(江南大学 物联网工程学院, 江苏 无锡 214122;无锡职业技术学院 物联网技术学院, 江苏 无锡 214122;国防科学技术大学 电子科学与工程学院, 湖南 长沙 410073)
Target Tracking Algorithm Based on Kalman Filtering with Quadratic Equality Constraints
CAO Ya-Lu,YANG Le,LIU Quan-Sheng,PENG Li,GUO Fu-Cheng
(School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China;School of Internet of Things Technology, Wuxi Institute of Technology, Wuxi 214122, China;College of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China)
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Received:May 02, 2013    Revised:August 22, 2013
> 中文摘要: 目标跟踪是无线传感器网络的重要应用之一.研究目标运动轨迹满足一个二次等式约束(quadraticequality constraint)的目标跟踪问题.在实际应用中,当飞行器进行盘旋或者车辆沿弯道行使时,其轨迹均近似满足一个二次等式约束.考虑在卡尔曼滤波(Kalman filtering,简称KF)算法中引入二次等式约束以提高目标跟踪精度.所提出的算法在每个采样时刻首先利用新获取的观测量和无约束卡尔曼滤波算法更新目标运动状态估计,然后利用带二次等式约束的极大似然估计(maximum likelihood estimator,简称MLE)修正目标运动状态估计.在求解约束极大似然问题时,将其看作一类广义信赖域子问题(generalized trust region sub-problem,简称GTRS),以获得全局最优解.仿真结果表明,该算法与现有带二次等式约束的卡尔曼滤波算法相比具有更高的跟踪精度.
Abstract:Target tracking is one of the essential applications of the wireless sensor network. This paper considers the scenario where the target motion trajectory satisfies a quadratic equality constraint. In practice, when an aircraft hovers or a ground vehicle travels along a curve, its trajectory can be represented approximately as a quadratic function. This study applies quadratic constraints in the well-known Kalman filter (KF) to improve its performance in target tracking. The proposed algorithm first utilizes newly obtained positioning measurements and the unconstrained KF to produce an updated state estimation and then refines it using a maximum likelihood estimator (MLE) with quadratic equality constraints. When solving the constrained MLE problem, this paper formulates it as a generalized trust region sub-problem (GTRS) in order to obtain its globally optimal solution. Simulation results show that the proposed algorithm outperforms previously developed nonlinear KF algorithms with quadratic equality constraints in terms of enhanced target tracking accuracy.
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基金项目:国家自然科学基金(61304264, 61305017); 江苏省自然科学基金(BK20130154); 江苏省产学研联合创新资金项目(BY2013015-33) 国家自然科学基金(61304264, 61305017); 江苏省自然科学基金(BK20130154); 江苏省产学研联合创新资金项目(BY2013015-33)
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CAO Ya-Lu,YANG Le,LIU Quan-Sheng,PENG Li,GUO Fu-Cheng.Target Tracking Algorithm Based on Kalman Filtering with Quadratic Equality Constraints.Journal of Software,2013,24(S1):24-32