基于高斯和近似的扩展切片高斯混合滤波器及其在多径估计中的应用

Extension of SGMF Using Gaussian Sum Approximation for Nonlinear/Non-Gaussian Model and Its Application in Multipath Estimation

全球卫星导航系统(Global navigation satellite system,GNSS)信号的多径估计问题实际上是条件线性状态空间模型下的状态估计问题.根据高斯和理论提出了适用于非高斯噪声环境的扩展切片高斯混合滤波(Extension of sliced Gaussian mixture filter,ESGMF)算法.该算法将非高斯噪声的状态概率密度函数(Probability density function,PDF)表示为高斯和的形式,将ESGMF通过一组并行的切片高斯混合滤波器(Sliced Gaussian mixture filter,SGMF)来实现.同时,在ESGMF算法中利用粒子滤波(Particle filter,PF)中重采样的思想对成指数增加的状态预测PDF的高斯混合个体进行约简,以提高贝叶斯推理的效率.该算法可以获得非高斯噪声下状态PDF的迭代解析表达式.最后,将ESGMF应用于GPS多径参数估计,仿真结果表明,ESGMF算法的估计精度优于基于PF和扩展卡尔曼滤波(Extended Kalman filter,EKF)的算法.

The multipath estimation of global navigation satellite system （GNSS） signal is actually the state estimation of nonlinear/non-Gaussian systems. The extension of sliced Gaussian mixture filter （ESGMF） based on Gaussian sum approximation is proposed for the state estimation of nonlinear/non-Gaussian state space, and the probability density function （PDF） expression of states is derived recursively for a time varying system. Resampling is applied to the prediction PDF to reduce the complexity of Bayesian inference. The simulation result of multipath estimation with ESGMF shows that the ESGMF algorithm performs better in accuracy than the algorithms based on particle filter （PF） and extended Kalman filter （EKF）.