A Recursive Restricted Total Least-Squares Algorithm

Rhode, Stephan; Usevich, Konstantin; Markovsky, Ivan; Gauterin, Frank

doi:10.1109/tsp.2014.2350959

Cited by 44 publications

(13 citation statements)

References 23 publications

(30 reference statements)

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“…where V Wy ∈ R b and V yy ∈ R . Following [4,56], the covariance Σ TLS of the TLS estimatê β TLS can be approximated as…”

Section: Total Least-squares (Idim-tls)mentioning

confidence: 99%

“…Conversely, ref. [20] proposed reformulating IDIM-LS under physicality constraints in a Semi-Definite Programming (SDP) perspective, writing (56) in the form of a Linear Matrix inequality (LMI). Provided that the reference frame L j of link j and its CoM frame C j have the same orientation, I j can indeed be related to the inertia tensor L j expressed in L j , using the Huygens-Steiner theorem…”

Section: Enforcing Physical Consistency Within Inertial Parameter Identification 71 Mathematical Formulation Of the Physical Consistency mentioning

confidence: 99%

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Inertial Parameter Identification in Robotics: A Survey

et al. 2021

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This work aims at reviewing, analyzing and comparing a range of state-of-the-art approaches to inertial parameter identification in the context of robotics. We introduce “BIRDy (Benchmark for Identification of Robot Dynamics)”, an open-source Matlab toolbox, allowing a systematic and formal performance assessment of the considered identification algorithms on either simulated or real serial robot manipulators. Seventeen of the most widely used approaches found in the scientific literature are implemented and compared to each other, namely: the Inverse Dynamic Identification Model with Ordinary, Weighted, Iteratively Reweighted and Total Least-Squares (IDIM-OLS, -WLS, -IRLS, -TLS); the Instrumental Variables method (IDIM-IV), the Maximum Likelihood (ML) method; the Direct and Inverse Dynamic Identification Model approach (DIDIM); the Closed-Loop Output Error (CLOE) method; the Closed-Loop Input Error (CLIE) method; the Direct Dynamic Identification Model with Nonlinear Kalman Filtering (DDIM-NKF), the Adaline Neural Network (AdaNN), the Hopfield-Tank Recurrent Neural Network (HTRNN) and eventually a set of Physically Consistent (PC-) methods allowing the enforcement of parameter physicality using Semi-Definite Programming, namely the PC-IDIM-OLS, -WLS, -IRLS, PC-IDIM-IV, and PC-DIDIM. BIRDy is robot-agnostic and features a complete inertial parameter identification pipeline, from the generation of symbolic kinematic and dynamic models to the identification process itself. This includes functionalities for excitation trajectory computation as well as the collection and pre-processing of experiment data. In this work, the proposed methods are first evaluated in simulation, following a Monte Carlo scheme on models of the 6-DoF TX40 and RV2SQ industrial manipulators, before being tested on the real robot platforms. The robustness, precision, computational efficiency and context of application the different methods are investigated and discussed.

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“…where V Wy ∈ R b and V yy ∈ R . Following [4,56], the covariance Σ TLS of the TLS estimatê β TLS can be approximated as…”

Section: Total Least-squares (Idim-tls)mentioning

confidence: 99%

Section: Enforcing Physical Consistency Within Inertial Parameter Identification 71 Mathematical Formulation Of the Physical Consistency mentioning

confidence: 99%

Inertial Parameter Identification in Robotics: A Survey

et al. 2021

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“…For the signal processing community, TLS emerges as the main tool for estimation in linear systems with imperfect knowledge of the input signals, which justifies several recent research efforts related to the TLS method [18][19][20][21]. However, the original formulation of the TLS method is based on the following model…”

Section: Total Least Squares (Tls)mentioning

confidence: 99%

Balanced least squares: Estimation in linear systems with noisy inputs and multiple outputs

Vía

Santamarı́a

2016

2016 IEEE Statistical Signal Processing Workshop (SSP)

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This paper revisits the linear model with noisy inputs, in which the performance of the total least squares (TLS) method is far from acceptable. Under the assumption of Gaussian noises, the maximum likelihood (ML) estimation of the system response is reformulated as a general balanced least squares (BLS) problem. Unlike TLS, which minimizes the trace of the product between the empirical and inverse theoretical covariance matrices, BLS promotes solutions with similar values of both the empirical and theoretical error covariance matrices. The general BLS problem is reformulated as a semidefinite program with a rank constraint, which can be relaxed in order to obtain polynomial time algorithms. Moreover, we provide new theoretical results regarding the scenarios in which the relaxation is tight, as well as additional insights on the performance and interpretation of BLS. Finally, some simulation results illustrate the satisfactory performance of the proposed method.

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“…18,19 And TLS method is tightly related to the maximum likelihood principal component analysis method introduced in chemometrics by Schuermans et al 20 However, the variable errors of measurement data are usually in an asymmetric way in practice. The generalized total least squares (GTLS) method 21,22 with noise covariance matrix can be regarded as a restricted total least squares (RTLS) method for dealing with the data, which are measured with unequal precision and contaminated with uncorrelated errors. However, an implementation for this approach seems challenging in practice.…”

Section: Introductionmentioning

confidence: 99%

An improved total least square calibration method for straightness error of coordinate measuring machine

Lin

Fan

et al. 2016

Proceedings of the Institution of Mechanical Engineers, Part B:

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The total least square method based on singular value decomposition for fitting straight line and plane surface has been developed to deal with the straightness calibration problem. Different from the ordinary least square method only taking into account the error of the dependent variable, total least square method considers the errors of all the variables in a symmetrical way. However, in practice, it is difficult to choose an optimal method for the variable errors of measurement data in an asymmetric way. This article presents an improved calibration method for straightness error of a coordinate measuring machine. The proposed method, named as improved total least square, could fit straight line and plane surface when the variables are in an asymmetric way. In improved total least square method, weight matrices with parameter λ set between the independent and dependent variables are introduced to augmented matrix. A procedure is developed to determine the parameter λ. Numerical cases and measurement experiment are given to prove the performance of improved total least square method.

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A Recursive Restricted Total Least-Squares Algorithm

Cited by 44 publications

References 23 publications

Inertial Parameter Identification in Robotics: A Survey

Inertial Parameter Identification in Robotics: A Survey

Balanced least squares: Estimation in linear systems with noisy inputs and multiple outputs

An improved total least square calibration method for straightness error of coordinate measuring machine

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