一种基于牛顿法的高斯非线性滤波器

On Gaussian nonlinear filter using Newton method

针对高斯型非线性滤波器在大初始估计误差和/或小量测误差条件下的估计性能恶化问题,提出一种新的高斯型非线性滤波器设计方法。从优化角度出发,将当前时刻状态视为未知参数,以高斯假设下状态-观测联合概率分布密度的对数作为代价函数,基于一阶线性化和牛顿下降方法推导了迭代观测更新方程,在此基础上设计了一种迭代型高斯非线性滤波器。通过典型仿真算例将所提算法与几种经典滤波器及近期提出的几种迭代型高斯滤波器进行了性能对比。结果表明,算法具有更好的收敛性和准确性,适于大初始误差条件下的非线性滤波问题。

To address the estimate performance degeneration for Gaussian nonlinear filter when encountering large initialization error and/ or accurate measurements, a novel Gaussian-type nonlinear filtering approach is proposed based on Newton method in optimization. The log joint probability of state and observation is taken as a cost function for optimization problem, and hence the state is regarded as unknown parameter at current observation time. Continuous measurement update equations for state and error matrix are derived by using the newton method in optimization community and first order Taylor expansion to nonlinear functions, a novel recursive Gaussian filter for nonlinear problems is devised using the continuous update equations. The performance of proposed method is tested by simulation in the comparison with classic Kalman filters and lately proposed recursive Gaussian type filters. The results support the superiority of the method in favor of present methods with good accuracy and convergence, which recommends its application to nonlinear filtering problem with large initialization error.