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Article

Trajectory PHD Filter for Adaptive Measurement Noise Covariance Based on Variational Bayesian Approximation

1
Laboratory of Array and Information Processing, College of Computer and Information, Hohai University, Nanjing 210098, China
2
College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, China
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The 28th Research Institute of China Electronics Technology Group Corporation, Nanjing 210007, China
*
Author to whom correspondence should be addressed.
Academic Editor: Marco Ferrari
Appl. Sci. 2022, 12(13), 6388; https://doi.org/10.3390/app12136388
Received: 23 May 2022 / Revised: 12 June 2022 / Accepted: 20 June 2022 / Published: 23 June 2022
(This article belongs to the Section Electrical, Electronics and Communications Engineering)
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. View Full-Text
Keywords: trajectory PHD filter; variational Bayesian approximation; noise covariance matrix; inverse Gamma distribution; estimation of trajectory trajectory PHD filter; variational Bayesian approximation; noise covariance matrix; inverse Gamma distribution; estimation of trajectory
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MDPI and ACS Style

Lu, X.; Jing, D.; Jiang, D.; Gao, Y.; Yang, J.; Li, Y.; Li, W.; Tao, J.; Liu, M. Trajectory PHD Filter for Adaptive Measurement Noise Covariance Based on Variational Bayesian Approximation. Appl. Sci. 2022, 12, 6388. https://doi.org/10.3390/app12136388

AMA Style

Lu X, Jing D, Jiang D, Gao Y, Yang J, Li Y, Li W, Tao J, Liu M. Trajectory PHD Filter for Adaptive Measurement Noise Covariance Based on Variational Bayesian Approximation. Applied Sciences. 2022; 12(13):6388. https://doi.org/10.3390/app12136388

Chicago/Turabian Style

Lu, Xingchen, Dahai Jing, Defu Jiang, Yiyue Gao, Jialin Yang, Yao Li, Wendong Li, Jin Tao, and Ming Liu. 2022. "Trajectory PHD Filter for Adaptive Measurement Noise Covariance Based on Variational Bayesian Approximation" Applied Sciences 12, no. 13: 6388. https://doi.org/10.3390/app12136388

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