Distributed scheduling of measurements in a sensor network for parameter estimation of spatio-temporal systems

Abstract

The main aim of the paper is to develop a distributed algorithm for optimal node activation in a sensor network whose measurements are used for parameter estimation of the underlying distributed parameter system. Given a fixed partition of the observation horizon into a finite number of consecutive intervals, the problem under consideration is to optimize the percentage of the total number of observations spent at given sensor nodes in such a way as to maximize the accuracy of system parameter estimates. To achieve this, the determinant of the Fisher information matrix related to the covariance matrix of the parameter estimates is used as the qualitative design criterion (the so-called D-optimality). The proposed approach converts the measurement scheduling problem to a convex optimization one, in which the sensor locations are given a priori and the aim is to determine the associated weights, which quantify the contributions of individual gaged sites to the total measurement plan. Then, adopting a pairwise communication scheme, a fully distributed procedure for calculating the percentage of observations spent at given sensor locations is developed, which is a major novelty here. Another significant contribution of this work consists in derivation of necessary and sufficient conditions for the optimality of solutions. As a result, a simple and effective computational scheme is obtained which can be implemented without resorting to sophisticated numerical software. The delineated approach is illustrated by simulation examples of a sensor network design for a two-dimensional convective diffusion process.

Construction of constrained experimental designs on finite spaces for a modified Ek-optimality criterion

“…As a nontrivial device to check the viability of the proposed technique, the problem of sensor selection for a distributed parameter system (DPS) will be used (cf. Uciński, 2005;Patan and Kowalów, 2018). Here the response y is defined implicitly as the solution of a partial differential equation (PDE).…”

Optimal sensor selection for prediction-based iterative learning control of distributed parameter systems

“…The resulting discrete optimization problem is then approximated based on relaxation which amounts to operating on the density of sensors in lieu of their individual positions. In particular the Fedorov's idea of directly constrained design measures [11] is used resulting in a simple and effective exchange algorithm being a dedicated adaptation of the techniques reported in [18,21,27].…”