A loosely coupled Inertial Navigation System (INS) and Global Positioning System (GPS) are studied, particularly considering the constant lever arm effect. A five-element vector, comprising a craft's horizontal velocities in the navigation frame and its position in the earth-centred and earth-fixed frame, is observed by GPS, and in the presence of lever arm effect, the nonlinear observation equation from the state vector to the observation vector is established and addressed by the correction stage of an unscented Kalman filter (UKF). The conditionally linear substructure in the nonlinear observation equation is exploited, and a computationally efficient refinement of the UKF called marginalized UKF (MUKF) is investigated to incorporate this substructure where fewer sigma points are needed, and the computational expense is cut down while the high accuracy and good applicability of the UKF are retained. A performance comparison between UKF and MUKF demonstrates that the MUKF can achieve, if not better, at least a comparable performance to the UKF, but at a lower computational expense.

This paper proposes an algorithm for the initial alignment method for rocket navigation systems. It uses the inertial freezing alignment to resolve the attitude matrix with respect to its fast and robust characteristics. Due to disturbances from the swaying base environment, such as people walking and wind effect, which would consequently result in a great lever arm effect, a Finite Impulse Response (FIR) filter is utilized to decrease the noise in the accelerometers' measurement. In addition, there are sensor errors in the system; the online estimation of gyroscopes' drift with a Kalman filter is adopted to achieve compensation. Numerical results from a simulated rocket initial alignment experiment are reported to demonstrate the effectiveness of the method.