A multi-gyro angular rate measurement method based on weight allocation

Abstract

The present invention relates to a multi-gyro angular rate measurement method based on weight allocation. After analyzing the respective shortcomings of the existing four-cross configuration and virtual gyro technology measurement methods, a weight function with respect to frequency is obtained by deriving the measurement accuracy models of the two methods, and a weight allocation measurement method is further proposed, which realizes the fusion of the advantages of the two methods and obtains the measurement expression of the angular rate of the spacecraft in the full frequency band of the multi-gyro. Since the weight allocation function of the four-cross configuration and virtual gyro technology is related to the measurement accuracy of the two measurement methods, and the measurement accuracy is a function of the dynamic frequency of the spacecraft, it is ensured that the angular rate of the spacecraft can be measured with high precision in different frequency bands. This method effectively improves the angular rate measurement accuracy of the spacecraft in the full frequency band. The present invention belongs to the field of inertial navigation technology and can be applied to the high-precision full-frequency band measurement of the attitude angular rate of the spacecraft.

Description

Technical Field

[0001] The present invention relates to a multi-gyro angular rate measurement method based on weight distribution, which is suitable for the occasion of adopting a rotor-type gyro configuration as a spacecraft attitude angular motion information measurement. Technical Background

[0002] Rotor gyros primarily include flexible gyros, magnetically levitated gyros, liquid-levitated gyros, electrostatically levitated gyros, triple-levitated gyros, and dual-levitated gyros. Due to their high measurement accuracy, they are currently the preferred choice for high-precision inertial navigation systems. When calculating the spacecraft's angular velocity, a single gyro must ignore the inertial coupling and cross-coupling terms caused by the spacecraft's angular motion, resulting in limited measurement accuracy. To achieve high-precision measurement of spacecraft angular velocity, multi-gyro configurations and virtual gyro technology are currently the primary approaches employed. Multi-gyro configurations, such as quad-cross, pyramid, pentagonal, and hexagonal pyramid configurations, utilize information exchange between multiple gyros within a configuration to achieve high-precision, high-bandwidth measurement of the spacecraft's attitude angular velocity, without neglecting the inertial coupling and cross-coupling terms caused by the spacecraft's angular motion. Virtual gyroscope technology refers to the method of combining multiple ordinary precision gyroscopes into an array and fusing them into a high-precision gyroscope. Its core lies in the design of software filters. That is, by analyzing and identifying the measurement values ​​of the gyroscope array, the optimal filter is designed to estimate the size of various gyroscope errors, and the measurement information is compensated and corrected to obtain a high-precision estimate of the input angular rate.

[0003] Errors in measuring spacecraft angular rate using a multi-gyro configuration are primarily due to individual gyro variations and configuration installation errors. Since these errors are systematic, they become significant when the spacecraft is operating in low dynamic conditions, leading to insufficient measurement accuracy at low frequencies. Virtual gyro technology essentially ignores the inertial coupling and cross-coupling terms caused by the spacecraft's angular motion when calculating angular rate, resulting in limited measurement accuracy at high frequencies. Summary of the Invention

[0004] The present invention addresses the difficulty of achieving high-precision measurement of spacecraft angular rate across the entire frequency band. By proposing a multi-gyro angular rate measurement method based on weight allocation, the method combines the precision advantages of both the four-cross configuration and virtual gyro technology across different frequency bands, achieving high-precision measurement of spacecraft angular rate across the entire frequency band. This method effectively improves the accuracy of spacecraft angular rate measurements across the entire frequency band.

[0005] The technical solution of the present invention:

[0006] After analyzing the shortcomings of the existing four-cross configuration and virtual gyro technology, a weight function for frequency was obtained by deriving the measurement accuracy models of the two methods. A weight distribution measurement method was further proposed to achieve the integration of the advantages of the two methods. The measurement expression of the spacecraft angular rate by multiple gyros was obtained. The specific steps include:

[0007] (1) Four-cross configuration measurement method

[0008] Spacecraft three-axis attitude angular rate ω under four-cross configuration bx ,ω by ,ω bz

[0009]

[0010] Among them, k I Indicates the torque coefficient of the gyro torquer; J r , J z Respectively represent the radial and axial moments of inertia of the gyro rotor; Ω represents the angular velocity of the gyro rotor; Respectively represent the deflection angular velocity of the 1st, 2nd, 3rd, and 4th gyro rotors around the OX axis; Respectively represent the deflection angular velocity of the 1st, 2nd, 3rd, and 4th gyro rotors around the OY axis; Represent the deflection angular acceleration of the 1st, 2nd, 3rd, and 4th gyro rotors around the OX axis respectively; Respectively represent the deflection angular acceleration of the 1st, 2nd, 3rd, and 4th gyro rotors around the OY axis; I α1 , I α2 , I α3 , I α4 I represents the current of the 1st, 2nd, 3rd and 4th gyro torque coils driving the rotor to deflect around OX; β1 , I β2 , I β3 , I β4 Respectively represent the currents of the 1st, 2nd, 3rd and 4th gyro torquer coils driving the rotor to deflect around OY;

[0011] (2) Virtual gyroscope technology

[0012] Gyro measurement error model

[0013]

[0014] Where i = 1, 2, 3, 4; y i represents the output signal of the i-th gyroscope; ω v Represents the true angular rate signal of the spacecraft; b i Represented by the random walk of the angular rate of the i-th gyroscope ω bi The bias drift caused byi is the random walk of the angle of the i-th gyroscope;

[0015] The virtual gyroscope state equation and measurement equation can be expressed as

[0016]

[0017] Where Z(t) = [y1 y2 y3 y4] T , represents the vector of gyro measurement output signal; F, H represent coefficient matrices; X(t) represents the state variable; represents the rate of change of the state variable, where

[0018] X(t)=[b T ω v ] T (4)

[0019] Combining formulas (3) and (4), we can get the spacecraft three-axis attitude angular rate ω vx ,ω vy ,ω vz ;

[0020] (3) Weight allocation

[0021] The measurement accuracy expressions of the four-cross configuration and virtual gyro technology are:

[0022]

[0023] Among them, η b , η v represent the measurement accuracy of the four-cross configuration and virtual gyro technology respectively; A, f represent the amplitude and frequency of the spacecraft attitude angular displacement respectively; λ b ,λ v They represent the system error coefficient and relative error coefficient of the gyroscope respectively, and the expressions are:

[0024]

[0025] Among them, σ b Individual differences of ghostwriter gyroscopes and systematic errors such as processing and assembly. Therefore, the weight expressions of the two methods of four-cross configuration and virtual gyroscope technology are obtained as follows:

[0026]

[0027] The weights of the two measurement results of the four-cross configuration and the virtual gyro technology are distributed to obtain the final spacecraft three-axis attitude angular rate ω x ,ω y ,ω z

[0028] ω=qb ω b +q v ω v (8)

[0029] Where ω=[ω x ω y ω z ] T ;ω b =[ω bx ω by ω bz ] T ;ω v =[ω vx ω vy ω vz ] T ;q b represents the weight of the four-cross configuration measurement result; q v Represents the weight of the virtual gyroscope measurement result.

[0030] Equation (5) shows that when the spacecraft is in a low-dynamic state, the measurement accuracy of the four-cross configuration method is limited within this frequency range due to the individual differences between the multiple gyros. However, the virtual gyro technology processes the angular rate output information of each gyro, so the individual gyro difference error has no effect on the measurement accuracy. When the spacecraft is in a high-dynamic state, the four-cross configuration method derives the spacecraft angular rate solution while retaining the inertial coupling term and the cross-coupling term, so the high dynamics have no effect on its measurement accuracy. When using the virtual gyro technology to measure the spacecraft angular rate, the single gyro angular rate information used is obtained by the traditional sensitive method. The measurement accuracy of the traditional sensitive method decreases as the spacecraft frequency increases. Therefore, the measurement accuracy of the virtual gyro technology decreases as the spacecraft frequency increases.

[0031] Overall, the virtual gyro technology offers relatively higher measurement accuracy when the spacecraft is in low dynamics, while the four-cross configuration offers greater measurement accuracy when the spacecraft is in high dynamics. Considering that the four-cross configuration requires four gyros, the four gyros can be considered as a single configuration to output angular velocity, or they can be considered individually, outputting four angular velocity results using traditional methods, and then achieving high-precision angular velocity measurement through information fusion. Therefore, the above two methods can be implemented simultaneously using the same four gyros. By assigning weights, the advantages of the two methods in different frequency bands are combined, achieving high-precision angular velocity measurement across the entire frequency band of the spacecraft using multiple gyros.

[0032] The inventive principle of the present invention is: after analyzing the respective shortcomings of the existing four-cross configuration and virtual gyroscope technology, a weight function about frequency is obtained by deriving the measurement accuracy models of the two methods, and a weight distribution measurement method is further proposed to achieve the integration of the advantages of the two methods, and the measurement expression of the spacecraft angular rate by multiple gyros is obtained.

[0033] Because virtual gyro technology offers higher measurement accuracy when the spacecraft is in low dynamics, while the four-cross configuration offers greater accuracy when the spacecraft is in high dynamics, both methods can be implemented simultaneously using the same four gyros. By weighting these two methods, their advantages across different frequency bands are combined, enabling multi-gyro high-precision measurement of spacecraft angular rates across the entire frequency band.

[0034] Compared with the existing solutions, the main advantage of the solution of the present invention is that the advantages of the four-cross configuration and virtual gyroscope technology in different frequency bands are integrated through weight distribution, thereby realizing high-precision measurement of the spacecraft angular rate in the entire frequency band. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Specific implementation plan diagram;

[0036] Figure 2 Measurement results and errors of the four-cross configuration at 1 Hz;

[0037] Figure 3 Measurement results and errors of virtual gyro technology at 1Hz;

[0038] Figure 4 Measurement results and errors of the weight allocation method at 1 Hz;

[0039] Figure 5 Measurement results and errors of the four-cross configuration at 10 Hz;

[0040] Figure 6 Measurement results and errors of virtual gyro technology at 10Hz;

[0041] Figure 7 Measurement results and errors of the weight allocation method at 10 Hz. Specific implementation plan

[0042] Specific embodiments of the present invention are as follows Figure 1 As shown in the figure, after analyzing the shortcomings of the existing four-cross configuration and virtual gyro technology, the weight function of frequency is obtained by deriving the measurement accuracy models of the two methods. A weight distribution measurement method is further proposed to achieve the integration of the advantages of the two methods. The measurement expression of the spacecraft angular rate by multiple gyros is obtained, which specifically includes the following steps:

[0043] (1) Four-cross configuration measurement method

[0044] Spacecraft three-axis attitude angular rate ω under four-cross configuration bx ,ω by ,ω bz

[0045]

[0046] Among them, k I Indicates the torque coefficient of the gyro torquer; J r , J z Respectively represent the radial and axial moments of inertia of the gyro rotor; Ω represents the angular velocity of the gyro rotor; Respectively represent the deflection angular velocity of the 1st, 2nd, 3rd, and 4th gyro rotors around the OX axis; Respectively represent the deflection angular velocity of the 1st, 2nd, 3rd, and 4th gyro rotors around the OY axis; Represent the deflection angular acceleration of the 1st, 2nd, 3rd, and 4th gyro rotors around the OX axis respectively; Respectively represent the deflection angular acceleration of the 1st, 2nd, 3rd, and 4th gyro rotors around the OY axis; I α1 , I α2 , I α3 , I α4 I represents the current of the 1st, 2nd, 3rd and 4th gyro torque coils driving the rotor to deflect around OX; β1 , I β2 , I β3 , I β4 Respectively represent the currents of the 1st, 2nd, 3rd and 4th gyro torquer coils driving the rotor to deflect around OY;

[0047] (2) Virtual gyroscope technology

[0048] Gyro measurement error model

[0049]

[0050] Where i = 1, 2, 3, 4; y i represents the output signal of the i-th gyroscope; ω v Represents the true angular rate signal of the spacecraft; b i Represented by the random walk of the angular rate of the i-th gyroscope ω bi The bias drift caused by i is the random walk of the angle of the i-th gyroscope;

[0051] The virtual gyroscope state equation and measurement equation can be expressed as

[0052]

[0053] Where Z(t) = [y1 y2 y3 y4] T , represents the vector of gyro measurement output signal; F, H represent coefficient matrices; X(t) represents the state variable; represents the rate of change of the state variable, where

[0054] X(t)=[b T ω v ] T (12)

[0055] Combining formulas (3) and (4), we can get the spacecraft three-axis attitude angular rate ω vx ,ω vy ,ω vz ;

[0056] (3) Weight allocation

[0057] The measurement accuracy expressions of the four-cross configuration and virtual gyro technology are:

[0058]

[0059] Among them, η b , η v represent the measurement accuracy of the four-cross configuration and virtual gyro technology respectively; A, f represent the amplitude and frequency of the spacecraft attitude angular displacement respectively; λ b ,λ v They represent the system error coefficient and relative error coefficient of the gyroscope respectively, and the expressions are:

[0060]

[0061] Among them, σ b Individual differences of ghostwriter gyroscopes and systematic errors such as processing and assembly. Therefore, the weight expressions of the two methods of four-cross configuration and virtual gyroscope technology are obtained as follows:

[0062]

[0063] The weights of the two measurement results of the four-cross configuration and the virtual gyro technology are distributed to obtain the final spacecraft three-axis attitude angular rate ω x ,ω y ,ω z

[0064] ω=q b ω b +q v ω v (16)

[0065] Where ω=[ω x ω y ω z ]T ;ω b =[ω bx ω by ω bz ] T ;ω v =[ω vx ω vy ω vz ] T ;q b represents the weight of the four-cross configuration measurement result; q v Represents the weight of the virtual gyroscope measurement result.

[0066] In order to verify the correctness and superiority of the method of the present invention, the angular velocity of the spacecraft OY axis is set to ω by = sin(2πt)° / s and ω by = sin(20πt)° / s, that is, the amplitude is 1° / s, and the frequencies are 1Hz and 10Hz respectively. The angular rate measurement results and errors obtained by the configuration method are as follows Figure 2 and Figure 5 As shown; the angular rate measurement results and errors estimated by MSCSG based on virtual gyroscope technology are shown as follows Figure 3 and Figure 6 As shown in the figure; the angular rate measurement results and errors obtained after weight distribution of the calculation results of the two methods are shown in the figure. Figure 4 and Figure 7 shown.

[0067] Combine Figure 2 、 Figure 3 、 Figure 4 It can be found that when the spacecraft dynamic frequency is 1Hz, the angular rate error measured by the four-cross configuration is about 0.05° / s, and the angular rate error measured by the virtual gyro technology is about 0.013° / s. Based on the weight distribution method proposed in this paper, the weights of the four-cross configuration and the virtual gyro technology are calculated to be 0.2 and 0.8 respectively, and the final angular rate measurement error is 0.02° / s. Figure 5 、 Figure 6 、 Figure 7It can be found that when the spacecraft dynamic frequency is 10Hz, the angular rate error measured by the four-cross configuration is about 0.008° / s, and the angular rate error measured by the virtual gyroscope technology is about 0.04° / s. Based on the weight allocation method proposed in this paper, the weights of the four-cross configuration and the virtual gyroscope technology are calculated to be 0.9 and 0.1, respectively, and the final angular rate measurement error is 0.013° / s. Overall, when the four-cross configuration is used alone, the measurement accuracy is at least 95%, and when the virtual gyroscope technology is used alone, the measurement accuracy is at least 96%. After using weight allocation to combine the advantages of the two in different frequency bands, the measurement accuracy is at least 98%, thus verifying that the present invention effectively reduces the contradiction between the spacecraft dynamic frequency and the angular rate measurement accuracy.

[0068] The contents not described in detail in this specification belong to the prior art known to those skilled in the art.

Claims

1. A multi-gyro angular rate measurement method based on weight allocation, characterized in that: The following steps are involved: (1) Four-cross configuration measurement method Spacecraft three-axis attitude angular rate ω under four-cross configuration bx ,ω by ,ω bz Among them, k I Indicates the torque coefficient of the gyro torquer; J r , J z Respectively represent the radial and axial moments of inertia of the gyro rotor; Ω represents the angular velocity of the gyro rotor; Respectively represent the deflection angular velocity of the 1st, 2nd, 3rd, and 4th gyro rotors around the OX axis; Respectively represent the deflection angular velocity of the 1st, 2nd, 3rd, and 4th gyro rotors around the OY axis; Represent the deflection angular acceleration of the 1st, 2nd, 3rd, and 4th gyro rotors around the OX axis respectively; Respectively represent the deflection angular acceleration of the 1st, 2nd, 3rd, and 4th gyro rotors around the OY axis; I α1 , I α2 , I α3 , I α4 I represents the current of the 1st, 2nd, 3rd and 4th gyro torque coils driving the rotor to deflect around OX; β1 , I β2 , I β3 , I β4 Respectively represent the currents of the 1st, 2nd, 3rd and 4th gyro torquer coils driving the rotor to deflect around OY; (2) Virtual gyroscope technology Gyro measurement error model Where i = 1, 2, 3, 4; y i represents the output signal of the i-th gyroscope; ω v Represents the true angular rate signal of the spacecraft; b i Represented by the random walk of the angular rate of the i-th gyroscope ω bi The bias drift caused by i is the random walk of the angle of the i-th gyroscope; The virtual gyroscope state equation and measurement equation are expressed as Where Z(t) = [y1 y2 y3 y4] T represents the vector of the gyro measurement output signal; F, H represent the coefficient matrix; X(t) represents the state variable; represents the rate of change of the state variable, where X(t)=[b T ω v ] T (4) Combining formulas (3) and (4), we can get the spacecraft three-axis attitude angular rate ω vx ,ω vy ,ω vz ; (3) Weight allocation The weights of the two measurement results of the four-cross configuration and the virtual gyro technology are distributed to obtain the final spacecraft three-axis attitude angular rate ω x ,ω y ,ω z ω=q b oh b +q v oh v (5) Where ω=[ω x ω y ω z ] T ;ω b =[ω bx ω by ω bz ] T ;ω v =[ω vx ω vy ω vz ] T ;q b represents the weight of the four-cross configuration measurement result; q v Represents the weight of the virtual gyroscope measurement result.

2. The multi-gyro angular rate measurement method based on weight allocation according to claim 1, characterized in that: The measurement accuracy expressions of the four-cross configuration and virtual gyro technology are: Among them, η b , η v represent the measurement accuracy of the four-cross configuration and virtual gyro technology respectively; f represents the frequency of the spacecraft attitude angular displacement; λ b ,λ v Represent the system error coefficient and relative error coefficient of the gyroscope respectively, and the expression is Among them, σ b represents the individual differences of the gyroscope and the processing and assembly system errors; A represents the amplitude of the spacecraft attitude angular displacement.

3. The multi-gyro angular rate measurement method based on weight allocation according to claim 2, characterized in that: The weight expressions of the four-cross configuration and virtual gyro technology are:

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