Equivalent approaches to equations of traditional transfer alignment and rapid transfer alignment

This paper deals with the equivalence between the traditional transfer alignment (TTA) equations and the rapid transfer alignment (RTA) equations proposed by Kain and Cloutier. The TTA and RTA equations are presented firstly, and the platform misalignment vector, the physical misalignment vector and the measurement misalignment vector introduced by Kain and Cloutier are explained. The relationships among three misalignment vectors are derived. The RTA equations can also be obtained using the relationships and the TTA equations. Therefore, the two kinds of equations are equivalent and can be put in the same framework, and the RTA equations are the special formulations of the TTA equations in the rapid alignment condition. The measurement misalignment vector makes the RTA equations concise which is both the state vector and the measurement vector in the Kalman filter and turns the computation of attitude matching into the computed body frame. The RTA equations are more suitable for the transfer alignment where the alignment time is critical, while the TTA equations are suitable for where the errors of the missile inertial measurement unit is needed to estimated. The method of velocity and attitude matching transfer alignment is used in the simulation study, and the results verify that the TTA and RTA equations have the good performance and have the same precision of less then 1 arc second in the same simulation environment after 10 seconds.