Adjusting the Errors-In-Variables Model: Linearized Least-Squares vs. Nonlinear Total Least-Squares

Schaffrin, Burkhard

doi:10.1007/1345_2015_61

Cited by 11 publications

(3 citation statements)

References 9 publications

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“…See also Skoglund et al (2015) and Teunissen (1990). The second point is that Errors-In-Variables (EIV) models in their time invariant cases have been investigated by several valuable publications (for example, Amiri-Simkooei, 2017; Neitzel, 2010; Snow, 2012; Fang, 2011; 2014; Shen et al, 2011; Schaffrin, 2016; Schaffrin et al, 2012; Schaffrin and Felus, 2008; Mahboub, 2012; 2014; 2016; Mahboub et al, 2013; 2015; Mahboub and Sharifi, 2013a; 2013b; Paláncz and Awange, 2012; Zhang et al, 2013; Jazaeri et al, 2014; Zeng et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

A Constrained Total Extended Kalman Filter for Integrated Navigation

Mahboub

Mohammadi

2018

J. Navigation

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In this contribution, an improved Extended Kalman Filter (EKF), named the Total Extended Kalman Filter (TEKF) is proposed for integrated navigation. It can consider the neglected random observed quantities which may appear in a dynamic model. In particular, this paper will consider the case of vision-based navigation. This algorithm is equipped with quadratic constraints and makes use of condition equations. The paper will show that the refined data from different sensors including a Global Positioning System (GPS) receiver, an Inertial Navigation System (INS) and remote sensors can be fused into a Constrained Total Extended Kalman Filter (CTEKF) algorithm. The CTEKF algorithm is applied to a case study in the Guilan province in the north of Iran. The results show the efficiency of the proposed algorithm.

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Section: Introductionmentioning

confidence: 99%

A Constrained Total Extended Kalman Filter for Integrated Navigation

Mahboub

Mohammadi

2018

J. Navigation

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“…Apparently, (9c) turns out to be a generalized form of formula (18a) in Schaffrin (2015) that allows treatment of EIV-Models with cross-covariances Q Ay that are non-zero. This would be part of a modified "Mahboub-type" algorithm after Mahboub (2012) and Schaffrin (2015).…”

mentioning

confidence: 99%

“…3. Schaffrin's (2015) algorithm, (7a)-( 7b) with (9c), referred to as D herein: This algorithm is encapsulated in equations (8b), ( 9), and (18b) of Schaffrin (2015). However, in light of ( 7b) and (9c), it now allows for a non-zero crosscovariance matrix Q yA .…”

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confidence: 99%

A Simple TLS-Treatment of the Partial EIV-Model as One with Singular Cofactor Matrices I: The Case of a KRONECKER Product for $$Q_A = Q_0\otimes Q_x$$

Jazaeri,

Schaffrin,

Snow

2023

International Association of Geodesy Symposia

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Following the pioneering work in the PhD dissertation by Snow (PhD thesis, Rep. No. 502, Div. of Geodetic Sci, School of Earth Sciences, The Ohio State University, Columbus, OH, USA, 2012), the two articles by Schaffrin et al. (J Geodetic Sci 4(1):28–36, 2014) and by Jazaeri et al. (Z für Vermessungswesen 139(4):229–240, 2014) provided a broad overview of the Total Least-Squares (TLS) adjustment within EIV-Models with singular cofactor matrices. Around the same time, Xu et al. (J Geodesy 86:661–675, 2012) proposed a specific algorithm to find the TLS solution within a partial EIV-Model, which has been improved by various authors since, including Shi et al. (J Geodesy 89(1):13–16, 2015), Wang et al. (Cehui Xuebao/Acta Geodaet et Cartograph Sinica 46(8):978–987, 2017), Zhao (Surv Rev 49(356):346–354, 2017), and Han et al. (Surv Rev 52(371):126–133, 2020), to name a few. On the other hand, it is easy to see that the partial EIV-Model is a special case of the general EIV-Model with singular cofactor matrices and thus does not need a separate class of algorithms unless they are more efficient than the standard algorithms. This, however, does not seem to be guaranteed as will be shown in this contribution for the straight-line adjustment under $$Q_A = Q_0 \otimes Q_x$$ Q A = Q 0 ⊗ Q x . As a consequence, we shall argue that, rather than discussing the partial EIV-Model, it would be more worthwhile to make the respective developments within an EIV-Model with singular cofactor matrices directly.

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Line fitting in Euclidean 3D space

Snow

Schaffrin

2016

Stud Geophys Geod

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Adjusting the Errors-In-Variables Model: Linearized Least-Squares vs. Nonlinear Total Least-Squares

Cited by 11 publications

References 9 publications

A Constrained Total Extended Kalman Filter for Integrated Navigation

A Constrained Total Extended Kalman Filter for Integrated Navigation

A Simple TLS-Treatment of the Partial EIV-Model as One with Singular Cofactor Matrices I: The Case of a KRONECKER Product for $$Q_A = Q_0\otimes Q_x$$

Line fitting in Euclidean 3D space

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