Distributed Fusion Prediction for Mixed Continuous-Discrete Linear Systems

The integration of information from a combination of different types of observed instruments (sensors) are often used in the design of high-accuracy control systems. Typical applications that benefit from this use of multiple sensors include industrial tasks, military commands, mobile robot navigation, multi-target tracking, and aircraft navigation (see (hall, 1992, Bar-Shalom, 1990, Bar-Shalom & Li, 1995, Zhu, 2002, Ren & Key, 1989) and references therein). One problem that arises from the use of multiple sensors is that if all local sensors observe the same target, the question then becomes how to effectively combine the corresponding local estimates. Several distributed fusion architectures have been discussed in (Alouani, 2005, Bar-Shalom & Campo, 1986, Bar-Shalom, 2006, Li et al., 2003, Berg & Durrant-Whyte, 1994, Hamshemipour et al., 1998) and algorithms for distributed estimation fusion have been developed in (Bar-Shalom & Campo, 1986, Chang et al., 1997, Chang et al, 2002, Deng et al., 2005, Sun, 2004, Zhou et al., 2006, Zhu et al., 1999, Zhu et al., 2001, Roecker & McGillem, 1998, Shin et al, 2006). To this end, the Bar-Shalom and Campo fusion formula (Bar-Shalom & Campo, 1986) for two-sensor systems has been generalized for an arbitrary number of sensors in (Deng et al., 2005, Sun, 2004, Shin et al., 2007) The formula represents an optimal mean-square linear combination of the local estimates with matrix weights. The analogous formula for weighting an arbitrary number of local estimates using scalar weights has been proposed in (Shin et al., 2007, Sun & Deng, 2005, Lee & Shin 2007). However, because of lack of prior information, in general, the distributed filtering using the fusion formula is globally suboptimal compared with optimal centralized filtering (Chang et al., 1997). Nevertheless, in this case it has advantages of lower computational requirements, efficient communication costs, parallel implementation, and fault-tolerance (Chang et al., 1997, Chang et al, 2002, Roecker & McGillem, 1998). Therefore, in spite of its limitations, the fusion formula has been widely used and is superior to the centralized filtering in real applications. The aforementioned papers have not focused on prediction problem, but most of them have considered only distributed filtering in multisensory continuous and discrete dynamic models. Direct generalization of the distributed fusion filtering algorithms to the prediction problem is impossible. The distributed prediction requires special algorithms one of which for discrete-time systems was presented in (Song et al. 2009). In this paper, we generalize the results of (Song et al. 2009) on mixed continuous-discrete systems. The continuous-discrete