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We study the problem of selecting most informative subset of a large observation set to enable accurate estimation of unknown parameters. This problem arises in a variety of settings in machine learning and signal processing including feature selection, phase retrieval, and target localization. Since for quadratic measurement models the moment matrix of the optimal estimator is generally unknown, majority of prior work resorts to approximation techniques such as linearization of the observation model to optimize the alphabetical optimality criteria of an approximate moment matrix. Conversely, by exploiting a connection to the classical Van Trees’ inequality, we derive new alphabetical optimality criteria without distorting the relational structure of the observation model. We further show that under certain conditions on parameters of the problem these optimality criteria are monotone and (weak) submodular set functions. These results enable us to develop an efficient greedy observation selection algorithm uniquely tailored for quadratic models, and provide theoretical bounds on its achievable utility.
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On Submodularity of Quadratic Observation Selection in Constrained Networked Sensing Systems
We study the problem of observation selection in a resource-constrained networked sensing system, where the objective is to select a small subset of observations from a large network to perform a state estimation task. When the measurements are gathered using nonlinear systems, majority of prior work resort to approximation techniques such as linearization of the measurement model to utilize the methods developed for linear models, e.g., (weak) submodular objectives and greedy selection schemes. In contrast, when the measurement model is quadratic, e.g., the range measurements in a radar system, by exploiting a connection to the classical Van Trees' inequality, we derive new optimality criteria without distorting the relational structure of the measurement model. We further show that under certain conditions these optimality criteria are monotone and (weak) submodular set functions. These results enable us to develop an efficient greedy observation selection algorithm uniquely tailored for constrained networked sensing systems following quadratic models and provide theoretical bounds on its achievable utility. Extensive numerical experiments demonstrate efficacy of the proposed framework.
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- Award ID(s):
- 1809327
- PAR ID:
- 10170196
- Date Published:
- Journal Name:
- 2019 American Control Conference (ACC)
- Page Range / eLocation ID:
- 4671 to 4676
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.23919/ACC.2019.8814899
