Geometric-algebra affine projection adaptive filter
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 o...
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Online Access: | https://doi.org/10.1186/s13634-021-00790-y |
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doaj-3efc3b7fc8234aa1845e4b6fc15e6a752021-09-19T11:21:41ZengSpringerOpenEURASIP Journal on Advances in Signal Processing1687-61802021-09-012021111310.1186/s13634-021-00790-yGeometric-algebra affine projection adaptive filterYuetao Ren0Yongfeng Zhi1Jun Zhang2The Research and Development Institute in Shenzhen, Northwestern Polytechnical UniversityThe Research and Development Institute in Shenzhen, Northwestern Polytechnical UniversityThe Research and Development Institute in Shenzhen, Northwestern Polytechnical UniversityAbstract 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.https://doi.org/10.1186/s13634-021-00790-yAdaptive filterGeometric algebraAffine projectionHypercomplex processColored signal |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Yuetao Ren Yongfeng Zhi Jun Zhang |
spellingShingle |
Yuetao Ren Yongfeng Zhi Jun Zhang Geometric-algebra affine projection adaptive filter EURASIP Journal on Advances in Signal Processing Adaptive filter Geometric algebra Affine projection Hypercomplex process Colored signal |
author_facet |
Yuetao Ren Yongfeng Zhi Jun Zhang |
author_sort |
Yuetao Ren |
title |
Geometric-algebra affine projection adaptive filter |
title_short |
Geometric-algebra affine projection adaptive filter |
title_full |
Geometric-algebra affine projection adaptive filter |
title_fullStr |
Geometric-algebra affine projection adaptive filter |
title_full_unstemmed |
Geometric-algebra affine projection adaptive filter |
title_sort |
geometric-algebra affine projection adaptive filter |
publisher |
SpringerOpen |
series |
EURASIP Journal on Advances in Signal Processing |
issn |
1687-6180 |
publishDate |
2021-09-01 |
description |
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. |
topic |
Adaptive filter Geometric algebra Affine projection Hypercomplex process Colored signal |
url |
https://doi.org/10.1186/s13634-021-00790-y |
work_keys_str_mv |
AT yuetaoren geometricalgebraaffineprojectionadaptivefilter AT yongfengzhi geometricalgebraaffineprojectionadaptivefilter AT junzhang geometricalgebraaffineprojectionadaptivefilter |
_version_ |
1717375764889862144 |