CN102519462B - Angular velocity based Euler angle exponent output method - Google Patents

Abstract

The invention discloses an angular velocity based Euler angle exponent output method, which is used for solving the technical problems that the Euler angle output precision is poor when the traditional aircraft maneuvers. The technical scheme is as follows: a pitch angle, a roll angle and a yaw angle is sequentially solved. The integral solution exponential type ultra-linear approximation of an Euler angle state equation is realized by defining a new parameter | Lambda |, and the determination of time updating iterative calculation accuracy of the Euler angle is ensured, and thus the accuracy of the output of a flight attitude of inertial equipment is improved.

Description

Eulerian angle index output intent based on angular velocity

Technical field

The present invention relates to a kind of aircraft maneuvering flight and determine method, particularly relate to a kind of Eulerian angle index output intent based on angular velocity.

Background technology

Inertial equipment has vital role in the movable body navigation with in controlling; The acceleration of rigid motion, angular velocity and attitude etc. all depend on inertial equipment output usually, and the output accuracy that therefore improves inertial equipment has clear and definite practical significance; In inertial equipment, acceleration adopts accelerometer, angular velocity to adopt the direct metering system of angular rate gyroscope, the attitude accuracy of rigid body requires when very high to adopt attitude gyro to measure as the flight test waits, but in a lot of applications, has the measurement such as angular velocity directly to resolve output; Main cause is because dynamically attitude sensor is expensive, volume is large, cause a lot of aircraft to adopt angular rate gyroscopes etc. to resolve three Eulerian angle, make the attitude time upgrade output and become the core contents such as navigation, also make it become one of principal element that affects the inertial navigation system precision, therefore design and adopt the rational attitude time to upgrade the hot subject that output intent just becomes research; From the document of publishing, attitude output is mainly adopted the direct method of approximation of Eulerian equation based on angular velocity or adopts approximate Runge Kutta method to resolve (Sun Li, Qin Yongyuan, attitude algorithms of SINS relatively, China's inertial technology journal, 2006, Vol.14 (3): 6-10; Pu Li, Wang TianMiao, Liang JianHong, Wang Song, An Attitude Estimate Approach using MEMS Sensors for Small UAVs, 2006, IEEE International Conference on Industrial Informatics, 1113-1117); Because three Eulerian angle in Eulerian equation are coupled mutually, belong to nonlinear differential equation, different with the error range under different flight state in different starting condition, be difficult to guarantee the Practical Project permissible accuracy.

Summary of the invention

The poor problem of Eulerian angle output accuracy, the invention provides a kind of Eulerian angle index output intent based on angular velocity when overcoming existing aircraft maneuvering flight.The method is according to solving successively the angle of pitch, roll angle, crab angle, and introduce four parameters, directly the expression formula of Eulerian angle is carried out to high-order approaches integration, make solving according to ultralinear of Eulerian angle approach, thereby can guarantee to determine the time renewal iterative computation precision of Eulerian angle and the output accuracy of inertance element.

The technical solution adopted for the present invention to solve the technical problems is: a kind of Eulerian angle index output intent based on angular velocity is characterized in comprising the following steps:

1, (a) is according to Eulerian equation:

In formula:

refer to respectively rolling, pitching, crab angle; P, q, r is respectively rolling, pitching, yaw rate; Parameter-definition is identical in full; The calculating of these three Eulerian angle is carried out according to the step that solves successively the angle of pitch, roll angle, crab angle;

(b) time of the angle of pitch upgrades and to solve formula and be:

In formula: $\left|\mathrm{\λ}\right|=\sqrt{{\∫}_{\mathrm{kT}}^{t}p{\∫}_{\mathrm{kT}}^t\mathrm{pd\τdt}+{\∫}_{\mathrm{kT}}^{t}q{\∫}_{\mathrm{kT}}^t\mathrm{pd\τdt}+{\∫}_{\mathrm{kT}}^{t}r{\∫}_{\mathrm{kT}}^t\mathrm{rd\τdt}},$ T is the sampling period, lower same;

2,, in the situation that the known angle of pitch, the time of roll angle upgrades and solves formula and be:

3, under the angle of pitch, roll angle known case, being solved to of crab angle:

$\mathrm{\ψ}\left(t\right)=\mathrm{\ψ}\left(\mathrm{kT}\right)+{\∫}_{\mathrm{kT}}^t[a_1\left(t\right)+a_2\left(t\right)]\mathrm{dt}$

In formula:

The invention has the beneficial effects as follows: owing to solving successively the angle of pitch, roll angle, crab angle, and introduce four parameters, directly the expression formula of Eulerian angle is carried out to high-order approaches integration, make solving according to ultralinear of Eulerian angle approach, thereby guaranteed the time renewal iterative computation precision of definite Eulerian angle and the output accuracy of inertance element.

Below in conjunction with embodiment, the present invention is elaborated.

Embodiment

1, (a) is according to rigid body attitude equation (Eulerian equation):

In formula:

refer to respectively rolling, pitching, crab angle; P, q, r is respectively rolling, pitching, yaw rate; Parameter-definition is identical in full; The calculating of these three Eulerian angle is carried out according to the step that solves successively the angle of pitch, roll angle, crab angle;

(b) time of the angle of pitch upgrades and to solve formula and be:

In formula: $\left|\mathrm{\λ}\right|=\sqrt{{\∫}_{\mathrm{kT}}^{t}p{\∫}_{\mathrm{kT}}^t\mathrm{pd\τdt}+{\∫}_{\mathrm{kT}}^{t}q{\∫}_{\mathrm{kT}}^t\mathrm{pd\τdt}+{\∫}_{\mathrm{kT}}^{t}r{\∫}_{\mathrm{kT}}^t\mathrm{rd\τdt}},$ T is the sampling period, lower same;

2,, in the situation that the known angle of pitch, the time of roll angle upgrades and solves formula and be:

3, under the angle of pitch, roll angle known case, being solved to of crab angle:

$\mathrm{\ψ}\left(t\right)=\mathrm{\ψ}\left(\mathrm{kT}\right)+{\∫}_{\mathrm{kT}}^t[a_1\left(t\right)+a_2\left(t\right)]\mathrm{dt}$

In formula:

When inertial equipment is directly exported to rolling, pitching, yaw rate p, q, r adopts three rank to approach while describing, and acquired results also approaches O (T ³), compare the direct method of approximation of Eulerian equation or adopt approximate Runge Kutta method the O (T of method such as to resolve ²) precision will height.

Claims (1)

1. the Eulerian angle index output intent based on angular velocity is characterized in that comprising the following steps:

Step 1, (a) are according to Eulerian equation:

In formula: refer to respectively rolling, pitching, crab angle; P, q, r is respectively rolling, pitching, yaw rate; The calculating of these three Eulerian angle is carried out according to the step that solves successively the angle of pitch, roll angle, crab angle;

(b) time of the angle of pitch upgrades and to solve formula and be:

In formula: $\left|\mathrm{\λ}\right|=\sqrt{{\∫}_{\mathrm{kT}}^{t}p{\∫}_{\mathrm{kT}}^t\mathrm{pd\τdt}+{\∫}_{\mathrm{kT}}^{t}q{\∫}_{\mathrm{kT}}^t\mathrm{qd\ιdt}+{\∫}_{\mathrm{kT}}^{t}r{\∫}_{\mathrm{kT}}^t\mathrm{rd\ιdt},}$ T is the sampling period;

Step 2, in the situation that the known angle of pitch, the time of roll angle upgrades and solves formula and be:

Step 3, under the angle of pitch, roll angle known case, being solved to of crab angle:

$\mathrm{\ψ}\left(t\right)=\mathrm{\ψ}\left(\mathrm{kT}\right)+{\∫}_{\mathrm{kT}}^t[a_1\left(t\right)+a_2\left(t\right)]\mathrm{dt}$

In formula: