Kullback–Leibler divergence based sensor placement in linear processes for efficient data reconciliation

Kullback–Leibler divergence (KLD) based sensor placement design (SPD) has been recently proposed for accurate estimation of variables using data reconciliation for steady-state linear processes. Use of KLD enables SPD for both Gaussian and non-Gaussian measurement noise cases. Additionally, it enables direct incorporation of the end-user specified estimation accuracies in the SPD procedure. In the current work, we establish several useful properties of the KLD based objective. We establish its invariance to the choice of primary variables. For the case when measurement noises are uncorrelated and Gaussian, we also establish its non-decreasing and submodular behavior. To solve the NP-hard SPD problem, we design a computationally efficient greedy algorithm. For the uncorrelated Gaussian measurement noise case, the algorithm finds provably near-optimal solution to the SPD problem. We also provide bounds for sensor placement obtained using any algorithm. We demonstrate the proposed approach on a phasor measurement unit, and a water distribution network. •Kullback–Leibler divergence based objective function for sensor placement presented.•The objective can accommodate any type of density function of the measurement noise.•Submodular nature of objective function established for the Gaussian noise case.•Greedy heuristic proposed to obtain near optimal solution to the NP-hard problem.•Approach demonstrated using a PMU, and a city-wide water distribution network.