Particle Filtering With Dependent Noise Processes
Particle Filtering With Dependent Noise Processes
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DOI：
10.1109/tsp.2012.2202653
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发表时间：
2012-09-01
影响因子：
5.4
通讯作者：
Gustafsson, Fredrik
中科院分区：
文献类型：
--
作者：
Saha, Saikat;Gustafsson, Fredrik
物理系统的建模往往导致离散的时间状态空间模型与相关的过程和测量噪声。对于线性高斯模型，卡尔曼滤波器处理这种情况，正如文献中所描述的那样。然而，对于非线性或非高斯模型，文献中描述的粒子滤波只提供了独立噪声情况下的一般解决方案。在这里，我们提出了一个扩展的粒子滤波理论，主要贡献如下：1)导出了最优建议分布；ii)对非线性模型中高斯噪声的特殊情况进行了详细的处理，得出了一种与相应的卡尔曼滤波器一样易于实现的具体算法；iii)将有效处理模型中线性高斯子结构的边缘（Rao-Blackwellized）粒子滤波器扩展到相关噪声；最后，iv)噪声过程的联合高斯分布的参数以递归的方式与状态联合估计。
Modeling physical systems often leads to discrete time state-space models with dependent process and measurement noises. For linear Gaussian models, the Kalman filter handles this case, as is well described in literature. However, for nonlinear or non-Gaussian models, the particle filter as described in literature provides a general solution only for the case of independent noise. Here, we present an extended theory of the particle filter for dependent noises with the following key contributions: i) The optimal proposal distribution is derived; ii) the special case of Gaussian noise in nonlinear models is treated in detail, leading to a concrete algorithm that is as easy to implement as the corresponding Kalman filter; iii) the marginalized (Rao-Blackwellized) particle filter, handling linear Gaussian substructures in the model in an efficient way, is extended to dependent noise; and, finally, iv) the parameters of a joint Gaussian distribution of the noise processes are estimated jointly with the state in a recursive way.