An Introduction to Twisted Particle Filters and Parameter Estimation in Non-Linear State-Space Models
An Introduction to Twisted Particle Filters and Parameter Estimation in Non-Linear State-Space Models
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DOI：
10.1109/tsp.2016.2563387
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发表时间：
2016-09-15
影响因子：
5.4
通讯作者：
Piche, Robert
中科院分区：
文献类型：
--
作者：
Ala-Luhtala, Juha;Whiteley, Nick;Piche, Robert
扭曲粒子滤波是最近由Whiteley和Lee为了提高状态空间模型中边缘似然估计的效率而提出的一类序贯蒙特卡罗方法。本文的目的是扩展扭曲粒子滤波的方法，建立易于理解的理论结果，传达其基本原理，并在粒子马尔科夫链蒙特卡罗中演示其在估计静态模型参数方面的实际性能。我们推导了扭曲粒子滤波器，它结合了系统或多项式重采样和来自历史粒子状态的信息，并给出了一个透明的证明，它确定了边缘似然估计的最佳算法。我们演示了如何逼近具有高斯噪声的非线性状态空间模型的最优算法，并将这种逼近应用于两个例子：距离和方位跟踪问题和具有蓝牙信号强度测量的室内定位问题。对于给定的CPU时间，我们在边际似然估计的方差和马尔可夫链自相关方面证明了比标准算法的改进，并使用估计的参数改善了跟踪性能。
Twisted particle filters are a class of sequential Monte Carlo methods recently introduced by Whiteley and Lee to improve the efficiency of marginal likelihood estimation in state-space models. The purpose of this article is to extend the twisted particle filtering methodology, establish accessible theoretical results which convey its rationale, and provide a demonstration of its practical performance within particle Markov chain Monte Carlo for estimating static model parameters. We derive twisted particle filters that incorporate systematic or multinomial resampling and information from historical particle states, and a transparent proof which identifies the optimal algorithm for marginal likelihood estimation. We demonstrate how to approximate the optimal algorithm for nonlinear state-space models with Gaussian noise and we apply such approximations to two examples: a range and bearing tracking problem and an indoor positioning problem with Bluetooth signal strength measurements. We demonstrate improvements over standard algorithms in terms of variance of marginal likelihood estimates and Markov chain autocorrelation for given CPU time, and improved tracking performance using estimated parameters.