We derive robust linear filtering and experimental design for systems governed by stochastic differential equations (SDEs) under model uncertainty. Given a model of signal and observation processes, an optimal linear filter is found by solving the Wiener-Hopf equation; with model uncertainty, it is desirable to derive a corresponding robust filter. This article assumes that the physical process is modeled via a SDE system with unknown parameters; the signals are degraded by blurring and additive noise. Due to time-dependent stochasticity in SDE systems, the system is nonstationary; and the resulting Wiener-Hopf equation is difficult to solve in closed form. Hence, we discretize the problem to obtain a matrix system to carry out the overall procedure. We further derive an intrinsically Bayesian robust (IBR) linear filter together with an optimal experimental design framework to determine the importance of SDE parameter(s). We apply the theory to an SDE-based pharmacokinetic two-compartment model to estimate drug concentration levels.

中文翻译：

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基于模型的随机微分方程系统鲁棒滤波与实验设计

我们为由模型不确定性下的随机微分方程 (SDE) 控制的系统推导出稳健的线性滤波和实验设计。给定信号和观测过程的模型，通过求解 Wiener-Hopf 方程找到最佳线性滤波器；对于模型不确定性，需要推导出相应的鲁棒滤波器。本文假设物理过程是通过未知参数的 SDE 系统建模的；信号会因模糊和加性噪声而劣化。由于 SDE 系统中的时间相关随机性，系统是非平稳的；并且由此产生的 Wiener-Hopf 方程很难以封闭形式求解。因此，我们将问题离散化以获得矩阵系统来执行整个过程。我们进一步推导出固有贝叶斯稳健 (IBR) 线性滤波器以及最佳实验设计框架，以确定 SDE 参数的重要性。我们将该理论应用于基于 SDE 的药代动力学两室模型来估计药物浓度水平。