Understanding and applying rapid transfer alignment equation

Aim. Ref.2 on rapid transfer alignment equation by Kain et al gives without proof an important and very useful relationship. We give the proof in order to gain insight into this relationship so as to apply it with full understanding. In the full paper, we explain our understanding and application of the understood relationship in some detail; in this abstract, we just add some pertinent remarks to listing the two topics of explanation. The first topic is: the proof of the relationship among platform misalignment vector, measurement misalignment vector and physical misalignment vector. Its three subtopics are: the relationship among the three misalignment vectors (subtopic 1.1), velocity error differential equation (subtopic 1.2) and attitude error differential equation (subtopic 1.3). In subtopic 1.1, we first define the three vectors and then derive the eq.(13) in the full paper as the relationship among them. In subtopic 1.2, we use the eq.(13) to demonstrate the consistency between the traditional transfer alignment (TTA) equation and the rapid transfer alignment (RTA) equation. In subtopic 1.3, we prove that there also exists the consistency between the TTA equation and the RTA equation and that the RTA equation is essentially a special form of the TTA equation. The second topic is: simulation results and their analysis. In this topic, we simulate for 10 seconds the velocity-matching and attitude-matching transfer alignment of the slave SINS (strapdown inertial navigation system) using the TTA equation and RTA equation respectively. The analysis of the simulation results, presented in Table 1 in the full paper, shows preliminarily that the misalignments obtained with the TTA equation and the RTA equation respectively are both less than 1 arc second.