线性加性噪声下随机Navier-Stokes信号的粒子滤波
Particle Filtering for Stochastic Navier-Stokes Signal Observed with Linear Additive Noise
摘要：
我们考虑一个非线性滤波问题，即信号服从随机Navier-Stokes方程，并通过加性噪声的线性映射进行观察。该装置与数值天气预报和气候建模的数据同化有关，其中类似的模型用于未知的海洋或风速。我们提出了一种粒子滤波方法，使用似然通知的重要性建议，自适应回火，和少量的适当的马尔可夫链蒙特卡罗步骤。我们为每个步骤提供了详细的设计，并在我们的数值示例中显示，它们对于实现良好的性能和效率都至关重要。
英文摘要：
We consider a non-linear filtering problem, whereby the signal obeys the stochastic Navier-Stokes equations and is observed through a linear mapping with additive noise. The setup is relevant to data assimilation for numerical weather prediction and climate modelling, where similar models are used for unknown ocean or wind velocities. We present a particle filtering methodology that uses likelihood informed importance proposals, adaptive tempering, and a small number of appropriate Markov Chain Monte Carlo steps. We provide a detailed design for each of these steps and show in our numerical examples that they are all crucial in terms of achieving good performance and efficiency.
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