迭代容积平方根粒子滤波

Iterated cubature square root particle filter

为解决先验概率作为重要性密度函数因未融入最新的观测信息而造成测量精度低的问题,提出了迭代容积粒子滤波。此算法采用Gauss-Newton迭代和容积卡尔曼滤波设计重要性密度函数,在迭代过程中不断修改新息的方差和协方差,使重要性密度函数更接近后验概率密度。此外,为确保状态协方差矩阵的正定性,采用了平方根滤波的思想,通过正交三角分解来代替每次迭代的矩阵开方操作。仿真实验证明,此算法可以提高滤波精度,适用于对精度要求很高但对运算时间要求不是很高的场合。

In order to solve the problem that the transition prior distribution as an importance density function does not include the lastest measuring information and only apply on the place of low precision,this paper proposed new particle filter named iterated cubature particle filter（ICPF）. The new algorithm developed the importance density function by Gauss-Newton iterate method and cubature Kalman filter（CKF）,the importance density function was more approximate the posterior density function because of improved innovation covariance and cross-covariance in the process of iteration. In addition,to ensure the positive definiteness of the state covariance matrix,it insteaded matrix square root operation in each iteration by orthogonal triangular decomposition for the use square root filtering. The simulation results indicate that the new algorithm can improve the accuracy of filter and is suitable for the situation that pay more attention to accuracy than time.