Bearings-Only Tracking Analysis via Information Geometry Xuezhi Wang*, Yongqiang Cheng†, and Bill Moran* †School of Electronic Science and Engineering, National University of Defense Technology, Changsha, Hunan, 410073, P.R.China Email: nudtyqcheng@gmail.com * Melbourne Systems Laboratory, Faculty of Engineering, University of Melbourne, Australia Email: xwang@unimelb.edu.au , b.moran@unimelb.edu.au Abstract – In this paper, the problem of bearings-only tracking with a single sensor is studied via the theory of information geometry, where Fisher information ma- trix plays the role of Riemannian metric. Under a given tracking scenario, the Fisher information distance be- tween two targets is approximately calculated over the window of surveillance region and is compared to the corresponding Kullback Leibler divergence. It is demon- strated that both “distances” provide a contour map that describes the information difference between the loca- tion of a target and a specified point. Furthermore, an analytical result for the optimal heading of a given con- stant speed sensor is derived based on the the properties of statistical manifolds. Keywords: Bearings-Only Tracking, Fisher Informa- tion Distance, Information Geometry, Optimal Sensor Heading. 1 Introduction The complexity of bearings-only tracking (BOT) with a single sensor combines the potential unobserv- ability of the underlying target state with strong non- linearity between measurement and and target state [1]. It is well understood in the literature that a necessary condition for the position and velocity of a constant ve- locity target to be fully observable is the availability of measurements acquired before and after an ownship manoeuvre [2]. Interestingly, necessary and sufficient conditions derived in [3] show that there is a class of sen- sor maneuvers for which full observability of the target state is not achieved. The potential lack of observabil- ity, and the nonlinearity in the measurement equation have constantly challenged the development of appro- priate filtering techniques [4] to solve the BOT problem optimally [5]. Information geometry pioneered by Cramer and Rao from 40s [6] and brought to maturity in the works of Amari [7], offers comprehensive results about statistical models simply by considering them as geometrical ob- jects and the statistical structures as geometrical struc- tures. As a powerful mathematical tool, it can also provide additional perspectives in the analysis of mea- surement of systems. The main tenet of information geometry is that many important structures in proba- bility theory, information theory and statistics can be treated as structures in differential geometry by regard- ing a space of probabilities as a differentiable mani- fold endowed with a Riemannian metric and a family of affine connections distinct from the canonical Levi- Cevita connection [8]. The manifold is proved to have a unique Riemannian metric given by the Fisher infor- mation matrix (FIM), and a dual pairs of affine con- nections [7]. For a given target tracking system for which the Fisher information matrix can be calculated, the Fisher information distance (FID) on the statistical manifold between two target states is well defined and can be used as a measure for target resolvability over the region of interest. Such an advantage was demonstrated in [9] and motivated this work. Alternatively, the Kullback Leibler divergence provides a simple way to approxi- mate the information distance without the knowledge of the statistical manifold. In this paper, the problem of bearings-only tracking with a single sensor is studied via information geome- try, where the Fisher information matrix plays the role of a Riemannian metric. Under a given tracking sce- nario, the FID between two targets is approximately calculated over the window of surveillance region and is compared to the corresponding Kullback Leibler diver- gence. It is demonstrated that both “distances” provide a contour map that describes the information difference