Interacting multiple model unscented filter for tracking a ballistic missile during its boost phase

Boost-phase detection of a ballistic missile is an attractive option for defense systems because boosting rockets are easy to detect and, in this phase, countermeasures are less effective. Nevertheless, it raises technical criticalities due to the short burn-out times and to the unknown features and behavior of the missile. The boosting trajectory of a ballistic missile, in fact, can be divided in at least three phases, each one characterized by a different steering strategy: the vertical arc, the pitch maneuver, and the gravity turn. Furthermore, the overall trajectory is very sensitive to variations in the parameters of the model and in the kick angle chosen during the pitch maneuver. Therefore, the tracking of a boosting missile presents two major difficulties: the identification of the missile parameters (ballistic coefficient, mass rate, thrust over weight ratio, etc.), and the determination of the steering strategy. The multiple models filter approach has been adopted in this paper to cope with these issues. In particular, an improved version of the Interacting Multiple Model Unscented Filter (IM-MUF) for tracking a missile has been introduced. Essentially, a modified form of the filter Markov Transition Matrix (MTM), ad hoc designed for the problem of tracking a ballistic missile during its boost phase, is proposed. The probabilities of the state transitioning from one dynamic model to another are given by the MTM elements. In the traditional approach, these probabilities are supposed constant and known. In this work these conservative hypotheses have been relaxed and these probabilities have been considered to be functions of the estimated state vector, thanks to specific features of the missile trajectory. A numerical, three-dimensional Monte Carlo simulation has been implemented in order to reconstruct a state vector composed by the position, velocity and missile parameters vectors. The modified IMMUF runs several models, each one accounting for one of the phases of flight with a different value of thrust direction, and combines estimations in order to provide the final estimation. Noisy measurements are obtained from a radar. The results show that the proposed IMMUF with the variable MTM outperform the traditional form of the IMMUF, by giving more accurate estimation.