Tracking and fusion in log-spherical state space with application to collision avoidance and kinematic ranging
This chapter is devoted to a special state representation for target tracking. The considered coordinates possess, in comparison with classical Cartesian ones, distinct advantages in particular in applications where angles are the only measurements available like, e.g. for jammed radar. In those applications, measurements are not Cartesian-complete and the range of a moving object under track is not observable unless the sensor platform performs manoeuvres. This chapter presents basic relations and properties of log-spherical coordinates. In particular, it is shown how those coordinates decouple the remaining coordinates from the unobservable range in angular-only tracking. The chapter discusses recursive filter algorithms and corresponding performance bounds. As an application example, it uses data fusion in a collision avoidance system based on a suite of sensors. The final topic is the so-called kinematic ranging, i.e. the extraction of range information from angular-only measurements by suitably chosen manoeuvres of the sensor platform. Presentation in this chapter covers both mathematical derivations as well as numerical simulation results.
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