Performance Analysis of Decentralized Kalman Filters under Communication Constraints

In target tracking, multi-sensor systems are becoming more and more popular [14]. The advantages especially for physically distributed sensors are obvious: multiple viewing angles, different strong points of different sensors, and a higher robustness due to the inherent redundancy. On the other hand, some kind of fusion is necessary to integrate the data from the different sensors and to extract the desired information about the targets. Traditionally, centralized fusion architectures have been used as their application is straightforward. All the data from the different sensors is sent to a single location to be fused. In recent years, increasing emphasis has been placed on distributed fusion where several fusion nodes exist in the network, like e.g., the Decentralized Kalman Filter (DKF) [11, 27], which is studied here, but also the covariance method [2], the federated filter [6, 7], a fusion system based on channel filters [23], and, most recently, a unified framework for optimal linear estimation fusion [16—21, 29]. As usual, the approaches based on Kalman filters are thereby mainly restricted to the linear Gaussian case. Furthermore, the unified framework is theoretically very insightful. As detailed in [17], the required generalized covariance matrix can, however, only be calculated accurately for some special cases. In many cases, it needs to be approximated numerically or even manually tuned. Finally, even if the covariance matrix can be determined accurately, this need not necessarily be possible in a recursive way so that no recursive estimator can be designed [16]. In a distributed fusion system, the sensor measurements are processed locally to produce state estimates, which are then transmitted between the fusion nodes. This approach is conceptually more complex as, even for statistically independent measurements, the local state estimates are correlated in time and among each other. In contrast to centralized fusion, there is also the danger of reusing information. Common information has to be detected and discarded in the fusion process. Additionally, the task of data association in tracking multiple targets, which is already difficult and still an active area of research for centralized architectures [4], becomes even more complex in the distributed case where only parts of the data are available at each fusion node. Finally, distributed fusion can even be inherently suboptimal [18]. A sufficient condition for distributed fusion to be optimal, however, is that the measurement noises are uncorrelated, which is often at least approximately given in real world scenarios. On the other hand, the advantages of such distributed fusion architectures are a higher robustness due to a redundancy of fusion nodes and a lower processing load at each fusion node. It is also easier to integrate or scale existing systems. Therefore, distributed fusion is espe-