In this paper, we focus on batch state estimation for linear systems. This problem is important in applications such as environmental field estimation, robotic navigation, and target tracking. Its difficulty lies on that limited operational resources among the sensors, e.g., shared communication bandwidth or battery power, constrain the number of sensors that can be active at each measurement step. As a result, sensor scheduling algorithms must be employed. Notwithstanding, current sensor scheduling algorithms for batch state estimation scale poorly with the system size and the time horizon. In addition, current sensor scheduling algorithms for Kalman filtering, although they scale better, provide no performance guarantees or approximation bounds for the minimization of the batch state estimation error. In this paper, one of our main contributions is to provide an algorithm that enjoys both the estimation accuracy of the batch state scheduling algorithms and the low time complexity of the Kalman filtering scheduling algorithms. In particular: 1) our algorithm is near-optimal: it achieves a solution up to a multiplicative factor 1/2 from the optimal solution, and this factor is close to the best approximation factor 1/e one can achieve in polynomial time for this problem; 2) our algorithm has (polynomial) time complexity that is not only lower than that of the current algorithms for batch state estimation; it is also lower than, or similar to, that of the current algorithms for Kalman filtering. We achieve these results by proving two properties for our batch state estimation error metric, which quantifies the square error of the minimum variance linear estimator of the batch state vector: a) it is supermodular in the choice of the sensors; b) it has a sparsity pattern (it involves matrices that are block tri-diagonal) that facilitates its evaluation at each sensor set.
Fast Catch-Up, Late Switching: Optimal Batch Size Scheduling via Functional Scaling Laws
School of Mathematical Sciences, Peking University（北京大学数学科学学院）；Center for Machine Learning Research, Peking University（北京大学机器学习研究中心）；School of Computer Science, Shanghai Jiao Tong University（上海交通大学计算机科学学院）；State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China（中国科学技术大学认知智能国家重点实验室）；Meituan, Beijing（美团（北京））；AI for Science Institute, Beijing（北京人工智能科学研究院）
Backpressure-based Mean-field Type Game for Scheduling in Multi-Hop Wireless Sensor Networks
NYUAD Research Institute New York University Abu Dhabi（纽约大学阿布扎比分校研究学院）；Department of Mathematics KTH Royal Institute of Technology（瑞典皇家理工学院数学系）；Engineering Division New York University Abu Dhabi（纽约大学阿布扎比分校工程学院）
