Girsanov定理在离散观测连续非线性系统粒子滤波中的应用
Application of Girsanov Theorem to Particle Filtering of Discretely Observed Continuous-Time Non-Linear Systems
摘要：
本文考虑了粒子滤波在连续-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，并且在离散时刻获得系统的噪声测量。它示出了如何Girsanov定理可用于评估似然比所需的重要性抽样。它还示出了如何的方法可以应用到一类模型，其中的驾驶噪声过程是在维数低于状态，因此状态和噪声的法律是不绝对连续的。还考虑了条件高斯模型和未知静态参数模型的Rao-Blackwellization。
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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