A Novel Least-Mean Kurtosis Adaptive Filtering Algorithm Based on Geometric Algebra
A novel least-mean kurtosis adaptive filtering algorithm based on geometric algebra (GA-LMK) is proposed for multidimensional signal processing. First, taking advantage of geometric algebra (GA) in terms of the representation of multidimensional signal, the GA-LMK algorithm represents a multidimensi...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
IEEE
2019-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/8735755/ |
| _version_ | 1819276193694744576 |
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| author | Rui Wang Yinmei He Chenyang Huang Xiangyang Wang Wenming Cao |
| author_facet | Rui Wang Yinmei He Chenyang Huang Xiangyang Wang Wenming Cao |
| author_sort | Rui Wang |
| collection | DOAJ |
| description | A novel least-mean kurtosis adaptive filtering algorithm based on geometric algebra (GA-LMK) is proposed for multidimensional signal processing. First, taking advantage of geometric algebra (GA) in terms of the representation of multidimensional signal, the GA-LMK algorithm represents a multidimensional signal as a GA multivector. Second, we extend the original least mean kurtosis (LMK) algorithm in GA space for multidimensional signal processing. The proposed GA-LMK algorithm minimizes the cost function of negated kurtosis of the error signal in GA space, and provides a way to make tradeoff problem between convergence rate and steady-state error. Third, we study the steady-state behavior of the GA-LMK algorithm under Gaussian noises to acquire conditions of misadjustment. The simulation results show that our proposed GA-LMK adaptive filtering algorithm can outperform significantly existing the state-of-the-art algorithms in terms of convergence rate and steady-state error. |
| first_indexed | 2024-12-23T23:36:20Z |
| format | Article |
| id | doaj.art-4f48052fa3bb4086b4955587aec36037 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-23T23:36:20Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-4f48052fa3bb4086b4955587aec360372022-12-21T17:25:51ZengIEEEIEEE Access2169-35362019-01-017782987831010.1109/ACCESS.2019.29223438735755A Novel Least-Mean Kurtosis Adaptive Filtering Algorithm Based on Geometric AlgebraRui Wang0https://orcid.org/0000-0002-7974-9510Yinmei He1Chenyang Huang2Xiangyang Wang3Wenming Cao4https://orcid.org/0000-0002-8174-6167School of Communication and Information Engineering, Key laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, Shanghai Institute for Advanced Communication and Data Science, Shanghai University, Shanghai, ChinaSchool of Communication and Information Engineering, Key laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, Shanghai Institute for Advanced Communication and Data Science, Shanghai University, Shanghai, ChinaSchool of Communication and Information Engineering, Key laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, Shanghai Institute for Advanced Communication and Data Science, Shanghai University, Shanghai, ChinaSchool of Communication and Information Engineering, Key laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, Shanghai Institute for Advanced Communication and Data Science, Shanghai University, Shanghai, ChinaCollege of Information Engineering, Shenzhen University, Shenzhen, ChinaA novel least-mean kurtosis adaptive filtering algorithm based on geometric algebra (GA-LMK) is proposed for multidimensional signal processing. First, taking advantage of geometric algebra (GA) in terms of the representation of multidimensional signal, the GA-LMK algorithm represents a multidimensional signal as a GA multivector. Second, we extend the original least mean kurtosis (LMK) algorithm in GA space for multidimensional signal processing. The proposed GA-LMK algorithm minimizes the cost function of negated kurtosis of the error signal in GA space, and provides a way to make tradeoff problem between convergence rate and steady-state error. Third, we study the steady-state behavior of the GA-LMK algorithm under Gaussian noises to acquire conditions of misadjustment. The simulation results show that our proposed GA-LMK adaptive filtering algorithm can outperform significantly existing the state-of-the-art algorithms in terms of convergence rate and steady-state error.https://ieeexplore.ieee.org/document/8735755/Geometric algebraleast-mean kurtosisgeometric calculusadaptive filters |
| spellingShingle | Rui Wang Yinmei He Chenyang Huang Xiangyang Wang Wenming Cao A Novel Least-Mean Kurtosis Adaptive Filtering Algorithm Based on Geometric Algebra IEEE Access Geometric algebra least-mean kurtosis geometric calculus adaptive filters |
| title | A Novel Least-Mean Kurtosis Adaptive Filtering Algorithm Based on Geometric Algebra |
| title_full | A Novel Least-Mean Kurtosis Adaptive Filtering Algorithm Based on Geometric Algebra |
| title_fullStr | A Novel Least-Mean Kurtosis Adaptive Filtering Algorithm Based on Geometric Algebra |
| title_full_unstemmed | A Novel Least-Mean Kurtosis Adaptive Filtering Algorithm Based on Geometric Algebra |
| title_short | A Novel Least-Mean Kurtosis Adaptive Filtering Algorithm Based on Geometric Algebra |
| title_sort | novel least mean kurtosis adaptive filtering algorithm based on geometric algebra |
| topic | Geometric algebra least-mean kurtosis geometric calculus adaptive filters |
| url | https://ieeexplore.ieee.org/document/8735755/ |
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