An Adaptive Online Smoother with Closed-Form Solutions and Information-Theoretic Lag Selection for Conditional Gaussian Nonlinear Systems
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条件高斯非线性系统的自适应在线平滑：闭式解与信息论滞后选择
- 研究问题
- 在部分观测、高维及时间相关性变化的动态系统中，如何利用邻近未来观测改善状态估计，同时控制历史存储成本？
- 方法与思路
- 作者为条件高斯非线性系统构造自适应滞后在线平滑器，利用状态不确定性的减少选择窗口，并以闭式公式计算。
- 材料陈述的贡献
- 摘要称，该方法降低计算和存储需求，并展示在线因果关系检测、拉格朗日数据同化与部分观测参数估计的应用。
- 阅读关注点
- 应核对允许闭式计算的系统结构、信息准则的定义、在线使用未来观测的延迟，以及极端事件下窗口调整的表现。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未给出适用系统的完整条件，不能推定覆盖任意非线性系统。
原文摘要
Data assimilation (DA) combines partial observations with dynamical models to improve state estimation. Filter-based DA uses only past and present data and is the prerequisite for real-time forecasts. Smoother-based DA exploits both past and future observations. It aims to fill in missing data, provide more accurate estimations, and develop high-quality datasets. However, the standard smoothing procedure requires using all historical state estimations, which is storage-demanding, especially for high-dimensional systems. This paper develops an adaptive-lag online smoother for a large class of complex dynamical systems with strong nonlinear and non-Gaussian features, which has important applications to many real-world problems. The adaptive lag allows the utilization of observations only within a nearby window, thus reducing computational complexity and storage needs. Online lag adjustment is essential for tackling turbulent systems, where temporal autocorrelation varies significantly over time due to intermittency, extreme events, and nonlinearity. Based on the uncertainty reduction in the estimated state, an information criterion is developed to systematically determine the adaptive lag. Notably, the mathematical structure of these systems facilitates the use of closed analytic formulae to calculate the online smoother and adaptive lag, avoiding empirical tunings as in ensemble-based DA methods. The adaptive online smoother is applied to studying three important scientific problems. First, it helps detect online causal relationships between state variables. Second, the advantage of reduced computational storage expenditure is illustrated via Lagrangian DA, a high-dimensional nonlinear problem. Finally, the adaptive smoother advances online parameter estimation with partial observations, emphasizing the role of the observed extreme events in accelerating convergence.