Angle speed-based Chebyshev approximate output method of quaternion numbers in ultimate flight of aircraft

Abstract

The invention discloses an angle speed-based Chebyshev approximate output method of quaternion numbers in an ultimate flight of an aircraft for solving the technical problem of poor accuracy of an inertial device for outputting the quaternion numbers when the traditional aircraft is in the ultimate flight. The technical scheme is that rolling, pitching and yaw angle speeds p, q and r are subjected to approximation description by the Shifted Chebyshev orthogonal polynomial to directly obtain a quaternion state-transition matrix so that iterative calculation precision of the quaternion numbers is determined. The order of the Shifted Chebyshev orthogonal polynomial of the rolling, pitching and yaw angle speeds p, q and r is determined according to an requirement of the engineering accuracy, super-linear approximation of a quaternion state matrix transfer equation phi e[(k+1)T, kT] can be realized, and the iterative calculation precision of the quaternion numbers is guaranteed so that the output accuracy of the inertial device when the aircraft is in the ultimate flight is improved.

Description

technical field [0001] The invention relates to an attitude output method of an airborne inertial device of an aircraft, in particular to a quaternion Chebyshev approximate output method based on angular velocity during extreme flight of an aircraft. Background technique [0002] Usually, the acceleration, angular velocity, and attitude of rigid body motion depend on the output of inertial equipment, so improving the output accuracy of inertial equipment has clear practical significance. Space motions such as aircraft, torpedoes, and spacecraft use differential equations of rigid body motion in most cases; and the differential equations describing the attitude of rigid bodies are the core of them, usually with three Euler angles, namely pitch, roll and yaw angles To describe, usually the pitch, roll and yaw angular velocities in the airborne inertial equipment are calculated and output. When the pitch angle of the rigid body is ±90°, the roll angle and yaw angle cannot be f...

AI Technical Summary

Problems solved by technology

[0004] In order to overcome the problem that the existing quaternion output error is large, the present invention provides a quaternion Chebyshev approximate output method based on the angular velocity of the aircraft limit flight, the method uses the shifted Chebyshev (Shifted Chebyshev) orthogonal polynomial pair The roll, pitch, and yaw angular velocities p, q, and r are approximated and described, and the quaternion state transition matrix is ​​directly obtained, which can ensure the iterative calculation accuracy of the quaternion, thereby improving the output of the quaternion of the inertial equipment during the extreme flight of the aircraft. Number precision

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