Name
Abstract | ||
|---|---|---|
The single-source localization problem (SSLP), which is nonconvex by its nature, appears in several important multidisciplinary fields such as signal processing and the global positioning system. In this paper, we cast SSLP as a Euclidean distance embedding problem and study a Lagrangian dual approach. It is proved that the Lagrangian dual problem must have an optimal solution under the generalized Slater condition. We provide a sufficient condition for the zero-duality gap and establish the equivalence between the Lagrangian dual approach and the existing Generalized Trust-Region Subproblem (GTRS) approach studied by Beck et. al. [“Exact and Approximate Solutions of Source Localization Problems,” IEEE Trans. Signal Process., vol. 56, pp. 1770–1778, 2008]. We also reveal new implications of the assumptions made by the GTRS approach. Moreover, the Lagrangian dual approach has a straightforward extension to the multiple-source localization problem. Numerical simulations demonstrate that the Lagrangian dual approach can produce localization of similar quality as the GTRS and can significantly outperform the well-known semidefinite programming solver ${\tt SNLSDP}$ for the multiple source localization problem on the tested cases. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1109/TSP.2013.2264814 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
semidefinite programming solver,orthogonal projection,sslp,signal processing,mathematical programming,gtrs approach,euclidean distance matrix,lagrangian dual approach,generalized trust-region subproblem approach,low-rank approximation,lagrangian duality,single-source localization problem,euclidean distance embedding problem,duality (mathematics),multiple-source localization problem,generalized slater condition,zero-duality gap,duality mathematics | Mathematical optimization,Weak duality,Duality (mathematics),Slater's condition,Duality (optimization),Lagrangian relaxation,Solver,Euclidean distance matrix,Semidefinite programming,Mathematics | Journal |
Volume | Issue | ISSN |
61 | 15 | 1053-587X |
Citations | PageRank | References |
5 | 0.45 | 14 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Houduo Qi | 1 | 437 | 32.91 |
| Naihua Xiu | 2 | 142 | 22.48 |
| Xiaoming Yuan | 3 | 1118 | 60.83 |