Global analysis of vessel motion patterns has become possible using satellite-based Automatic Identification System (AIS). The concept of space-based AIS needs several satellites to provide complete coverage and high detection probability. However, in early development stages, often only one satellite is launched and due to its limitation of orbit and footprint, received AIS messages are discontinuous. In this paper, we have analysed real AIS data obtained by satellite to form a global maritime surveillance picture. Furthermore, we propose to take advantage of the tensor CANDECOMP/PARAFAC (CP) decomposition to analyse three mode characteristics of the data, which are location, vessel and time. For incomplete data, we exploit the link prediction technique based on tensor factorisation to recover vessel tracks in a specified area. A variant of temporal link prediction based on CP is presented. We illustrate the usefulness of exploiting the three-mode structure of AIS data by simulation, and demonstrate that the track recovery result has acceptable precision.