On the Distribution of Positioning Errors in Wireless Sensor Networks: A Simulative Comparison of Optimization Algorithms

Recent advances in the technology of wireless electronic devices have made possible to build ad-hoc wireless sensor networks (WSNs) using inexpensive nodes consisting of low power processors, a modest amount of memory, and simple wireless transceivers. Over the last years, many novel applications have been envisaged for distributed WSNs in the area of monitoring, communication, and control. One of the key enabling and indispensable services in WSNs is localization (i.e., positioning), given that the availability of nodes´ location may represent the fundamental support for various protocols (e.g., routing) and applications (e.g., habitat monitoring). In the depicted context, the present contribution reports our recent research advances along two main directions: i) first of all, we provide a comparative analysis of various optimization algorithms that can be used for atomic location estimation, which include: triangulation, steepest descent, non-linear least squares, conjugate gradient, and an enhanced version of the Steepest Descent (ESD) that is introduced in this paper, and ii) then, we provide a statistical characterization of location errors, by showing that the distribution of error positions can be well approximated by the family of Pearson distributions. In particular, we will show that i) the ESD algorithm may be competitive with the other algorithms in terms of estimation accuracy and numerical complexity, and ii) the knowledge of location error distribution may be efficiently used to speed-up the analysis of iterative-based positioning algorithms by avoiding the need of simulating the whole location discovery algorithm and allowing simulation at the atomic level only.