Three-dimensional axial assignment problems with decomposable cost coefficients
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
CONDENSATION—Conditional Density Propagation forVisual Tracking
International Journal of Computer Vision
Approximating discrete collections via local improvements
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Distributed sensor network for real time tracking
Proceedings of the fifth international conference on Autonomous agents
Robust Monte Carlo localization for mobile robots
Artificial Intelligence
Estimation with Applications to Tracking and Navigation
Estimation with Applications to Tracking and Navigation
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The focus of attention problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
An Optimal Approach to Collaborative Target Tracking with Performance Guarantees
Journal of Intelligent and Robotic Systems
Adaptive online camera coordination for multi-camera multi-target surveillance
Computer Vision and Image Understanding
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In this paper, we consider the problem of assigning sensors to track targets so as to minimize the expected error in the resulting estimation for target locations. Specifically, we are interested in how disjoint pairs of bearing or range sensors can be best assigned to targets to minimize the expected error in the estimates. We refer to this as the focus of attention (FOA) problem. In its general form, FOA is NP-hard and not well approximable. However, for specific geometries we obtain significant approximation results: a 2-approximation algorithm for stereo cameras on a line, a (1 + ε)-approximation algorithm for any constant ε when the cameras are equidistant, and a 1.42-approximation algorithm for equally spaced range sensors on a circle. In addition to constrained geometries, we further investigate the problem for general sensor placement. By reposing as a maximization problem--where the goal is to maximize the number of tracks with bounded error--we are able to leverage results from maximum set-packing to render the problem approximable. We demonstrate the utility of these algorithms in simulation for a target tracking task, and for localizing a team of mobile agents in a sensor network. These results provide insights into sensor/target assignment stragies, as well as sensor placement in a distributed network.