通用的连续-离散非线性Yau滤波I：扩散矩阵与状态无关的仿射线性状态模型
Universal, Continuous-Discrete Nonlinear Yau Filtering I: Affine, Linear State Model with State-Independent Diffusion Matrix
摘要：
连续-离散滤波问题需要解称为福克-普朗克-柯尔莫哥洛夫前向方程（FPKfe）的偏微分方程。本文指出，对于具有仿射线性漂移和状态无关扩散矩阵的状态模型，仅用线性代数技巧就能得到基本解。特别是，不需要解微分方程。此外，对时间步长的大小或测量模型没有限制。还讨论了重要的计算方面，是至关重要的潜在的实时实现高维问题。这个解是普适的，因为初始分布可以是任意的。
英文摘要：
The continuous-discrete filtering problem requires the solution of a partial differential equation known as the Fokker-Planck-Kolmogorov forward equation (FPKfe). In this paper, it is pointed out that for a state model with an affine, linear drift and state-independent diffusion matrix the fundamental solution can be obtained using only linear algebra techniques. In particular, no differential equations need to be solved. Furthermore, there are no restrictions on the size of the time step size, or on the measurement model. Also discussed are important computational aspects that are crucial for potential real-time implementation for higher-dimensional problems. The solution is universal in the sense that the initial distribution may be arbitrary.
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