Particle Filters.ppt

Introduction Sequential Monte Carlo Methods in Practice, Springer-Verlag,2001 IEEE Transactions on Signal Processing Special issue on Monte Carlo Methods for Statistical Signal Processing 2002,50(2) Proceedings of the IEEE, Special Issue on Sequential State Estimation, 2004,92(3) Beyond the Kalman Filter: Particle Filters for Tracking Applications, Artech House Publishers, 2004. Monte Carlo Method Ulam von Neumann Metropolis Fermi Buffon 投针实验 Monte Carlo Methods Important Sampling Rejection Sampling Metropolis-Hastings Gibbs采样 Sequential Monte Carlo Bootstrap filtering (Gordon 1993) Condensation algorithm(Isard and Blake 1996 ) Particle filtering (Doucet 2001) Sequential Monte Carlo 20世纪50年代，Hammersley便采用基于序贯重要性采样(Sequential importance sampling,SIS)的蒙特卡洛方法解决统计学问题。 20世纪60年代后期，Handschin与Mayne使用序贯蒙特卡洛方法解决自动控制领域的相关问题。 20世纪70年代，Handschin、Akashi,Zaritskii Sequential Monte Carlo Tanizaki、Geweke等采用基于重要性采样的蒙特卡洛方法成功解决了一系列高维积分问题。 Smith与Gelfand提出的采样-重采样思想为Bayesian推理提供了一种易于实现的计算策略。 Smith与Gordon等人合作，于20世纪90年代初将重采样(Resampling)步骤引入到粒子滤波中,提出Bootstrap滤波算法。 美国海军集成水下监控系统中的Nodestar便是粒子滤波应用的一个实例 Applications of Particle Filters Navigation, Positioning, Tracking Channel equalization Fundamental Concepts Bayesian inference Monte Carlo Simulation Sequential Importance Sampling Resampling Bayesian Inference X is unknown-a random variable or set (vector) of random variables Y is observed-also a set of random variables We wish to infer X by observing Y. The probability distribution p(x) models our prior knowledge of X. The conditional probability distribution p(Y|X) models the relationship between Y and X. Bayesian Filtering General problem statement State Space Formulation Bayes Theorem The conditional distribution p(x|y) represents posterior information about x given y. Recursive Bayesian Estimation Recursive Bayesian Estimation Monte Carlo Sampling Monte Carlo Simulation The posterior distribution p(x|y) may be difficult or impossible to compute in closed form. A