A Normalized Adaptive Filtering Algorithm Based on Geometric Algebra
In this paper, we extend the original Normalized Least Mean Fourth (NLMF) and Normalized Least Mean Square (NLMS) adaptive filtering algorithms into Geometric Algebra (GA) space to enable them to process multidimensional signals. We redefine the cost functions and propose the GA based NLMF and NLMS...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9091885/ |
| _version_ | 1798002052303945728 |
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| author | Rui Wang Meixiang Liang Yinmei He Xiangyang Wang Wenming Cao |
| author_facet | Rui Wang Meixiang Liang Yinmei He Xiangyang Wang Wenming Cao |
| author_sort | Rui Wang |
| collection | DOAJ |
| description | In this paper, we extend the original Normalized Least Mean Fourth (NLMF) and Normalized Least Mean Square (NLMS) adaptive filtering algorithms into Geometric Algebra (GA) space to enable them to process multidimensional signals. We redefine the cost functions and propose the GA based NLMF and NLMS algorithms (GA-NLMF & GA-NLMS). We take full advantage of the ability of GA to represent multidimensional signals in GA space. GA-NLMS minimizes the cost function of the normalized mean square of the error signal, and remain stable as the input signal of the filter increases. GA-NLMS has fast convergence rate but higher steady-state error. The GA-NLMF algorithm minimizes the cost function of the normalized mean fourth of the error signal. Simulation results show that our proposed GA-NLMS adaptive filtering algorithm outperforms original NLMS algorithm in terms of convergence rate and steady-state error, and GA-NLMF outperforms both NLMF and GA-NLMS algorithms. GA-NLMF has faster convergence rate and lower steady state error, which is proved in the experiments. |
| first_indexed | 2024-04-11T11:46:03Z |
| format | Article |
| id | doaj.art-e9b6cf50dec74c8a85c50d651f5a958b |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-11T11:46:03Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-e9b6cf50dec74c8a85c50d651f5a958b2022-12-22T04:25:35ZengIEEEIEEE Access2169-35362020-01-018928619287410.1109/ACCESS.2020.29942309091885A Normalized Adaptive Filtering Algorithm Based on Geometric AlgebraRui Wang0https://orcid.org/0000-0002-7974-9510Meixiang Liang1Yinmei He2Xiangyang Wang3Wenming Cao4https://orcid.org/0000-0002-8174-6167Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, School of Communication and Information Engineering, Shanghai Institute for Advanced Communication and Data Science, Shanghai University, Shanghai, ChinaKey Laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, School of Communication and Information Engineering, Shanghai Institute for Advanced Communication and Data Science, Shanghai University, Shanghai, ChinaKey Laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, School of Communication and Information Engineering, Shanghai Institute for Advanced Communication and Data Science, Shanghai University, Shanghai, ChinaKey Laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, School of Communication and Information Engineering, Shanghai Institute for Advanced Communication and Data Science, Shanghai University, Shanghai, ChinaCollege of Information Engineering, Shenzhen University, Shenzhen, ChinaIn this paper, we extend the original Normalized Least Mean Fourth (NLMF) and Normalized Least Mean Square (NLMS) adaptive filtering algorithms into Geometric Algebra (GA) space to enable them to process multidimensional signals. We redefine the cost functions and propose the GA based NLMF and NLMS algorithms (GA-NLMF & GA-NLMS). We take full advantage of the ability of GA to represent multidimensional signals in GA space. GA-NLMS minimizes the cost function of the normalized mean square of the error signal, and remain stable as the input signal of the filter increases. GA-NLMS has fast convergence rate but higher steady-state error. The GA-NLMF algorithm minimizes the cost function of the normalized mean fourth of the error signal. Simulation results show that our proposed GA-NLMS adaptive filtering algorithm outperforms original NLMS algorithm in terms of convergence rate and steady-state error, and GA-NLMF outperforms both NLMF and GA-NLMS algorithms. GA-NLMF has faster convergence rate and lower steady state error, which is proved in the experiments.https://ieeexplore.ieee.org/document/9091885/Geometric algebranormalized least mean fourthnormalized least mean squareadaptive filters |
| spellingShingle | Rui Wang Meixiang Liang Yinmei He Xiangyang Wang Wenming Cao A Normalized Adaptive Filtering Algorithm Based on Geometric Algebra IEEE Access Geometric algebra normalized least mean fourth normalized least mean square adaptive filters |
| title | A Normalized Adaptive Filtering Algorithm Based on Geometric Algebra |
| title_full | A Normalized Adaptive Filtering Algorithm Based on Geometric Algebra |
| title_fullStr | A Normalized Adaptive Filtering Algorithm Based on Geometric Algebra |
| title_full_unstemmed | A Normalized Adaptive Filtering Algorithm Based on Geometric Algebra |
| title_short | A Normalized Adaptive Filtering Algorithm Based on Geometric Algebra |
| title_sort | normalized adaptive filtering algorithm based on geometric algebra |
| topic | Geometric algebra normalized least mean fourth normalized least mean square adaptive filters |
| url | https://ieeexplore.ieee.org/document/9091885/ |
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