Multifidelity sensor placement in Bayesian state estimation problems

Abstract

We study optimal sensor placement for Bayesian state estimation problems in which sensors vary in cost and fidelity, resulting in a budget-constrained multifidelity optimal experimental design problem. Sensor placement optimality is quantified using the D-optimality criterion, and the problem is approached by leveraging connections with the column subset selection problem in numerical linear algebra. We implement a greedy approach for this problem, whose computational efficiency we improve using rank-one updates via the Sherman-Morrison formula. We additionally present an iterative algorithm that, for each feasible allocation of sensors, greedily optimizes over each sensor fidelity subject to previous sensor choices, repeating this process until a termination criterion is satisfied. To our knowledge, these algorithms are novel in the context of cost-constrained multifidelity sensor placement. We evaluate our methods on several benchmark state estimation problems, including reconstructions of sea surface temperature and flow around a cylinder, and empirically demonstrate improved performance over random designs.