Improved analytical solution with optimization constraints using TDOA and FDOA measurements for USV/AUV collaborative localization

The paper introduces an enhanced constrained two-step weighted least squares (WLS) analytic localization algorithm designed to determine the AUV’s position and velocity within the collaborative localization system, utilizing time difference of arrival and frequency difference of arrival measurements. This algorithm integrates optimization constraints between intermediate variables and target motion parameters, producing precise analytical solution based on WLS minimization criterion. The proposed process not only reduces computational burden by providing an analytical solution but also enhances estimation accuracy through the incorporation of optimization constraints. Analytical assessments and statistical simulations highlight the superior estimation accuracy of the proposed algorithm, and demonstrate that the position and velocity estimation accuracy align with the Cramér-Rao lower bound under appropriate measurement noise conditions.