由于多伯努利滤波器直接近似递推了多目标状态的后验概率密度，使得多目标跟踪问题在基于随机有限集理论框架下的求解及目标状态的估计显得更为直观。本文针对一个状态可分解(线性/非线性)的状态空间模型，分析基于Rao-Blackwell定理的滤波估计方法，结合噪声的去相关构造线性状态的滤波方程。文中详细推导并提出Rao-Blackwellized粒子势均衡多目标多伯努利滤波器的一般实现形式，包括给出多伯努利非线性状态粒子滤波的实现形式，并结合非线性滤波结果给出多伯努利线性状态的递推滤波公式。本文提出的滤波器实现方法能够在更低维的状态空间上进行采样，滤波器的整体跟踪性能得到提高。多目标跟踪的仿真实验结果验证了该算法的有效性。%The multi-Bernoulli filter propagates approximately the multi-target posterior density so that solving target tracking problem and extracting target state based on random finite set are more tractable. Considering a state space model whose state can be divided into linear and nonlinear part, this paper analyzes the Rao-Blackwell theorem based filtering algorithm. Then, using the corresponding algorithm of decorrelation of state noises, we presents the filtering formula for linear state. Moreover, this paper proposes a Rao-Blackwellized particle cardinality balanced multi-target multi-Bernoulli filter. This algorithm firstly implements the particle filtering for multi-Bernoulli nonlinear state, and the filtering formula of multi-Bernoulli linear state is derived afterwards based on the nonlinear filtering result. The proposed filter can sample particle in a lower dimensional state space and improve the overall target tracking performance. The simulation results of the multi-target tracking show the effectiveness of the proposed approach.
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