Averaging Quaternions

Markley, F. Landis; Cheng, Yang; Crassidis, John L.; Oshman, Yaakov

doi:10.2514/1.28949

Cited by 306 publications

(158 citation statements)

References 8 publications

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“…Thus, the translation and rotation parts of the transformation matrix are split, and the rotation matrices are transformed into quaternions. Markley et al (2007) proposed an exact solution for averaging quaternions based on minimizing a weighted sum of squared Frobenius norms. However, as the differences between rotations in our case are small, we use an approximate solution also provided by Markley et al (2007), where quaternions are averaged using , ) (…”

Section: Calibrationmentioning

confidence: 99%

See 1 more Smart Citation

Augmented Reality in Forest Machine Cabin

Palonen¹,

Hyyti

Visala³

2017

IFAC-PapersOnLine

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Augmented reality human machine interface is demonstrated in the cabin of a forest machine outdoors for the first time in real time. In this work, we propose a system setup and a real-time capable algorithm to augment the operator's visual field with measurements from the forest machine and its environment. In the demonstration, an instrumented forestry crane and a lidar are used to model the pose of the crane and its surroundings. In our approach, a camera and an inertial measurement unit are used to estimate the pose of the operator's head in difficult lighting conditions with the help of planar markers placed on the cabin structures. Using the estimate, a point cloud and a crane model are superimposed on the video feed to form an augmented reality view. Our system is tested to work outdoors using a forest machine research platform in real time with encouraging initial results.

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Section: Calibrationmentioning

confidence: 99%

“…The selected method has two known flaws (Markley et al, 2007). The first flaw is that the resulting quaternion is no longer a unit quaternion.…”

Section: Calibrationmentioning

confidence: 99%

Augmented Reality in Forest Machine Cabin

Palonen¹,

Hyyti

Visala³

2017

IFAC-PapersOnLine

View full text Add to dashboard Cite

show abstract

“…Certainly, if ( ( ), ( ) ) of all CCD are known, then can be directly calibrated by Equation (28) using GCPs. (3) According to the equivalent relationship between the attitude matrix and the attitude quaternion, along with quaternion theory [44], the difference between the on-board and post-processed attitudes can be calculated by ∆ = ⊗ , where denotes the post-processed attitude, and denotes the on-board attitude. The quaternion deviation∆ can be transformed to the Euler angle defined in J2000 [45,46].…”

Section: Attitude Accuracy Comparison and Evaluationmentioning

confidence: 99%

High-Precision Attitude Post-Processing and Initial Verification for the ZY-3 Satellite

et al. 2014

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Abstract:Attitude data, which is the important data strongly correlated with the geometric accuracy of optical remote sensing satellite images, are generally obtained using a real-time Extended Kalman Filter (EKF) with star-tracker and gyro data for current high-resolution satellites, such as Orb-view, IKONOS, Quickbird,Pleiades, and ZY-3.We propose a forwardbackward Unscented Kalman Filter (UKF) for post-processing, and the proposed method employs UKF to suppress noise by using an unscented transformation (UT) rather than an EKF in a nonlinear attitude system. Moreover, this method makes full use of the collected data in the fixed-interval and computational resources on the ground, and it determines optimal attitude results by forward-backward filtering and weighted smoothing with the raw star-tracker and gyro data collected for a fixed period. In this study, the principle and implementation of the proposed method are described. The post-processed attitude was compared with the on-board attitude, and the absolute accuracy was evaluated by the two methods. One method compares the positioning accuracy of the object space coordinates with the post-processed and on-board attitude data without using ground control points OPEN ACCESSRemote Sens. 2015, 7 112 (GCPs). The other method compares the tie-point residuals of the image coordinates after a free net adjustment. In addition, the internal and external parameters of the camera were accurately calibrated before use for an objective evaluation of the attitude accuracy. The experimental results reveal that the accuracy of the post-processed attitude is superior to the accuracy of the on-board processed attitude. This method has been applied to the ZiYuan-3 satellite system for processing the raw star-tracker and gyro data daily.

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“…CFC was performed asking the users to change the probe position 40 times in a water tank with a planar membrane in the bottom, changing the configuration of a mechanical linkage that held the probe still while the DRF poses were acquired and averaged. 36 In the experiments, the water temperature was monitored constantly using a digital multimeter (IDM-62T, ISO-tech, United Kingdom).…”

Section: Figmentioning

confidence: 99%

Accurate calibration method for 3D freehand ultrasound probe using virtual plane

et al. 2011

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Purpose : In this paper a new, easy‐to‐manufacture and easy‐to‐use ultrasound (US) probe calibration phantom for 3D freehand scanning is presented and evaluated, together with a new method for achieving an accurate and user‐robust calibration using virtual plane. Methods : The phantom allows the optically tracked US probe to perform two rotations and two translations while keeping the image of a tensioned wire in the image plane. This approach allows obtaining a sharp image of the wire independently from the probe pose. The virtual plane allows the calibration algorithm to converge minimizing the required number of US probe tracked poses. The US image and position data are synchronized via a CORBA interface, created within the Image Guided Surgery Toolkit (IGSTK) framework. The calibration algorithm and the calibration protocol were evaluated in a set of experiments carried out by different test‐users. Results : The calibration method proved to be accurate and precise: 3D point reconstruction accuracy resulted 0.2 mm as mean value, while the precision was 0.4 mm as standard deviation. Conclusions : The technique showed to be suitable for medical applications from morphological diagnosis to intraoperative surgical planning adaption.

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Averaging Quaternions

Cited by 306 publications

References 8 publications

Augmented Reality in Forest Machine Cabin

Augmented Reality in Forest Machine Cabin

High-Precision Attitude Post-Processing and Initial Verification for the ZY-3 Satellite

Accurate calibration method for 3D freehand ultrasound probe using virtual plane

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