Localization using boundary sensors: An analysis based on graph theory
We consider sensors, such as fibers, lasers, and pyroelectric motion detectors, that fire when objects cross a boundary. A moving object can be localized by analyzing sequences of boundary crossings. We consider the number of distinct sequences and object positions that can be achieved using boundary sensors in one- and two-dimensional spaces. For 1D systems we use representations of sensor sequences on graphs to derive limits on the number of object locations that can be monitored by a given sensor population and sequence length. For 2D systems we show that in certain circumstances the ratio of the number of unique sensor sequences to the number of unique object paths is exponential in the sequence length and we argue that the probability of unique identification is high for sufficiently large sequences. We also prove the triangle grid can track an object with error limited to a small neighborhood.
boundary sensor theory sensor sequence algorithm design deployment sequence deployment graph sequence graph