On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms

Schaffrin, Burkhard; Felus, Yaron A.

doi:10.1007/s00190-007-0186-5

Cited by 89 publications

(37 citation statements)

References 15 publications

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“…It can be seen from the table that regular shape of the error measurement is within 2%. 3)Irregular area measurement by compass Conventional calculation of the irregular area is approximated by the regular area [114,15,16] ,and the area can be obtained from the regular's. The table 5 is a regular processing of irregular circle area, where the radian of circular evenly is divided, approximating for four, five, hexagon area error.…”

Section: ) Measurement Of Multilateral Area By Compassmentioning

confidence: 99%

Research on Measurement Technology of Length and Area Based on COMPASS Positioning

Cao¹,

Yang²

2018

Proceedings of the 2018 International Conference on Mathematics, Modelling, Simulation and Algorithms (MMSA 2018)

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Abstract-This paper studies the Compass Positioning and WI-FI positioning etc. for single point positioning and measurement of distance between two points in the error range. As a reference, GPS measurement data with accurate positioning is shown else. On this basis, calculation rules of the area measurement by which the Compass system of irregular region mining point positions into regular polygon approximation is explored, and then the rule method is used to calculate the cumulative area measurement for complex and irregular terrain. It can be shown with irregular area. The experimental data and the measurement results show that the relative error of Bei-dou Positioning length, within distance between 100-200m,is less than 5%,and area measurement error of the regular shape is within 3%.

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Section: ) Measurement Of Multilateral Area By Compassmentioning

confidence: 99%

Research on Measurement Technology of Length and Area Based on COMPASS Positioning

Cao¹,

Yang²

2018

Proceedings of the 2018 International Conference on Mathematics, Modelling, Simulation and Algorithms (MMSA 2018)

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“…Felus and Schaffrin [11] developed a Structured Total Least Squares algorithm to solve a planar linear conformal transformation with a particularly structured coefficient matrix A. Moreover, they proposed [12] a method based on the non-linear Euler-Lagrange condition equations for estimating a planar affine transformation by a multivariate TLS problem. Results showed that the differences between the TLS and the classical LS estimated parameters are small [12]; nevertheless they could affect significantly the final accuracy of the transformed coordinates.…”

Section: Errors-in-variables Model and Total Leastmentioning

confidence: 99%

“…Moreover, they proposed [12] a method based on the non-linear Euler-Lagrange condition equations for estimating a planar affine transformation by a multivariate TLS problem. Results showed that the differences between the TLS and the classical LS estimated parameters are small [12]; nevertheless they could affect significantly the final accuracy of the transformed coordinates. TLS solutions for the 3D datum and affine transformations are also derived in [13] and [14], respectively.…”

Section: Errors-in-variables Model and Total Leastmentioning

confidence: 99%

Errors-in-Variables Anisotropic Extended Orthogonal Procrustes Analysis

Maset

Crosilla

Fusiello

2017

IEEE Geosci. Remote Sensing Lett.

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Abstract-This paper presents a novel total least squares solution of the anisotropic row-scaling Procrustes problem. Ordinary least squares Procrustes approach finds the transformation parameters between origin and destination sets of observations minimizing errors affecting only the destination one. In this study, we introduce the Errors-In-Variables model in the anisotropic Procrustes analysis problem and present a solution that can deal with the uncertainty affecting both sets of observations. The algorithm is applied to solve the image exterior orientation problem. Experiments show that the proposed total least squares method leads to an accuracy in the parameters estimation that is higher than the one reached with the ordinary least squares anisotropic Procrustes solution when the number of points, whose coordinates are known in both the image and the external systems, is small.

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“…The above approach in its multivariate generalization, where the vector y turns into a n × d matrix Y and the vector ξ into a m × d matrix Ξ with d as dimension, has been applied quite successfully to the affine transformation; see, e.g., Schaffrin and Felus (2008), and Schaffrin and Wieser (2009) This works so well since, in this case, the matrix A remains unstructured. For the similarity transformation, however, the structure of A must be imprinted on E A as well, a fact that had already been emphasized by Felus and Schaffrin (2005).…”

Section: A Brief Review Of the Tls Approach Within An Eiv-modelmentioning

confidence: 99%

Modifying Cadzow's algorithm to generate the optimal TLS-solution for the structured EIV-Model of a similarity transformation

Schaffrin

Neitzel

Uzun

et al. 2012

Journal of Geodetic Science

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Abstract:In 2005, Felus and Schaffrin discussed the problem of a Structured Errors-in-Variables (EIV) Model in the context of a parameter adjustment for a classical similarity transformation. Their proposal, however, to perform a Total Least-Squares (TLS) adjustment, followed by a Cadzow step to imprint the proper structure, would not always guarantee the identity of this solution with the optimal Structured TLS solution, particularly in view of the residuals. Here, an attempt will be made to modify the Cadzow step in order to generate the optimal solution with the desired structure as it would, for instance, also result from a traditional LS-adjustment within an iteratively linearized GaussHelmert Model (GHM). Incidentally, this solution coincides with the (properly) Weighted TLS solution which does not need a Cadzow step.

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On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms

Cited by 89 publications

References 15 publications

Research on Measurement Technology of Length and Area Based on COMPASS Positioning

Research on Measurement Technology of Length and Area Based on COMPASS Positioning

Errors-in-Variables Anisotropic Extended Orthogonal Procrustes Analysis

Modifying Cadzow's algorithm to generate the optimal TLS-solution for the structured EIV-Model of a similarity transformation

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