{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/132486"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/132486","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Near-Optimal Sensor Placement for Detection of Poisson Distributed Targets","abstract":"In this dissertation, we address the problem of sensor placement for detecting uncertain targets. We model target arrivals using a Poisson process to capture the inherent randomness of event occurrences and emphasize the importance of accounting for uncertainty in the sensor placement strategy. To tackle this, we propose a computationally efficient approximation method based on a lower bound derived from Jensen's inequality. This approach leverages the mean of the uncertain target model to yield a suboptimal yet tractable solution suitable for real-time applications. We evaluate the accuracy of this approximation by quantifying its deviation from the original formulation and providing an upper bound on the approximation error. While the initial framework is formulated in a 1-dimensional spatial domain along a line segment for simplicity, we extend it to a 2-dimensional setting to handle uncertain linear target trajectories using a log-Gaussian Cox line process. Furthermore, we develop an improved closed-form approximation that incorporates both the mean and variance of the target distribution using a second-order Taylor series expansion, offering increased accuracy and a tighter error bound. The effectiveness of our proposed methods is demonstrated using real-world ship traffic data from the Hampton Roads channels in Virginia, USA, obtained from the Office for Coastal Management and the Bureau of Ocean Energy.","abstract_html":"In this dissertation, we address the problem of sensor placement for detecting uncertain targets. We model target arrivals using a Poisson process to capture the inherent randomness of event occurrences and emphasize the importance of accounting for uncertainty in the sensor placement strategy. To tackle this, we propose a computationally efficient approximation method based on a lower bound derived from Jensen's inequality. This approach leverages the mean of the uncertain target model to yield a suboptimal yet tractable solution suitable for real-time applications. We evaluate the accuracy of this approximation by quantifying its deviation from the original formulation and providing an upper bound on the approximation error. While the initial framework is formulated in a 1-dimensional spatial domain along a line segment for simplicity, we extend it to a 2-dimensional setting to handle uncertain linear target trajectories using a log-Gaussian Cox line process. Furthermore, we develop an improved closed-form approximation that incorporates both the mean and variance of the target distribution using a second-order Taylor series expansion, offering increased accuracy and a tighter error bound. 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We model target arrivals using a Poisson process to capture the inherent randomness of event occurrences and emphasize the importance of accounting for uncertainty in the sensor placement strategy. To tackle this, we propose a computationally efficient approximation method based on a lower bound derived from Jensen's inequality. This approach leverages the mean of the uncertain target model to yield a suboptimal yet tractable solution suitable for real-time applications. We evaluate the accuracy of this approximation by quantifying its deviation from the original formulation and providing an upper bound on the approximation error. While the initial framework is formulated in a 1-dimensional spatial domain along a line segment for simplicity, we extend it to a 2-dimensional setting to handle uncertain linear target trajectories using a log-Gaussian Cox line process. Furthermore, we develop an improved closed-form approximation that incorporates both the mean and variance of the target distribution using a second-order Taylor series expansion, offering increased accuracy and a tighter error bound. The effectiveness of our proposed methods is demonstrated using real-world ship traffic data from the Hampton Roads channels in Virginia, USA, obtained from the Office for Coastal Management and the Bureau of Ocean Energy."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["This dissertation explores how to place sensors in an area to detect moving targets such as ships when their locations and movements are uncertain. We use a mathematical approach to model how targets might randomly appear over time and space, and we show that in our numerical simulations, accounting for this uncertainty leads to better sensor placement decisions. We use a statistical tool to estimate when and where targets are likely to appear including uncertainty. To make this process practical for real-time use, we develop a computationally efficient approximation method that gives a good quality solution. We also measure how close this method comes to the original problem and show that the error stays within a mathematically established range. Our research starts with a simple one-dimensional case, where sensors are placed along a straight line to detect target arrivals, and then expands to a more realistic two-dimensional setting where targets follow uncertain lines. We further improve our method by considering both the average behavior and variation in target movement, leading to even better results. Finally, we demonstrate the effectiveness of our approach using real-world ship traffic data from the Hampton Roads area in Virginia, USA."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Doctor of Philosophy"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Near-Optimal Sensor Placement for Detection of Poisson Distributed Targets"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Stilwell, Daniel J."],"dc:contributor.committeemember":["Doan, Thinh Thanh","Xiong, Wenjie","De Sturler, Eric","Williams, Ryan K."],"dc:contributor.department":["Electrical Engineering"],"dc:creator":["Kim, Min Gyu"],"dc:date.accessioned":["2025-05-16T08:01:34Z"],"dc:date.available":["2025-05-16T08:01:34Z"],"dc:date.issued":["2025-05-15"],"dc:description.abstract":["In this dissertation, we address the problem of sensor placement for detecting uncertain targets. 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Furthermore, we develop an improved closed-form approximation that incorporates both the mean and variance of the target distribution using a second-order Taylor series expansion, offering increased accuracy and a tighter error bound. The effectiveness of our proposed methods is demonstrated using real-world ship traffic data from the Hampton Roads channels in Virginia, USA, obtained from the Office for Coastal Management and the Bureau of Ocean Energy."],"dc:description.abstractgeneral":["This dissertation explores how to place sensors in an area to detect moving targets such as ships when their locations and movements are uncertain. We use a mathematical approach to model how targets might randomly appear over time and space, and we show that in our numerical simulations, accounting for this uncertainty leads to better sensor placement decisions. We use a statistical tool to estimate when and where targets are likely to appear including uncertainty. To make this process practical for real-time use, we develop a computationally efficient approximation method that gives a good quality solution. We also measure how close this method comes to the original problem and show that the error stays within a mathematically established range. Our research starts with a simple one-dimensional case, where sensors are placed along a straight line to detect target arrivals, and then expands to a more realistic two-dimensional setting where targets follow uncertain lines. We further improve our method by considering both the average behavior and variation in target movement, leading to even better results. 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