Real-time Estimation of Dynamic Lever Arm Effect of Transfer Alignment for Wing’s Elastic Deformation
Chenghao Geng, Falin Wu, Shan Xu, Xueyan Zhang, Fan Si, Yan Zhao, Beihang University, P.R. China
Location: Big Sur
When the carrier dose angular motion, the master strapdown inertial navigation system (M-SINS) installed on carrier and the wing-mounted slave strapdown inertial navigation system (S-SINS) will measure different motion information because of the difference of installation position between M-SINS and S-SINS. The difference of motion information between M-SINS and S-SINS will lead to lever arm effect error, which seriously affects the accuracy of transfer alignment of wing-mounted S-SINS. The precise acquisition of the length of lever arm is prerequisite for compensating the error. In traditional compensation method, the length of lever arm is regarded as a fixed value. However, in practical application, elastic deformation will occur on the wing of carrier under the influence of the load on the wing and turbulence. This phenomenon will lead to the length of lever arm becoming a variable. Under this condition, if the length of lever arm is still regarded as a fixed value, great errors will be produced on the measurements of the filter, which will cause severely negative impact on the accuracy of transfer alignment. To compensate the lever arm effect error during the process of transfer alignment of wing-mounted S-SINS, a real-time estimation method of dynamic lever arm is proposed in this paper. The proposed method estimates the length of the dynamic lever arm in real time by adding the length into state variables of transfer alignment. Firstly, in order to establish the error equations of S-SINS system with lever arm effect error, both the relations between the length of the dynamic lever arm and dynamic flexural deformation angle, and between the output of M-SINS and S-SINS are derived. The expressions of lever-arm velocity error and lever-arm acceleration error are derived from the relations aforementioned, and both of them are added into the error equations of S-SINS system as parameters to establish the complete error equations of S-SINS system with lever arm effect error. Then, the filter model of S-SINS system is designed, which contains state equation and measurement equation of the system. On the one hand, the state matrix, which is the core of state equation, is derived according to the error equations of S-SINS. The length of lever arm is added into state equation as state variable. On the other hand, the measurement equation is inferred from the relation between the output of M-SINS and S-SINS with velocity plus angular velocity matching method. Finally, the process of transfer alignment is implemented using unscented Kalman Filter (UKF) because of the nonlinearity of the system. And the length of dynamic lever arm is estimated by UKF as one of state variables. The estimated length of dynamic lever arm can be introduced to the expressions of lever-arm velocity error and lever-arm acceleration error to calculate the error caused by lever arm effect. To validate the proposed method, a simulation experiment is conducted in MATLAB. The simulation experiment uses second-order Markov process to simulate the elastic deformation of wing. The simulation results indicate that the proposed method is able to estimate the change of the dynamic lever arm caused by the elastic deformation of wing in real-time, and achieves the high accuracy estimation of misalignment angle after compensating the lever arm effect error.