Initialization of ballistic targets tracking filters with detection probability lower than unity

Radar tracking of a projectile flying in the Earth´s atmosphere is a very complex issue to cope with, due to the need of (suboptimal) nonlinear filtering techniques. Almost all cases found in literature assume that the target trajectory is observable from the firing point to the impact point on the ground, namely the trajectory observation gets under way from the first available measurement. The radar track initiation time is actually a stochastic quantity that has to be treated by means of a statistical procedure. In this paper a preliminary analysis of the effect of a more realistic filter initialization is proposed.