Distributed sensor networks are growing in popularity for a large number of sensing applications ranging from environmental monitoring to military target classification and tracking. However, knowledge of the individual sensor positions is a prerequisite to obtaining meaningful information from measurements made by the sensors. With the scale of sensor networks rapidly increasing due to advances in communications and MEMS technology, an automatic localization service based on inter-sensor measurements is becoming an essential element in modern networks. This dissertation studies fundamental aspects of localization performance while deriving general results for singular estimation problems.
Because inter-sensor measurements, such as distances or angles-of-arrival (AOA), are invariant to absolute positioning of the sensor scene, localizing sensors with an absolute reference, e.g., latitude and longitude, is inherently a singular estimation problem suffering from non-identifiability of the absolute location parameters. This results in a corresponding singular Fisher information matrix.
We consider means of regularizing the absolute localization problem and devise novel performance characterizations by showing that the location parameters have a natural decomposition into relative configuration and centroid transformation components based on the singularity of the problem. A linear representation of the transformation manifold, which includes representations of rotation, translation, and scaling, is used for decomposition of general localization error covariance matrices. The unified statistical framework presented – which naturally generalizes to non-localization problems – allows us to quantify and bound performance in the relative and transformation domains. These tools facilitate analysis of relative-only algorithms while enabling new algorithm development to finely tune performance in each subdomain. The analysis is applied to a novel closed-form AOA-based localization algorithm presented in the dissertation.
Finally, we consider anchor nodes, with a priori known positions, as a specific form of regularization and address optimal anchor selection and placement strategies for minimum mean-square localization error. We present a novel sensor placement heuristic based on minimizing principal angles between the anchor-induced constraint subspace and the non-identifiable transformation subspace. This work provides analytical justification for the frequent, but empirical, observation that perimeter-placement of anchors is desirable.