A Gauss–Newton Iterative Method for Emitter Localization Using Joint TDOA/FDOA/DDR Measurements

To address the problems of complex auxiliary-variable constraints and degraded localization accuracy under low signal-to-noise ratio (SNR) conditions in existing moving emitter localization algorithms based on joint TDOA/FDOA/DDR measurements, this paper proposes a three-measurement localization algorithm that combines weighted least squares (WLS) initialization with Gauss–Newton iteration. First, a pseudo-linear equation system is constructed by jointly using the TDOA, FDOA, and DDR measurements. A WLS estimator is then used to obtain the initial joint estimate of the source position and velocity. Next, a nonlinear WLS model is established with the original weighted residuals as the optimization objective. The source state parameters are directly refined through Gauss–Newton iteration, without using auxiliary-variable penalty terms or semidefinite relaxation. Simulation results show that the proposed algorithm achieves high localization accuracy and stable convergence in both near-field and far-field scenarios. It approaches the Cramér–Rao lower bound in the relatively low-SNR region and has the lowest average running time among the compared algorithms.