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Adaptive beamforming 1

Gradient operator 1

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adaptive filtering 1

deep-sea coblat-crusts 1

design of self-adaptive circuit 1

giant magnetostrictive material (GMM) self-sensing actuator 1

least means square (LMS) self-adapting algorithm 1

microtopography 1

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Study on the ultrasonic distance measurement system for seabed coblat crusts microtopography based on LMS

Liu Ai’jun,Zhou Zhijin,Bu Yingyong,Long Yingchun

Strategic Study of CAE 2009, Volume 11, Issue 8, Pages 79-82

Abstract: Through continuous adjustment of the quantity of delay time, the minimum mean square (LMS) error was

Keywords： deep-sea coblat-crusts microtopography LMS single-beam measurement adaptive filtering

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Signal separation technology for diphase opposition giant magnetostrictive self-sensing actuator

Xinhua WANG, Shuwen SUN, Jian ZHEN, Qianyi YA, Deguo WANG,

Frontiers of Mechanical Engineering 2010, Volume 5, Issue 2, Pages 176-183 doi: 10.1007/s11465-010-0001-5

Abstract: technology for the giant magnetostrictive self-sensing actuator comes true by the least means square (LMS

Keywords： giant magnetostrictive material (GMM) self-sensing actuator least means square (LMS) self-adapting algorithm

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Properties of a general quaternion-valued gradient operator and its applications to signal processing

Meng-di Jiang, Yi Li, Wei Liu,w.liu@sheffield.ac.uk

Frontiers of Information Technology & Electronic Engineering 2016, Volume 17, Issue 2, Pages 83-95 doi: 10.1631/FITEE.1500334

Abstract: The gradients of a -valued function are often required for ic algorithms. The HR provides a viable framework and has found a number of applications. However, the applications so far have been limited to mainly real-valued functions and linear -valued functions. To generalize the operator to nonlinear functions, we define a restricted version of the HR operator, which comes in two versions, the left and the right ones. We then present a detailed analysis of the properties of the operators, including several different product rules and chain rules. Using the new rules, we derive explicit expressions for the derivatives of a class of regular nonlinear -valued functions, and prove that the restricted HR gradients are consistent with the gradients in the real domain. As an application, the derivation of the least mean square algorithm and a nonlinear adaptive algorithm is provided. Simulation results based on vector sensor arrays are presented as an example to demonstrate the effectiveness of the -valued signal model and the derived algorithm.

Keywords： Quaternion Gradient operator Signal processing Least mean square (LMS) algorithm Nonlinear adaptive