Fixed Point Iteration Based Algorithm for Asynchronous TOA-Based Source Localization

This paper investigates the problem of source localization using signal time-of-arrival (TOA) measurements in the presence of unknown start transmission time. Most state-of-art methods are based on convex relaxation technologies, which possess global solution for the relaxed optimization problem. However, computational complexity of the convex optimization–based algorithm is usually large, and need CVX toolbox to solve it. Although the two stage weighted least squares (2SWLS) algorithm has very low computational complexity, its estimate performance is susceptible to sensor geometry and threshold phenomenon. A new algorithm that is directly derived from maximum likelihood estimator (MLE) is developed. The newly proposed algorithm is named as fixed point iteration (FPI); it only involves simple calculations, such as addition, multiplication, division, and square-root. Unlike state-of-the-art methods, there is no matrix inversion operation and can avoid the unstable performance incurred by singular matrix. The FPI algorithm can be easily extended to the scenario with sensor position errors. Finally, simulation results demonstrate that the proposed algorithm reaches a good balance between computational complexity and localization accuracy.