# Large-Scale Automatic Vessel Monitoring Based on Dual-Polarization Sentinel-1 and AIS Data
## Materials and Methods
### SAR and AIS Data Comparison  
In order to assess the effectiveness of ship SAR-based detections, the identified targets are compared with vessel positions extracted from AIS data flows. The AIS data was collected from databases containing messages acquired by both terrestrial stations and SAT-AIS systems. Even if, according to the the International Convention for Safety of Life at Sea (SOLAS), it is required that all ships exceeding 300 tons engaged on international voyages, cargo ships of 500 tons and above not engaged on international voyages and all passenger ships were required to carry AIS transponders [60], not all existing vessels were monitored by AIS systems. In addition, AIS systems can present communication losses due to the physical limitations of their components, such as very high frequency (VHF) propagation losses or multipath effects of the signal reception. Due to these limitations, in this study we considered the AIS information as a cross-comparison datatest for the evaluation of SAR-based vessel detection results, and not as a complete ground-truth dataset. In general, AIS transponders broadcast the position of the vessel at different time intervals ranging from two seconds for fast manoeuvring targets, to three minutes for anchored vessels [61]. However, for different scenarios including deliberate partial switch of the AIS transponder or surveillance of areas out of the reception range of terrestrial antennas, the time span between the reception of two AIS positions can be higher than three minutes. Therefore, for low frequency AIS data flows, it is not necessarly possible to extract the AIS positions at the specific SAR image acquisition time. In order to overcome this limitation and to compare SAR and AIS datasets it is necessary to first interpolate the AIS positions [22]. In case the SAR acquisition time lies between two AIS positions close in time (few seconds) a linear interpolation was sufficient while for larger gaps between the AIS positions a more complex interpolation procedure is desirable [62]. In this study, for each area of interest corresponding to the SAR image coverage, we extract the AIS ship positions for a time range of \(\pm\)X minutes with respect to the SAR acquisition time, denoted hereafter \(t_{SAR}\). The values of X may vary for instance, from 15 min to one or even two hours depending on the traffic density or the number of terrestrial antennas in the area of interest. Under normal conditions, we receive more than one AIS position per ship during this 2 \(\times\) X minutes time interval. However, as mentioned before, not all the ships are able to report AIS messages in a very short 2 \(\times\) X minutes time interval (e.g., X \(\leq\) 1 min). To overcome this difference, all AIS positions were interpolated in order to predict the position at \(t_{SAR}\). In this context, the following procedure is proposed. First, trajectories were extracted for ships that reported more than one position before and after \(t_{SAR}\), under the assumption of constant speed and heading. The closest position to \(t_{SAR}\) from the AIS trajectory is retained for each unique vessel identified by its Maritime Mobile Service Identity (MMSI) series. The heading and speed computed between the consecutive positions for each trajectory are compared with the AIS heading and speed and heading provided by the metadata reports. If the compared numbers are similar enough, the interpolation process continues for all points and the interpolated positions corresponding to \(t_{SAR}\) are retained for each vessel. In addition, we take into account the following two cases. For the first one, we consider that the reported positions have all timestamps before \(t_{SAR}\) and assume that speed and heading are constant. Therefore, the ship position is predicted for a time interval equalling the difference in seconds between \(t_{SAR}\) and the latest AIS position timestamp. For the second case, we considered that the timestamps of the AIS reported positions are after \(t_{SAR}\).