# VHF Omnidirectional Range (VOR) Experimental Positioning for Stratospheric Vehicles
## 1 Introduction  
In the extremely complex scenario of the so-called New Space Economy, stratospheric missions are obtaining an increasingly important role due to their effective capabilities of performing quasi-satellite tasks with lower development and installation costs, when compared to orbital platforms [1]. To support the emerging mission concepts for stratospheric payloads and for this transfer from _space_ science to _near-space_ missions [1, 2], the future operations of stratospheric airships, High Altitude Platform Stations (HAPSs), and stratospheric vehicles will require an improvement of the navigation systems reliability for achieving more accurate navigation, station-keeping tasks, and positioning [3, 4, 5, 6, 7, 8]. The utilization of a secondary navigation system, as back-up for than Global Navigation Satellite System (GNSS), can introduce a further improvement to the navigation systems reliability and to the mission execution itself [9, 10, 11]. Aeronautical Navigational aids (NavAids) can support these new concept mission profiles with an extension of their usual service volume. Passive NavAids, such as the VHF Omnidirectional Range (VOR, [12, 13, 14]), can support the missions by requiring only passive Radio-Frequency (RF) airborne hardware, thus simplifying the architecture of the additional navigation systems on-board the stratospheric platforms. Although GNSS is currently already redundant (with several governmental systems active and operational) and aeronautical ground-based NavAids can be supporting similar missions only when overflying land, these NavAids can provide further support to stratospheric missions with an additional, independent navigation system.  
These navigation systems are generally not allowing the users to directly achieve positioning, while the absolute position determination is in general possible through further processing of the measurements. For example, the VOR system outputs the radialinformation, which equals the bearing angle of the line between the airborne receiver and the VOR ground station with respect to the Magnetic North, without any information on the actual position of the receiver [12]. If intersecting two radials, it is possible to calculate the latitude and longitude of the receiver.  
The STRATONAV experiment, developed at Sapienza University of Rome for the REXUS/BEXUS Programme (aiming at launching European student experiments on-board stratospheric balloons and sounding rockets, [15]) has proven in 2016 the well-functioning of the VOR navigation system in stratospheric flight, while flying on a stratospheric balloon in Northern Sweden with an apogee of 32.2 km. The data analysis, described in [16], confirmed that the reliability of such navigation system in stratospheric flight is comparable to the current accuracy standards predicted by the International Civil Aviation Organization (ICAO, [12; 17]) and they can satisfy the previous standard rates introduced in the first years of VOR operations.  
After the accuracy determination analysis carried out with the data collected in stratosphere, the STRATONAV data have been re-processed with the aim of achieving positioning and ground-track estimation of the balloon trajectory by means of the VOR measurements stand-alone. This paper reports the results from the VOR-based positioning analysis carried out on the stratospheric balloon data from STRATONAV. The needed materials and methods, from an introduction on VOR to the data analysis principles and data collection processes adopted on STRATONAV, will be described in Section 2, while the obtained results from the conducted analyses will be presented in Section 3, before moving to the conclusions in Section 4.