Method for approximately outputting quaternion numbers with arbitrary step size in orthogonal series during extreme flight of aircraft

Abstract

The invention discloses a method for approximately outputting quaternion numbers with arbitrary step size in orthogonal series during the extreme flight of an aircraft, and aims to solve the technical problem that the accuracy of the quaternion numbers outputted by inertia equipment during the extreme flight of the conventional aircraft is poor. The technical scheme is that a plurality of parameters are introduced in, and approximation in an improved recurrence form similar to the Chebyshev orthogonal polynomial is performed to the rolling angular speed p, the pitch angular speed q and the yaw angular speed r, so that the transfer matrix of the state of the quaternion numbers can be obtained directly, and the accuracy of the iterative computation for confirming the quaternion numbers can be guaranteed. The invention can be used for confirming the order of the orthogonal polynomial with arbitrary step size of the rolling angular speed p, the pitch angular speed q and the yaw angular speed r as per the requirement of the engineering accuracy, realizes the ultra-linear approximation of the state equation transfer matrix phi e [(k+1)T, kT] of the quaternion numbers, and guarantees the accuracy of the iterative computation for confirming the quaternion numbers, thereby improving the outputting accuracy of the inertia equipment during the extreme flight of the aircraft.

Description

technical field [0001] The invention relates to an attitude output method of airborne inertial equipment of an aircraft, in particular to an approximate output method of quaternion arbitrary step-length orthogonal series during extreme flight of the 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 ca...

AI Technical Summary

Problems solved by technology

[0004] In order to overcome the problem of large error in the existing quaternion output, the present invention provides an approximate output method of quaternion arbitrary step-length orthogonal series when the aircraft is in extreme flight. , The yaw angular velocity p, q, r is expanded and approximated by an improved recursive form similar to the Chebyshev orthogonal polynomial, and the quaternion state transition matrix is ​​directly obtained, which can ensure the iterative calculation accuracy of the quaternion, thereby improving the aircraft Inertial device output quaternion accuracy during extreme flight

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