Information geometry of target tracking sensor networks

In this paper, the connections between information geometry and performance of sensor networks for target tracking are explored to pursue a better understanding of placement, planning and scheduling issues. Firstly, the integrated Fisher information distance (IFID) between the states of two targets is analyzed by solving the geodesic equations and is adopted as a measure of target resolvability by the sensor. The differences between the IFID and the well known Kullback–Leibler divergence (KLD) are highlighted. We also explain how the energy functional, which is the “integrated, differential” KLD, relates to the other distance measures. Secondly, the structures of statistical manifolds are elucidated by computing the canonical Levi–Civita affine connection as well as Riemannian and scalar curvatures. We show the relationship between the Ricci curvature tensor field and the amount of information that can be obtained by the network sensors. Finally, an analytical presentation of statistical manifolds as an immersion in the Euclidean space for distributions of exponential type is given. The significance and potential to address system definition and planning issues using information geometry, such as the sensing capability to distinguish closely spaced targets, calculation of the amount of information collected by sensors and the problem of optimal scheduling of network sensor and resources, etc., are demonstrated. The proposed analysis techniques are presented via three basic sensor network scenarios: a simple range-bearing radar, two bearings-only passive sonars, and three ranges-only detectors, respectively.