3-D Target Localization Based on Frequency-of-Arrival via Multiple Satellites

This paper presents JLAS-FOA, an algorithm for joint localization and time synchronization of stationary nodes using Frequency-of-Arrival (FOA) measurements under clock asynchrony. Unlike prior work neglecting satellite coordinate/velocity noise and clock mismatches, we model node position and clock drift as unknowns, explicitly incorporating noisy ephemeris data and clock frequency errors. A maximum likelihood formulation is linearized via the Gauss-Newton method, solved using weighted least squares (WLS) to iteratively refine estimates. The Cramér-Rao Lower Bound (CRLB) is derived to characterize estimation limits, revealing accuracy degradation from satellite position/velocity noise. The algorithm ensures asymptotically unbiased convergence by minimizing weighted residuals, offering an optimal solution without requiring perfect satellite state information. This work provides a robust framework for high-precision localization and synchronization in satellite reception scenarios, balancing theoretical rigor with computational efficiency.