Quaternion Laguerre approximate output method based on angular speed used during extreme flight of flying vehicle

Abstract

The invention discloses a quaternion Laguerre approximate output method based on an angular speed used during extreme flight of a flying vehicle, which is used for solving the technical problem of poor quaternion output accuracy of inertia equipment during extreme flight of the conventional flying vehicle. In a technical scheme, approximate approach description is performed on a rolling angular speed, a pitching angular speed and a yawing angular speed p, q and r by adopting a Shifted Lagnuerre orthogonal polynomial to directly obtain a quaternion state transfer matrix, so that the iterative computation accuracy of a determined quaternion is ensured. Shifted Lagnuerre orthogonal polynomial orders for the rolling angular speed, the pitching angular speed and the yawing angular speed p, q and r can be determined according to engineering accuracy, so that ultra-linear approximation for a quaternion state equation transfer matrix phie[(k+1)T, kT] is realized, the iterative computation accuracy of the determined quaternion is ensured, and the output accuracy of the inertia equipment during extreme flight of the flying vehicle is increased.

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 Laguerre approximate output method based on an angular velocity when the aircraft is in extreme flight. 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 ...

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 Laguerre approximate output method based on the angular velocity of the aircraft's limit flight, the method adopts the shifted Laguerre (Shifted Laguerre) orthogonal polynomial pair The roll, pitch, and yaw angular velocities p, q, and r are approximated and described, and the state transition matrix of the quaternion is obtained directly, so that the iterative calculation accuracy of the quaternion can be guaranteed

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