3D Coordinate-coupled Variable Structure Multiple Model Estimator for Maneuvering Target Tracking
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摘要: 在3维空间机动目标跟踪过程中，目标运动先验未知和坐标耦合误差会引起运动模型-模式失配，而模型-模式失配会引起状态估计有偏。该文根据目标运动速度正交条件修正状态转移矩阵，利用原始-对偶正则约束空间测量到球面可行域，结合自适应转弯率模型和无迹卡尔曼滤波(UKF)，进行模型状态滤波并融合状态估计的一致输出，推导3维变结构多模型无迹卡尔曼滤波(VSMMUKF)算法。实验结果表明，相比多模重要性无迹卡尔曼滤波(MIUKF)算法，VSMMUKF计算量相当，能够更准确地拟合3维空间点目标机动运动。相比于交互多模型最大最小粒子滤波(IMM-MPF)算法，VSMMUKF跟踪固定翼无人机(UAV)的滤波精度提升了2.8%～59.9%，整体算法负担减小了1个数量级。Abstract: In the 3D maneuvering target tracking, unknown prior and coordinate coupling errors can cause model-mode mismatch and state estimation bias. In this paper, the state transition matrices are modified based on the target velocity-orthogonal condition, the spherical feasible domain is approximated by using the primal-dual regularization, and the adaptive turn rate model is combined in the frame of Unscented Kalman Filtering (UKF) to estimate the model-conditioned state, attaining the consistent output processing. 3D Variable Structure Multi-Model UKF (VSMMUKF) algorithm is derived. Simulation results show that, compared to the Multimode Importance UKF (MIUKF) algorithm, VSMMUKF can more accurately fit the maneuvering motion of 3D spatial point target with the comparable computational complexity; Compared to the Interactive Multi-model Maximum Minimum Particle Filtering (IMM-MPF) algorithm, the filtering accuracy of VSMMUKF for tracking a fixed-wing Unmanned Aerial Vehicle (UAV) has improved by 2.8%～59.9%, and the overall computation burden has reduced an order of magnitude.
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表 1 表100轮蒙特卡罗实验统计滤波误差(均值、最大值及协方差)和实验运行时间
算法 位置均方根误差 $ x $轴上滤波误差 $ y $轴上滤波误差 $ z $轴上滤波误差 运行时间 (s) 均值 (m) 标准差 (m) 最大值 (m) 标准差 (m) 最大值 (m) 标准差 (m) 最大值 (m) 标准差 (m2) MIUKF 18.34 10.10 –25.41 10.19 27.28 10.70 17.04 5.42 1.36 IMM-MPF 9.69 4.68 –14.05 4.94 16.63 6.06 8.36 2.18 16.05 VSMUKF 3.88 2.05 –5.45 2.24 6.97 2.66 –5.11 2.12 5.93 
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