δ-广义标记多伯努利滤波器的非线性应用扩展
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摘要
针对非线性模型下δ-广义标记多伯努利(δ-GLMB)滤波器的序贯蒙特卡洛(SMC)实现过程计算复杂度过高、难以实现快速准确滤波的问题,给出了δ-GLMB滤波器的积分卡尔曼高斯混合(QK-GM)实现过程。该算法基于Gauss-Hermite数值积分规则获取一组带权重的积分点,利用这些积分点求取多目标密度函数的均值和协方差矩阵。将该算法与已有的扩展卡尔曼高斯混合(EK-GM)实现、无味卡尔曼高斯混合(UK-GM)实现和SMC实现在不同的杂波强度和检测概率条件下就多目标跟踪精度和时间消耗等方面做了较为详细的对比,结果表明,与SMC实现方法相比,QK-GM-δ-GLMB算法能以完全可接受的时间开销为代价,将多目标跟踪精度提高10%以上。该算法为δ-GLMB滤波器在非线性场景中的应用提供了一种新的实现方法。
Quadrature Kalman Gaussian mixture(QK-GM) implementation for δ-generalized labeled multi-Bernoulli(δ-GLMB) filter is proposed to solve the problem that the sequential Monte Carlo(SMC) implementation for δ-GLMB filter in nonlinear model is too complex to realize fast and accurate filtering. The algorithm is based on the Gauss-Hermite quadrature rule to obtain a set of weighted quadrature points, and these points are then utilized to calculate mean values and covariance matrixes of the multiobjective density functions. The proposed QK-GM implementation is compared with the existing algorithms, including extended Kalman Gaussian mixture(EK-GM), unscented Kalman Gaussian mixture(UK-GM) and SMC implementation, in detail in terms of tracking accuracy and time consumption for multi-target tracking in the presence of different clutter densities and detection probabilities. Simulation results and a comparison with SMC method show that the QK-GM implementation of δ-GLMB filter improves the multi-target tracking accuracy by more than 10% at the expense of a completely acceptable time cost. The proposed algorithm may provide a new method for applications of δ-GLMB filter in nonlinear scenes.
Quadrature Kalman Gaussian mixture(QK-GM) implementation for δ-generalized labeled multi-Bernoulli(δ-GLMB) filter is proposed to solve the problem that the sequential Monte Carlo(SMC) implementation for δ-GLMB filter in nonlinear model is too complex to realize fast and accurate filtering. The algorithm is based on the Gauss-Hermite quadrature rule to obtain a set of weighted quadrature points, and these points are then utilized to calculate mean values and covariance matrixes of the multiobjective density functions. The proposed QK-GM implementation is compared with the existing algorithms, including extended Kalman Gaussian mixture(EK-GM), unscented Kalman Gaussian mixture(UK-GM) and SMC implementation, in detail in terms of tracking accuracy and time consumption for multi-target tracking in the presence of different clutter densities and detection probabilities. Simulation results and a comparison with SMC method show that the QK-GM implementation of δ-GLMB filter improves the multi-target tracking accuracy by more than 10% at the expense of a completely acceptable time cost. The proposed algorithm may provide a new method for applications of δ-GLMB filter in nonlinear scenes.
引文
[1] MAHLER R.Statistical multisource-multitarget information fusion [M].Norwood,MA,USA:Artech House,2007:655-682.
[2] MAHLER R.Advances in statistical multisource-multitarget information fusion [M].Norwood,MA,USA:Artech House,2014:435-500.
[3] BLACKMAN S,POPOLI R.Design and analysis of modern tracking systems [M].Norwood,MA,USA:Artech House,1999:98-120.
[4] BAR-SHALOM Y,WILLETT P K,TIAN X.Tracking and data fusion:a handbook of algorithms [M].Bloomfield,CT,USA:YBS Publishing,2011:308-367.
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[7] MAHLER R.PHD filters of higher order in target number [J].IEEE Transactions on Aerospace and Electronic Systems,2007,43(4):1523-1543.
[8] VO B T,VO B N.Labeled random finite sets and multi-object conjugate priors [J].IEEE Transactions on Signal Processing,2013,61(13):3460-3475.
[9] VO B N,VO B T,PHUNG D.Labeled random finite sets and the Bayes multi-target tracking filter [J].IEEE Transactions on Signal Processing,2014,62(24):6554-6567.
[10] VO B N,VO B T,HOANG H.An efficient implementation of the generalized labeled multi-Bernoulli filter [J].IEEE Transactions on Signal Processing,2017,65(8):1975-1987.
[11] ATHANS M,WISHNER R P,BERTOLINI A.Suboptimal state estimation for continuous time nonlinear systems from discrete noisy measurements [J].IEEE Transactions on Automatic Control,1968,13(5):504-514.
[12] JULIER S J,UHLMANN J K,DURRANT-WHYTE H F.A new method for the particular transformation of means and covariances in filters and estimators [J].IEEE Transactions on Automatic Control,2000,45(3):477-482.
[13] 巫春玲,韩崇昭.平方根求积分卡尔曼滤波器 [J].电子学报,2009,37(5):987-992.WU Chunling,HAN Chongzhao.Square-root quadrature Kalman filter [J].Acta Electronica Sinica,2009,37(5):987-992.
[14] 巫春玲,韩崇昭.求积分卡尔曼粒子滤波算法 [J].西安交通大学学报,2009,43(2):25-28.WU Chunling,HAN Chongzhao.Quadrature Kalman filter [J].Journal of Xi’an Jiaotong University,2009,43(2):25-28.
[15] ARASARATNAM I,HAYKIN S,ELLIOTT R J.Discrete-time nonlinear filtering algorithms using Gauss-Hermite quadrature [J].Proceedings of the IEEE,2007,95(5):953-977.
[16] VO B N,MA W.The Gaussian mixture probability hypothesis density filter [J].IEEE Transactions on Signal Processing,2006,54(11):4091-4104.
[17] SCHUHMACHER D,VO B T,VO B N.A consistent metric for performance evaluation of multi-object filters [J].IEEE Transactions on Signal Processing,2008,56(8):3447-3457.
[2] MAHLER R.Advances in statistical multisource-multitarget information fusion [M].Norwood,MA,USA:Artech House,2014:435-500.
[3] BLACKMAN S,POPOLI R.Design and analysis of modern tracking systems [M].Norwood,MA,USA:Artech House,1999:98-120.
[4] BAR-SHALOM Y,WILLETT P K,TIAN X.Tracking and data fusion:a handbook of algorithms [M].Bloomfield,CT,USA:YBS Publishing,2011:308-367.
[5] MALLICK M,CORALUPPI S,CARTHEL C.Multi-target tracking using multiple hypothesis tracking,in integrated tracking,classification,and sensor management:theory and applications [M].New York,USA:Wiley,2012:165-190.
[6] MAHLER R.Multi-target Bayes filtering via first-order multi-target moments [J].IEEE Transactions on Aerospace and Electronic Systems,2003,39(4):1152-1178.
[7] MAHLER R.PHD filters of higher order in target number [J].IEEE Transactions on Aerospace and Electronic Systems,2007,43(4):1523-1543.
[8] VO B T,VO B N.Labeled random finite sets and multi-object conjugate priors [J].IEEE Transactions on Signal Processing,2013,61(13):3460-3475.
[9] VO B N,VO B T,PHUNG D.Labeled random finite sets and the Bayes multi-target tracking filter [J].IEEE Transactions on Signal Processing,2014,62(24):6554-6567.
[10] VO B N,VO B T,HOANG H.An efficient implementation of the generalized labeled multi-Bernoulli filter [J].IEEE Transactions on Signal Processing,2017,65(8):1975-1987.
[11] ATHANS M,WISHNER R P,BERTOLINI A.Suboptimal state estimation for continuous time nonlinear systems from discrete noisy measurements [J].IEEE Transactions on Automatic Control,1968,13(5):504-514.
[12] JULIER S J,UHLMANN J K,DURRANT-WHYTE H F.A new method for the particular transformation of means and covariances in filters and estimators [J].IEEE Transactions on Automatic Control,2000,45(3):477-482.
[13] 巫春玲,韩崇昭.平方根求积分卡尔曼滤波器 [J].电子学报,2009,37(5):987-992.WU Chunling,HAN Chongzhao.Square-root quadrature Kalman filter [J].Acta Electronica Sinica,2009,37(5):987-992.
[14] 巫春玲,韩崇昭.求积分卡尔曼粒子滤波算法 [J].西安交通大学学报,2009,43(2):25-28.WU Chunling,HAN Chongzhao.Quadrature Kalman filter [J].Journal of Xi’an Jiaotong University,2009,43(2):25-28.
[15] ARASARATNAM I,HAYKIN S,ELLIOTT R J.Discrete-time nonlinear filtering algorithms using Gauss-Hermite quadrature [J].Proceedings of the IEEE,2007,95(5):953-977.
[16] VO B N,MA W.The Gaussian mixture probability hypothesis density filter [J].IEEE Transactions on Signal Processing,2006,54(11):4091-4104.
[17] SCHUHMACHER D,VO B T,VO B N.A consistent metric for performance evaluation of multi-object filters [J].IEEE Transactions on Signal Processing,2008,56(8):3447-3457.