Anchor-free TDOA self-localization

We present an approach for the localization of passive receiver nodes in a communication network. In our settings the positions of the nodes are unknown. The only source of information is the time when environmental sound or ultrasound signals are received. The discrete signals occur at unknown positions and times, but they can be distinguished. The clocks of the receivers are synchronized, so the time differences of arrival (TDOA) of the signals can be computed. The goal is to determine the relative positions of all receiver nodes and implicitly the positions and times of the environmental signals. Our novel approach, the Iterative Cone Alignment algorithm, solves iteratively a non-linear optimization problem of time differences of arrival (TDOA) by a physical spring-mass simulation. Here, our algorithm shows a smaller tendency to get stuck in local minima than a non-linear least-squares approach. The approach is tested in numerous simulations and in a real-world setting where we demonstrate and evaluate a tracking system for a moving ultrasound beacon without the need to initially calibrate the positions of the receivers. Using our approach we estimate the trajectory of a moving model train with a precision in the range of centimeters.