共查询到20条相似文献，搜索用时 31 毫秒
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Total least squares (TLS) can solve the issue of parameter estimation in the errors-invariables (EIV) model, however, the estimated parameters are affected or even severely distorted when the observation vector and coefficient matrix are contaminated by gross errors. Currently, the use of existing robust TLS (RTLS) methods for the EIV model is unreasonable. Original residuals are directly used in most studies to construct the weight factor function, thus the robustness for the structure space is not considered. In this study, a robust weighted total least squares (RWTLS) algorithm for the partial EIV model is proposed based on Newton-Gauss method and the equivalent weight principle of general robust estimation. The algorithm utilizes the standardized residuals to construct the weight factor function and employs the median method to obtain a robust estimator of the variance component. Therefore, the algorithm possesses good robustness in both the observation and structure spaces. To obtain standardized residuals, we use the linearly approximate cofactor propagation law for deriving the expression of the cofactor matrix of WTLS residuals. The iterative procedure and precision assessment approach for RWTLS are presented. Finally, the robustness of RWTLS method is verified by two experiments involving line fitting and plane coordinate transformation. The results show that RWTLS algorithm possesses better robustness than the general robust estimation and the robust total least squares algorithm directly constructed with original residuals. 相似文献
3.
Increasing numerical efficiency of iterative solution for total least-squares in datum transformations 总被引：1，自引：0，他引：1
Cartesian coordinate transformation between two erroneous coordinate systems is considered within the Errors-In-Variables (EIV) model. The adjustment of this model is usually called the total Least-Squares (LS). There are many iterative algorithms given in geodetic literature for this adjustment. They give equivalent results for the same example and for the same user-defined convergence error tolerance. However, their convergence speed and stability are affected adversely if the coefficient matrix of the normal equations in the iterative solution is ill-conditioned. The well-known numerical techniques, such as regularization, shifting-scaling of the variables in the model, etc., for fixing this problem are not applied easily to the complicated equations of these algorithms. The EIV model for coordinate transformations can be considered as the nonlinear Gauss-Helmert (GH) model. The (weighted) standard LS adjustment of the iteratively linearized GH model yields the (weighted) total LS solution. It is uncomplicated to use the above-mentioned numerical techniques in this LS adjustment procedure. In this contribution, it is shown how properly diminished coordinate systems can be used in the iterative solution of this adjustment. Although its equations are mainly studied herein for 3D similarity transformation with differential rotations, they can be derived for other kinds of coordinate transformations as shown in the study. The convergence properties of the algorithms established based on the LS adjustment of the GH model are studied considering numerical examples. These examples show that using the diminished coordinates for both systems increases the numerical efficiency of the iterative solution for total LS in geodetic datum transformation: the corresponding algorithm working with the diminished coordinates converges much faster with an error of at least 10-5 times smaller than the one working with the original coordinates. 相似文献
4.
Variance component estimation in errors-in-variables models and a rigorous total least-squares approach 总被引：1，自引：0，他引：1
Vahid Mahboub 《Studia Geophysica et Geodaetica》2014,58(1):17-40
A method for variance component estimation (VCE) in errors-in-variables (EIV) models is proposed, which leads to a novel rigorous total least-squares (TLS) approach. To achieve a realistic estimation of parameters, knowledge about the stochastic model, in addition to the functional model, is required. For an EIV model, the existing TLS techniques either do not consider the stochastic model at all or assume approximate models such as those with only one variance component. In contrast to such TLS techniques, the proposed method considers an unknown structure for the stochastic model in the adjustment of an EIV model. It simultaneously predicts the stochastic model and estimates the unknown parameters of the functional model. Moreover the method shows how an EIV model can support the Gauss-Helmert model in some cases. To make the VCE theory into EIV model more applicable, two simplified algorithms are also proposed. The proposed methods can be applied to linear regression and datum transformation. We apply these methods to these examples. In particular a 3-D non-linear close to identical similarity transformation is performed. Two simulation studies besides an experimental example give insight into the efficiency of the algorithms. 相似文献
5.
Data-snooping procedure applied to errors-in-variables models 总被引：1，自引：0，他引：1
The theory of Baarda’s data snooping — normal and F tests respectively based on the known and unknown posteriori variance — is applied to detect blunders in errors-invariables (EIV) models, in which gross errors are in the vector of observations and/or in the coefficient matrix. This work is a follow-up to an earlier work in which we presented the formulation of the weighted total least squares (WTLS) based on the standard least squares theory. This method allows one to directly apply the existing body of knowledge of the least squares theory to the errors-in-variables models. Among those applications, data snooping methods in an EIV model are of particular interest, which is the subject of discussion in the present contribution. This paper generalizes the Baarda’s data snooping procedure of the standard least squares theory to an EIV model. Two empirical examples, a linear regression model and a 2-D affine transformation, using simulated and real data are presented to show the efficacy of the presented formulation. It is highlighted that the method presented is capable of detecting outlying equations (rather than outlying observations) in a straightforward manner. Further, the WTLS method can be used to handle different TLS problems. For example, the WTLS problem for the conditions and mixed models, the WTLS problem subject to constraints and variance component estimation for an EIV model can easily be established. These issues are in progress for future publications. 相似文献
6.
An algorithmic approach to the total least-squares problem with linear and quadratic constraints 总被引：5，自引：0，他引：5
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. 相似文献
7.
Studia Geophysica et Geodaetica - In this contribution, an iterative algorithm for variance-covariance component estimation based on the structured errors-in-variables (EIV) model is proposed. We... 相似文献
8.
Vahid Mahboub Mohammad Saadatseresht Alireza A. Ardalan 《Studia Geophysica et Geodaetica》2017,61(1):19-34
An applicable algorithm for Total Kalman Filter (TKF) approach is proposed. Meanwhile, we extend it to the case in which we can consider arbitrary weight matrixes for the observation vector, the random design matrix and possible correlation between them. Also the updated dispersion matrix of the predicted unknown is given. This approach makes use of condition equations and straightforward variance propagation rules. It is applicable to data fusion within a dynamic errors-in-variables (DEIV) model, which usually appears in the determination of the position and attitude of mobile sensors. Then, we apply for the first time the TKF algorithm and its extended version named WTKF to a DEIV model and compare the results. The results show the efficiency of the proposed WTKF algorithm. In particular in the case of large weights, WTKF shows approximately 25% improvement in contrast to TKF approach. 相似文献
9.
Unscented transformation with scaled symmetric sampling strategy for precision estimation of total least squares 总被引：2，自引：0，他引：2
The errors-in-variables (EIV) model is a nonlinear model, the parameters of which can be solved by singular value decomposition (SVD) method or the general iterative algorithm. The existing formulae for covariance matrix of total least squares (TLS) parameter estimates don’t fully consider the randomness of quantities in iterative algorithm and the biases of parameter estimates and residuals. In order to reflect more reasonable precision information for TLS adjustment, the derivative-free unscented transformation with scaled symmetric sampling strategy, i.e. scaled unscented transformation (SUT), is introduced and implemented. In this contribution, we firstly discuss the existing various solutions of TLS adjustment and covariance matrices of TLS parameter estimates and derive the general first-order approximate cofactor matrices of random quantities in TLS adjustment. Secondly, based on the combination of TLS iterative algorithm and calculation process of SUT, we design the two SUT algorithms to calculate the biases and the second-order approximate covariance matrices. Finally, the straight line fitting model and plane coordinate transformation model are used to demonstrate that applying SUT for precision estimation of TLS adjustment is feasible and effective. 相似文献
10.
The spectrum of high frequency Earth rotation variations contains strong harmonic signal components mainly excited by ocean tides along with much weaker non-harmonic fluctuations driven by irregular processes like the diurnal thermal tides in the atmosphere and oceans. In order to properly investigate non-harmonic phenomena a representation in time domain is inevitable. We present a method, operating in time domain, which is easily applicable within Earth rotation estimation from Very Long Baseline Interferometry (VLBI). It enables the determination of diurnal and subdiurnal variations, and is still effective with merely diurnal parameter sampling. The features of complex demodulation are used in an extended parameterization of polar motion and universal time which was implemented into a dedicated version of the Vienna VLBI Software VieVS. The functionality of the approach was evaluated by comparing amplitudes and phases of harmonic variations at tidal periods (diurnal/semidiurnal), derived from demodulated Earth rotation parameters (ERP), estimated from hourly resolved VLBI ERP time series and taken from a recently published VLBI ERP model to the terms of the conventional model for ocean tidal effects in Earth rotation recommended by the International Earth Rotation and Reference System Service (IERS). The three sets of tidal terms derived from VLBI observations extensively agree among each other within the three-sigma level of the demodulation approach, which is below 6 μas for polar motion and universal time. They also coincide in terms of differences to the IERS model, where significant deviations primarily for several major tidal terms are apparent. An additional spectral analysis of the as well estimated demodulated ERP series of the ter- and quarterdiurnal frequency bands did not reveal any significant signal structure. The complex demodulation applied in VLBI parameter estimation could be demonstrated a suitable procedure for the reliable reproduction of high frequency Earth rotation components and thus represents a qualified tool for future studies of irregular geophysical signals in ERP measured by space geodetic techniques. 相似文献
11.
A. H. ELSheikh C. C. Pain F. Fang J. L. M. A. Gomes I. M. Navon 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(4):877-897
A new parameter estimation algorithm based on ensemble Kalman filter (EnKF) is developed. The developed algorithm combined with the proposed problem parametrization offers an efficient parameter estimation method that converges using very small ensembles. The inverse problem is formulated as a sequential data integration problem. Gaussian process regression is used to integrate the prior knowledge (static data). The search space is further parameterized using Karhunen–Loève expansion to build a set of basis functions that spans the search space. Optimal weights of the reduced basis functions are estimated by an iterative regularized EnKF algorithm. The filter is converted to an optimization algorithm by using a pseudo time-stepping technique such that the model output matches the time dependent data. The EnKF Kalman gain matrix is regularized using truncated SVD to filter out noisy correlations. Numerical results show that the proposed algorithm is a promising approach for parameter estimation of subsurface flow models. 相似文献
12.
Peiliang Xu 《Studia Geophysica et Geodaetica》2013,57(3):339-352
The effects of incorrect weights on the weighted least squares (WLS) estimate, its accuracy, relative goodness and reliability have been thoroughly investigated in statistical and geodetic literature. Although the variance of unit weight has been one of the most important quantities in statistics and geodesy, little has been done to understand the effect of incorrect weights of observations and incorrect prior information on this quantity, except for an earlier study of Koch who showed that incorrect weights of observations would create a bias in the estimation of the variance of unit weight, though they do not affect the unbiasedness of the WLS estimates of parameters and the corrections to the observations. Since Koch did not directly give the formula to compute the bias, we will derive the bias of the estimated variance of unit weight due to incorrect weights of observations in this paper. In the case of incorrect prior information, both incorrect prior mean and incorrect prior weights can independently contribute a bias to the estimate of the variance of unit weight. Two simulated examples clearly show that the bias of the estimated variance of unit weight due to incorrect weights can be much larger than the variance of unit weight itself. 相似文献
13.
The usual least-squares adjustment within an Errors-in-Variables (EIV) model is often described as Total Least-Squares Solution
(TLSS), just as the usual least-squares adjustment within a Random Effects Model (REM) has become popular under the name of
Least-Squares Collocation (without trend). In comparison to the standard Gauss-Markov Model (GMM), the EIV-Model is less informative
whereas the REM is more informative. It is known under which conditions exactly the GMM or the REM can be equivalently replaced
by a model of condition equations or, more generally, by a Gauss-Helmert Model. Similar equivalency conditions are, however,
still unknown for the EIV-Model once it is transformed into such a model of condition equations. In a first step, it is shown
in this contribution how the respective residual vector and residual matrix look like if the TLSS is applied to condition
equations with a random coefficient matrix to describe the transformation of the random error vector. The results are demonstrated
using a numeric example which shows that this approach may be valuable in its own right. 相似文献
14.
卫星激光测距（SLR）技术作为卫星精密定轨手段和轨道检核重要方法,激光反射器已经成为重力卫星和测高卫星等低轨卫星的基本载荷.经典的SLR台站坐标是使用动力学方法计算的,本文根据多颗低轨卫星（LEO）多历元的激光观测数据,采用几何方法开展地面SLR测站坐标计算.通过组建低轨卫星群实现对全球激光站的动态观测,为了合理配置不同低轨卫星间观测值权重,削弱低轨卫星群可能存在的系统性偏差,提出采用方差分量估计组合的最小二乘法进行解算.实测结果显示,解算出SLR台站坐标框架解与SLRF2014差异平均值在25.1 mm,外符合精度达到1~2 cm.该方法避免了复杂动力学模型,SLR台站坐标的几何计算方法既可以作为激光测站框架解算手段之一,同时将LEO卫星群作为空间并址站实现不同技术地球参考框架间的融合. 相似文献
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Detailed paleomagnetic data from the Wairoa Syncline, a middle Miocene to the present forearc basin on the East Coast of the North Island, New Zealand, show that the rate of clockwise rotation for the last 5 Ma has been 7–8°/Ma of which less than 1.5°/Ma can be explained by apparent polar wander due to motion of the Australian or Pacific plates. This rotation is similar to a present-day rate of 7°/Ma determined from geodetic data. Between 5 and 20 Ma ago the rate of tectonic rotation is poorly determined and may be between 0° and 2°/Ma.
The change in the rate of rotation of the Wairoa Syncline around 5 Ma is probably related to a markedly different tectonic style in the New Zealand region within the last 5 Ma, associated with a change in position of the Euler poles of rotation for the Pacific-Australian plates. 相似文献
16.
Due to their high aspect ratio fractures are often conceptualized as lower-dimensional structures embedded into the surrounding host matrix. This simplification is typically made within the context of numerical simulation, for the inverse estimation of the matrix-diffusion coefficient from break-through curves or for the derivation of analytical solutions describing flow and transport in a fracture–matrix system. It is generally justified by the so called Lauwerier assumption stating that the transversal dispersion inside the fracture is infinitely fast therefore hampering the formation of gradients across the width of the fracture. In this study we want to verify the applicability of such lower-dimensional modeling. To that end we investigate the occurrence of fracture-scale gradients in a simplified fracture–matrix model by virtue of analytical as well as numerical investigations. The relevant processes modeled are advection, dispersion, matrix diffusion and linear decay. In addition, we also investigate the impact on the inverse estimation of matrix-diffusion coefficients through analytical solutions, which assume a lower-dimensional fracture. Results show that a lower-dimensional modeling of fractures will only lead to errors for early periods of the time-dependent solution. Such errors may however, extent to the steady state if fast radioactive decay is considered. The estimation of the matrix-diffusion coefficient too is affected by the assumption of a lower-dimensional fracture. We see errors as big as 20% for the estimation procedure, the value of which depends on the ratio of the matrix-diffusion vs. the transversal dispersion coefficient. Our analysis suggest that a lower-dimensional representation of fractures is justified for many typical conditions and that special attention must only be paid in a confined number of cases. 相似文献
17.
To study contaminant transport in groundwater, an essential requirement is robust and accurate estimation of the transport parameters such as dispersion coefficient. The commonly used inverse error function method (IEFM) may cause unacceptable errors in dispersion coefficient estimation using the breakthrough curves (BTCs) data. We prove that the random error in the measured concentrations, which might be described by a normal distribution, would no longer follow the normal distribution after the IEFM transformation. In this study, we proposed a new method using the weighted least squares method (WLSM) to estimate the dispersion coefficient and velocity of groundwater. The weights were calculated based on the slope of the observed BTCs. We tested the new method against other methods such as genetic algorithm and CXTFIT program and found great agreement. This new method acknowledged different characteristics of solute transport at early, intermediate, and late time stages and divided BTCs into three sections for analysis. The developed method was applied to interpret three column tracer experiments by introducing continuous, constant‐concentration of sodium chloride (NaCl) into columns filled with sand, gravel, and sand‐gravel media. This study showed that IEFM performed well only when the observed data points were located in the linear (intermediate time) section of BTCs; it performed poorly when data points were in the early and late time stages. The new WLSM method, however, performed well for data points scattering over the entire BTCs and appeared promising in parameter estimation for solute transport in a column. 相似文献
18.
以旋转椭球体面上某点为原点建立一个大地坐标单位活动坐标架. 通过平移, 使活动坐标架的原点与以椭球中心为原点的笛卡尔单位标架的原点相重合. 然后再通过两次标架旋转, 使活动坐标架与笛卡尔单位标架完全重合. 本文给出了使两个单位标架相重合的转换关系式, 以及该点位移在两个单位标架中的坐标转换式； 在此基础上, 考虑该点的位移及活动坐标架皆为该点大地坐标的函数, 经复杂推导, 分别给出了该点位移向量的微分在大地坐标系中的分量以及该点分别沿坐标曲线的弧微分表达式, 继而导出了该点的位移梯度矩阵; 最后推导出了椭球坐标系的应变张量与转动张量表达式, 并对转动张量的几何含义进行了较详细的解释, 且采用曲面理论对球面与椭球面的应变张量间的内在关系进行了讨论. 相似文献
19.
Expression of strain and rotation tensor in geodetic coordinates 总被引：1，自引：0，他引：1
In this paper, unit moving trihedron is first constructed for a point on the surface of a revolution ellipsoid. Via translation, the origin of the trihedron coincides with that of Cartesian coordinates established at the center of the ellipsoid, and then through two coordinate rotations, the trihedron completely coincides with the Cartesian coordi-nates. Transformation formulae between the moving trihedron and unit Cartesian coordinate frameworks as well as transformation of point displacement between two unit coordinate frameworks are presented. Based on the above transformation formulae between two different coordinate frameworks, due to the fact that the displacement and moving trihedron of the point are both functions of the geodetic coordinates, components in the corresponding axis for differential of displacement vector and geodetic curves arc differential at the point in geodetic system can be obtained through complicated derivation. Displacement gradient matrix at the point in geodetic system is also given. Finally, expressions of strain and rotation tensor in geodetic coordinates are presented. Geometric meanings of the rotation tensor are explained in detail. The intrinsic relationship between strain tensors of sphere and ellip-soid are also discussed. 相似文献
20.
Bayesian model averaging assessment on groundwater management under model structure uncertainty 总被引：1，自引：1，他引：0
This study introduces Bayesian model averaging (BMA) to deal with model structure uncertainty in groundwater management decisions. A robust optimized policy should take into account model parameter uncertainty as well as uncertainty in imprecise model structure. Due to a limited amount of groundwater head data and hydraulic conductivity data, multiple simulation models are developed based on different head boundary condition values and semivariogram models of hydraulic conductivity. Instead of selecting the best simulation model, a variance-window-based BMA method is introduced to the management model to utilize all simulation models to predict chloride concentration. Given different semivariogram models, the spatially correlated hydraulic conductivity distributions are estimated by the generalized parameterization (GP) method that combines the Voronoi zones and the ordinary kriging (OK) estimates. The model weights of BMA are estimated by the Bayesian information criterion (BIC) and the variance window in the maximum likelihood estimation. The simulation models are then weighted to predict chloride concentrations within the constraints of the management model. The methodology is implemented to manage saltwater intrusion in the “1,500-foot” sand aquifer in the Baton Rouge area, Louisiana. The management model aims to obtain optimal joint operations of the hydraulic barrier system and the saltwater extraction system to mitigate saltwater intrusion. A genetic algorithm (GA) is used to obtain the optimal injection and extraction policies. Using the BMA predictions, higher injection rates and pumping rates are needed to cover more constraint violations, which do not occur if a single best model is used. 相似文献