. Experimental results indicate that this combined method can indeed improve ambiguity search efficiency for both the single constellation and dual constellations, respectively, showing the potential for processing high-dimension integer parameters in multi-GNSS environment.     

遥感数据自动分类中应用辅助数据的原理

本文从目视解译信息空间的模拟、模式维数对模式样本集线性可分性的影响、模式空间各模式类别可分性测度OIF指数及迹准则判断原理等模式识别原理出发,初步讨论了在遥感影象自动分类中利用辅助数据的理论依据,并以藏北西扎地区草资源调查中利用辅助数据进行自动分类的实例说明辅助数据提高自动分类精度的有效性。     

一种提取北部湾沿海地区水体信息的动态阈值方法

准确地获取水体分布信息与水体变化规律在流域综合治理等方面具有重要意义。本文基于高分六号(GF-6)影像与Landsat 8影像,选取北部湾海域作为测试研究区,在海洋水体指数(OWI)基础上,针对水体光谱特性,分析了水体像元OWI与归一化植被指数之间的相关性,基于两种指数动态平衡,提出了一个稳定性较高的动态阈值的水体提取方法,并进行了试验验证。试验结果表明,动态阈值方法能够稳定、准确地提取水体信息,避免了人为设定阈值存在的误差,并且本文提出的指数无论是针对国产高分影像还是其他光学影像,都具有较好的普适性,可应用于沿海海岸线的监测等方面。     

空间数据模糊聚类的有效性评价

基于模糊划分中存在的分类不确定性因素和空间数据的空间位置特征,提出了一种新的空间数据模糊聚类有效性函数。实验结果表明,这种新的有效性函数能够对模糊聚类结果的有效性进行正确的评价,特别是对于空间数据模糊聚类有效性评价,其分类效果较理想,同其他有效性指标相比,能得到较优的分类数。