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摘要翻译：
本文研究了粒子滤波在连续-离散最优滤波问题中的应用，其中系统模型是随机微分方程，在离散时刻得到系统的噪声测量值。给出了Girsanov定理如何用于重要抽样所需的似然比的估计。文中还说明了该方法如何应用于一类驱动噪声过程的维数低于状态，因而状态和噪声的规律不是绝对连续的模型。本文还考虑了条件高斯模型和未知静态参数模型的Rao-Blackwellidation问题。
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英文标题：
《Application of Girsanov Theorem to Particle Filtering of Discretely
Observed Continuous-Time Non-Linear Systems》
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作者：
Simo S\"arkk\"a and Tommi Sottinen
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最新提交年份：
2008
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分类信息：
一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Statistics 统计学
二级分类：Computation 计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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英文摘要：
This article considers the application of particle filtering to continuous-discrete optimal filtering problems, where the system model is a stochastic differential equation, and noisy measurements of the system are obtained at discrete instances of time. It is shown how the Girsanov theorem can be used for evaluating the likelihood ratios needed in importance sampling. It is also shown how the methodology can be applied to a class of models, where the driving noise process is lower in the dimensionality than the state and thus the laws of state and noise are not absolutely continuous. Rao-Blackwellization of conditionally Gaussian models and unknown static parameter models is also considered.
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PDF链接：
https://arxiv.org/pdf/705.1598
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