Why You Shouldn’t Use TDOA for Multilateration

The maximum likelihood problem arising from multilateration or source localization via signal times of arrival (TOA) leads to a nonlinear least squares problem in target position and target transmission time (TTT). Since we are not interested in the latter, it is usually eliminated from the equation system. We eliminate the TTT in closed form, which is simpler to design, easier to implement, and faster to compute than the often used pairwise time differences of arrival (TDOAs). We propose an unweighted nonlinear least squares formulation of the multilateration problem whose minimization with the Levenberg-Marquardt algorithm is very fast. Julia source code is available here (others added on request): https://github.com/KIT-ISAS/MFI2025_MLAT-TOA