On Submodularity of Quadratic Observation Selection in Constrained Networked Sensing Systems
Mahsa Ghasemi, Abolfazl Hashemi, Ufuk Topcu, Haris Vikalo · 2019
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.