Positioning Optimization Methods Using TOA/TDOA Under NLOS Conditions

Source positioning is a central issue in cellular or wireless sensor networks.In a localization problem,the positioning of an unknown target is obtained from a set of measurements observed at some known sensors,such as time of arrival(TOA)?time difference of arrival(TDOA).Traditional localization methods assume that the target signals arrive at the known sensors all in a straight-line way,which is the so-called line-of-sight(LOS)assumption.However,this assumption often collapses in practice,particularly in city communities.In such circumstances,the target signals often follow non-line-of-sight(NLOS)propergation way due to the building reflections or diffraction,resulting in non-line-of-sight(NLOS)errors that can degrade the localization accuracy sharply.This study focuses on how to reduce the adverse effect of NLOS errors on the positioning accuracy and on how to get better estimation performance.This study focuses on the TOA/TDOA positioning optimization methods under NLOS conditions.The main work includes:1.For the robust positioning problem under NLOS conditions with TOA measurements,two convex-relaxation-based methods,one using the semi-definite relaxation(SDR)and another resorting to the second-order cone relaxation(SOCR)to handle the involved nonconvex constraints,are studied,which both transform the initial noncovex positioning problem into a convex one for seeking a robust solution.In view of the big computational burden of these two methods,a general-trust-regionsubproblems(GTRS)-based method is also studied,which transforms the initial positioning problem into a GTRS problem and exploits a simple binary search to obtain a robust localization solution with low computational costs.2.For the robust positioning problem under the bounded NLOS assumption with TDOA measurements,two scenarios are discussed: one assumes that the NLOS path state is unknown,where the original TDOA positioning problem is transformed into a robust least squares(RLS)problem,and then the two convex relaxation strategies,i.e.,SDR and SOCR techniques,are applied to deal with the nonconvex RLS problem to achieve a robust target position estimate.Another presumes that the NLOS path state is known and the LOS and NLOS measurement data can be processed separately,where a weighted term is added to the NLOS measurement data to obtain a robust weighted least-squares(RWLS)problem and the resulting RWLS problem is solved by the SOCR technique to get a robust target location estimate.3.For the TOA-based multi-target cooperative positioning problem under the NLOS conditions,a SDP-based multi-target cooperative positioning algorithm in the literature is studied first,which estimates the source location as well as the NLOS errors to reduce the influence of the NLOS error on the positioning performance.Then,a new multi-target cooperative positioning algorithm based on concave convex procedure is also studied,which uses the minimum absolute deviation criterion to construct the cost function and solves it with the concave convex optimization procedure.When the percentage of the NLOS path number is lower than the medium level,this algorithm can reduce the influence of the NLOS errors effectively.