Localization of a Passive Object in 3-D by Propagation Time Delays to A Rigid Body Receiver of Unknown Location

Self-localization of sensor nodes is the first step towards the positioning of an intended object. This paper proposes the use of a rigid body with sensors attached as a receiver network for the localization of an object, using the signal propagation time delays from the transmitters through the object to the sensors. We show that it is conceivable to locate the object without requiring the location, consisting of the position and orientation, of the rigid body. Such an interesting conclusion is supported by a new time delay model that is independent of the location of the rigid body. The model leads directly to the formulation of a quadratically constrained quadratic program problem for locating the object, from which an efficient closed-form estimator and a noise-resilient semidefinite programming solution are derived. When a noisy position of the rigid body is available, we evaluate the possible amount of improvement that can be gained and develop the positioning solutions for this case as well. Simulations validate well the theoretical development and the optimal performance of the proposed estimators.