An Optimal Tightly-coupled Stellar-inertial Integrated Navigation Method based on Star Reprojection
Dongkai Dai, Wenfeng Tan, Jiaxing Zheng, Xingshu Wang, and Shiqiao Qin, National University of Defense Technology, China
Stellar and inertial integrated navigation system can provide high-precision and reliable navigation information autonomously for long-duration sea, aircraft, and spacecraft missions. In the stellar/inertial integration, the accumulated error of inertial navigation system (INS) can be restrained by star trackers, which are capable of providing 3-axis attitude information by using at least 3 stars in the field of view (FOV). Unfortunately, the FOV of star tracker for daytime application should be minimized in order to improve the signal-to-noise ratio (SNR) under strong background light condition, so there are usually not enough bright stars in the FOV for attitude determination. To overcome this limitation, we propose a new tightly-coupled stellar-inertial integration algorithm based on star reprojection.
The star reprojection error is an image geometric error of estimated star positions with respect to the measured ones when given intrinsic parameters and attitude information of the star tracker. In the proposed method, the attitude for reprojection error calculation is provided by the INS, so the navigation errors and inertial sensor errors will induce corresponding reprojection errors, then estimated and compensated by using the observation of reprojection errors. Firstly, the measurement model of a star tracker is introduced, and the accurate mathematic relationship between star spot reprojection errors and the navigation errors of INS is established. Secondly, the navigation error and systemic error of the INS are modeled as dynamic state-space models. Finally, the navigation error and systematic errors are simultaneously estimated by a Kalman filter by using the observations of star reprojection error. In addition, the intrinsic parameter errors and the fix angles of the star tracker can be modeled in the state-space equations simultaneously, and estimated in the Kalman filter, so the proposed method can also be used for dynamic calibration of the star tracker.
The feasibility of the proposed method is investigated by numerical simulations. The simulations use real trajectory data measured by the INS/GNSS integrated system in a real ship-borne experiment to generate inertial sensors and star tracker data. Firstly, the performance of stellar-inertial integration with small FOV is validated. The navigation errors related to the various error sources (for example, star tracker noise, inertial sensor error and fix angle error) are tested. Then, the simulations compare the performances of different integration methods, i.e. the reprojection error based method and the attitude error based method when a wide FOV star tracker is used for integrated navigation. The simulation results show that the proposed method can work well even when there are not enough stars in FOV for attitude determination, and the reprojection error based method can get better performance than that of the attitude error based method. That is induced by the different statistical characteristic of the observation errors in Kalman filter.
The proposed tightly-coupled integrated algorithm, which uses star reprojection error as observation, can obtain the optimal estimation of state-space variables and result in higher navigation accuracy. There is no limitation on star number in FOV for the proposed method, so the ratio of valid star tracker data will be remarkably improved when working in daytime. Moreover, the proposed method can also be adopted to calibrate star trackers under dynamic condition, and it is essential for long-endurance application.