Quaternion superlinear output method based on angular velocities for aircraft during extreme flight

Abstract

The invention discloses a quaternion superlinear output method based on angular velocities for an aircraft during extreme flight, which is used for solving the technical problem of poor precision of quaternion outputted by existing inertial equipment when an aircraft is in extreme flight. The technical scheme includes that expansion of a state transition matrix of a linear time varying system is analyzed to redefine relevant parameters, accordingly, three antecedent terms of an approximate expression are completely identical to three antecedent terms of the expansion of the state transition matrix of the linear time varying system, a certain approximation degree is realized for consequent higher order terms, superlinear approximation of a quaternion state equation transition matrix phie[(k+1)T, kT] is realized by means of defining new parameters and an absolute lambda, a quaternion state transition matrix second-order approximant is directly obtained, calculation precision of specified quaternion is ensured, and output precision of inertial equipment is improved when the aircraft is in extreme flight.

Description

technical field [0001] The invention relates to an attitude output method of an aircraft airborne inertial device, in particular to a quaternion superlinear 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 be fixed. At th...

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 a method for superlinear output of quaternion based on angular velocity when the aircraft is in extreme flight. The method redefines The relevant parameters make the first three terms of the approximate expression exactly the same as the first three terms of the expansion of the state transition matrix of the linear time-varying system, and have a certain degree of approximation to the following high-order terms, so as to ensure the calculation accuracy of the quaternion, thereby improving Inertial equipment output quaternion accuracy during extreme flight of aircraft

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