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The integrated navigation systems are utilized in the largest number of modern ships (Yang,2009; Qiu, 2013; Xiong, 2001). The integrated navigation systems fuse the observations sampled by multiple navigation devices, such as, Global Position System (GPS), Inertial Navigation System (INS) and Celestial Navigation System (CNS), to obtain the more accurate and reliable navigational state information of the target ship, compared with the navigation system with single device (Wu, 2009; Li, 2014; Liu, 2011; Guo, 2015).
With the development of communication technology and computer science, the Automatic Identification System (AIS) has been growing popularity in ports and ships. The stars, ship-based radars, shore-based radars, AIS stations and maritime aircrafts make up a self-organizing wireless monitoring network to obtained various navigation information for ships. The ship equipped AIS broadcasts its ship identification, speed, course, location, and such other navigation state information to the shore-based AIS stations and other ships equipped AIS. It makes that the ship equipped AIS can obtain not only the observations sampled by its own navigation devices, but also the navigation state information about other ships in certain sea area, which may serve as the relative observation of the target ship. The adjacent ships in certain sea area around the target ship, in some sense, can be taken as the “relative navigation devices”, which are the new navigation information source for the navigation systems. From the point of view of information processing, integrated utilizing the navigation information sampled by the inherent navigation devices in the target ship and the relative navigation information broadcasted by “relative navigation devices” is expected to obtain a more accurate and reliable navigational state information. It is called relative integrated navigation (Li, 2011). The work of (Ge, 2008) presented a ship relative integrated navigation algorithm to deal with the synchronous navigation observations obtained by the inherent navigation devices and relative navigation devices. The single difference of GPS pseudo-range was taken in account for the relative navigation problem (Wang, 2012). For the observation asynchronously sampled by multiple navigation devices or broadcasted by “relative navigation devices”, a novel asynchronous integrated navigation method was also proposed (Ge, 2008). The delay phenomenon of transmitting the (relative) navigation information are considered (Liu, 2014), and a relative integrated navigation approach for the kinds of the scenario with delay navigation information was developed from the out-of-sequence-measurement fusion method. It is noted that most of the traditional integrated navigation methods (Yang, 2009; Qiu, 2013; Xiong, 2001; Wu, 2009; Li, 2014; Liu, 2011; Guo, 2015) and above relative integrated navigation methods (Ge, 2008; Wang, 2012; Liu, 2014) were all given on the basis of the assumption that the system noises and observation noises satisfy the Gaussian distribution with known statistic characteristics. However, the statistic characteristics of system noises and observation noises are usually difficult to accurately acquire in practical, because that the ships sailing on the sea are often disturbed by the wind, storm, surge, current and other sea condition or meteorological factors, which lead to complex yaw phenomenon and dynamic positioning location change.
Aiming at this problem, the property that the energies of the system noise and the observation noise are limited in finite horizon are utilized to describe the system. On this basis, two traditional integrated navigation methods are given (Liu, 2010; Zhao, 2002) to fuse the observations sampled by INS and GPS. These two methods, nevertheless, are both difficult to develop for the integrated navigation with observations sampled multiple general navigation devices, especially for the integrated navigation scenarios with relative navigation information. Therefore, it is the motivation of our research to design a novel relative integrated navigation method for general multiple navigation information sampled by the inherent navigation devices in the target ship and the relative navigation information broadcasted by “relative navigation devices”.