Randomized Sensor Selection for Nonlinear Systems With Application to Target Localization
Shaunak D. Bopardikar, Osama En-Nasr, Xiaobo Tan
Abstract
Given a nonlinear dynamical system, this letter considers the problem of selecting a subset of the total set of sensors that has provable guarantees on standard metrics related to the nonlinear observability Gramian. The key contribution is a simple randomized algorithm that samples the sensors uniformly without replacement, and yields probabilistic guarantees on the minimum eigenvalue or the inverse of the condition number of the nonlinear observability Gramian relative to that of the complete set of sensors. Numerical studies reveal that the utility of the theoretical results lies in the regime of large total number of sensors wherein the combinatorial nature of the problem presents a significant computational challenge. The results are demonstrated numerically on a problem of moving target localization using an extended Kalman filter in two scenarios: one using range sensors and another with time-difference-of-arrival measurements. A graceful degradation of performance with a decreased number of sensors is observed when compared to the use of all of the sensors for localization. It is also observed that for certain metrics, the proposed approach provides an improvement over a heuristic that selects the sensors in a greedy manner based on the contribution of an additional sensor toward the observability Gramian metric.
BibTeX
@inproceedings{ral2019_randomizedsensor,
title = {Randomized Sensor Selection for Nonlinear Systems With Application to Target Localization},
author = {Shaunak D. Bopardikar and Osama En-Nasr and Xiaobo Tan},
booktitle = {RA-L 2019},
year = {2019}
}