TOA-based source localization using ML estimation

Abstract

This paper proposes the Time of arrival (TOA) measurement model for finding the position of a stationary emitting source for Line-of-Sight (LOS) scenario. Here Maximum Likelihood Estimation (MLE) is used as the positioning algorithm. For approximation of the roots of the solution, which directly corresponds to the source location, the optimization techniques used are Gauss-Newton, Gradient descent and Newton-Raphson methods. Two different cases are considered for investigation in this paper. The first case compares the three different optimization techniques in terms of convergence rate. In the second case the error values obtained from two different scenarios are compared, one involving a single trial only, while the second scenario uses Monte Carlo method of simulations. Firstly, the error values, for both the coordinates (two-dimensional), obtained by getting the difference between the measured source positions and the initially guessed source position are obtained for a single trial. Later using Monte Carlo simulation method, the Root-Mean-Square (RMS) error values, for both the coordinates (two-dimensional), for the optimization techniques are obtained. To improve the performance of the algorithm, Monte Carlo simulation has been used for multiple trials.