Sparse-Grid Based Estimation for Situational Awareness

本计画的目标是建立一个稀疏网格滤波架构，以在计算限制下精确估计非线性及非高斯动态系统。本研究的动机是具有挑战性的情境感知问题。情境意识关注的是环境中正在发生的事情以及未来将发生的事情。它是至关重要的决策在各种领域包含大的不确定性和丰富的动态。研究方法是使用高精度稀疏网格作为非高斯不确定性的有效和准确的表示，并递归地传播和更新稀疏网格。该研究将产生一个统一的基于点的过滤框架，计算效率高的非线性滤波算法，并解决空间态势感知中的估计问题。可提供的资料包括研究成果文件、用于稀疏网格滤波/空间态势感知的MATLAB工具箱、工程专业学生教育和研讨会，以及学生在空间物体跟踪方面的实践经验。如果成功，态势感知解决方案将有助于提供有关空间/地面环境的及时准确的信息，数据和服务，并减少对轨道和地面基础设施的危害。它将对空间和运输系统的安全运行作出巨大贡献，从而对经济和国家安全产生直接影响。基于稀疏网格的估计，从更广泛的角度来看，提供了一类精确和计算效率高的算法来解决许多高维和非线性动态系统，如多智能体系统，传感器网络和电力系统的复杂估计问题。通过课程设计，学生项目参与和推广的各种活动，将研究成果融入教育计划，将有助于招募和留住少数民族学生，并激励年轻学生追求他们的职业生涯在工程或科学。

The objective of this project is to establish a sparse grid filtering framework for accurate estimation of nonlinear and non-Gaussian dynamic systems under computational constraints. This research is motivated by challenging situational awareness problems. Situational awareness is concerned with what is happening in the environment and what will happen in the future. It is critical to decision making in a variety of domains containing large uncertainties and rich dynamics. The research approach is to use a high-accuracy sparse grid as an efficient and accurate representation of non-Gaussian uncertainty and recursively propagate and update the sparse grid. The research will result in a unified point-based filtering framework, computationally efficient nonlinear filtering algorithms, and a solution to the estimation problems in space situational awareness. Deliverables include documentation of research results, a MATLAB toolbox for sparse grid filtering/space situational awareness, engineering student education and seminars, and student hands-on experience in space object tracking. If successful, the situational awareness solution will help provide timely and accurate information, data, and services regarding the space/ground environment, and reduce hazards to infrastructure in orbit and on the ground. It will make a great contribution to the safe operation of space and transportation systems and thus have a direct impact on the economy and national security. The sparse-grid based estimation, in a broader perspective, provides a class of accurate and computationally efficient algorithms to solve complex estimation problems for many high dimensional and nonlinear dynamical systems such as multi-agent systems, sensor networks, and power systems. The integration of the research results into the education programs through a variety of activities in curriculum design, student project involvement, and outreach will help recruit and retain minority students and motivate young students to pursue their careers in engineering or science.