Retrieval of Euler rotation angles from 3D similarity transformation based on quaternions

Uygur, Süreyya Özgür; Aydin, Cüneyt; Akyılmaz, O.

doi:10.1080/14498596.2020.1776170

Cited by 16 publications

(6 citation statements)

References 47 publications

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“…Now, Equation (9) is defined to convert the accelerometer and magnetometer quaternion data to their quaternion derivative, that

J_{m}

and

J_{a}

are Jacobian matrices of magnetometer and accelerometer [43, 44], and their values are as follows:

{\overset{q}{true}}_{m, t} + {\overset{q}{true}}_{a, t} = J_{m} m_{u, t} {{false|}_{J_{m} = \frac{d s_{i, t}}{d q}} + J_{a} a_{u, t} |}_{J_{a} = \frac{d a_{g, t}}{d q}} .

…”

Section: Methodsmentioning

confidence: 99%

Diagnosing gait disorders based on angular variations of knee and ankle joints utilizing a developed wearable motion sensor

Akhavanhezaveh

Abbasi-Kesbi

2021

Healthcare Tech Letters

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Here, a sensory motion system is developed to diagnose gait disorders using the estimation of angular variations in the knee and ankle joints. The sensory system includes two transmitter sensors and a central node, where each transmitter comprises three sensors of accelerometer, gyroscopes, and magnetometer to estimate the angular movements in the ankle and knee joints. By using a proposed filter, the angular variation is estimated in a personal computer employing the raw data of the motion sensors that are sent by the central node. The obtained results of the presented filter in comparison to an actual reference illustrate that the root mean square error is less than 1.01, 1.34, and 1.61 degrees, respectively, for the angles of and and that illustrate an improvement of 40% than the previous work. Moreover, a quantity value is defined based on the correlation between knee and ankle angles that show the amount of correctness in gating. Thus, the proposed system can be utilized for people who suffer problems in gait and help them to improve their movements.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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“…Now, Equation (9) is defined to convert the accelerometer and magnetometer quaternion data to their quaternion derivative, that

J_{m}

and

J_{a}

are Jacobian matrices of magnetometer and accelerometer [43, 44], and their values are as follows:

{\overset{q}{true}}_{m, t} + {\overset{q}{true}}_{a, t} = J_{m} m_{u, t} {{false|}_{J_{m} = \frac{d s_{i, t}}{d q}} + J_{a} a_{u, t} |}_{J_{a} = \frac{d a_{g, t}}{d q}} .

…”

Section: Methodsmentioning

confidence: 99%

Diagnosing gait disorders based on angular variations of knee and ankle joints utilizing a developed wearable motion sensor

Akhavanhezaveh

Abbasi-Kesbi

2021

Healthcare Tech Letters

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“…Besides, 7 sets of initial values of parameters in which the absolute value of rotation angle is from 90° to 180°, are adopted and listed in Table 7. It is known there are two sets of solution of rotation angles from the rotation matrix see Uygur et al (2020). Both sets are equally correct and we do not have to care, which set of angles is used for describing the object rotation.…”

Section: Iterative Computationmentioning

confidence: 99%

Extended WTLS iterative algorithm of 3D similarity transformation based on Gibbs vector

Zeng

He²,

Le-geng

et al. 2021

Acta Geod Geophys

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Considering coordinate errors of both control points and non-control points, and different weights between control points and non-control points, this contribution proposes an extended weighted total least squares (WTLS) iterative algorithm of 3D similarity transformation based on Gibbs vector. It treats the transformation parameters and the target coordinate of non-control points as unknowns. Thus it is able to recover the transformation parameters and compute the target coordinate of non-control points simultaneously. It is also able to assess the accuracy of the transformation parameters and the target coordinates of non-control points. Obviously it is different from the traditional algorithms that first recover the transformation parameters and then compute the target coordinate of non-control points by the estimated transformation parameters. Besides it utilizes a Gibbs vector to represent the rotation matrix. This representation does not introduce additional unknowns; neither introduces transcendental function like sine or cosine functions. As a result, the presented algorithm is not dependent to the initial value of transformation parameters. This excellent performance ensures the presented algorithm is suitable for the big rotation angles. Two numerical cases with big rotation angles including a real world case (LIDAR point cloud registration) and a simulative case are tested to validate the presented algorithm. Keywords3D similarity transformation • Weighted total least squares (WTLS) • Iterative algorithm • Initial value of parameter • Big rotation angels * Huaien Zeng

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“…Mercan et al [28] presented an iterative algorithm formulated as a GH model of adjustment for the solution of weighted symmetric similarity transformation problems, which takes advantage of quaternion's unique representation of 3D orthogonal rotation matrix. Later, Uygur et al [29] showed how to evaluate the rotation angles and the full covariance matrix of the transformation parameters from the estimation results in asymmetric and symmetric 3D similarity transformations based on quaternions.…”

Section: Quaternion's Application In Point Cloud Registrationmentioning

confidence: 99%

A Closed-Form Solution to Linear Feature-Based Registration of LiDAR Point Clouds

et al. 2021

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Due to the high complexity of geo-spatial entities and the limited field of view of LiDAR equipment, pairwise registration is a necessary step for integrating point clouds from neighbouring LiDAR stations. Considering that accurate extraction of point features is often difficult without the use of man-made reflectors, and the initial approximate values for the unknown transformation parameters must be estimated in advance to ensure the correct operation of those iterative methods, a closed-form solution to linear feature-based registration of point clouds is proposed in this study. Plücker coordinates are used to represent the linear features in three-dimensional space, whereas dual quaternions are employed to represent the spatial transformation. Based on the theory of least squares, an error norm (objective function) is first constructed by assuming that each pair of corresponding linear features is equivalent after registration. Then, by applying the extreme value analysis to the objective function, detailed derivations of the closed-form solution to the proposed linear feature-based registration method are given step by step. Finally, experimental tests are conducted on a real dataset. The derived experimental result demonstrates the feasibility of the proposed solution: By using eigenvalue decomposition to replace the linearization of the objective function, the proposed solution does not require any initial estimates of the unknown transformation parameters, which assures the stability of the registration method.

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Retrieval of Euler rotation angles from 3D similarity transformation based on quaternions

Cited by 16 publications

References 47 publications

Diagnosing gait disorders based on angular variations of knee and ankle joints utilizing a developed wearable motion sensor

Diagnosing gait disorders based on angular variations of knee and ankle joints utilizing a developed wearable motion sensor

Extended WTLS iterative algorithm of 3D similarity transformation based on Gibbs vector

A Closed-Form Solution to Linear Feature-Based Registration of LiDAR Point Clouds

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