高斯渐进贝叶斯滤波器

Gaussian progressive Bayesian filter

中文关键词  非线性滤波  渐进贝叶斯  卡尔曼滤波器  一阶动态系统  Monte Carlo方法

英文关键词  nonlinear filtering  progressive Bayesian  Kalman filter  first order dynamic system  Monte Carlo method

中文摘要

      渐进贝叶斯方法将先验分布到后验分布的演化描述为一阶动态系统, 通过在伪时间上连续地引入观测信 息实现后验状态估计. 该方法的一般形式解, 即动态系统的时间导数, 是难以得到的. 本文提出一种高斯型渐进贝 叶斯滤波器. 首先在线性高斯条件下推导了时间导数的解析解; 然后证明了在该条件下, 由该解析解确定的一阶动 态系统与常量状态估计的Kalman-Bucy滤波器是一致的, 且由此导出的高斯渐进贝叶斯滤波器与卡尔曼滤波器是 一致的. 最后利用一阶Taylor展开推导了滤波器在非线性高斯条件下的近似解表达式, 并采用Monte Carlo方法给出 了具体实现方法. 通过若干仿真算例表明, 新滤波器具有较高的精度, 且在一定精度条件下的时间复杂度低于一般 粒子滤波器.

英文摘要

      Progressive Bayesian methods formulate the evolution from prior distribution to posterior distribution as a first order dynamic system, by incorporating the measurements in a continuous pesudo-time manner, to perform posterior state estimation. The general solution of time derivative of this dynamic system is usually nontrivial. A novel Gaussian type progressive Bayesian filter is proposed in this paper. First, the solution to this time-derivative is derived under linear Gaussian condition. Then, it is proved that the first order dynamic system determined by the derived solution is consistent with a Kalman-Bucy filter for constant state estimation, and the resultant Gaussian progressive Bayesian filter is consistent with Kalman filter. Thirdly, the filter is extended to the nonlinear case and an approximate solution is derived by using first order Taylor expansion. The corresponding Monte Carlo method for implementing the proposed filter for nonlinear problem is given. Simulation results demonstrate higher accuracy provided by the new filter, with lower time complexity than the particle filter at given accuracy.