Accurate Semidefinite Relaxation Method for 3-D Rigid Body Localization Using AOA
Gang Wang, K. C. Ho
Abstract
This paper addresses the rigid body localization problem using angle-of-arrival measurements. We formulate the problem as a constrained weighted least squares (CWLS) minimization problem with the rotation matrix and position vector as variables, which is a challenging non-convex problem. To approximately solve this problem, we first relax it as a convex semidefinite program (SDP), and then tighten the relaxed problem by adding some reasonable second-order cone constraints. Simulations show that the tightened SDP problem is able to reach the performance of the original CWLS problem, making its solution achieve the Cramer-Rao lower bound accuracy, when the noise level is not too high.
Topics & Concepts
Relaxation (psychology)Semidefinite programmingMathematical optimizationConvex optimizationOptimization problemComputational complexity theoryMinificationPosition (finance)Regular polygonRotation matrixSecond-order cone programmingMathematicsAlgorithmComputer scienceUpper and lower boundsRotation (mathematics)Mathematical analysisArtificial intelligenceGeometryPsychologyEconomicsSocial psychologyFinanceIndoor and Outdoor Localization TechnologiesRobotics and Sensor-Based LocalizationTarget Tracking and Data Fusion in Sensor Networks