  We study the problem of scheduling sensors in a resource-constrained linear
dynamical system, where the objective is to select a small subset of sensors
from a large network to perform the state estimation task. We formulate this
problem as the maximization of a monotone set function under a matroid
constraint. We propose a randomized greedy algorithm that is significantly
faster than state-of-the-art methods. By introducing the notion of curvature
which quantifies how close a function is to being submodular, we analyze the
performance of the proposed algorithm and find a bound on the expected mean
square error (MSE) of the estimator that uses the selected sensors in terms of
the optimal MSE. Moreover, we derive a probabilistic bound on the curvature for
the scenario where{\color{black}{ the measurements are i.i.d. random vectors
with bounded $\ell_2$ norm.}} Simulation results demonstrate efficacy of the
randomized greedy algorithm in a comparison with greedy and semidefinite
programming relaxation methods.
