Sensor Scheduling with Guarantees for Greedy Approximation of Non-Submodular mean-squared error metric

We address sensor scheduling in linear time-invariant (LTI) dynamical systems, aiming to optimize the utilization of a limited number of sensors, which is inherently an NP-hard problem. We explore complex scenarios where the metric is a non-submodular mean squared error (MSE) for state estimation. Despite the challenges posed by non-submodular metrics in deriving a performance guarantee for greedy solutions over multiple time steps, we develop a sequential sensor scheduling framework that ensures performance guarantees for the greedy algorithm across the entire sequence while leveraging concepts of the submodularity ratio and the curvature. Thus, we propose a theoretical performance guarantee for the greedy approximation using the sequential analysis for sensor scheduling. Our simulation results demonstrate that our proposed guarantee for sensor scheduling effectively bounds the performance across various system cases.