Analysis of Position and Timing Solutions for an APNT-System - A Look on Convergence, Accuracy and Integrity

Abstract

Alternative Position Navigation and Timing (APNT) considers different possible ranging sources like DME, UAT, LDACS, etc… for which multipath is a major threat. Therefore code smoothing with Doppler measurement techniques have been considered in this paper. But ranging errors are not the only issues encountered in APNT; in fact the positioning algorithm needs to be revisited as the linearization assumption for GNSS does not apply for the short range case. Indeed, two problems have been observed while applying the Newton-Raphson approach for the LDACS data collected during the 2012 flight trials: the initial point when taken too far away from the true position prevents the iterative positioning algorithm to converge; and when the initial point is close to the solution but the ranging errors are too large we also observed a convergence problem of the Newton-Raphson algorithm. From this observation, we have decided to investigate the performance of a direct method. A hybrid method taking advantage of both approaches (initial point provided by a direct method followed by the Newton-Raphson method) has been suggested and compared with the stand alone direct method. This paper describes these methods and their performances are assessed based on simulations over Germany using DME stations as ranging source locations. We show that the direct and hybrid methods provide a solution also when the Newton-Raphson algorithm does not converge.