Semidefinite Programming for Unified TDOA-Based Localization Under Unknown Propagation Speed
Hengnian Qi, Xiaoping Wu, Liangquan Jia
Abstract
By assuming signal propagation speed to be unknown, a convex rank unconstrained semidefinite programming (RUSDP) algorithm is designed to obtain the unified solution for near-field and far-field TDOA-based localization. Then the rank constrained semidefinite programming (RCSDP) is further proposed by availing of the rank constraint. The simulations show the validity of the RUSDP and RCSDP algorithms whether the source is in the near-field or in the far-field. The RCSDP performs significantly better than the RUSDP due to the tighter relaxation.
Topics & Concepts
Semidefinite programmingSemidefinite embeddingMultilaterationRelaxation (psychology)Rank (graph theory)Mathematical optimizationComputer scienceField (mathematics)Constraint (computer-aided design)Convex optimizationRegular polygonAlgorithmMathematicsQuadratically constrained quadratic programQuadratic programmingCombinatoricsSocial psychologyGeometryAzimuthPsychologyPure mathematicsIndoor and Outdoor Localization TechnologiesDirection-of-Arrival Estimation TechniquesSparse and Compressive Sensing Techniques