# Optimum Design of Hybrid Sensor Networks for Parameter Estimation of Spatiotemporal Processes

Dariusz Ucinski^{*}

A major difficulty in the modelling and calibration of processes described by partial differential equations is the impossibility to measure process variables over the entire spatial domain. This leads to the question of how to optimally place sensors. Common sensor placement strategies exploit the Fisher information matrix associated with the parameters to be identified. A revived interest in optimal sensor location accompanies advances in Sensor Networks (SNs) which highly increase the flexibillity of observation systems. In the contribution, a mobile sensor network is considered which includes a number of mobile nodes which can move in a given spatial domain and, therefore, we would like their trajectories to be optimal in a sense. In addition to that, the data from mobile sensors are to be complemented by the ones gathered by a given number of nodes selected from among a greater number of nodes whose locations in space are fixed. Therefore, a decision must be made about which subset of non-mobile sensors is to be activated. Mathematically, the problem is a mixed discrete optimal control one and, due to its potential high dimensionality, naive solutions are deemed to failure. The branch-and-bound method is applied to drastically reduce the search space. The key idea behind it is alternation between two relaxed problems, namely a discrete optimization one related to stationary sensors and an optimal control one associated with moving sensors.

Mathematics Subject Classification: 62K05 93E12 90B80 93C20 49J15

Keywords: optimal sensor location; partial differential equations; D-optimum design; optimal control; branch and bound

Minisymposion: Optimal Design of Spatio-Temporal Networks and Systems