Geometric-algebra affine projection adaptive filter

Geometric algebra (GA) is an efficient tool to deal with hypercomplex processes due to its special data structure. In this article, we introduce the affine projection algorithm (APA) in the GA domain to provide fast convergence against hypercomplex colored signals. Following the principle of minimal...

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Published inEURASIP journal on advances in signal processing Vol. 2021; no. 1; pp. 1 - 13
Main Authors Ren, Yuetao, Zhi, Yongfeng, Zhang, Jun
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 17.09.2021
Springer
Springer Nature B.V
SpringerOpen
Subjects
Adaptive filter
Adaptive filters
Affine projection
Aircraft
Algebra
Algorithms
Analysis
Calculus
Colored signal
Convergence
Cost function
Data structures
Differentiation
Engineering
Geometric algebra
Hypercomplex process
Ill posed problems
Lagrange multiplier
Optimization
Quantum Information Technology
R&D
Research & development
Sensors
Signal processing
Signal,Image and Speech Processing
Spintronics
Stability analysis
Geometric algebra
Hypercomplex process
Affine projection
Adaptive filter
Colored signal
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Abstract Geometric algebra (GA) is an efficient tool to deal with hypercomplex processes due to its special data structure. In this article, we introduce the affine projection algorithm (APA) in the GA domain to provide fast convergence against hypercomplex colored signals. Following the principle of minimal disturbance and the orthogonal affine subspace theory, we formulate the criterion of designing the GA-APA as a constrained optimization problem, which can be solved by the method of Lagrange Multipliers. Then, the differentiation of the cost function is calculated using geometric calculus (the extension of GA to include differentiation) to get the update formula of the GA-APA. The stability of the algorithm is analyzed based on the mean-square deviation. To avoid ill-posed problems, the regularized GA-APA is also given in the following. The simulation results show that the proposed adaptive filters, in comparison with existing methods, achieve a better convergence performance under the condition of colored input signals.
AbstractList Geometric algebra (GA) is an efficient tool to deal with hypercomplex processes due to its special data structure. In this article, we introduce the affine projection algorithm (APA) in the GA domain to provide fast convergence against hypercomplex colored signals. Following the principle of minimal disturbance and the orthogonal affine subspace theory, we formulate the criterion of designing the GA-APA as a constrained optimization problem, which can be solved by the method of Lagrange Multipliers. Then, the differentiation of the cost function is calculated using geometric calculus (the extension of GA to include differentiation) to get the update formula of the GA-APA. The stability of the algorithm is analyzed based on the mean-square deviation. To avoid ill-posed problems, the regularized GA-APA is also given in the following. The simulation results show that the proposed adaptive filters, in comparison with existing methods, achieve a better convergence performance under the condition of colored input signals.
Abstract Geometric algebra (GA) is an efficient tool to deal with hypercomplex processes due to its special data structure. In this article, we introduce the affine projection algorithm (APA) in the GA domain to provide fast convergence against hypercomplex colored signals. Following the principle of minimal disturbance and the orthogonal affine subspace theory, we formulate the criterion of designing the GA-APA as a constrained optimization problem, which can be solved by the method of Lagrange Multipliers. Then, the differentiation of the cost function is calculated using geometric calculus (the extension of GA to include differentiation) to get the update formula of the GA-APA. The stability of the algorithm is analyzed based on the mean-square deviation. To avoid ill-posed problems, the regularized GA-APA is also given in the following. The simulation results show that the proposed adaptive filters, in comparison with existing methods, achieve a better convergence performance under the condition of colored input signals.
ArticleNumber 82
Audience Academic
Author Zhi, Yongfeng
Ren, Yuetao
Zhang, Jun
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Keywords Geometric algebra
Hypercomplex process
Affine projection
Adaptive filter
Colored signal
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  doi: 10.1109/WACV.2016.7477642
– volume: 36
  start-page: 1042
  issue: 9
  year: 2013
  ident: 790_CR19
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.2660
– volume: 311
  start-page: 375
  year: 2017
  ident: 790_CR23
  publication-title: Appl. Math. Comput.
  doi: 10.1016/j.amc.2017.05.027
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Snippet Geometric algebra (GA) is an efficient tool to deal with hypercomplex processes due to its special data structure. In this article, we introduce the affine...
Abstract Geometric algebra (GA) is an efficient tool to deal with hypercomplex processes due to its special data structure. In this article, we introduce the...
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SubjectTerms Adaptive filter
Adaptive filters
Affine projection
Aircraft
Algebra
Algorithms
Analysis
Calculus
Colored signal
Convergence
Cost function
Data structures
Differentiation
Engineering
Geometric algebra
Hypercomplex process
Ill posed problems
Lagrange multiplier
Optimization
Quantum Information Technology
R&D
Research & development
Sensors
Signal processing
Signal,Image and Speech Processing
Spintronics
Stability analysis
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Title Geometric-algebra affine projection adaptive filter
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Volume 2021
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