CN103954351B - The measuring method of the micro-angular oscillation of a kind of space vehicle - Google Patents

Abstract

The measuring system of the micro-angular oscillation of a kind of space vehicle disclosed by the invention and method, acceleration is measured combination and is arranged in space vehicle carrier coordinate system, measure the carrier low frequency directly related with micro-angular oscillation, trace level linearly coupled, measure, in conjunction with acceleration, the relative position relation combined with space vehicle carrier barycenter again and carry out data processing, micro-angular oscillation of computer memory aircraft. The invention solves the difficult problem that the micro-angular oscillation of aircraft under space environment is measured, there is the feature of highly reliable, high precision, small volume and low cost.

Description

Method for measuring micro-angular vibration of spacecraft

Technical Field

The invention relates to a method for measuring micro-angular vibration of a spacecraft, belonging to the technical field of inertia.

Background

When the spacecraft is in orbit, flutter can occur under the action of a movable part or an external mechanical environment, and the flutter is mainly represented by steady-state sinusoidal response, random fluctuation or angular jitter of damped oscillation. The magnitude (typically above 0.1 arcsec) and frequency spectrum (0.1-500 Hz) of the flutter varies depending on the source of the disturbance and the aircraft structure. The micro-angular vibration disturbance of the spacecraft can influence the imaging precision or the aiming precision of a camera or an aiming system, and meanwhile, the accuracy of a space science experiment is also reduced. Therefore, the method can accurately measure the micro magnitude angular vibration of the spacecraft in real time, and has important significance in the application field of aerospace vehicles as the reference data for analyzing and compensating the angular vibration condition.

At present, satellites such as ZY, GF and the like in China use vibration sensors to measure the microgravity acceleration environment of an aircraft, and the micro-level line vibration of the on-orbit aircraft in a certain frequency band is measured, so that a basis is provided for various scientific researches, but the angular vibration of the aircraft cannot be directly measured, and the angular vibration condition of the aircraft is further analyzed and compensated. The laser gyro can meet the requirements of micro-angle vibration measurement indexes on measurement accuracy and measurement bandwidth, but due to the limitations of size, power consumption and environmental adaptability, the laser gyro is not reported to be applied to micro-angle vibration measurement of a space vehicle at home and abroad at present. China develops a micro-angular vibration measurement sensor for a space aircraft based on the magnetohydrodynamics principle, and due to the limitation of technical and process levels, indexes such as precision, reliability, volume, service life and the like of the sensor cannot meet the requirements of practical engineering application in a short time. Therefore, with the continuous expansion of the application of the spatial technology in the military and civil fields in China, an effective method for measuring the micro-angular vibration of the space aircraft needs to be explored urgently to meet the requirement of the aircraft in the space environment on the measurement of the micro-angular vibration.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: aiming at the defects of the prior art, the method for measuring the micro-angular vibration of the spacecraft, which is high in reliability, high in precision, small in size and low in cost, is provided, and the problem that the micro-angular vibration of the spacecraft cannot be accurately measured in China is solved.

The technical solution of the invention is as follows:

a system for measuring micro-angular vibration of a spacecraft comprises an acceleration measuring assembly, a resistance sampling circuit and a blocking amplifying circuit;

the acceleration measurement combination outputs the measured vibration of the aircraft carrier line in a current mode, the resistance sampling circuit converts a current signal into a voltage signal, the DC blocking amplification circuit performs secondary amplification on the voltage signal and filters a DC component in the signal to obtain a voltage signal corresponding to the line vibration, and then the low-frequency line vibration calibration device is used for calibrating the accelerometer measurement combination, so that the voltage signal can be converted into low-frequency and trace-level line vibration.

The acceleration measurement combination is realized by adopting a three-axis high-precision quartz flexible accelerometer, and the accelerometer measurement combination is respectively placed on an X axis, a Y axis and a Z axis of a spacecraft carrier coordinate system.

The resistance sampling circuit comprises an operational amplifier A1, resistors R1, R2 and R3 and a capacitor C1; the positive input end of the operational amplifier A1 is grounded, the reverse input end is connected with one ends of R2 and C1, the other end of R2 is connected with one ends of R1 and R3, the other ends of R3 and C1 are both connected with the output end of the operational amplifier A1, and the other end of R1 is grounded.

The DC blocking amplifying circuit comprises an operational amplifier A2, resistors R4, R5 and R6 and a capacitor C2; one end of the capacitor C2 is connected with the output end of the operational amplifier A1, the other end of the capacitor C2 is connected with the positive input end of the operational amplifier and the resistor R4, the other end of the resistor R4 is grounded, the reverse input end of the operational amplifier A2 is connected with the R5 and the R6, the other end of the resistor R5 is grounded, and the other end of the resistor R6 is connected with the output end of the operational amplifier A2.

A measuring method based on a micro-angular vibration measuring system comprises the following steps:

(1) arranging an acceleration measurement combination in a spacecraft carrier coordinate system, and measuring the low-frequency and microscale line vibration of a carrier;

the line vibration obtained by the acceleration measurement combination measurement can be expressed as:

$a=\mathrm{\ω}\×\mathrm{\ω}\×r+\stackrel{\·}{\mathrm{\ω}}\×r$

wherein omega is the rotating angular speed of the spacecraft carrier,acceleration of the rotation angle of a spacecraft carrierAnd degree, r is the position vector of the mass point relative to the mass center O of the carrier.

(2) And (3) carrying out data processing on the low-frequency and trace-level line vibration obtained by measurement in the step (1) by utilizing the relative position relation between the acceleration measurement combination and the mass center of the spacecraft carrier, and further calculating to obtain the micro-angle vibration of the spacecraft.

The accelerometer measurement combination is respectively arranged on three points B, C and D on an X axis, a Y axis and a Z axis of a spacecraft carrier coordinate system, and the position vector of the accelerometer measurement combination relative to a spacecraft carrier mass center O is R_BO、R_CO、R_DOThe line vibration measured for each measurement combination is as follows:

$a_B=\stackrel{\·}{\mathrm{\ω}}\×R_{\mathrm{BO}}+\mathrm{\ω}\×\mathrm{\ω}\×R_{\mathrm{BO}}$

$a_C=\stackrel{\·}{\mathrm{\ω}}\×R_{\mathrm{CO}}+\mathrm{\ω}\×\mathrm{\ω}\×R_{\mathrm{CO}}$

$a_D=\stackrel{\·}{\mathrm{\ω}}\×R_{\mathrm{DO}}+\mathrm{\ω}\×\mathrm{\ω}\×R_{\mathrm{DO}}$

a_B、a_Cand a_DLinear vibration vectors obtained by measuring and combining the measurement of the accelerometers are respectively a space vehicle carrier coordinate system X, Y and a Z axis, omega is the rotating angular speed of a space vehicle carrier,the angular acceleration of rotation of the spacecraft carrier.

The method for processing the data of the low-frequency and microscale line vibration in the step (2) is as follows: establishing X, Y and Z-axis angular accelerationAnd line vibration a_B、a_C、a_DThe relationship between:

${\stackrel{\·}{\mathrm{\ω}}}_X=\frac{a_C^Z}{{2R}_{\mathrm{CO}}}-\frac{a_D^Y}{{2R}_{\mathrm{DO}}}$

${\stackrel{\·}{\mathrm{\ω}}}_Y=\frac{a_D^X}{{2R}_{\mathrm{DO}}}-\frac{a_B^Z}{{2R}_{\mathrm{BO}}}$

${\stackrel{\·}{\mathrm{\ω}}}_Z=\frac{a_B^Y}{{2R}_{\mathrm{BO}}}-\frac{a_C^X}{{2R}_{\mathrm{CO}}}$

wherein,measuring linear vibration along the Y axis and the Z axis of an aircraft carrier coordinate system measured by an accelerometer arranged at a point B on the X axis of the aircraft carrier coordinate system;measuring linear vibration along the X axis and the Z axis of an aircraft carrier coordinate system measured by an accelerometer arranged at a point C on the Y axis of the aircraft carrier coordinate system;to flyAn accelerometer placed at a point D on the Z axis of the aircraft carrier coordinate system measures linear vibration along the X axis and the Y axis of the aircraft carrier coordinate system measured by the combination;

the four-order Runge-Kutta method is used for integral operation, and the micro-angle vibration of the spacecraft can be obtained:

${\mathrm{\ω}}_X\left(t\right)=\mathrm{\ω}(t-T)+\frac{T}{6}{\stackrel{\·}{\mathrm{\ω}}}_X(t-T)+\frac{2T}{3}{\stackrel{\·}{\mathrm{\ω}}}_X(t-\frac{1}{2}T)+\frac{1}{6}{\stackrel{\·}{\mathrm{\ω}}}_X\left(t\right)$

${\mathrm{\ω}}_Y\left(t\right)=\mathrm{\ω}(t-T)+\frac{T}{6}{\stackrel{\·}{\mathrm{\ω}}}_Y(t-T)+\frac{2T}{3}{\stackrel{\·}{\mathrm{\ω}}}_Y(t-\frac{1}{2}T)+\frac{1}{6}{\stackrel{\·}{\mathrm{\ω}}}_Y\left(t\right)$

${\mathrm{\ω}}_Z\left(t\right)=\mathrm{\ω}(t-T)+\frac{T}{6}{\stackrel{\·}{\mathrm{\ω}}}_Z(t-T)+\frac{2T}{3}{\stackrel{\·}{\mathrm{\ω}}}_Z(t-\frac{1}{2}T)+\frac{1}{6}{\stackrel{\·}{\mathrm{\ω}}}_Z\left(t\right)$

wherein T represents the current sampling time, and T is the sampling period.

Compared with the prior art, the invention has the following advantages:

(1) the invention establishes the corresponding relation between the angular acceleration and the linear vibration in the space microgravity environment, provides a theoretical basis for the measurement of the micro-angular vibration of the spacecraft, and solves the problem that the existing equipment cannot carry out high-precision measurement of the micro-angular vibration of the spacecraft.

(2) The acceleration measurement combination provided by the invention selects the high-precision quartz flexible accelerometer as a sensitive element, and has the characteristics of high precision, small volume and strong environmental adaptability.

(3) The resistance sampling circuit adopts a T-shaped resistance network to reduce the influence of circuit aliasing noise and external environment temperature and humidity changes on signals. The DC blocking amplifying circuit mode of firstly isolating the DC component and then amplifying is adopted, so that the amplification of the DC signal is avoided, and the signal-to-noise ratio of the signal is improved.

(4) The invention measures and combines the low-frequency and trace-level linear vibration directly related to the micro-angular vibration by the accelerometer, obtains the micro-angular vibration of the spacecraft by utilizing mathematical operation, has simple structure and economic method, and has wide application prospect in the field of measuring the micro-angular vibration of the spacecraft, wherein the carrier has limited volume, special working environment and high requirement on measuring precision.

Drawings

FIG. 1 is a schematic diagram of the system of the present invention;

FIG. 2 is a diagram of a resistance sampling circuit according to the present invention;

fig. 3 is a dc blocking amplifying circuit diagram of the present invention.

Detailed Description

The invention will be further explained with reference to the drawings.

As shown in FIG. 1, the system for measuring micro-angular vibration of a spacecraft of the present invention comprises an acceleration measurement assembly, a resistance sampling circuit, and a blocking amplification circuit; the acceleration measurement combination outputs the measured vibration of the aircraft carrier line in a current mode, the resistance sampling circuit converts a current signal into a voltage signal, the DC blocking amplification circuit performs secondary amplification on the voltage signal and filters a DC component in the signal to obtain a voltage signal corresponding to the line vibration, and then the low-frequency line vibration calibration device is used for calibrating the accelerometer measurement combination, so that the voltage signal can be converted into low-frequency and trace-level line vibration.

The acceleration measurement combination is realized by adopting a three-axis high-precision quartz flexible accelerometer, and the accelerometer measurement combination is respectively placed on an X axis, a Y axis and a Z axis of a spacecraft carrier coordinate system.

As shown in fig. 2, the resistance sampling circuit includes an operational amplifier a1, resistors R1, R2, R3, and a capacitor C1; the positive input end of the operational amplifier A1 is grounded, the reverse input end is connected with one ends of R2 and C1, the other end of R2 is connected with one ends of R1 and R3, the other ends of R3 and C1 are both connected with the output end of the operational amplifier A1, and the other end of R1 is grounded.

As shown in fig. 3, the dc blocking amplifier circuit includes an operational amplifier a2, resistors R4, R5, R6, and a capacitor C2; one end of the capacitor C2 is connected with the output end of the operational amplifier A1, the other end of the capacitor C2 is connected with the positive input end of the operational amplifier and the resistor R4, the other end of the resistor R4 is grounded, the reverse input end of the operational amplifier A2 is connected with the R5 and the R6, the other end of the resistor R5 is grounded, and the other end of the resistor R6 is connected with the output end of the operational amplifier A2.

As shown in fig. 1, a measuring method based on a micro-angular vibration measuring system includes the following steps:

(1) arranging an acceleration measurement combination in a spacecraft carrier coordinate system, and measuring the low-frequency and microscale line vibration of a carrier;

the line vibration resulting from the acceleration measurement combination measurement can be expressed as:

$a=\mathrm{\ω}\×\mathrm{\ω}\×r+\stackrel{\·}{\mathrm{\ω}}\×r$

wherein omega is the rotating angular speed of the spacecraft carrier,the rotating angular acceleration of the spacecraft carrier is shown, and r is a position vector of a mass point relative to the mass center O of the carrier.

(2) And (3) carrying out data processing on the low-frequency and trace-level line vibration obtained by measurement in the step (1) by utilizing the relative position relation between the acceleration measurement combination and the mass center of the spacecraft carrier, and further calculating to obtain the micro-angle vibration of the spacecraft.

The accelerometer measurement combination is respectively arranged on three points B, C and D on an X axis, a Y axis and a Z axis of a spacecraft carrier coordinate system, and the position vector of the accelerometer measurement combination relative to a spacecraft carrier mass center O is R_BO、R_CO、R_DOThe line vibration measured for each measurement combination is as follows:

$a_B=\stackrel{\·}{\mathrm{\ω}}\×R_{\mathrm{BO}}+\mathrm{\ω}\×\mathrm{\ω}\×R_{\mathrm{BO}}$

$a_C=\stackrel{\·}{\mathrm{\ω}}\×R_{\mathrm{CO}}+\mathrm{\ω}\×\mathrm{\ω}\×R_{\mathrm{CO}}$

$a_D=\stackrel{\·}{\mathrm{\ω}}\×R_{\mathrm{DO}}+\mathrm{\ω}\×\mathrm{\ω}\×R_{\mathrm{DO}}$

a_B、a_Cand a_DLinear vibration vectors obtained by measuring and combining the measurement of the accelerometers are respectively a space vehicle carrier coordinate system X, Y and a Z axis, omega is the rotating angular speed of a space vehicle carrier,the angular acceleration of rotation of the spacecraft carrier.

The method for processing the data of the low-frequency and microscale line vibration in the step (2) is as follows: establishing X, Y and Z-axis angular accelerationAnd line vibration a_B、a_C、a_DThe relationship between:

${\stackrel{\·}{\mathrm{\ω}}}_X=\frac{a_C^Z}{{2R}_{\mathrm{CO}}}-\frac{a_D^Y}{{2R}_{\mathrm{DO}}}$

${\stackrel{\·}{\mathrm{\ω}}}_Y=\frac{a_D^X}{{2R}_{\mathrm{DO}}}-\frac{a_B^Z}{{2R}_{\mathrm{BO}}}$

${\stackrel{\·}{\mathrm{\ω}}}_Z=\frac{a_B^Y}{{2R}_{\mathrm{BO}}}-\frac{a_C^X}{{2R}_{\mathrm{CO}}}$

wherein,measuring linear vibration along the Y axis and the Z axis of an aircraft carrier coordinate system measured by an accelerometer arranged at a point B on the X axis of the aircraft carrier coordinate system;measuring linear vibration along the X axis and the Z axis of an aircraft carrier coordinate system measured by an accelerometer arranged at a point C on the Y axis of the aircraft carrier coordinate system;measuring linear vibration along the X axis and the Y axis of an aircraft carrier coordinate system measured by an accelerometer measuring combination placed at a D point on the Z axis of the aircraft carrier coordinate system;

the four-order Runge-Kutta method is used for integral operation, and the micro-angle vibration of the spacecraft can be obtained:

${\mathrm{\ω}}_X\left(t\right)=\mathrm{\ω}(t-T)+\frac{T}{6}{\stackrel{\·}{\mathrm{\ω}}}_X(t-T)+\frac{2T}{3}{\stackrel{\·}{\mathrm{\ω}}}_X(t-\frac{1}{2}T)+\frac{1}{6}{\stackrel{\·}{\mathrm{\ω}}}_X\left(t\right)$

${\mathrm{\ω}}_Y\left(t\right)=\mathrm{\ω}(t-T)+\frac{T}{6}{\stackrel{\·}{\mathrm{\ω}}}_Y(t-T)+\frac{2T}{3}{\stackrel{\·}{\mathrm{\ω}}}_Y(t-\frac{1}{2}T)+\frac{1}{6}{\stackrel{\·}{\mathrm{\ω}}}_Y\left(t\right)$

${\mathrm{\ω}}_Z\left(t\right)=\mathrm{\ω}(t-T)+\frac{T}{6}{\stackrel{\·}{\mathrm{\ω}}}_Z(t-T)+\frac{2T}{3}{\stackrel{\·}{\mathrm{\ω}}}_Z(t-\frac{1}{2}T)+\frac{1}{6}{\stackrel{\·}{\mathrm{\ω}}}_Z\left(t\right)$

wherein T represents the current sampling time, and T is the sampling period.

The combined measuring range of the accelerometer in the invention is +/-0.1 g, the resolution is 5ug, and the position vector of the center of mass O of the carrier relative to the spacecraft is R_BO、R_CO、R_DOall are 1m, the full-scale range +/-0.1G of the accelerometer measurement combination is output +/-0.125 mA (the scale factor of the selective sensitive element is 1.25mA/G), the resistance sampling circuit is shown in FIG. 2 and is realized by adopting a T-type resistance network, wherein the capacitance C1 is 47pF and is used for preventing the circuit from self-excitation, the R1 is 1K omega, the R2 is 500 omega, the R3 is 10K omega, the circuit gain is G R2 × (1+ R3/R1+ R3/R2), the resistance sampling circuit gain is 15500V/A through calculation, and the output voltage signal range is-1.9375- + 1.9375V.

As the micro-angular vibration measurement bandwidth of the spacecraft is required to be 0.1-150Hz, the direct-current component of the voltage signal obtained by resistance sampling needs to be filtered. In order to improve the signal-to-noise ratio of the signal, the signal after the direct-current component is filtered is amplified for the second time, the amplification factor is 2 times, the range of the output voltage signal is-3.875V to +3.875V, the DC blocking amplification circuit is shown in FIG. 3, and the signal cutoff frequency of the DC blocking circuit is 0.0096 Hz. The size of the capacitor C2 is 3.3uF, R4 ═ 5M Ω, R5 ═ 5K Ω, and R5 ═ 6K Ω.

The embodiment is already applied to a certain high-resolution satellite, and flight data show that the micro-angular vibration measurement bandwidth of the spacecraft of the embodiment reaches 0.1-150Hz, the angular resolution is 0.01 arc second, the measurement precision is better than 10%, and the micro-angular vibration measurement requirement of the spacecraft can be met.

The technology not disclosed by the invention belongs to the technical field.

Claims (9)

1. A system for measuring the micro-angular vibration of a spacecraft, comprising: the accelerometer comprises an accelerometer measurement combination, a resistance sampling circuit and a blocking amplifying circuit;

the accelerometer measurement combination outputs measured aircraft carrier line vibration in a current form, the resistance sampling circuit converts a current signal into a voltage signal, the DC blocking amplification circuit performs secondary amplification on the voltage signal and filters a direct current component in the signal to obtain a voltage signal corresponding to the line vibration, then the low-frequency line vibration calibration device is used for calibrating the accelerometer measurement combination, the voltage signal can be converted into low-frequency and trace-level line vibration, the relative position relation between the accelerometer measurement combination and the mass center of a spacecraft carrier is used for performing data processing on the measured low-frequency and trace-level line vibration, and then the micro-angle vibration of the spacecraft is calculated.

2. The system for measuring the micro-angular vibration of the spacecraft of claim 1, wherein: the accelerometer measurement combination is realized by adopting a three-axis high-precision quartz flexible accelerometer, and the accelerometer measurement combination is respectively placed on an X axis, a Y axis and a Z axis of a spacecraft carrier coordinate system.

3. The system for measuring the micro-angular vibration of the spacecraft of claim 1, wherein: the resistance sampling circuit comprises an operational amplifier A1, resistors R1, R2 and R3 and a capacitor C1; the positive input end of the operational amplifier A1 is grounded, the reverse input end is connected with one ends of R2 and C1, the other end of R2 is connected with one ends of R1 and R3, the other ends of R3 and C1 are both connected with the output end of the operational amplifier A1, and the other end of R1 is grounded.

4. A system for measuring the micro-angular vibration of a spacecraft as claimed in claim 3, wherein: the DC blocking amplifying circuit comprises an operational amplifier A2, resistors R4, R5 and R6 and a capacitor C2; one end of the capacitor C2 is connected with the output end of the operational amplifier A1, the other end of the capacitor C2 is connected with the positive input end of the operational amplifier A2 and the resistor R4, the other end of the R4 is grounded, the reverse input end of the operational amplifier A2 is connected with the R5 and the R6, the other end of the R5 is grounded, and the other end of the R6 is connected with the output end of the operational amplifier A2.

5. A system for measuring the micro-angular vibration of a spacecraft as claimed in claim 3, wherein: the capacitor C1 has a size of 47pF to prevent the circuit from self-exciting, and R1 ═ 1K Ω, R2 ═ 500 Ω, and R3 ═ 10K Ω.

6. The system for measuring the micro-angular vibration of the spacecraft of claim 4, wherein: the size of the capacitor C2 is 3.3uF, 5M Ω for R4, 5K Ω for R5, and 5K Ω for R6.

7. A measuring method based on the measuring system of the micro-angular vibration of the spacecraft of claim 1, characterized by the following steps:

(1) arranging an accelerometer measurement combination in a spacecraft carrier coordinate system, and measuring low-frequency and microscale line vibration of a carrier;

the line vibration measured by the accelerometer measurement combination can be expressed as:

$a=\mathrm{\ω}\×\mathrm{\ω}\×r+\stackrel{\·}{\mathrm{\ω}}\×r$

wherein omega is the rotating angular speed of the spacecraft carrier,the rotating angular acceleration of the spacecraft is shown, and r is a position vector of a mass point relative to the mass center O of the carrier;

(2) and (3) carrying out data processing on the low-frequency and trace-level line vibration obtained in the step (1) by utilizing the relative position relation between the accelerometer measurement combination and the mass center of the spacecraft carrier, and further calculating to obtain the micro-angle vibration of the spacecraft.

8. The measurement method according to claim 7, characterized in that: the accelerometer measurement combination is respectively arranged on three points B, C and D on an X axis, a Y axis and a Z axis of a spacecraft carrier coordinate system, and the position vector of the accelerometer measurement combination relative to a spacecraft carrier mass center O is R_BO、R_CO、R_DOThe line vibration measured for each measurement combination is as follows:

$a_B=\stackrel{\·}{\mathrm{\ω}}\×R_{BO}+\mathrm{\ω}\×\mathrm{\ω}\×R_{BO}$

$a_C=\stackrel{\·}{\mathrm{\ω}}\×R_{CO}+\mathrm{\ω}\×\mathrm{\ω}\×R_{CO}$

$a_D=\stackrel{\·}{\mathrm{\ω}}\×R_{DO}+\mathrm{\ω}\×\mathrm{\ω}\×R_{DO}$

a_B、a_Cand a_DLinear vibration vectors, directions respectively, obtained for combined measurements of accelerometer measurementsA spacecraft carrier coordinate system X, Y and a Z axis, omega is the rotating angular speed of the spacecraft carrier,the angular acceleration of rotation of the spacecraft carrier.

9. The measurement method according to claim 8, characterized in that: the method for processing the data of the low-frequency and microscale line vibration in the step (2) is as follows: establishing X, Y and Z-axis rotational angular accelerationAnd line vibration a_B、a_C、a_DThe relationship between:

${\stackrel{\·}{\mathrm{\ω}}}_X=\frac{a_C^Z}{2R_{CO}}-\frac{a_D^Y}{2R_{DO}}$

${\stackrel{\·}{\mathrm{\ω}}}_Y=\frac{a_D^X}{2R_{DO}}-\frac{a_B^Z}{2R_{BO}}$

${\stackrel{\·}{\mathrm{\ω}}}_Z=\frac{a_B^Y}{2R_{BO}}-\frac{a_C^X}{2R_{CO}}$

wherein,measuring linear vibration along the Y axis and the Z axis of an aircraft carrier coordinate system measured by an accelerometer arranged at a point B on the X axis of the aircraft carrier coordinate system;measuring linear vibration along the X axis and the Z axis of an aircraft carrier coordinate system measured by an accelerometer arranged at a point C on the Y axis of the aircraft carrier coordinate system;measuring linear vibration along the X axis and the Y axis of an aircraft carrier coordinate system measured by an accelerometer measuring combination placed at a D point on the Z axis of the aircraft carrier coordinate system;

the four-order Runge-Kutta method is used for integral operation, and the micro-angle vibration of the spacecraft can be obtained:

${\mathrm{\ω}}_X\left(t\right)=\mathrm{\ω}(t-T)+\frac{T}{6}{\stackrel{\·}{\mathrm{\ω}}}_X(t-T)+\frac{2T}{3}{\stackrel{\·}{\mathrm{\ω}}}_X(t-\frac{1}{2}T)+\frac{1}{6}{\stackrel{\·}{\mathrm{\ω}}}_X\left(t\right)$

${\mathrm{\ω}}_Y\left(t\right)=\mathrm{\ω}(t-T)+\frac{T}{6}{\stackrel{\·}{\mathrm{\ω}}}_Y(t-T)+\frac{2T}{3}{\stackrel{\·}{\mathrm{\ω}}}_Y(t-\frac{1}{2}T)+\frac{1}{6}{\stackrel{\·}{\mathrm{\ω}}}_Y\left(t\right)$

${\mathrm{\ω}}_Z\left(t\right)=\mathrm{\ω}(t-T)+\frac{T}{6}{\stackrel{\·}{\mathrm{\ω}}}_Z(t-T)+\frac{2T}{3}{\stackrel{\·}{\mathrm{\ω}}}_Z(t-\frac{1}{2}T)+\frac{1}{6}{\stackrel{\·}{\mathrm{\ω}}}_Z\left(t\right)$

wherein T represents the current sampling time, and T is the sampling period.