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Efficient Deterministic Algorithm for Huge-Sized Noisy Sensor Localization Problems via Canonical Duality Theory

This paper presents a new deterministic method and a polynomial-time algorithm for solving general huge-sized sensor network localization problems. The problem is first formulated as a nonconvex minimization, which was considered as an NP-hard based on conventional theories. However, by the canonical duality theory, this challenging problem can be equivalently converted into a convex dual problem. By introducing a new optimality measure, a powerful canonical primal–dual interior (CPDI) point algorithm is developed which can solve efficiently huge-sized problems with hundreds of thousands of sensors. The new method is compared with the popular methods in the literature. Results show that the CPDI algorithm is not only faster than the benchmarks but also much more accurate on networks affected by noise on the distances.