Nonlinear filtering with signal dependent observation noise
Nonlinear filtering with signal dependent observation noise
复制标题
具有信号相关观测噪声的非线性滤波
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
J. Xiong
中科院分区：
文献类型：
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作者：
D. Crisan;M. Kouritzin;J. Xiong
本文研究了非经典框架下的滤波问题：假设观测方程由信号相关噪声驱动。我们证明了信号的条件分布的支集在二次变差过程的导数的相应水平集上。根据噪声的内在维数，我们区分两种情况：在第一种情况下，条件分布具有离散支持，我们推导出条件分布的显式表示。在第二种情况下，过滤问题等价于定义在流形上的经典问题，我们推导出条件分布的演化方程。所得结果应用于观测噪声为Ornstein-Uhlenbeck过程的滤波问题。
The paper studies the filtering problem for a non-classical frame- work: we assume that the observation equation is driven by a signal dependent noise. We show that the support of the conditional distri- bution of the signal is on the corresponding level set of the derivative of the quadratic variation process. Depending on the intrinsic dimension of the noise, we distinguish two cases: In the first case, the conditional distribution has discrete support and we deduce an explicit represen- tation for the conditional distribution. In the second case, the filtering problem is equivalent to a classical one defined on a manifold and we deduce the evolution equation of the conditional distribution. The re- sults are applied to the filtering problem where the observation noise is an Ornstein-Uhlenbeck process.