ITR/AP: Optimal Nonlinear Estimation in the Geosciences

ITR/AP：地球科学中的最优非线性估计

• 批准号: 0113649
• 负责人: Nicholas Ercolani
• 金额: $ 25.46万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-09-01 至 2005-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0113649&HistoricalAwards=false
• 关键词: ITR; AP; Optimal; Nonlinear; Estimation

This project develops a new technique for estimation of the state of a stochastic dynamical system, given some partial and imperfect information from measurements. Unlike traditional linear estimation methods, such as least-squares variational methods or Kalman Filter approach, this new technique is capable of handling highly nonlinear dynamics--and thus non-Gaussian statistics-- in a way that approaches the optimality of the formally exact solution by Kushner, Stratonovitch, Pardoux (KSP). Just as KSP, the new method computes the conditional statistics of the system given the measurements. However, when applied to problems of interest in information technology, such as large-scale geoscience or environmental data assimilation, the new method does not lead to functional stochastic equations that are hopelessly intractable to solve, as does KSP. The approach pursued in this project is instead to approximate the conditional statistics by means of a variational formulation, which yields the conditional mean as the minimizer of an appropriate cost function and the covariance as its Hessian. The cost function proposed is calculated by a Rayleigh-Ritz or moment-closure scheme, which should render the problem tractable to numerical computation. The main research that will be done is to develop suitable statistical techniques to model the system for the Rayleigh-Ritz calculation, to work out efficient algorithms for the numerical optimization of the cost function, and to compare with existing suboptimal estimation schemes. In many areas of the geosciences of practical importance, it is crucial to combine information from observations with the results of a sophisticated numerical model to produce the best estimate of the past or future state of the system. In the case of a chemical or radioactive spill observed by monitoring a few well sites, one wants to track the contaminant plume backward in time to its source. This must be accomplished with only statistical knowledge about the properties of the aquifer and groundwater flow field and with the measurements themselves subject to error. In numerical weather prediction, the goal is instead to combine the latest observations from satellite arrays with the output of large-scale, meteorological computer models to predict the future state of the weather. Again, the models contain stochastic or chaotic elements which prevent perfect prediction based upon partial and imperfect information. The modeling methods and numerical algorithms developed in this project should provide a practical scheme to compute the best estimate in the face of such randomness in the model and uncertainty in the observations.

该项目开发了一种新技术，用于鉴于测量结果的某些部分和不完美的信息，以估算随机动力系统的状态。 与传统的线性估计方法（例如最小二乘变异方法或卡尔曼滤波器方法）不同，这种新技术能够以一种方法来处理高度非线性动力学 - 因此，非高斯统计数据 - 以一种方法来实现Kushner，Stratonovitch，Pardoux，Pardoux（kssp）正式精确解决方案的最佳性。 正如KSP一样，新方法计算给定测量值的系统的条件统计数据。 但是，当应用于信息技术感兴趣的问题（例如大规模地球科学或环境数据同化）时，新方法不会像KSP一样导致功能随机方程，这些方程无可救药地解决。 相反，该项目中采用的方法是通过差异公式近似条件统计的方法，该公式将有条件的平均值作为适当的成本函数的最小化器和协方差为其Hessian。 提出的成本函数由雷利 - 里茨（Rayleigh-Ritz）或力矩闭合方案计算，这应该使问题可用于数值计算。 将要做的主要研究是开发合适的统计技术来对雷利 - 里兹计算的系统进行建模，以便为成本函数的数值优化制定有效的算法，并与现有的次优估计方案进行比较。 在实际重要性的地球科学领域的许多领域中，将观测值的信息与复杂的数值模型的结果结合起来至关重要，以产生对系统过去或将来状态的最佳估计。如果通过监测一些井站点观察到化学或放射性溢出物，则希望及时向后跟踪污染物的羽流到其来源。 这必须仅通过有关含水层和地下水流场的性质的统计知识以及测量本身会遇到错误的统计知识来实现​​。在数字天气预测中，目标是将卫星阵列中最新观察结果与大规模的气象计算机模型的输出相结合，以预测天气的未来状态。 同样，这些模型包含随机或混乱的元素，这些元素可以基于部分和不完美的信息来防止完美的预测。 该项目中开发的建模方法和数值算法应提供一个实用方案，以计算模型中这种随机性和观测值不确定性的最佳估计。