平方根递推更新GMP-PHDF

传统高斯混合粒子概率假设密度滤波器(Gaussian mixture particle probability hypothesis density filter,GMP PHDF)采用先验状态转移概率密度作为重要性密度函数,会出现粒子退化问题。而递推更新高斯滤波器依据测量函数梯度渐进式地进行状态更新,可获得更为接近于真实分布的后验估计,但其协方差矩阵易非正定而导致递推中断。对此,本文首先分析平方根递推更新高斯滤波器(square-root recursive update Gaussian filter,SR-RUGF)的实现思路,并给出基于容积卡尔曼滤波(cubature Kalman filter,CKF)的SR RUGF实现步骤。在此基础上,利用SR RUGF为GMP PHDF构建重要性密度函数,进而提出基于平方根递推更新的GMP-PHDF(square-root recursive update GMP-PHDF, SRRU-GMP-PHDF)算法。仿真结果表明,算法可以很好地利用量测信息,获得更高精度的估计结果。

Square-root recursive update GMP-PHDF

In the traditional Gaussian mixture particle probability hypothesis density filter (GMP-PHDF), the prior state transition probability density is used as a sample important density function, which will lead to a particle degradation problem. The posterior estimation that is more approximate to the real posterior distribution, can be obtained by the incremental state update procedure of the recursive update Gaussian filter according to the gradient of the measurement function, where, however, the non positive definite covariance matrix will cause recursive interruption. Thus, the implementation idea of the square-root recursive update Gaussian filter (SR-RUGF) is analyzed, and the implementation steps of SR-RUGF based on the cubature Kalman filter (CKF) are given subsequently. On this basis, a sample important density function is constructed by using SR-RUGF, based on which a square root recursive update GMP-PHDF (SRRU-GMP-PHDF) is derived. Simulation results demonstrate that the proposed algorithm can assimilate the measurement information commendably and obtain estimation results with higher accuracy.