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Exact Linear Closed-Form Solutions to the 3D TDOA Source Localization Problem

Presents the first exact, purely algebraic closed-form solvers for time-difference-of-arrival source localization in full three-dimensional space with four and five sensors. The five-sensor case reduces to inverting one 3x3 linear system with no sign-ambiguity resolution; the four-sensor case adds a single quadratic whose two-fold ambiguity is resolved by residual minimization or priors. Linearity makes the solvers fast, iteration-free, and suitable for on-platform SLAM, PNT/GPS, and acoustic/EM geolocation.