An infinity-norm based flexible semidefinite programming technique for elliptical localization

This paper focuses on elliptical localization for a multi-static passive radar, when an uncooperative transmitter is considered. We take two factors into account: the error in transmitter position and the range-dependent measurement noise. When no prior is provided on the error's bound or variance, it is found that most existing algorithms become invalid. Following this and based on the infinity-norm optimization criterion, a min-max flexible semidefinite programming (MMF-SDP) technique is developed to achieve novel estimation results. MMF-SDP works by decomposing the noise components into independent ones and then treating them as optimization parameters. Relationship between the noise components on different measurements is also explored, which helps guarantee a rank-one semidefinite relaxation. Numerical results collaborate with our theory and the superiority of MMF-SDP is also illustrated.