Performance analysis of parameter estimator on non-linear iterative methods for ultra-wideband positioning

ABSTRACT Ultra-wideband is a promising technology in indoor positioning due to its accurate time resolution and good penetration. Since the positioning model is non-linear, iterative methods are often considered for solving the localisation problem. However, the positioning system is prone to become ill-posed. The iterative methods cannot easily converge to a global optimal solution. In this paper, the convergence property of four non-linear iterative methods is analytically reviewed under ill-conditioned configuration. For the iteration, three types of initial values are selected. Experimental results are given to demonstrate that although the barycentre method can converge correctly, it is inefficient with too many iterations. In addition, with a good initial value, the Gauss–Newton method can converge effectively, and it sometimes converges to a false local optimisation solution when selecting a bad initial value. Moreover, both the regularised Gauss–Newton method and closed-form Newton method can converge to the global optimum effectively with fewer iterations. This study shows that the closed-form Newton method has higher efficiency of convergence than the other methods. Meanwhile, to make complete use of measurements available to improve the accuracy, the result of non-iterative method is generally used as the initial value of the iterative method.