Positional accuracy improvement: a comparative study in Shanghai,China

With the rapid development of geospatial data capture technologies such as the Global Positioning System, more and higher accuracy data are now readily available to upgrade existing spatial datasets having lower accuracy using positional accuracy improvement (PAI) methods. Such methods may not achieve survey-accurate spatial datasets but can contribute to significant improvements in positional accuracy in a cost-effective manner. This article addresses a comparative study on PAI methods with applications to improve the spatial accuracy of the digital cadastral for Shanghai. Four critical issues are investigated: (1) the choice of improvement model in PAI adjustment; five PAI models are presented, namely the translation, scale and translation, similarity, affine, and second-order polynomial models; (2) the choice of estimation method in PAI adjustment; three estimation methods in PAI adjustment are proposed, namely the classical least squares (LS) adjustment, which assumes that only the observation vector contains error, the general least squares (GLS) adjustment, which regards both the ground and map coordinates of control points as observations with errors, and the total least squares (TLS) adjustment, which takes the errors in both the observation vector and the design matrix into account; (3) the impact of the configuration of ground control points (GCPs) on the result of PAI adjustment; 12 scenarios of GCP configurations are tested, including different numbers and distributions of GCPs; and (4) the deformation of geometric shape by the above-mentioned transformation models is presented in terms of area and perimeter.

The empirical experiment results for six test blocks in Shanghai demonstrated the following. (1) The translation model hardly improves the positional accuracy because it accounts only for the shift error within digital datasets. The other four models (i.e., the scale and translation, similarity, affine, and second-order polynomial models) significantly improve the positional accuracy, which is assessed at checkpoints (CKPs) by calculating the difference between the updated coordinates transformed from the map coordinates and the surveyed coordinates. On the basis of the refined Akaike information criterion, the two best optimal transformation models for PAI are determined as the scale and translation and affine transformation models. (2) The weighted sum of square errors obtained using the GLS and TLS methods are much less than those obtained using the classical least squares method. The result indicates that both the GLS and TLS estimation methods can achieve greater reliability and accuracy in PAI adjustment. (3) The configuration of GCPs has a considerable effect on the result of PAI adjustment. Thus, an optimal configuration scheme of GCPs is determined to obtain the highest positional accuracy in the study area. (4) Compared with the deformations of geometric shapes caused by the transformation models, the scale and translation model is found to be the best model for the study area.     

A TEST OF SIGNIFICANCE FOR PARTIAL LEAST SQUARES REGRESSION

Partial least squares (PLS) regression is a commonly used statistical technique for performingmultivariate calibration, especially in situations where there are more variables than samples. Choosingthe number of factors to include in a model is a decision that all users of PLS must make, but iscomplicated by the large number of empirical tests available. In most instances predictive ability is themost desired property of a PLS model and so interest has centred on making this choice based on aninternal validation process. A popular approach is the calculation of a cross-validated r~2 to gauge howmuch variance in the dependent variable can be explained from leave-one-out predictions. Using MonteCarlo simulations for different sizes of data set, the influence of chance effects on the cross-validationprocess is investigated. The results are presented as tables of critical values which are compared againstthe values of cross-validated r~2 obtained from the user's own data set. This gives a formal test forpredictive ability of a PLS model with a given number of dimensions.     

地理数据线性回归中的稳健估计方法

在线性回归中，常用最小二乘估计求线性方程的回归系数。但最小二乘估计受异常值影响较大，当样本数据存在异常值时，估计出的回归系数会产生较大偏差。稳健估计是最小二乘估计的改进，能在不排除异常数据的情况下，达到减弱异常数据对结果的影响。利用稳健估计提出黄土地区沟谷密度与侵蚀量的回归方程，并和最小二乘估计得到的回归方程比较，前者具有更回归效果。     

A ROBUST PLS PROCEDURE

A robust partial least squares(PLS)regression algorithm is developed.This is achieved by substitutionof the univariate regression steps in the iterative PLS2 algorithm by a robust alternative.The anglebetween loading vectors from both perturbed and unperturbed solutions is used as a measure ofrobustness.By means of a perturbation study on a structure-activity data set,it is demonstrated thatthe stability of the robust method is superior to standard PLS.     

THE KERNEL ALGORITHM FOR PLS

A fast and memory-saving PLS regression algorithm for matrices with large numbers of objects ispresented.It is called the kernel algorithm for PLS.Long(meaning having many objects,N)matricesX (N×K)and Y(N×M)are condensed into a small(K×K)square‘kernel’matrix X~TYY~TX of sizeequal to the number of X-variables.Using this kernel matrix X~TYY~TX together with the small covariancematrices X~TX(K×K),X~TY(K×M)and Y~TY(M×M),it is possible to estimate all necessaryparameters for a complete PLS regression solution with some statistical diagnostics.The newdevelopments are presented in equation form.A comparison of consumed floating point operations isgiven for the kernel and the classical PLS algorithm.As appendices,a condensed matrix algebra versionof the kernel algorithm is given together with the MATLAB code.     

基于动态因子的区域生态安全评价——以河北省万全县为例

本文以河北省万全县为例, 探索在GIS 和RS 技术支持下进行区域生态安全综合评价的 方法。数据包括1992 年8 月的TM影像、2002 年8 月的ETM+和SPOT 影像、1∶5 万DEM等; 选取 植被指数变化、土地利用类型变化和土壤有机质含量变化三类动态评价因子; 采用综合指数法构 建了基于生态退化的动态评价模型; 应用最小二乘原理客观地计算出了模型中各指标的权重; 并最终在ArcGIS 9.0/Spatial Analyst 模块中生成了生态安全评价图, 使模型得以实现。结果表明 该县南部河川区生态安全要优于中部丘陵区和北部山区; 相对不安全区域占到全县总面积的 50.1%, 虽然不安全区域总体分布较为散落, 但在北部和中部相对集中; 总体生态安全评价值为 2.3, 标志着本地区的生态安全级别较低, 应引起当地政府的高度重视。另外, 采用动态评价因子, 比采用静态评价因子具有一定优势; 采用最小二乘原理计算模型中权重系数的方法比较实用和 科学, 降低了人为影响因素, 也可以避免主观判断产生的错误, 为评价模型中权重系数的确定提 供了一种新的方法和选择。     

Estimation of pH optima and tolerances of diatoms in lake sediments by the methods of weighted averaging,least squares and maximum likelihood,and their use for the prediction of lake acidity

Ecological optima and tolerances with respect to autumn pH were estimated for 63 diatom taxa in 47 Finnish lakes. The methods used were weighted averaging (WA), least squares (LS) and maximum likelihood (ML), the two latter methods assuming the Gaussian response model.WA produces optimum estimates which are necessarily within the observed lake pH range, whereas there is no such restriction in ML and LS. When the most extreme estimates of ML and LS were excluded, a reasonably close agreement among the results of different estimation methods was observed. When the species with unrealistic optima were excluded, the tolerance estimates were also rather similar, although the ML estimates were systematically greater.The parameter estimates were used to predict the autumn pH of 34 other lakes by weighted averaging. The ML and LS estimates including the extreme optima produced inferior predictions. A good prediction was obtained, however, when prediction with these estimates was additionally scaled with inverse squared tolerances, or when the extreme values were removed (censored). Tolerance downweighting was perhaps more efficient, and when it was used, no additional improvement was gained by censoring. The WA estimates produced good predictions without any manipulations, but these predictions tended to be biased towards the centroid of the observed range of pH values.At best, the average bias in prediction, as measured by mean difference between predicted and observed pH, was 0.082 pH units and the standard deviation of the differences, measuring the average random prediction error, was 0.256 pH units.     

A new methodology for measuring coastline recession using buffering and non‐linear least squares estimation

Coastline recession is one of the best indicators of coastal erosion. Three methods for computing coastline recession – the baseline approach, the dynamic segmentation approach and the area‐based approach – have been used, each of which has one or more drawbacks. To overcome these problems, a new methodology for measuring coastline recession is proposed, using buffering and non‐linear least squares estimation. The proposed method was compared with the three existing methods with respect to two simulated cases and two real coastlines. Test results confirmed that the new method is more reliable than the three other methods, all of which are susceptible to variability of recession, scale, number of line segments, length of coastlines and direction of the baseline. The proposed method, incorporating two physically meaningful values – magnitude and variability of coastline recession according to the mean and standard deviation of coastline offsets, respectively – presents itself as an effective alternative method of assessing coastline recession.     

THE PERFORMANCE OF LEAST SQUARES AND ROBUST REGRESSION IN THE CALIBRATION OF ANALYTICAL METHODS UNDER NON-NORMAL NOISE DISTRIBUTIONS

By means of Monte Carlo simulations a comparison has been made between ordinary least squaresregression and robust regression. The robust regression procedure is based on the Huber estimate and iscomputed by means of the iteratively reweighted least squares algorithm. The performance of bothprocedures has been evaluated for estimation of the parameters of a calibration function and fordetermination of the concentration of unknown samples. The influence of the distributionalcharacteristics skewness and kurtosis has been studied, and the number of measurements used forconstructing the calibration curve has also been taken into account, Under certain conditions robustregression offers an advantage over least squares regression.     

基于改进植被指数土壤水分遥感反演

以渭-库绿洲为例,基于Landsat8 OLI遥感数据,考虑到短波红外特征与土壤水分有很好的关联,将短波红外波段引入可见光-近红外波段构成的传统植被指数中,旨在建立新的植被指数监测土壤水分。基于改进前后共8种植被指数,通过灰色关联分析（GRA）筛选出3种高关联度植被指数,再用偏最小二乘回归（PLSR）进行建模,然后用该模型对研究区土壤水分反演,并对其空间分布格局进一步分析。结果显示：（1）在传统植被指数的基础上引入信息量较大的短波红外,可大幅度降低植被指数间的VIF,消除其多重共线性。（2）通过GRA分析可知,改进后的植被指数与土壤水分之间的关联度均要高于传统植被指数。（3）通过GRA分析筛选出3种高关联度植被指数建立得到精度较高,稳定性较好的PLSR模型,并反演研究区土壤水分分布状况,土壤水分总体上至西向东,由北到南降低,然而土壤水分最小值主要分布在绿洲—荒漠交错带,使得交错带成为“生态裂谷”。研究表明：将短波红外波段引入到可见光-近红外植被指数中,建立的新植被指数可获得较好的土壤水分空间分布反演结果。     

Responses of aboveground biomass of alpine grasslands to climate changes on the Qinghai-Tibet Plateau

Aboveground biomass in grasslands of the Qinghai-Tibet Plateau has displayed an overall increasing trend during 2003-2016, which is profoundly influenced by climate change. However, the responses of different biomes show large discrepancies, in both size and magnitude. By applying partial least squares regression, we calculated the correlation between peak aboveground biomass and mean monthly temperature and monthly total precipitation in the preceding 12 months for three different grassland types (alpine steppe, alpine meadow, and temperate steppe) on the central and eastern Qinghai-Tibet Plateau. The results showed that mean temperature in most preceding months was positively correlated with peak aboveground biomass of alpine meadow and alpine steppe, while mean temperature in the preceding October and February to June was significantly negatively correlated with peak aboveground biomass of temperate steppe. Precipitation in all months had a promoting effect on biomass of alpine meadow, but its correlations with biomass of alpine steppe and temperate steppe were inconsistent. It is worth noting that, in a warmer, wetter climate, peak aboveground biomass of alpine meadow would increase more than that of alpine steppe, while that of temperate steppe would decrease significantly, providing support for the hypothesis of conservative growth strategies by vegetation in stressed ecosystems.     

火焰原子吸收法测定和计算误差的减小

通过对火焰原子吸收法样品分析误差产生的各主要环节的分析和实验的验证 ,指出在盐湖资源开发过程产生的混合样品分析中 ,样品稀释倍数、光谱干扰、电离干扰和计算方法是影响结果准确性的主要因素 ,进一步提出了减小误差的办法 ,并给出了用Excel处理数据的示例表格和相应的VBA程序代码。     

Seamless multivariate affine error-in-variables transformation and its application to map rectification

Affine transformation that allows the axis-specific rotations and scalars to capture the more transformation details has been extensively applied in a variety of geospatial fields. In tradition, the computation of affine parameters and the transformation of non-common points are individually implemented, in which the coordinate errors only of the target system are taken into account although the coordinates in both target and source systems are inevitably contaminated by random errors. In this article, we propose the seamless affine error-in-variables (EIV) transformation model that computes the affine parameters and transforms the non-common points simultaneously, importantly taking into account the errors of all coordinates in both datum systems. Since the errors in coefficient matrix are involved, the seamless affine EIV model is nonlinear. We then derive its least squares iterative solution based on the Euler–Lagrange minimization method. As a case study, we apply the proposed seamless affine EIV model to the map rectification. The transformation accuracy is improved by up to 40%, compared with the traditional affine method. Naturally, the presented seamless affine EIV model can be applied to any application where the transformation estimation of points fields in the different systems is involved, for instance, the geodetic datum transformation, the remote sensing image matching, and the LiDAR point registration.     

MLR和PLSR的沙壤土盐分含量光谱检测对比研究

为了快速有效检测南疆地区典型土壤（沙壤土）的盐分含量变化,利用光谱仪和电导仪测得南疆阿拉尔市红枣种植区盐渍土近红外高光谱和电导率数据,基于7种不同光谱预处理方法和2种特征波长选择算法,分别建立多元线性回归（MLR）和偏最小二乘回归（PLSR）的土壤盐分监测模型。结果表明：7种预处理方法中,归一化,多元散射,变量标准化和一阶导数能够有效提高土壤盐分的预测模型精度。基于多元逐步回归（SMR）波长选择方法的多元线性回归（SMLR）模型的R_val²>0.948 9,RPD>6.294 9,RMSEP<0.435 6;基于连续投影算法（SPA）的多元线性回归（SPA-MLR）模型的R_val²>0.956 8,RPD>6.922 1,RMSEP<0.361 6,预测结果要优于偏最小二乘回归（PLSR）模型,其中基于归一化处理后的SMLR和SPA-MLR的预测精度最为理想,分别为R_val²=0.979 2,RPD=9.907 8,RMSEP=0.287 6和R_val²=0.980 5,RPD=10.50,RMSEP=0.278 3,而且筛选的特征波长较少。说明归一化是更有效的光谱预处理方法,多元线性回归（MLR）更适合建立南疆典型沙壤土盐分含量的预测模型。     

SHORT COMMUNICATION PLS FITS CLOSER THAN PCR

PLS1 regression is generally viewed as lying in between PCR and OLS regression.Proof is given thatthe coefficient of determination,R~2,for a PLS multivariate calibration model is at least as high as thatfor a PCR model with the same number of components.It appears that PLS can be linked to acorrelation-weighted polynomial regression of a constant response on the eigenvalues of the covariancematrix of the predictor variables.