Near-optimal sensor scheduling for batch state estimation: Complexity, algorithms, and limits
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Near-Optimal Sensor Scheduling.pdf
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Author(s)
Tzoumas, Vasileios
Pappas, George J.
Jadbabaie-Moghadam, Ali
Date Issued
December 2016
Journal
2016 IEEE 55th Conference on Decision and Control (CDC)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Tzoumas, Vasileios; Jadbabaie, Ali and Pappas, George J. “Near-Optimal Sensor Scheduling for Batch State Estimation: Complexity, Algorithms, and Limits.” 2016 IEEE 55th Conference on Decision and Control (CDC), December 2016, Las Vegas, Nevada, USA, Institute of Electrical and Electronics Engineers (IEEE), December 2016
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
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DOI of Published Version
https://doi.org/10.1109/CDC.2016.7798669
