An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics
Aimed at the problems in which the performance of filters derived from a hypothetical model will decline or the cost of time of the filters derived from a posterior model will increase when prior knowledge and second-order statistics of noise are uncertain, a new filter is proposed. In this paper, a...
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MDPI AG
2021-11-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/21/22/7673 |
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| author | Lin Cao Chuyuan Zhang Zongmin Zhao Dongfeng Wang Kangning Du Chong Fu Jianfeng Gu |
| author_facet | Lin Cao Chuyuan Zhang Zongmin Zhao Dongfeng Wang Kangning Du Chong Fu Jianfeng Gu |
| author_sort | Lin Cao |
| collection | DOAJ |
| description | Aimed at the problems in which the performance of filters derived from a hypothetical model will decline or the cost of time of the filters derived from a posterior model will increase when prior knowledge and second-order statistics of noise are uncertain, a new filter is proposed. In this paper, a Bayesian robust Kalman filter based on posterior noise statistics (KFPNS) is derived, and the recursive equations of this filter are very similar to that of the classical algorithm. Note that the posterior noise distributions are approximated by overdispersed black-box variational inference (O-BBVI). More precisely, we introduce an overdispersed distribution to push more probability density to the tails of variational distribution and incorporated the idea of importance sampling into two strategies of control variates and Rao–Blackwellization in order to reduce the variance of estimators. As a result, the convergence process will speed up. From the simulations, we can observe that the proposed filter has good performance for the model with uncertain noise. Moreover, we verify the proposed algorithm by using a practical multiple-input multiple-output (MIMO) radar system. |
| first_indexed | 2024-03-10T05:04:36Z |
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| id | doaj.art-ec86489691784b5e81708c9f0c22f5cc |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-10T05:04:36Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
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| series | Sensors |
| spelling | doaj.art-ec86489691784b5e81708c9f0c22f5cc2023-11-23T01:27:46ZengMDPI AGSensors1424-82202021-11-012122767310.3390/s21227673An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order StatisticsLin Cao0Chuyuan Zhang1Zongmin Zhao2Dongfeng Wang3Kangning Du4Chong Fu5Jianfeng Gu6Key Laboratory of the Ministry of Education for Optoelectronic Measurement Technology and Instrument, Beijing Information Science and Technology University, Beijing 100101, ChinaKey Laboratory of the Ministry of Education for Optoelectronic Measurement Technology and Instrument, Beijing Information Science and Technology University, Beijing 100101, ChinaKey Laboratory of the Ministry of Education for Optoelectronic Measurement Technology and Instrument, Beijing Information Science and Technology University, Beijing 100101, ChinaBeijing TransMicrowave Technology Company, Beijing 100080, ChinaKey Laboratory of the Ministry of Education for Optoelectronic Measurement Technology and Instrument, Beijing Information Science and Technology University, Beijing 100101, ChinaDepartment of Communication and Electronics Engineering, School of Computer Science and Engineering, Northeastern University, Shenyang 110169, ChinaMoonshot Health, 3700 St-Patrick Street, Suite 102, Montreal, QC H4E 1A2, CanadaAimed at the problems in which the performance of filters derived from a hypothetical model will decline or the cost of time of the filters derived from a posterior model will increase when prior knowledge and second-order statistics of noise are uncertain, a new filter is proposed. In this paper, a Bayesian robust Kalman filter based on posterior noise statistics (KFPNS) is derived, and the recursive equations of this filter are very similar to that of the classical algorithm. Note that the posterior noise distributions are approximated by overdispersed black-box variational inference (O-BBVI). More precisely, we introduce an overdispersed distribution to push more probability density to the tails of variational distribution and incorporated the idea of importance sampling into two strategies of control variates and Rao–Blackwellization in order to reduce the variance of estimators. As a result, the convergence process will speed up. From the simulations, we can observe that the proposed filter has good performance for the model with uncertain noise. Moreover, we verify the proposed algorithm by using a practical multiple-input multiple-output (MIMO) radar system.https://www.mdpi.com/1424-8220/21/22/7673MIMO radarKalman filterBayesian robustnessuncertain noiseposterior noise statisticsproposal distribution |
| spellingShingle | Lin Cao Chuyuan Zhang Zongmin Zhao Dongfeng Wang Kangning Du Chong Fu Jianfeng Gu An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics Sensors MIMO radar Kalman filter Bayesian robustness uncertain noise posterior noise statistics proposal distribution |
| title | An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics |
| title_full | An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics |
| title_fullStr | An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics |
| title_full_unstemmed | An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics |
| title_short | An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics |
| title_sort | overdispersed black box variational bayesian kalman filter with inaccurate noise second order statistics |
| topic | MIMO radar Kalman filter Bayesian robustness uncertain noise posterior noise statistics proposal distribution |
| url | https://www.mdpi.com/1424-8220/21/22/7673 |
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