This paper studies selecting a subset of the system's output to minimize the state estimation mean square error (MSE). This results in the maximization problem of a set function defined on possible sensor selections subject to a cardinality constraint. We consider to solve it approximately by a greedy search. Since the MSE function is not submodular nor supermodular, the well-known performance guarantees for the greedy solutions do not hold in the present case. Thus, we use the quantities---the submodularity ratio and the curvature---to evaluate the degrees of submodularity and supermodularity of the objective function. By using the properties of the MSE function, we approximately compute these quantities and derive a performance guarantee for the greedy solutions. It is shown that the guarantee is less conservative than those in the existing results.
@article{arxiv.2004.04355,
title = {Sensor placement minimizing the state estimation mean square error: Performance guarantees of greedy solutions},
author = {Akira Kohara and Kunihisa Okano and Kentaro Hirata and Yukinori Nakamura},
journal= {arXiv preprint arXiv:2004.04355},
year = {2020}
}