Closed–Form Elliptic Location with an Arbitrary Array Topology

An efficient noniterative algorithm for active localization of objects is developed. It is based on intersecting elliptic curves defined by uncertain range-sum measurements between a signal source, the objects, and a number of arbitrarily located receivers. Measurement errors are modelled as being unknown but bounded in amplitude by a closed convex set. Based on this set-theoretic uncertainty model, an error propagation analysis is performed, that allows one to accurately bound estimation errors. For discriminating object primitives and for discarding erroneous measurements, a hypothesis test is derived. The algorithm's computational load is much lower than for grid-based methods and iterative techniques. A recursive formulation is provided to support real-time applications.