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摘要: 针对杂波环境下的多个机动目标跟踪问题, 本文将多模型概率假设密度(Multiple-model probability hypothesis density, MM-PHD)滤波器和平滑算法相结合, 提出了MM-PHD前向--后向平滑器. 为了避免引入复杂的随机有限集(Random finite set, RFS)理论, 本文根据PHD的物理空间(Physical space)描述法推导得到了MM-PHD平滑器的后向更新公式. 由于MM-PHD前向--后向平滑器的递推公式中包含有多个积分, 因此它在非线性非高斯条件下没有解析的表达形式. 故本文又给出了它的序贯蒙特卡洛(Sequential Monte Carlo, SMC)实现. 100次蒙特卡洛(Monte Carlo, MC)仿真实验表明, 与MM-PHD滤波器相比, MM-PHD平滑器能够更加精确地估计多个机动目标的个数和状态, 但MM-PHD平滑器存在一定的时间滞后, 并且需要耗费更大的计算代价.Abstract: By integrating the multiple-model probability hypothesis density (MM-PHD) filter with the smoothing algorithms, an MM-PHD forward-backward smoother is proposed in this paper for tracking multiple maneuvering targets in clutter. To avoid use of complex random finite set (RFS) theory, the backward updated equation of the MM-PHD smoother can be derived according to the physical-space explanation of the PHD. Since the MM-PHD forward-backward smoother involves multiple integrals, this renders its recursion analytically intractable in the nonlinear and non-Gaussian conditions. Thus, the sequential Monte Carlo (SMC) method is used to implement the smoother. 100 Monte Carlo (MC) simulation results show that the proposed MM-PHD smoother significantly outperforms the MM-PHD filter in estimating the number and states of the multiple maneuvering targets, although the MM-PHD smoother will have time lag and more expansive computation requirement.
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