最小二乘拟合GNSS位置时间序列分析

针对GNSS位置时间序列包含的线性趋势及其变化可能干扰后续分析并掩盖动力学因素信息的问题,该文使用最小二乘方法分析时间序列的线性趋势并减弱时间序列中阶跃的影响。分析了最小二乘方法用于GNSS位置时间序列分析的可行性及利用该方法分别获取趋势变化点前后的线性趋势,据此估计时间序列趋势变化的大小进而可以对时间序列进行修复。该方法用于GNSS位置时间序列的初步分析,可以方便有效地去除线性趋势变化对后续时间序列分析的影响,同时拟合结果本身也能反应出时间序列的变化特征。     

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加权最小二乘法与AR组合模型在极移预测中的应用研究

分析了极移预测的重要性,介绍了目前极移预测的主要方法.根据目前常用预测模型中周年项和钱德勒项的时变性质,在极移预测方法上进行了一种新的尝试,即利用加权最小二乘法与AR组合模型对极移进行预测.为进一步优选模型中的加权函数,设计了3种选权方案,并通过对比,给出了极移X、Y序列各自合适的选权方案.通过实验最终验证了这种新方法对极移预测的精度提高有一定作用,可作为极移预测的一种参考方法;但该方法作为极移预测的一种新的尝试,在选权方案优选时,其物理激发上的理论依据仍需进一步探讨.     

基于ERDAS8．7LPS模块正射影像图的制作

LPS模块是ERDAS公司与Leica公司在原有的IMAGINE OrthoBase基础上进行改进后的产品。LPS将正射的过程进行了流水线式的梳理。本文以航空遥感所获得的数字图像为例，介绍了应用LPS模块进行数字图像正射校正处理的操作流程，并指出制作过程中的注意事项，以期对航空正射影像图的制作具有一定的借鉴作用。     

Least-squares prediction in linear models with integer unknowns

The prediction of spatially and/or temporal varying variates based on observations of these variates at some locations in space and/or instances in time, is an important topic in the various spatial and Earth sciences disciplines. This topic has been extensively studied, albeit under different names. The underlying model used is often of the trend-signal-noise type. This model is quite general and it encompasses many of the conceivable measurements. However, the methods of prediction based on these models have only been developed for the case the trend parameters are real-valued. In the present contribution we generalize the theory of least-squares prediction by permitting some or all of the trend parameters to be integer valued. We derive the solution for least-squares prediction in linear models with integer unknowns and show how it compares to the solution of ordinary least-squares prediction. We also study the probabilistic properties of the associated estimation and prediction errors. The probability density functions of these errors are derived and it is shown how they are driven by the probability mass functions of the integer estimators. Finally, we show how these multimodal distributions can be used for constructing confidence regions and for cross-validation purposes aimed at testing the validity of the underlying model. Dedicated to the memory of Dr. Tech.hc. Torben Krarup (1919–2005).     

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.     

Least-squares variance component estimation

Least-squares variance component estimation (LS-VCE) is a simple, flexible and attractive method for the estimation of unknown variance and covariance components. LS-VCE is simple because it is based on the well-known principle of LS; it is flexible because it works with a user-defined weight matrix; and it is attractive because it allows one to directly apply the existing body of knowledge of LS theory. In this contribution, we present the LS-VCE method for different scenarios and explore its various properties. The method is described for three classes of weight matrices: a general weight matrix, a weight matrix from the unit weight matrix class; and a weight matrix derived from the class of elliptically contoured distributions. We also compare the LS-VCE method with some of the existing VCE methods. Some of them are shown to be special cases of LS-VCE. We also show how the existing body of knowledge of LS theory can be used to one’s advantage for studying various aspects of VCE, such as the precision and estimability of VCE, the use of a-priori variance component information, and the problem of nonlinear VCE. Finally, we show how the mean and the variance of the fixed effect estimator of the linear model are affected by the results of LS-VCE. Various examples are given to illustrate the theory.     

用脊回法反演重力异常的多层密度及其界面

将研究区域划分成具有固定宽度的矩形网格，以网格密度和厚度作为模型参数，在此基础上形成重力异常的反演目标函数，计算出对模型参数的偏导数矩阵，然后采用脊回归法对重力异常进行反演而同时得到密度及其界面。以此方法对理论模型进行了反演试验。     

On the sensitivity of the results of least-squares adjustments concerning the stochastic model

A proper perturbation theory of a mathematical model and the quantities derived by means of least-squares adjustments is indispensable if the results have to be interpreted in a wider context. The sensitivity of some characteristic results of least-squares adjustments such as the estimated values of the parameters and their variance–covariance matrix due to imminent uncertainties of the stochastic model is discussed in detail. Linearizations are used with rigorous error measures and interval mathematics. Numerical examples conclude the investigations. Received: 27 December 1997 / Accepted: 19 April 1999