Sensors' allocation for estimating scalar fields by wireless sensor networks

Our aim is to consider the problem of allocating sensors and frequencies of their activation in such a way that the balance between the estimation accuracy of a scalar field and energy consumption is optimized. To this end we propose an extension of the theory of optimal experiment designs by including terms for transmission energy consumption or penalties for region coverage into the optimality criterion. We state the optimality conditions, which serve as a base for a numerical algorithm for searching sensors' positions and frequencies of their activations. Examples of optimal allocations for a variety of basis, spanning spatial fields, are also provided.