基于弱形式解的粒子流滤波器

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.

Weak solution based particle flow filter

A weak solution based particle flow filter is proposed for the difficulties of particle velocity field computation existed in the present particle flow filter. By regarding the particle velocity field as the gradient of the potential function, a weak formulation of partial differential equation(PDE) in which the velocity field is satisfied is derived. Subsequently, a weak solution with low computation is derived by using Galerkin method and Monte-Carlo integral. Simulation results show that local convergence of Gaussian approximation based filter occurs under certain initial conditions whereas the particle flow filter is nevertheless effective, with preferable tracking accuracy and robustness.