Quaternion error free estimation of reentry ballistic targets

A common approach followed in state estimation of reentry ballistic targets is to formulate the problem where the process model is written in the Earth fixed inertial frame, where as the measurement model is written in the body frame of the interceptor. In such a formulation, to relate the states with the measurement vector, a transformation matrix is required to transform the position and velocity vectors from inertial frame to body frame and vice-versa. This matrix is constructed using the attitude quaternion information of the interceptor as obtained from its inertial navigation system. In a practical situation, however, when the time of flight is high, the navigation error build up is usually large, which introduces large errors in the transformation matrix. Due to this, the performance of the estimator is found to be not very good, even though the seeker gives good measurement data. To avoid this problem, a new estimation formulation is proposed in this paper, where the process model is written in the body frame of the interceptor. This formulation needs body rate information of the interceptor instead of the attitude quaternion, which does not degrade much with the time of flight. Hence, this new formulation is quite effective in estimating the target states accurately, thereby improving the mission performance substantially, even in presence of large navigation errors in the attitude quaternion. Extensive simulation results show the effectiveness of the proposed approach.