The minimum positional error incurred by any connectivity-based positioning algorithm for mobile wireless systems

A very important problem in many wireless ad-hoc networks, including wireless sensor networks, is positioning or the determination of geographical locations of the wireless nodes. Positioning is used both in infrastructural aspects of sensor networks, like geographic routing and topology maintenance, and in applications like wildlife tracking. Connectivity-based positioning algorithms in mobile wireless systems are studied in this work. These algorithms compute node positions based only on the connectivity, i.e. the neighborhood information of each node. Many algorithms have been proposed for positioning in stationary node systems and bounds on positional error of algorithms have been derived. The design and analysis of positioning algorithms for mobile node systems is a more challenging problem. Node mobility increases the amount of positional information available to a positioning algorithm. The work in this paper establishes a bound on the positional error for connectivity-based algorithms in mobile systems. The formulation from the analysis is used to investigate the benefit of this additional positional information on reducing positional error. There is a limit to the usefulness of positional information from previous node positions due to movement. This captures an important performance tradeoff: historical positional information can yield reduced positional error but requires more connectivity information from the network which requires greater computational resources.