An algorithmic approach to the total least-squares problem with linear and quadratic constraints

Proper incorporation of linear and quadratic constraints is critical in estimating parameters from a system of equations. These constraints may be used to avoid a trivial solution, to mitigate biases, to guarantee the stability of the estimation, to impose a certain “natural” structure on the system involved, and to incorporate prior knowledge about the system. The Total Least-Squares (TLS) approach as applied to the Errors-In-Variables (EIV) model is the proper method to treat problems where all the data are affected by random errors. A set of efficient algorithms has been developed previously to solve the TLS problem, and a few procedures have been proposed to treat TLS problems with linear constraints and TLS problems with a quadratic constraint. In this contribution, a new algorithm is presented to solve TLS problems with both linear and quadratic constraints. The new algorithm is developed using the Euler-Lagrange theorem while following an optimization process that minimizes a target function. Two numerical examples are employed to demonstrate the use of the new approach in a geodetic setting.     

基于手机短信自动定位的地震灾情速报系统

基于手机自动定位的地震灾情速报系统是依托目前手机广泛使用于福建省各乡镇、街道以及绝大部分行政村这一有利条件而研制的。在分析地震灾情速报系统工作流程的基础上设计了该系统,并划分系统功能模块。讨论了系统实现中的关键技术,如反距离权重插值、基于ArcGISServer的开发WebGIS系统架构等。最后通过地震事件实例展示了系统的实际应用效果。     

对部分简单形体产生的自然电位进行定量分析

本文提出了一种新的特征点法,并在前人的基础上改进了一种数值计算方法(最小二乘法),以此来确定部分具有自然电位异常简单地质体的形态(形态系数)、埋藏深度、极化角和电偶极矩。特征点法通过剖面上三个特殊点(两个极值点和零电位点)的值以及它们相互间的距离便可快速求取地质体各参数。改进的最小二乘法则是在前人的基础上加入了零电位点的计算及其它处理方法,以此来获得准确性更高的地质体各参数。两种方法都被用来计算加入±5%随机误差的理论模型数据,并在土耳其的一个实际野外数据中得到测试。结果表明所求的参数与实际参数具有较好的一致性。     

Assimilating satellite SST/SSH and in-situ T/S profiles with the Localized Weighted Ensemble Kalman Filter

The Localized Weighted Ensemble Kalman Filter(LWEnKF) is a new nonlinear/non-Gaussian data assimilation(DA) method that can effectively alleviate the filter degradation problem faced by particle filtering, and it has great prospects for applications in geophysical models. In terms of operational applications, along-track sea surface height(AT-SSH), swath sea surface temperature(S-SST) and in-situ temperature and salinity(T/S) profiles are assimilated using the LWEnKF in the northern South China ...     

单位权方差公式的统一推证

本文从二次型的期望公式出发，推导了经典最小二乘平差、最小二乘滤波、最小二乘推估和最小二乘配置的验后单位权方差的估计公式。     

基于偏最小二乘回归的融雪型洪水预报模型

本文采用偏最小二乘回归法对新疆塔什库尔干河流的实测流量资料进行分析,建立了日平均流量的偏最小二乘回归模型,采用建立的模型对2001年日平均流量进行了预报。研究分析表明,结果比较合理,这为融雪型洪水预报提供了一种新的思路和研究方法。     

Drivers of water pollutant discharge in urban agglomerations and their scale effects: Empirical analysis of 305 counties in the Yangtze River Delta

Revealing the drivers and scale effects of water pollutant discharges is an important issue in the study of the environmental consequences during urban agglomeration evolution. It is also a prerequisite for realizing collaborative water pollutant reduction and environmental governance in urban agglomerations. This paper takes 305 counties in the Yangtze River Delta (YRD) as an example and selects chemical oxygen demand (COD) and ammonia nitrogen (NH₃-N) as two distinctive pollutant indicators, using the Spatial Lag Model (SLM) and Spatial Error Model (SEM) to estimate the drivers of water pollutant discharges in 2011 and 2016. Then the Multiscale Geographically Weighted Regression (MGWR) model is constructed to diagnose the scale effect and spatial heterogeneity of the drivers. The findings show that the size of population, the level of urbanization, and the economic development level show global-level increase impacts on water pollutant discharges, while the level of industrialization, social fixed assets investment, foreign direct investment, and local fiscal decentralization are local-level impacts. The spatial heterogeneity of local drivers presents the following characteristics: Social fixed assets investment has a strong promoting effect on both COD and NH₃-N discharges in the Hangzhou-Jiaxing-Huzhou region and the coastal area of the YRD; industrialization has a promoting effect on COD discharges in the Taihu Lake basin and Zhejiang province; foreign direct investment has a local inhibitory effect on NH₃-N discharge, and the pollution halo effect is more prominent in the marginal areas of the YRD such as northern Jiangsu, northern Anhui, and southern Zhejiang; local fiscal decentralization has a noticeable inhibitory effect on COD discharge in the central areas of the YRD, reflecting the positive impacts on improved local environmental awareness and stronger constraints of multilevel environmental regulations in the urban agglomeration. Therefore, it is recommended to guide greener development to reduce the water pollutant discharge; to embed an environmental push-back mechanism in the fields of industrial production, capital investment, and financial income and expenditure; and to establish a high-quality development pattern of urban agglomerations systematically compatible with the carrying capacity of the water environment.     

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A meshless method for axisymmetric problems in continuously nonhomogeneous saturated porous media

A meshless method based on the local Petrov–Galerkin approach is proposed to analyze 3-d axisymmetric problems in porous functionally graded materials. Constitutive equations for porous materials possess a coupling between mechanical displacements for solid and fluid phases. The work is based on the u–u formulation and the incognita fields of the coupled analysis in focus are the solid skeleton displacements and the fluid displacements. Independent spatial discretization is considered for each phase of the model, rendering a more flexible and efficient methodology. Both displacements are approximated by the moving least-squares (MLS) scheme. The paper presents in the first time a general meshless method for the numerical analysis of axisymmetric problems in continuously nonhomogeneous saturated porous media. Numerical results are given for boreholes in continuously nonhomogeneous porous medium with prescribed misfit and exponential variation of material parameters in the excavation zone.     

基于选权迭代法的抗差整体最小二乘及其应用

在测量数据处理中,观测向量与系数矩阵同时存在偶然误差时,整体最小二乘法能够得到更高精度的参数解,但整体最小二乘法无抗差能力,观测向量中的粗差将对参数求解产生较大影响。为解决上述问题,采用拉格朗日极值法推导了基于选权迭代法的抗差整体最小二乘计算公式,通过三维坐标转换参数求解实例对3种选权迭代法进行分析。结果表明,IGG法在抗差整体最小二乘解法中抗差效果最好。