随机连续-离散非线性系统参数和状态估计的数据同化
Data Assimilation for Combined Parameter and State Estimation in Stochastic Continuous-Discrete Nonlinear Systems
摘要：
数据同化（DA）提供了一个通用的框架，估计动力系统的贝叶斯推理的概念的基础上。这构成了不同的线性和非线性滤波和平滑技术的共同基础，从而更好地理解每种方法的特性和局限性。在这项研究中，四个非线性滤波器的随机连续动态与离散测量系统推断为不同的近似解的福克-普朗克方程的贝叶斯更新的预测步骤。每种过滤方法的特点和缺点进行了讨论，在每种情况下，在介绍的近似原始贝叶斯问题。引入的连续-离散（CD）滤波器，然后实现解决的状态和参数的组合估计问题的非线性系统描述的随机微分方程（ESTA），即连续搅拌釜式反应器（CSTR）。每个过滤器的性能指标，如估计误差，计算成本，以及量化正确的不确定性的能力，进行了比较和调查归因于假设的近似引入的每一类过滤器的推导。
英文摘要：
Data assimilation (DA) provides a general framework for estimation in dynamical systems based on the concepts of Bayesian inference. This constitutes a common basis for the different linear and nonlinear filtering and smoothing techniques which gives a better understanding of the characteristics and limitations of each approach. In this study, four nonlinear filters for systems governed by stochastic continuous dynamics with discrete measurements are inferred as different approximate solutions to the Fokker-Planck equation in the prediction step of the Bayesian update. The characteristics and drawbacks of each filtering approach are discussed in light of the introduced approximations to the original Bayesian problem in each case. The introduced continuous-discrete (CD) filters are then implemented to solve the combined estimation problem of the state and parameter variables in a nonlinear system described by a stochastic differential equation (SDE), namely, the continuous stirred-tank reactor (CSTR). The performance measures for each filter, such as estimation errors, computational cost, and the ability to quantify the correct uncertainty, are compared and investigated with attribution to the assumed approximations introduced in the derivation of each class of filters.
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