A Quaternion Gradient Operator and Its Applications

Mandic, Danilo P.; Jahanchahi, Cyrus; Took, Clive Cheong

doi:10.1109/lsp.2010.2091126

Cited by 179 publications

(170 citation statements)

References 11 publications

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“…It is called pseudogradient by Mandic et al who propose a quaternion gradient operator in [12]. Using their new derivative rules, we obtain ∂J/∂x * = φ H ǫ − 1/2 ǫ H φ.…”

Section: Resultsmentioning

confidence: 99%

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Sparse Approximations for Quaternionic Signals

Barthélemy

Larue

Mars

2013

Adv. Appl. Clifford Algebras

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Abstract. In this paper, we introduce a new processing procedure for quaternionic signals through consideration of the well-known orthogonal matching pursuit (OMP), which provides sparse approximation. Due to quaternions noncommutativity, two quaternionic extensions are presented: the right-multiplication quaternionic OMP, that can be used to process right-multiplication linear combinations of quaternionic signals, and the left-multiplication quaternionic OMP, that can be used to process left-multiplication linear combinations. As validation, these quaternionic OMP are applied to simulated data. Deconvolution is carried out and presented here with a new spikegram that is designed for visualization of quaternionic coefficients, and finally these are compared to multivariate OMP.

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“…It is called pseudogradient by Mandic et al who propose a quaternion gradient operator in [12]. Using their new derivative rules, we obtain ∂J/∂x * = φ H ǫ − 1/2 ǫ H φ.…”

Section: Resultsmentioning

confidence: 99%

“…(8.8) become: In the same way, we can conclude that the atom which produces the strongest decrease of the MSE ǫ 2 2 is the most correlated to the residue. As for the Q-OMPr, the quaternion gradient operator [12], which gives ∂J/∂x * = ǫφ H − 1/2 φǫ H , does not allow to select the optimal atom.…”

Section: Selection Step For Q-omplmentioning

confidence: 99%

Sparse Approximations for Quaternionic Signals

Barthélemy

Larue

Mars

2013

Adv. Appl. Clifford Algebras

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“…According to the steepest descent method applied to quaternion function, (12,13) the parameters of the multilayer quaternion neural network are given as…”

Section: Quaternion Neural Networkmentioning

confidence: 99%

Design of Quaternion-Neural-Network-Based Self-Tuning Control Systems

2017

Sensors and Materials

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In this study, we investigate the control performance of an adaptive controller using a multilayer quaternion neural network. The control system is a self-tuning controller, the control parameters of which are tuned online by the quaternion neural network to track plant output to follow the desired output generated by a reference model. A proportional-integral-derivative (PID) controller is used as a conventional controller, the parameters of which are tuned by the quaternion neural network. Computational experiments to control a single-input single-output (SISO) discrete-time nonlinear plant are conducted to evaluate the capability and characteristics of the quaternion-neural-networkbased self-tuning PID controller. Experimental results show the feasibility and effectiveness of the proposed controller.

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“…According to [7], [8], the conjugate gradient gives the maximum steepness direction for the optimization surface. Therefore, the conjugate gradient ∇ w * J 0 [n] will be used to derive the update of the coefficient weight vector.…”

Section: Its Gradient Is Given Bymentioning

confidence: 99%

Study of wind profile prediction with a combination of signal processing and computational fluid dynamics

Jiang

Liu

2017

2017 IEEE International Symposium on Circuits and Systems (ISCAS)

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ReuseUnless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. Abstract-Wind profile prediction at different scales plays a crucial role for efficient operation of wind turbines and wind power prediction. This problem can be approached in two different ways: one is based on statistical signal processing techniques and both linear and nonlinear models can be employed either separately or combined together for profile prediction; on the other hand, wind/atmospheric flow analysis is a classical problem in computational fluid dynamics (CFD) in applied mathematics, which employs various numerical methods and algorithms, although it is an extremely time-consuming process with high computational complexity. In this work, a new method is proposed based on synergy's between the signal processing approach and the CFD approach, by alternating the operations of a quaternion-valued least mean square (QLMS) algorithm and the large eddy simulation (LES) in CFD. As demonstrated by simulation results, the proposed method has a much lower computational complexity while maintaining a comparable prediction result.Index Terms-wind profile prediction, linear prediction, quaternion-valued signal processing, computational fluid dynamics

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A Quaternion Gradient Operator and Its Applications

Cited by 179 publications

References 11 publications

Sparse Approximations for Quaternionic Signals

Sparse Approximations for Quaternionic Signals

Design of Quaternion-Neural-Network-Based Self-Tuning Control Systems

Study of wind profile prediction with a combination of signal processing and computational fluid dynamics

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