A high-accuracy SINS attitude update algorithm based on Legendre polynomial

The large-acceleration motion of HFV (hypersonic flight vehicle), the high-speed rolling of spinning missile, and the large-maneuver flight of fighter aircraft has put forward higher performance demand for SINS (strapdown inertial navigation system). The high-accuracy positing will be realized under the high-dynamic maneuver environment after decreasing measurement error of IMU (inertial measurement unit), meanwhile the algorithm of SINS must be improved. The conventional algorithm calculates the flight attitude with determining the compensation term of coning error, after ignoring the high-order term of the Bortz equation. To improve the algorithm accuracy of SINS under high-dynamic maneuver environment, a high-accuracy algorithm, which uses Legendre polynomial to complete angular velocity function approximation and takes the numerical method of quaternion differential equation as core, is proposed herein. The high-order coning error is compensated in the numerical solving period in the proposed novel algorithm, because no approximation exists in deducing process. The attitude calculating simulations are finished in coning motion condition and high-dynamic maneuver condition respectively. Compared with the quadruple-cross-product compensation algorithm which has the highest accuracy at present, the attitude error of proposed algorithm is less than its 1/ 3 in coning motion condition. And algorithm accuracy is raised an order of magnitude under the high-dynamic maneuver environment. The high-accuracy algorithm based on Legendre polynomial has reference significance for accurate positing of future HFV, atomic gyroscope INS research and high-accuracy algorithm design of SINS. ©2022 Journal of Northwestern Polytechnical University.