渐进扩展卡尔曼滤波器

Progressive Extended Kalman Filter

渐进贝叶斯方法将贝叶斯更新步骤等效为伪时间上的连续演化过程,以实现对状态的后验估计.本文基于渐进贝叶斯框架,导出一种新的高斯型非线性滤波算法.在线性高斯条件下推导了渐进贝叶斯方法的精确解;证明了对于由线性高斯解确定的动态系统,其均值和协方差矩阵满足的微分方程与常数状态估计的Kalman-Bucy滤波器是一致的.对于非线性系统,利用一阶Taylor展开推导了近似解表达式,进而导出渐进扩展卡尔曼滤波器.仿真算例表明新滤波器性能较扩展卡尔曼滤波器有大幅提高,且避免了窄形似然函数带来的滤波性能恶化问题.

Progressive Bayesian methods formulate the Bayesian update as continuously pseudo-time probability density evolution to perform posterior state estimation. In this paper we derive a novel Gaussian nonlinear filter based on progressive Bayesian framework. A progressive Bayesian solution is firstly derived under linear Gaussian condition. It is proved that the moment evolution of the dynamic system determined by linear Gaussian solution possess the consistency with Kalman-Bucy filter for constant state estimation. For nonlinear system,by using first order Taylor expansion,an approximate solution is derived and the resultant progressive extended Kalman filter is presented. Simulation results demonstrate the superior performance of progressive extended Kalman filter over extended Kalman filter,moreover the performance degrading of nonlinear filtering caused by narrowshape likelihood is avoided.