Abstract:

To address the non-convergence problem of the traditional Gauss-Newton iterative method in time difference of arrival (TDOA) and frequency difference of arrival (FDOA) location due to the inaccurate iterative initial value,a Gauss-Newton iterative algorithm based on the constrained weighted least square (CWLS) is proposed.First,the nonlinear positioning equation in the positioning problem is transformed into a set of pseudo-linear equations about the target position and velocity.Initial values of the target position and velocity are estimated step by step.In order to realize the accurate estimation of the initial value,the equality constraint relationship between the target position and the auxiliary variable are relaxed to the second-order cone programming (SOCP) condition.The stochastic robust least square (SRLS) is introduced to construct a new linear relation.When the weighted least square solution does not meet the SOCP condition,the semi-definite programming (SDP) is used to solve the estimated solution of the target position.The target velocity is solved by the obtained target position.After obtaining the initial values of the target parameters,the Gaussian Newton iterative equations for the target position and velocity in the TDOA-FDOA localization system are established.Target parameters are solved by the Gaussian Newton iterative process,which does not require the introduction of auxiliary parameters and can directly obtain the target parameters.Simulation experiments show that the proposed algorithm has a good localization effect on both near-field and far-field targets,and that its robustness and high localization accuracy are better than those of the existing classical two-stage weighted algorithm.At the same time,simulation results show the necessity of optimizing the initial values when the Newton iterative equations are used.

Key words: passive localization, time difference of arrival, frequency difference of arrival, gauss-newton iteration, Cramér-Rao lower bound