On high precision bearings only tracking for manoeuvring targets

For the three-dimensional bearings-only problems of the type considered here, the singularities that can occur - the observer being in the plane of target motion, the track passing through the observer - can be recognised with just five consecutive observation pairs. The key parameter, the angular rate of turn of the target, can be found from five observations in the generic case and four scalar observations in the sub-generic case. In the intermediate singular case, where the track and the observer are coplanar, seven scalar observations are required. If a single initial range is available, all subsequent positions of the target can be computed in the generic and singular cases. Such computation is possible in the sub-generic case only if an initial velocity vector is also available.