A Connection Between the Kalman Filter and an Optimized LMS Algorithm for Bilinear Forms
The system identification problem becomes more challenging when the parameter space increases. Recently, several works have focused on the identification of bilinear forms, which are related to the impulse responses of a spatiotemporal model, in the context of a multiple-input/single-output system....
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-12-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/11/12/211 |
| _version_ | 1819289638244712448 |
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| author | Laura-Maria Dogariu Silviu Ciochină Constantin Paleologu Jacob Benesty |
| author_facet | Laura-Maria Dogariu Silviu Ciochină Constantin Paleologu Jacob Benesty |
| author_sort | Laura-Maria Dogariu |
| collection | DOAJ |
| description | The system identification problem becomes more challenging when the parameter space increases. Recently, several works have focused on the identification of bilinear forms, which are related to the impulse responses of a spatiotemporal model, in the context of a multiple-input/single-output system. In this framework, the problem was addressed in terms of the Wiener filter and different basic adaptive algorithms. This paper studies two types of algorithms tailored for the identification of such bilinear forms, i.e., the Kalman filter (along with its simplified version) and an optimized least-mean-square (LMS) algorithm. Also, a comparison between them is performed, which shows interesting similarities. In addition to the mathematical derivation of the algorithms, we also provide extensive experimental results, which support the theoretical findings and indicate the good performance of the proposed solutions. |
| first_indexed | 2024-12-24T03:10:02Z |
| format | Article |
| id | doaj.art-92c9242ed375412985e3ccfa09b75764 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-12-24T03:10:02Z |
| publishDate | 2018-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-92c9242ed375412985e3ccfa09b757642022-12-21T17:17:51ZengMDPI AGAlgorithms1999-48932018-12-01111221110.3390/a11120211a11120211A Connection Between the Kalman Filter and an Optimized LMS Algorithm for Bilinear FormsLaura-Maria Dogariu0Silviu Ciochină1Constantin Paleologu2Jacob Benesty3Department of Telecommunications, University Politehnica of Bucharest, 1-3, Iuliu Maniu Blvd., 061071 Bucharest, RomaniaDepartment of Telecommunications, University Politehnica of Bucharest, 1-3, Iuliu Maniu Blvd., 061071 Bucharest, RomaniaDepartment of Telecommunications, University Politehnica of Bucharest, 1-3, Iuliu Maniu Blvd., 061071 Bucharest, RomaniaEnergy Materials Telecommunications Research Centre, National Institute of Scientific Research (INRS-EMT), University of Quebec, Montreal, QC H5A 1K6, CanadaThe system identification problem becomes more challenging when the parameter space increases. Recently, several works have focused on the identification of bilinear forms, which are related to the impulse responses of a spatiotemporal model, in the context of a multiple-input/single-output system. In this framework, the problem was addressed in terms of the Wiener filter and different basic adaptive algorithms. This paper studies two types of algorithms tailored for the identification of such bilinear forms, i.e., the Kalman filter (along with its simplified version) and an optimized least-mean-square (LMS) algorithm. Also, a comparison between them is performed, which shows interesting similarities. In addition to the mathematical derivation of the algorithms, we also provide extensive experimental results, which support the theoretical findings and indicate the good performance of the proposed solutions.https://www.mdpi.com/1999-4893/11/12/211adaptive filterKalman filteroptimized LMS algorithmbilinear formssystem identification |
| spellingShingle | Laura-Maria Dogariu Silviu Ciochină Constantin Paleologu Jacob Benesty A Connection Between the Kalman Filter and an Optimized LMS Algorithm for Bilinear Forms Algorithms adaptive filter Kalman filter optimized LMS algorithm bilinear forms system identification |
| title | A Connection Between the Kalman Filter and an Optimized LMS Algorithm for Bilinear Forms |
| title_full | A Connection Between the Kalman Filter and an Optimized LMS Algorithm for Bilinear Forms |
| title_fullStr | A Connection Between the Kalman Filter and an Optimized LMS Algorithm for Bilinear Forms |
| title_full_unstemmed | A Connection Between the Kalman Filter and an Optimized LMS Algorithm for Bilinear Forms |
| title_short | A Connection Between the Kalman Filter and an Optimized LMS Algorithm for Bilinear Forms |
| title_sort | connection between the kalman filter and an optimized lms algorithm for bilinear forms |
| topic | adaptive filter Kalman filter optimized LMS algorithm bilinear forms system identification |
| url | https://www.mdpi.com/1999-4893/11/12/211 |
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