半参数模型与最小二乘配置模型的比较

针对重力高程异常估值的计算,采用半参数模型L=BX+S+Δ和最小二乘配置模型两种方法来计算,通过算例比较,分析半参数模型和最小二乘配置法的区别与联系。     

利用半参数模型精化GPS绝对定位中残余的系统偏差

为了减弱GPS单点定位中残余的系统偏差对参数估值精度的影响,在误差方程中引入一非参数分量来表示测量中残余的系统误差,即利用半参数模型来精化GPS绝对定位的函数模型。最后利用实测GPS数据检验了此算法的有效性,计算结果表明在一定程度上该算法不仅能够提高参数估值的精度,而且还能提取出平差模型中残余的系统偏差。但因为半参数模型在测量数据处理中的应用才刚刚起步,还有许多问题值得在理论与实践上进行深入的探讨与研究。     

偏差改正的Partial EIV模型方差分量估计

针对Partial EIV模型的方差分量估计中未考虑参数估值偏差所带来的影响,将Partial EIV模型视为非线性函数得到参数估值的偏差及二阶近似协方差表达式,计算得到偏差改正后的参数估值,结合方差分量估计方法,更新由参数估值影响的矩阵变量,给出了基于偏差改正的方差分量估计迭代方法。试验结果表明,参数估值及其协方差主要受参数估值偏差大小的影响,加入偏差改正能够得到更加合理的参数估值及方差分量估值,偏差改正后的方差分量估值可更加合理地评估参数估值的精度信息。     

均值平移模型的理论研究及分析

均值平移模型是处理含粗差观测值的常用模型之一.文中证明了均值平移模型的参数估值及残差二次型与剔除模型的参数估值和残差二次型完全相等,并进一步分析了均值平移模型粗差检验的性质.     

正规化矩阵正定时半参数估计量的统计性质

利用补偿最小二乘原理构造加权惩罚平方和,得到半参数模型中正规化矩阵正定时参数和半参数的估计量.从偶然误差的统计特征出发,详细讨论这种平差方法得到的参数估值的一些统计性质,并对半参数平差与最小二乘法的参数估计值进行比较.理论分析表明,通过选取合适的平滑参数,半参数平差方法优于最小二乘法.另外从数理统计的角度对平滑参数的选取进行分析,得到平滑参数的取值范围,也给出了平滑参数对模型精度的影响.     

均值平移模型的理论研究及分析

均值平移模型是处理含粗差观测值的常用模型之一,文中证明了均值平移模型的参数估值及残差二次型与剔除模型的参数估值和残差二次型完全相等,并进一步分析了均值平移模型粗差检验的性质。     

乘性误差模型参数估计及精度评定的Sterling插值方法

乘性误差模型加权最小二乘参数估值是观测值的非线性函数,观测值的权是加权最小二乘参数估值的非线性函数.已有的乘性误差模型参数估计方法理论上可以达到二阶无偏,但精度评定方法只能达到一阶精度,并且参数估计逐步的迭代过程使得参数及改正数的每一步估值都具有随机性,使得最终的参数估值与观测值为复杂的非线性关系.考虑到非线性迭代过程...     

用L-曲线法确定半参数模型中的平滑因子

提出了一种新的方法——L-曲线法确定平滑因子。通过确定合适的平滑因子，更好地控制了残差部分V^TPV与光滑度部分S^TRS之间的平衡，得到了更准确的参数估值。通过算例，将基于L-曲线法确定平滑因子的半参数模型解算方法和其他方法进行了比较。结果表明，用L-曲线法确定平滑因子后，提高了半参数模型计算结果的精度，可以更好地将观测值中的系统误差分离出来。     

一种选取补偿最小二乘正则化参数的改进方法

为了改进半参数模型补偿最小二乘估计中的正则化参数选取方法,该文设计了3种方案:L-曲线法、虚拟观测法以及该文提出的改进方法以比较正则化参数的优劣。模拟算例表明,该文提出的改进方法可以有效评价正则化参数,得到的参数估值精度更高,是一种较为有效的选取补偿最小二乘最佳正则化参数的方法。     

基于卡尔曼滤波的AR模型及应用

时间序列参数估值的时变性与预报模型的定常性之间的差异,使得预报精度随着预报步数的增加而显著降低。基于此,构建基于卡尔曼滤波和自适应卡尔曼滤波的AR模型以实时更新其参数估值,取得了较好的拟合效果并提高了预报精度。     

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.     

基于EIV模型的稳健估计

EIV（error-in-variables）模型同时考虑观测向量和系数矩阵的误差,自提出以来便得到广泛应用。目前针对EIV模型的整体最小二乘解法（TLS）假设观测值仅含有偶然误差,当观测值存在粗差时其解并不是最优的。文中通过选定合适的权函数,结合加权整体最小二乘迭代算法,导出基于EIV模型的稳健整体最小二乘迭代解法（RTLS）。线性拟合实验表明,文中方法能对粗差进行定位,且估计量受粗差影响较小,具有稳健性。     

Robust estimation of geodetic datum transformation

The robust estimation of geodetic datum transformation is discussed. The basic principle of robust estimation is introduced. The error influence functions of the robust estimators, together with those of least-squares estimators, are given. Particular attention is given to the robust initial estimates of the transformation parameters, which should have a high breakdown point in order to provide reliable residuals for the following estimation. The median method is applied to solve for robust initial estimates of transformation parameters since it has the highest breakdown point. A smooth weight function is then used to improve the efficiency of the parameter estimates in successive iterative computations. A numerical example is given on a datum transformation between a global positioning system network and the corresponding geodetic network in China. The results show that when the coordinates are contaminated by outliers, the proposed method can still give reasonable results. Received: 25 September 1997 / Accepted: 1 March 1999     

一种用于运动姿态评估的视觉伺服机器人

针对人们在运动中出现的姿态不标准且无人监督指导等问题，本文设计了一种用于运动姿态评估的视觉伺服机器人。这款机器人首先通过一种带有注意力机制的目标跟踪算法对运动目标进行跟踪，并与机器人的伺服电机结构协同工作以调整摄像头的角度，从而实现对在特定区域内运动的目标进行跟踪拍摄。然后由其姿态评估系统提取运动姿态，并与标准姿态进行比对评估。经验证，该机器人对人体运动姿态的质量高低具有较高的区分度，能对用户的多种姿态给予有效的评价，从而实现运动辅助及康复训练指导的目的。     

Variance-covariance estimation of GPS Networks

Summary It is quite easy to estimate the variance-covariance (VCV) matrix for single session surveys or local networks, but difficult where these local networks are combined together to form a regional network. Our main aim is to develop an appropriate VCV model to combine all the different types of networks, either global, regional or local. By careful estimation and combination of the individual VCVs of the local networks, we can form a unique VCV for local, regional and global networks. Different techniques are used to derive appropriate models for the variancecovariance components of the Global Positioning System (GPS) networks. The VCV models were estimated using homogeneous and heterogeneous data. The variance-covariance components are empirically derived using (a) the covariance of the observations of homogeneous data, (b) a combination of the covariance of the observationsP ^–1 and the covariance of the signal componentsC _ss (for either homogeneous and/or heterogeneous data), (c) only the variances are used to determine the variancecovariance, their covariances being zeros. We compare the solutions of the VCV developed for homogeneous and/or heterogeneous data with other developed VCVs. It was observed that the derived VCV model for the combined homogeneous and/or heterogeneous data of case (b) gives the best estimates in all cases.     

半参数模型的累积估计

文献 [1]用累积法研究了线性回归模型 ,得到了与最小二乘法相当的效果。本文将运用此法研究半参数模型得到了参数 β及非参数s (ti)的估计量 ;而后模拟一个例子 ,说明了此法的有效性。运用累积法不仅能得到与补偿最小二乘法相当的效果 ,而且弥补了补偿最小二乘法的一些不足。若该法与补偿最小二乘法结合在一起使用 ,将会得到较理想的结果。     

Optimal weighting in linear function estimation

Summary Considering a geometrical treatment (Elfving, 1952) of the Schreiber problem of optimum allocation of weights, the problem can be reduced to a pair of dual problems of linear programming (Belayev, 1972). In case the estimated value is a function of the direct independent observations (Belaev, 1976) the optimum weights must be proportional to the partial derivatives of this function with respect to the observations.     

Satellite clock bias estimation for iGPS

The High Integrity GPS program seeks to provide enhanced navigation performance by combining conventional GPS with a communications and ranging broadcast from the Iridium^® Communications System. Through clock and message aiding, it would enable existing GPS receivers to acquire and track in more challenging environments. As is the case for standard GPS, accurate and precise timing is key to performance. An approach is presented for estimating the bias of each Iridium satellite clock using satellite-to-ground and satellite-to-satellite measurements. The satellite clock bias estimates are based on a Kalman filter that incorporates code-type observations from the measurements at 10 s intervals. Filter parameters are set based on the expected behavior of the clocks, allowing for discontinuous bias and frequency adjustments due to ground commands. Typical results show the current filter to be accurate to within 200 ns while always meeting the initial system specification of half a microsecond.     

Robust estimation by expectation maximization algorithm

A mixture of normal distributions is assumed for the observations of a linear model. The first component of the mixture represents the measurements without gross errors, while each of the remaining components gives the distribution for an outlier. Missing data are introduced to deliver the information as to which observation belongs to which component. The unknown location parameters and the unknown scale parameter of the linear model are estimated by the EM algorithm, which is iteratively applied. The E (expectation) step of the algorithm determines the expected value of the likelihood function given the observations and the current estimate of the unknown parameters, while the M (maximization) step computes new estimates by maximizing the expectation of the likelihood function. In comparison to Huber’s M-estimation, the EM algorithm does not only identify outliers by introducing small weights for large residuals but also estimates the outliers. They can be corrected by the parameters of the linear model freed from the distortions by gross errors. Monte Carlo methods with random variates from the normal distribution then give expectations, variances, covariances and confidence regions for functions of the parameters estimated by taking care of the outliers. The method is demonstrated by the analysis of measurements with gross errors of a laser scanner.     

Total evaporation estimation for accurate water accounting purposes: an appraisal of various available estimation methods

The estimation of total evaporation is fundamental for water accounting, considering its influence on water availability. Moreover, the current increase in water consumption (e.g. in sub-Saharan Africa and the world over), land cover/use changes, deteriorating water quality and the climate change projections in most regions of the world underscore the need to understand water loss. So far, different approaches have been developed and implemented in estimating the variations of total evaporation, with varying accuracies. The aim of this work was therefore, to provide a review of these different approaches for estimating total evaporation, as well as a detailed discussion of their strengths and weaknesses. Findings from this review have shown that total evaporation estimates derived, using ground-based meteorological and micro-meteorological methods are inadequate for representing its large-scale spatial variations. On the other hand, remote sensing technology, which acquires data at different resolutions (i.e. radiometric, spectral, spatial and temporal), provides timely, up-to-date and relatively accurate spatial estimates of total evaporation over large geographic coverage, for sustainable and effective water accounting, which is key for well-informed and improved management of water resources at both catchment and regional scales. In this regard, more details on the remote sensing-based methods of estimating total evaporation are provided, especially considering the robust technological advancements and its potential in characterizing earth features over time and space. This work has also managed to identify research gaps and challenges in the accurate estimation of total evaporation, using remote sensing, especially with the emergence of more advanced sensors and the characteristics of the landscape.