An H∞-based approach for robust sensor localization

In this paper, we consider the problem of sensor localization, i.e., finding the positions of an arbitrary number of sensors located in a Euclidean space, ℝm, given at least m+1 anchors with known locations. Assuming that each sensor knows pairwise distances in its neighborhood and that the sensors lie in the convex hull of the anchors, we provide a DIstributed LOCalization algorithm in Continuous-Time, named DILOCCT, that converges to the sensor locations. This representation is linear and is further decoupled in the coordinates. By adding a proportional controller in the feed-forward loop of each location estimator, we show that the convergence speed of DILOC-CT can be made arbitrarily fast. Since a large gain may result into unwanted transients especially in the presence of disturbance introduced, e.g., by communication noise in the network, we use H_∞ theory to design local controllers that guarantee certain global performance while maintaining the desired steady-state. Simulations are provided to illustrate the concepts described in this paper.