Filtering boundary value discrete time linear systems

The Aegis Combat System [1] is used to protect US Navy vessels from planes and missiles. The computer-based command-and-decision element is the core of the Aegis Combat System. This interface makes the ACS capable of simultaneous operation against almost all kinds of threats. The Aegis Ballistic Missile Defense System program is intended to enable the Aegis system to act in a sea-based ballistic missile defense function, to counter short- and medium-range ballistic missiles of the variety typically employed by a number of potential opponent states. It works by firing a large amount of projectiles at the incoming missiles. Critical to the success of this system are real time accurate estimates of the trajectories of the incoming missiles. This requires filtering of the noisy measurements but what distinguishes it from standard filtering is that we know where the missiles are heading. (If they are not heading toward the ship or the target that the ship is protecting then we don´t care about them.) In effect we are interested in filtering a system that has boundary constraints. Hence we consider the problem of filtering a linear system that satisfies boundary conditions rather than initial conditions.