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针对粒子流滤波器中粒子速度场计算复杂,难以滤波求解的问题,提出一种基于弱形式解的粒子流滤波器.通过将粒子速度场等效为势函数的梯度,推导该速度场所满足的偏微分方程的弱形式;应用Galerkin有限元法和蒙特卡罗积分法,推导出一个易于计算的弱形式常数近似解.仿真算例表明,在一定初始条件下,多峰型后验分布会使高斯假设滤波器局部收敛,而粒子流滤波器是有效的,且具有较高的跟踪精度和较好的鲁棒性.
Aiming at the problem that particle velocity field is complex and hard to be solved by particle filter in particle filter, a particle filter based on weak form solution is proposed. The particle velocity field is equivalent to the gradient of potential function, A weak form of partial differential equations is obtained. An approximate solution of weak form constant is derived by using Galerkin finite element method and Monte Carlo integration method. The simulation results show that under certain initial conditions, multimodal posterior distribution Gaussian hypothesis filter local convergence, and particle stream filter is effective, and has high tracking accuracy and better robustness.