Robust navigation using angle of arrival measurements

The majority of conventional radionavigation systems are based on Time of Arrival (TOA) measurements of RF signals. By far the most common method is pseudoranging, mainly a result of the undisputed success of Global Navigation Satellite Systems (GNSS) as a ubiquitous technology, especially in aviation. With all its successes, however, there are limitations to pseudorange-based positioning, at least as embodied in GNSS. Well-publicized issues include its susceptibility to Radio Frequency Interference (RFI) in the forms of jamming and spoofing. A commonly cited solution is using array antennas, which enable adaptive beamforming as a mitigation; of interest here is that they also allow the estimation of the Angle of Arrival (AOA) of any signal including signals of opportunity. The concept of using AOA data is not new, having a significant history in direction finding during and post WW II. A well-established strategy for positioning algorithms, in general (i.e. range, pseudorange, Doppler, bearings, and combinations of these), consists of solving a set of simultaneous measurement equations using an iterative least squares algorithm; such algorithms for AOA measurements with known vehicle orientation previously have appeared. What is less well known, and of specific interest to us, is that the iterative AOA algorithm has poor convergence; this is in marked contrast to the TOA case. The error surface for range-based positioning is region-wise a paraboloid and points down toward a solution. The angles, or bearing, error surface displays concavity in large regions, the bane of convergence. To address this convergence concern one might attempt to modify the iteration to not take a full update step, but only some fraction of it. This, of course, leads to its own design and analysis problems. Instead, in this paper we consider two alternative algorithms for estimating position from a set of bearing measurements. The first of these is non-iterative in nature, so always provide an answer (i.e. have no convergence problems); the other is a new method which converts the bearings into ranges and reformulates the problem as an iterative range problem which has the good convergence characteristics of ranging-based positioning.