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Li B.,Tongji University | Li B.,Xian Research of Surveying and Mapping | Shen Y.,Tongji University | Zhang X.,Guangdong University of Technology | And 2 more authors.
International Journal of Geographical Information Science | Year: 2013

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. © 2013 Taylor and Francis Group, LLC. Source


Li B.,Tongji University | Wang M.,Tongji University | Yang Y.,Xian Research of Surveying and Mapping
Survey Review | Year: 2016

Different from the traditional linear regression model that captures only the errors of dependent variables (responses), this contribution presents a new multiple linear regression model where, besides the errors of responses, the errors of explanatory variables and their correlations with response errors are rigorously taken into account. The new regression model is typically a non-linear errors-in-variables (EIV) model, which is referred to as the error-affected and correlated linear regression (ECLR) in this paper. Considering the fact that only part of elements in design matrix A of the regression model are random, the authors express error matrix EA of A as a function of EX consists of all non-zero random errors. Then, the authors can easily formulate the stochastic model without the effect of non-random elements in A. An iterative solution is derived based on the Euler–Lagrange minimisation problem for ECLR. The authors further show that ECLR is very general and some of the existing linear regression methods, the ordinary least squares (OLS), the total least squares (TLS) and the weighted total least squares (WTLS), are the special cases. The experiments show that the ECLR method generally has a better performance than the OLS, TLS and WTLS methods in terms of the difference between the solution and the true values when the explanatory variables and responses are significantly correlated. © 2016 Survey Review Ltd. Source


Zheng H.,Xian Research of Surveying and Mapping | Tang X.,Xian Research of Surveying and Mapping | Chen G.,Xian Research of Surveying and Mapping | Liu Z.,Xian Research of Surveying and Mapping
Acta Geodaetica et Cartographica Sinica | Year: 2010

For InSAR data processing, baselines are vitally parameters and play important role for acquisition height of ground point. In the InSAR system based on formation-flying satellites, baselines changes continuously due to continuous movement of each satellite. So a credible and accurate method is needed. Baseline detection is one of important ways to get high-precision baseline. As a consequence, there are few experiences to use for reference in this work. This paper focuses on study the baseline detection in the formation-flying satellites, which test baseline parameters of InSAR formed by hi-dynamic and distributed satellites using the hi-precision ground area data. Based on analysis, an improved-model of baseline detection based on baseline linear fitting is presented. The tests of the method have been done using with the ERS real data. The result shows the method make great improvement and can be implemented in practice. Source

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