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Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

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Quaternion-valued nonlinear adaptive filtering.

Bukhari Che Ujang¹, Clive Cheong Took, Danilo P Mandic

¹Department of Electrical and Electronic Engineering, Imperial College London, London, UK. che.che-ujang07@imperial.ac.uk

IEEE Transactions on Neural Networks

|June 30, 2011

Summary

This summary is machine-generated.

Researchers developed new nonlinear adaptive filters using quaternion-valued functions. These filters offer a unified framework for gradient-based learning, improving estimation for complex signals.

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Area of Science:

Signal Processing
Adaptive Filtering
Quaternion Signal Processing

Background:

Traditional adaptive filters face limitations with complex-valued signals.
Developing nonlinear adaptive quaternion-valued models is challenging due to strict analyticity conditions.

Purpose of the Study:

To propose a class of nonlinear quaternion-valued adaptive filtering algorithms.
To establish a unifying framework for gradient-based learning in the quaternion domain.
To enhance filter optimality for both circular and noncircular quaternion signals.

Main Methods:

Utilizing locally analytic nonlinear activation functions, bypassing stringent global analyticity requirements.
Applying stochastic gradient learning algorithms that only need local analyticity.
Introducing widely linear versions of filters using augmented quaternion statistics for second-order optimality.

Main Results:

Demonstrated that quaternion-valued transcendental functions can serve as activation functions.
Derived algorithms with a generic form similar to real- and complex-valued counterparts.
Showcased improved performance for circular and noncircular quaternion signals through simulations.

Conclusions:

The proposed nonlinear adaptive quaternion filters provide a flexible and powerful framework.
The methods effectively handle second-order noncircularity in quaternion signals.
Simulations confirm the approach's validity on synthetic and real-world data.