Trajectory PHD Filter for Adaptive Measurement Noise Covariance Based on Variational Bayesian Approximation
In order to solve the problem that the measurement noise covariance may be unknown or change with time in actual multi-target tracking, this paper brings the variational Bayesian approximation method into the trajectory probability hypothesis density (TPHD) filter and proposes a variational Bayesian...
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MDPI AG
2022-06-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/12/13/6388 |
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| author | Xingchen Lu Dahai Jing Defu Jiang Yiyue Gao Jialin Yang Yao Li Wendong Li Jin Tao Ming Liu |
| author_facet | Xingchen Lu Dahai Jing Defu Jiang Yiyue Gao Jialin Yang Yao Li Wendong Li Jin Tao Ming Liu |
| author_sort | Xingchen Lu |
| collection | DOAJ |
| description | In order to solve the problem that the measurement noise covariance may be unknown or change with time in actual multi-target tracking, this paper brings the variational Bayesian approximation method into the trajectory probability hypothesis density (TPHD) filter and proposes a variational Bayesian TPHD (VB-TPHD) filter to obtain measurement noise covariance adaptively. By modeling the unknown covariance as the random matrix that obeys the inverse gamma distribution, VB-TPHD filter minimizes the Kullback–Leibler divergence (KLD) and estimates the sequence of multi-trajectory states with noise covariance matrices simultaneously. We propose the Gaussian mixture VB-TPHD (AGM-VB-TPHD) filter under adaptive newborn intensity for linear Gaussian models and also give the extended Kalman (AEK-VB-TPHD) filter and unscented Kalman (AUK-VB-TPHD) filter in nonlinear Gaussian models. The simulation results prove the effectiveness of the idea that the VB-TPHD filter can form robust and stable trajectory filtering while learning adaptive measurement noise statistics. Compared with the tag-VB-PHD filter, the estimated error of the VB-TPHD filter is greatly reduced, and the estimation of the trajectory number is more accurate. |
| first_indexed | 2024-03-09T22:09:04Z |
| format | Article |
| id | doaj.art-0f03ee1f792b414eb3d64b8f78b0b4c5 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-09T22:09:04Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-0f03ee1f792b414eb3d64b8f78b0b4c52023-11-23T19:35:45ZengMDPI AGApplied Sciences2076-34172022-06-011213638810.3390/app12136388Trajectory PHD Filter for Adaptive Measurement Noise Covariance Based on Variational Bayesian ApproximationXingchen Lu0Dahai Jing1Defu Jiang2Yiyue Gao3Jialin Yang4Yao Li5Wendong Li6Jin Tao7Ming Liu8Laboratory of Array and Information Processing, College of Computer and Information, Hohai University, Nanjing 210098, ChinaLaboratory of Array and Information Processing, College of Computer and Information, Hohai University, Nanjing 210098, ChinaLaboratory of Array and Information Processing, College of Computer and Information, Hohai University, Nanjing 210098, ChinaCollege of Energy and Electrical Engineering, Hohai University, Nanjing 210098, ChinaLaboratory of Array and Information Processing, College of Computer and Information, Hohai University, Nanjing 210098, ChinaLaboratory of Array and Information Processing, College of Computer and Information, Hohai University, Nanjing 210098, ChinaLaboratory of Array and Information Processing, College of Computer and Information, Hohai University, Nanjing 210098, ChinaLaboratory of Array and Information Processing, College of Computer and Information, Hohai University, Nanjing 210098, ChinaThe 28th Research Institute of China Electronics Technology Group Corporation, Nanjing 210007, ChinaIn order to solve the problem that the measurement noise covariance may be unknown or change with time in actual multi-target tracking, this paper brings the variational Bayesian approximation method into the trajectory probability hypothesis density (TPHD) filter and proposes a variational Bayesian TPHD (VB-TPHD) filter to obtain measurement noise covariance adaptively. By modeling the unknown covariance as the random matrix that obeys the inverse gamma distribution, VB-TPHD filter minimizes the Kullback–Leibler divergence (KLD) and estimates the sequence of multi-trajectory states with noise covariance matrices simultaneously. We propose the Gaussian mixture VB-TPHD (AGM-VB-TPHD) filter under adaptive newborn intensity for linear Gaussian models and also give the extended Kalman (AEK-VB-TPHD) filter and unscented Kalman (AUK-VB-TPHD) filter in nonlinear Gaussian models. The simulation results prove the effectiveness of the idea that the VB-TPHD filter can form robust and stable trajectory filtering while learning adaptive measurement noise statistics. Compared with the tag-VB-PHD filter, the estimated error of the VB-TPHD filter is greatly reduced, and the estimation of the trajectory number is more accurate.https://www.mdpi.com/2076-3417/12/13/6388trajectory PHD filtervariational Bayesian approximationnoise covariance matrixinverse Gamma distributionestimation of trajectory |
| spellingShingle | Xingchen Lu Dahai Jing Defu Jiang Yiyue Gao Jialin Yang Yao Li Wendong Li Jin Tao Ming Liu Trajectory PHD Filter for Adaptive Measurement Noise Covariance Based on Variational Bayesian Approximation Applied Sciences trajectory PHD filter variational Bayesian approximation noise covariance matrix inverse Gamma distribution estimation of trajectory |
| title | Trajectory PHD Filter for Adaptive Measurement Noise Covariance Based on Variational Bayesian Approximation |
| title_full | Trajectory PHD Filter for Adaptive Measurement Noise Covariance Based on Variational Bayesian Approximation |
| title_fullStr | Trajectory PHD Filter for Adaptive Measurement Noise Covariance Based on Variational Bayesian Approximation |
| title_full_unstemmed | Trajectory PHD Filter for Adaptive Measurement Noise Covariance Based on Variational Bayesian Approximation |
| title_short | Trajectory PHD Filter for Adaptive Measurement Noise Covariance Based on Variational Bayesian Approximation |
| title_sort | trajectory phd filter for adaptive measurement noise covariance based on variational bayesian approximation |
| topic | trajectory PHD filter variational Bayesian approximation noise covariance matrix inverse Gamma distribution estimation of trajectory |
| url | https://www.mdpi.com/2076-3417/12/13/6388 |
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