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Given a network of receivers and transmitters, the process of determining their positions from measured pseudoranges is known as network self-calibration. In this paper we consider 2D networks with synchronized receivers but unsynchronized transmitters and the corresponding calibration techniques, known as Time-Difference-Of-Arrival (TDOA) techniques. Despite previous work, TDOA self-calibration is computationally challenging. Iterative algorithms are very sensitive to the initialization, causing convergence issues. In this paper, we present a novel approach, which gives an algebraic solution to two previously unsolved scenarios. We also demonstrate that our solvers produce an excellent initial value for non-linear optimisation algorithms, leading to a full pipeline robust to noise.

Sensor Networks TDOA Self-Calibration: 2D Complexity Analysis and Solutions