Research On Time Difference Positioning And Robust Beamforming Algorithms In Passive Positioning Systems

Passive localization refers to how to determine the position of a target without emitting electromagnetic wave by receiving stations,but by passively receiving the radiating,reflecting or scattering electromagnetic wave from the radiant target.Due to the outstanding concealing,anti-reconnaissance and anti-jamming ability,passive localization has been widely used in the following fields such as electronic warfare and navigation,and will be applied in the following scenarios such as unmanned aerial vehicle network,intelligent transportation and internet of things.Furthermore,the passive localization technology based on time difference of arrival(TDOA)has attracted extensive attention and research,because of its high positioning precision,low requirement of receiving system,and strong networking ability.In this paper,we focus on the TDOA-based passive localization methods and beamforming algorithms.The main contributions are as follows:1)To improve the location accuracy,we proposed a quadratic-optimization method for TDOA-based passive multi-satellite localization with only Earth constraint by utilizing the fact of target locating on the Earth.The positioning problem is casted as a quadratically constrained quadratic optimization problem.Then the approximate analytic solution of target position is obtained by using Lagrange multipliers method.Simulation results show that the proposed algorithm can achieve the Cramer-Rao lower bound with Earth constraint in three typical scenarios.The localization performance of proposed method is superior to some existing methods like two-stage weighted least square and approximate maximum likelihood algorithms.Moreover,due to the acquisition of target approximate analytic solution,the proposed method can effectively lower the complexity and avoid initial value choice and convergence of iterative algorithms.2)To evaluate the importance of Earth constraint(EC)and variable constraint(VC)on the aspect of improving localization performance,we designed a weighted method.The proposed method separates the original quadratic optimization problem with both EC and VC into two independent solvable optimization problems with each keeping only EC or VC.Then the weighted coefficient is used to synthesize the associated optimal solutions of the two sub-problems to a new solution.The weighted factor is also utilized to evaluate the importance of EC and VC.Simulation results show that compared to VC,EC has a dominant impact on location performance.Abandoning the VC from the original optimization problem will not affect the overall localization performance.Hence,the operation of ignoring VC can reduce the computational complexity for TDOA-based location problem without degrading the localization performance.3)Considering the localization problem in interference environment,a robust beamformer in hybrid analog and digital beamforming structure is proposed by exploiting diagonal loading method and convex optimization technique.For the purpose of suppressing interference and enhancing the robustness to the estimate error of direction of arrival(DOA),the proposed hybrid beamforming is designed by minimizing the output receive power and harvesting the gain at the direction of DOA estimation and its tolerating maximum estimating error greater than 1.Simulation results show that the robustness of the proposed beamformer outperforms the diagonal-loading-based beamformer in hybrid structure.And for the medium or large scale antenna arrays,the proposed hybrid beamforming method can significantly reduce the number of radio frequency chains and effectively strike a good balance between system performance and hardware cost.