Constant-speed target tracking via bearings-only measurements

The observability properties of the constant-speed target tracking problem via bearings-only measurements are investigated. It is shown that there exists a one-dimensional unobservable foliation which is computed. Explicit formulas are given to recover the observable part. It is shown that the direction of target trajectory is observable and that the whole state is observable if either the norm of the velocity or the distance is also known. A nonlinear observer which has a parallel structure and tolerates faults on distance measurements is presented. Finite-dimensional filters for the approximating models in the case of noisy measurements are given on the basis of output function polynomial approximations