基于变尺度变换减少Sigma点的粒子滤波算法研究

A Particle Filter Algorithm Based on Scaled UKF with Reduced Sigma Points

为了减少传统无味粒子滤波(Unscented particle filter,UPF)算法的计算负担,提出了最小斜度单形无味转换(Minimal skew simplex UT,MSSUT)方法,这种方法是用最小斜度无味卡尔曼滤波来产生粒子的重要性函数.它不仅能够扩大重要性分布与系统状态的后验概率密度的重叠性,而且能够通过减少Sigma点来减少计算负担.但是,随着状态空间维数的增加,Sigma点集的覆盖半径增大,导致了Sigma点集的聚集性变差.辅助随机变量变尺度无味变换(Auxiliary random variable formulation of the scaled unscented transformation,ASUT)能够克服Sigma点集分布扩展的缺点.所以,提出了一种高维空间中改进的变尺度最小斜度无味粒子滤波(Scaled minimal skew simplex unscented particle filter,SMSSUPF)算法.仿真结果表明:在高维状态空间中,与传统的无味粒子滤波(UPF)相比,计算复杂度和计算负担显著减少.与最小斜度无味粒子滤波(Minimal skew simplex unscented particle filter,MSSUPF)相比,SMSSUPF减少了系统噪声方差和测量噪声方差所带来的估计误差.

In order to reduce the computation burden of con- ventional unscented particle filter （UPF）, a method for particle filter based on minimal skew simplex unscented transformation （MSSUT） is proposed. This method uses a minimal skew sim- plex unscented Kalman filter to generate importance distribu- tion of the particle filter. It can extend its overlaps and pos- terior probability density, and reduce the computation burden by reducing sigma points. However, the sigma point set cover- age radius expands over dimension of state space, which results in the deterioration of the aggregation of sigma points. Auxil- iary random variable formulation of the scaled transformation can overcome the defect of sigma point set distribution expan- sion. So a scaled minimal skew simplex unscented particle filter （SMSSUPF） is introduced. It is shown by simulation that com- pared with conventional unscented particle filter, the computa- tion complexity of SMSSUPF can be reduced, the computation burden can be reduced, and compared with spherical simplex unscented particle filter （MSSUPF）, SMSSUPF can reduce the system noise and the measurement noise variance estimation error.