Quaternion-Based Rapid Transfer Alignment With Linear State Equation Under Arbitrary Misalignments for Airdrop

Abstract

In the in-flight transfer alignment of a Precision Airdrop System (PADS) equipped with inertial navigation systems (INS), achieving rapid high-precision alignment under unknown installation angles and limited carrier maneuvering remains challenging. This study proposes a unified nonsingular rapid transfer alignment scheme for arbitrary misalignments. An inertial frame is defined, and the attitude matrix of the secondary INS (S-INS) is decomposed into a chained product of the main INS (M-INS) attitude matrix, installation matrix and body attitude variation matrices. A matching scheme is constructed using inertial-frame integrals of specific force and angular velocity. By taking the installation attitude quaternion as the state, a model comprising a linear state equation and second-order nonlinear measurement equation is established. Time updates follow standard Kalman filter procedures, whereas measurement updates adopt the second-order Extended Kalman Filter (SEKF) framework with only two extra correction terms. Furthermore, a simplified linear Kalman filter (LKF) scheme is developed by discarding error terms for short-duration transfer alignment. Accordingly, the time update process is eliminated, and the algorithm essentially becomes a weighted recursive least-squares method. Simulation and flight-test results show that the proposed SEKF converges within 10 seconds, yielding horizontal alignment RMSE below 0.035° and heading alignment RMSE below 0.045°. It outperforms conventional methods in both convergence speed and estimation accuracy, which fully satisfies practical alignment requirements for PADS.