On the asymptotic behavior of sensors' allocation algorithm in stochastic distributed systems

Joint Online Parameter Estimation and Optimal Sensor Placement for the Partially Observed Stochastic Advection-Diffusion Equation

“…It is thus possible to compute the asymptotic objective function J ( θ, o), and to obtain the optimal sensor placement ô = arg min o∈Ω ny J ( θ, o), prior to receiving any observations. In this scenario, it may be preferable to use a (non-stochastic) gradient descent algorithm on the asymptotic objective function directly in order to obtain the optimal sensor placement (e.g., [1,4]).…”

“…In comparison, the partially observed, continuous-time case has received relatively little attention. 1 This method was first proposed by Gerencser et al [51], who derived a RML estimator for the parameters of a finite dimensional, partially observed, linear diffusion process using the Itô-Venzel formula (e.g., [109]), and provided an almost sure convergence result for this estimator without proof. This analysis was later extended in [52], in which the authors established the almost sure convergence of a modified version of the estimator in [51],…”

“…Several authors have also considered optimal sensor placement with respect to asymptotic versions of these objective functions (e.g., [1,4,90,104,112,113]). In this case, the optimal sensor placements are obtained, possibly recursively, as the minima of the asymptotic objective function J (θ, o) = 1 t lim t→∞ J t (θ, o).…”