带非线性约束的自适应高斯和卡尔曼滤波目标跟踪算法
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摘要
无线传感网络中运动目标状态通常满足某种非线性状态约束,为了提高对传感网络中运动目标的跟踪精度,降低非高斯噪声对状态估计的影响,避免高斯项数在迭代过程中的冗余累积,提出一种带非线性约束的权值自适应高斯和卡尔曼滤波算法;算法在每个时刻计算目标当前状态的高斯子项集合,并对每个高斯子项分别以无迹卡尔曼滤波进行状态估计;设计了一种高斯子项权值自适应策略动态调节子项权值,以实现无约束状态下的全局估计;将目标的非线性状态约束引入滤波器结构中时,考虑将其看作一类无约束状态估计的约束投影问题,通过状态约束信息先验来修正运动目标的状态估计;仿真结果表明,该算法与目前的非线性约束卡尔曼滤波相比具有更高的跟踪精度。
The state of the moving target in the wireless sensor network usually satisfies a certain nonlinear constraint.In order to improve the tracking accuracy of moving targets in the sensor network,and avoid redundant accumulation of Gaussian terms in the iterative process at the same time,a self-adaptive Gaussian sum Kalman filter with nonlinear constraints is proposed.Firstly,the algorithm calculates the Gaussian subitems of the target state,and the state estimation is performed by unscented Kalman filter for each Gaussian subitem;Then an adaptive strategy of Gaussian subitem weight is designed to dynamically adjust the subitem weight throughout the filtering process,which results that the global estimate is obtained under unconstrained conditions.Finally,nonlinear state constraint of the target is introduced into the filter.Considering it as a constrained projection problem for unconstrained state estimation,the state estimation of moving targets in sensor networks is corrected by using constraint information.Simulation results show that the proposed algorithm outperforms previously developed Kalman filter algorithms with nonlinear constraints in term of improving target tracking accuracy.
The state of the moving target in the wireless sensor network usually satisfies a certain nonlinear constraint.In order to improve the tracking accuracy of moving targets in the sensor network,and avoid redundant accumulation of Gaussian terms in the iterative process at the same time,a self-adaptive Gaussian sum Kalman filter with nonlinear constraints is proposed.Firstly,the algorithm calculates the Gaussian subitems of the target state,and the state estimation is performed by unscented Kalman filter for each Gaussian subitem;Then an adaptive strategy of Gaussian subitem weight is designed to dynamically adjust the subitem weight throughout the filtering process,which results that the global estimate is obtained under unconstrained conditions.Finally,nonlinear state constraint of the target is introduced into the filter.Considering it as a constrained projection problem for unconstrained state estimation,the state estimation of moving targets in sensor networks is corrected by using constraint information.Simulation results show that the proposed algorithm outperforms previously developed Kalman filter algorithms with nonlinear constraints in term of improving target tracking accuracy.
引文
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[14]Yang C,Blasch E.Kalman filtering with nonlinear state constraints[J].IEEE Transactions on Aerospace&Electronic Systems,2009,45(1):70-84.14.
[15]Bruno O S,et al.State estimation for linear and non-linear equality-constrained systems[J].Control,2009,82(5):918-936.
[16]Teixeira,et al.Unscented filtering for equality-constrained nonlinear systems[A].American Control Conference IEEE Xplore[C].2008:39-44.
[2]孟静,陈罡,高晓丁.多移动机器人的目标跟踪研究[J].计算机测量与控制,2016,24(4):141-145.
[3]Leong P H,Arulampalam S,Lamahewa T A,et al.A Gaussian-sum based cubature Kalman filter for Bearings-Only tracking[J].IEEE Transactions on Aerospace&Electronic Systems,2013,49(2):1161-1176.
[4]Mendel J.Optimal filtering[J].IEEE Transactions on Automatic Control,1980,25(3):615-616.
[5]Simon D,Chia T L.Kalman filtering with state equality constraints[J].IEEE Transactions on Aerospace Electronic Systems,2002,38(1):128-136.
[6]Caputi M,Moose R L.A modified Gaussian sum approach to estimation of non-Gaussian signals[J].IEEE Transactions on Aerospace&Electronic Systems,1993,29(2):446-451.
[7]Horwood J T,Aragon N D,Poore A B.Adaptive Gaussian Sum Filters for Space Surveillance Tracking[J].Journal of the Astronautical Sciences,2011,56(8):1777-1790.
[8]Gokce M,Kuzuoglu M.Unscented Kalman filter-aided Gaussian sum filter[J].Radar Sonar&Navigation Iet,2015,9(5):589-599.
[9]Wang L,Cheng X.Algorithm of gaussian sum filter based on high-order UKF for dynamic state estimation[J].Control Automation&Systems,2015,13(3):652-661.
[10]Kottakki K K,Bhushan M,Bhartiya S.Optimization based constrained Gaussian sum unscented Kalman Filter[J].Ifac Papers online,2016,49(1):59-64.
[11]Kottakki K K,Bhushan M,Bhartiya S.Monte Carlo Gaussian sum filter for state estimation of nonlinear dynamical systems[J].IFAC-Papers OnLine,2016,49(1):65-70.
[12]Jiang H N,Cai Y.Bearings-only tracking with a Gaussiansum based ensemble Kalman filter[A].Chinese Control and Decision Conference[C].2017:4823-4828.
[13]Simon D.Kalman filtering with state constraints:a survey of linear and nonlinear algorithms[J].Iet Control Theory&Applications,2010,4(8):1303-1318.
[14]Yang C,Blasch E.Kalman filtering with nonlinear state constraints[J].IEEE Transactions on Aerospace&Electronic Systems,2009,45(1):70-84.14.
[15]Bruno O S,et al.State estimation for linear and non-linear equality-constrained systems[J].Control,2009,82(5):918-936.
[16]Teixeira,et al.Unscented filtering for equality-constrained nonlinear systems[A].American Control Conference IEEE Xplore[C].2008:39-44.