Feasibility analysis on optimal sensor selection in cyber-physical systems

A fundamental question for observation systems based on wireless sensor network (WSN) is to achieve the best tradeoff between estimation precision and many design factors. One challenge of this kind is to select a small number of sensors, if possible, to observe the environment, and thus conserve precious onboard battery energy by transmitting only valuable data to the base station. Although many sensor selection methods have been proposed, the analysis on this problem is relatively limited. Based on the theory of optimal experimental design and convex analysis, we present some feasibility analysis on the optimal sensor selection problem. Equipped with Fisher information matrix, we show that there exists a threshold, which we named Carathéodor´s limit, such that the optimal estimation is always feasible as far as the number of selected sensors is no less than that limit. We also investigated on the difference between the total sample number and the total sensor number. Discussions on some necessary conditions of sensor density and sensor deployment patterns are included too. We argue that sensor selection methods have potentials to save significant amount of energy for a large class of embedded wireless sensor networks without sacrificing estimation accuracy.