Performance analysis of sensor self-localization algorithms

In this paper the self-localization problem for sensor networks is discussed. We suggest to use the configuration of sensors that has overall maximum probability, given the observations. In a Bayesian framework this corresponds to maximum a posteriori (MAP) estimation. However, there is a main reservation concerning this approach: The computational problem of solving the complex nonlinear optimization problem seems at first glance to be enormous. We suggest in the present paper to reduce the computational burden by a simple coordinatewise greedy algorithm, which is nothing else than the successful iterative conditional modes (ICM) algorithm from spatial statistics and image analysis. The advantages are that it is 1) distributed, 2) simple and 3) easy to implement. A theoretical lower bound on the average mean square error (AMSE) for all localization estimators in multihop sensor networks is presented under suitable regularity conditions on the sensor positions. A simulation study is conducted and it is shown that the AMSE of the proposed estimator for a variety of parameters is close to the lower bound on the AMSE.