Relative and Absolute Errors in Sensor Network Localization

This paper considers the accuracy of sensor node location estimates from self-calibration in sensor networks. The location parameters are shown to 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 shown to coincide with the nullspace of the unconstrained Fisher information matrix (FIM). To regularize the absolute localization problem, we consider constraints on the coordinate locations and the impact of these constraints on relative and absolute location error. A geometric interpretation of the constrained Cramer-Rao bound (CRB) is provided based on the principal angles between the measurement subspace and the constraint subspace. Examples illustrate the utility of this error decomposition.