Sensor Localization Error Decomposition: Theory and Applications

In this paper we consider performance characterizations of self-localization algorithms for sensor networks. The location parameters have a natural decomposition into relative configuration and centroid transformation components based on the influence of measurements and prior information in the problem. A linear representation of the transformation parameter space, which includes rotations and translations, is used for decomposition of general localization error covariance matrices. The proposed decomposition may be applied to any estimator, the posterior Cramér-Rao bound (CRB) in a Bayesian setting, or a traditional CRB. Along with the CRB itself, the relative-transformation decomposition provides insight into how external inputs effect absolute localization performance. This partitioning of error is also useful to higher level applications in a sensor network that utilize results of the localization service and must account for its uncertainty. Examples are presented and an application demonstrates the utility of relative error decomposition to the problem of angle-of-arrival estimation with sensor location uncertainty.