A dual-gyroscope self-calibration method applicable to rate integral hemispherical resonator gyroscopes

Abstract

This invention belongs to the field of inertial navigation technology, specifically relating to a dual-gyroscope self-calibration method applicable to rate integral hemispherical resonator gyroscopes (HRGs). This invention uses two coaxial rate integral hemispherical resonator gyroscopes (HRGs) and employs a Kalman filtering method to estimate and compensate for the damping mismatch error of the two HRGs in real time, thus achieving dual-gyroscope self-calibration of the rate integral HRGs. Because the estimated value of the damping mismatch error is subtracted, the final output accuracy is higher than the original accuracy of the two HRGs. By using two HRGs, this invention achieves real-time calibration and compensation of HRG damping mismatch error without excessively increasing the volume, significantly reducing the impact of damping mismatch error on HRG accuracy. Compared to traditional damping mismatch error compensation methods that can only be calibrated under static conditions, this invention can accurately calibrate HRG damping mismatch error parameters under dynamic conditions, significantly reducing the impact of environmental changes on the compensation effect and improving the environmental adaptability of the HRG.

Description

Technical Field

[0001] This invention belongs to the field of inertial navigation technology, specifically relating to a dual-gyroscope self-calibration method applicable to rate integral hemispherical resonant gyroscopes (HRGs), suitable for various applications of rate integral HRGs. Background Art

[0002] In recent years, HRGs have seen rapid development in various application fields. Their working principle is based on the energy transfer caused by the Coriolis effect between two vibration modes of a hemispherical resonator. As a new type of inertial device, HRGs have characteristics such as large range, long lifespan, and high reliability. They are also capable of achieving measurement accuracy similar to or even higher than existing optical gyroscopes in a smaller size, and are considered to be the next-generation gyroscope with the best overall performance.

[0003] Currently, HRG (Hyper-Rate Integration) mainly exists in two application modes: force balance mode and rate integration mode. The former has high measurement accuracy, but its small range and bandwidth limit its application in the navigation field; while the latter, the rate integration mode, theoretically has an infinite range and an extremely stable scaling factor, making it suitable for inertial navigation scenarios. However, in practical applications, the rate integration mode requires the harmonic oscillator mode shape to precess freely across the entire angular range, which makes the damping mismatch caused by the circumferential non-uniformity of the harmonic oscillator a factor of error that must be considered.

[0004] In existing research, no comprehensive solution has been publicly disclosed for HRG damping mismatch error. The current mainstream error suppression method involves identifying the HRG damping mismatch error parameters before the gyroscope starts operating, and then applying control forces using electrodes during operation to counteract the gyroscope output bias caused by the damping mismatch. However, this method does not consider changes in the gyroscope's physical parameters due to environmental variations. Therefore, HRGs using this method for error suppression are extremely sensitive to environmental changes such as temperature, making practical application difficult without temperature control.

[0005] Based on the above analysis, if the physical parameters related to damping mismatch in the HRG can be estimated in real time, the impact of environmental changes on the rate integral HRG output can be reduced while suppressing the damping mismatch error, thus significantly improving the output accuracy of the HRG. Summary of the Invention

[0006] To reduce the impact of environmental factors such as temperature changes on the damping mismatch error compensation effect of rate integral HRG, this invention proposes a dual-gyroscope self-calibration method suitable for rate integral HRG. By using the outputs of two coaxial rate integral HRGs, the physical parameters inside the two rate integral HRGs are estimated in real time, thereby realizing real-time compensation for HRG damping mismatch error. This method can effectively improve the measurement accuracy of rate integral HRG.

[0007] The technical solution adopted in this invention is: a dual-gyroscope self-calibration method suitable for rate integral hemispherical resonant gyroscopes, comprising the following steps:

[0008] S1 mounts two identical rate integral HRGs on the base, ensuring their sensing axes are parallel. The two HRGs are then connected to the control circuit, which outputs the following data to the calculation module. The two rate integral HRGs are named HRG_A and HRG_B respectively:

[0009] The azimuth angle of the harmonic oscillator mode at time k in HRG_A

[0010] The azimuth angle of the harmonic oscillator mode at time k in HRG_B

[0011] It should be noted that the azimuth angle θ of the harmonic oscillator mode at time k k It represents the cumulative rotation angle of the harmonic oscillator after the self-rate integral HRG is energized, i.e., θ. k =θ0 + 2π × number of revolutions the standing wave has made: If the standing wave angle at time 0 (i.e., the angle between the harmonic oscillator mode shape and the x-axis electrode in the rate integral HRG) θ0 = π / 2, and the standing wave has rotated 2 revolutions in the positive direction from time 0 to time i, then θ i =π / 2 + 2 × 2π = 4.5π. During the process from time i to time j, the standing wave rotates one revolution in the opposite direction. Therefore, θ j =π / 2+2×2π-1×2π=3.5π;

[0012] In the above explanation, the subscript k indicates the value of the corresponding variable at time k; the superscripts A and B indicate that the corresponding variable is a parameter of HRG_A or HRG_B, respectively, and the same applies below.

[0013] S2 controls both rate integrals HRG to perform virtual rotation at a constant rate Ω0.

[0014] S3 establishes the continuous-time Kalman filter error equation:

[0015] In the rate integral HRG, if only the error caused by damping mismatch is considered, and random noise is ignored, the azimuth angle θ of the harmonic oscillator mode shape can be described by the following differential equation:

[0016]

[0017] Where G is the angular gain in rate integral mode; Ω is the angular rate applied to the gyroscope from the outside; Δ(1 / τ)=1 / τ1-1 / τ2 is the anisotropic damping coefficient, where τ1 and τ2 are the decay times of the main mode and secondary mode of the harmonic oscillator, respectively; This indicates taking the derivative with respect to θ; θ τ Let θ be the azimuth angle of the damping axis. From equation (1), it can be seen that since θ is the known gyroscope output, if Δ(1 / τ) and θ can be estimated in real time... τ Then the value of the second term in the formula (i.e., the error caused by damping mismatch) can be obtained and compensated for by calculation, and there is no need to worry about environmental changes affecting Δ(1 / τ) and θ. τ Changes can lead to inaccurate compensation.

[0018] By performing an identity transformation on equation (1), we can obtain equation (2):

[0019]

[0020] The intermediate variables a and b are represented as follows:

[0021]

[0022] As shown in equation (2), since both coaxial HRGs experience the same external angular velocity Ω and undergo a virtual rotation at a constant rate Ω0, the terms Ω and Ω0 can be eliminated by subtraction. At this point, only a and b are unknowns in the equation, and Kalman filtering can be used to estimate the intermediate variables a and b in real time, achieving the same result as the real-time estimation of Δ(1 / τ) and θ. τ Same effect.

[0023] From the above analysis, we can see that for HRG_A and HRG_B, we have:

[0024]

[0025] Subtracting equation (4) and equation (5) yields:

[0026]

[0027] Since the intermediate variables a and b change slowly over time, a first-order Markov process can be used to describe the time-varying process of a and b; from the above analysis, the error equation for continuous-time Kalman filtering can be obtained:

[0028]

[0029] in, As an intermediate variable, it represents and The difference; δa A and δb A They represent a respectively A and b A rate of change; δa B and δb B They represent a respectively B and b B The rate of change; further, the continuous-time Kalman filter error equation in fractional form can be obtained:

[0030]

[0031] S4 establishes a Kalman filter.

[0032] S4.1 Define the state vector X of the Kalman filter system at time k. k as follows:

[0033]

[0034] In equation (9), each variable is the value of the corresponding variable in S3 at time k.

[0035] The formula for one-step state prediction using the S4.2 Kalman filter is as follows:

[0036]

[0037] in X represents the state variable at time k-1. k-1 The estimated value is set to an initial value when k=0. 0 1×9 Represents a 1×9 dimensional zero matrix; Φ represents the one-step prediction of the state variable from time k-1 to time k; k / k-1 The state transition matrix from time k-1 to time k is as follows:

[0038]

[0039] In equation (11), I is the identity matrix, T is the sampling interval, and F k-1 Let F be the value of the continuous-time state transition matrix F of the Kalman filter at time k-1. From equation (8), we know that:

[0040]

[0041] S4.3 One-step prediction mean square error matrix P of the state from time k-1 to time k k / k-1 The calculation formula is as follows:

[0042]

[0043] In equation (13), P k-1 This represents the mean square error matrix for one-step prediction of the state at time k-1. When k=0, its initial value is set to P. 0-1 P 0-1 The specific values ​​are obtained from the actual performance of the gyroscope (such as zero-bias instability and random walk) and engineering experience; Q is the system noise covariance matrix, and its specific values ​​are also obtained from the actual performance of the gyroscope and engineering experience.

[0044] S4.4 Filter gain K at time k k The calculation formula is as follows:

[0045] K k =P k / k-1 H T HP k / k-1 H T +R) -1 (14)

[0046] In equation (14), H is the measurement matrix:

[0047] H = [1 0 0 0 0 0 0 0 0] (15)

[0048] In equation (14), R is the observation noise covariance matrix, the specific value of which is obtained from the actual performance of the gyroscope and engineering experience. The estimated state variables at time S4.5 k. The calculation formula is as follows:

[0049]

[0050] In equation (16), Z k For the observations at time k:

[0051]

[0052] S4.6 The mean square error matrix P of the state estimation at time k k The calculation formula is as follows:

[0053]

[0054] S5 performs HRG damping mismatch error parameter estimation and compensation:

[0055] S5.1 Initialize the timer by setting k = 0;

[0056] S5.2 sequentially executes S4.2-S4.6 to perform one round of Kalman filtering parameter estimation, obtaining the state vector X at time k. k The estimated value Pick The second element in The estimated value Pick The third element in The estimated value Pick The 4th element in The estimated value Pick The 5th element in The estimated value

[0057] S5.3 If k≥1, compensate for the HRG damping mismatch error:

[0058] S5.3.1 Calculate the angular increments of HRG_A and HRG_B from time k-1 to time k before compensation. and

[0059]

[0060]

[0061] S5.3.2 Calculate the angular increments of HRG_A and HRG_B from time k-1 to time k after compensation. and

[0062]

[0063] S5.4 take and The mean value is used as the output of the dual gyroscope system at time k.

[0064]

[0065] S5.5 Let k = k + 1;

[0066] S5.6 executes S5.2-S5.5 repeatedly until the current measurement ends, then exits the loop.

[0067] This invention utilizes two coaxial rate integrals (HRGs) and employs a Kalman filtering method to estimate and compensate for the damping mismatch error between the two HRGs in real time, thus achieving dual-gyroscope self-calibration of the rate integral HRGs. Because the estimated damping mismatch error is subtracted, the final output... Its accuracy is higher than the original accuracy of both HRGs.

[0068] The present invention has the following technical effects:

[0069] 1. By using two HRGs, the present invention achieves real-time calibration and compensation of HRG damping mismatch error without excessively increasing the volume, thus significantly reducing the impact of damping mismatch error on HRG accuracy.

[0070] 2. Compared with traditional damping mismatch error compensation methods that can only be calibrated under static conditions, this invention can accurately calibrate HRG damping mismatch error parameters under dynamic conditions.

[0071] 3. Compared with traditional HRG damping mismatch error compensation methods, this invention can significantly reduce the impact of environmental changes on the compensation effect and improve the environmental adaptability of HRG. Attached Figure Description

[0072] Figure 1 The self-calibration method proposed in this invention: implementation process

[0073] Figure 2 Graph showing the change of applied external angular rate over time

[0074] Figure 3 : intermediate parameter a A The estimated value

[0075] Figure 4 : intermediate parameter a B The estimated value

[0076] Figure 5 : intermediate parameter b A The estimated value

[0077] Figure 6 : intermediate parameter b B The estimated value

[0078] Figure 7 Angular rate error of HRG before and after compensation Detailed Implementation

[0079] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

[0080] To make the technical methods and advantages of this application clearer, the present invention will be further described below with reference to the accompanying drawings. The specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0081] The implementation process of the rate integral hemispherical resonator gyroscope dual-axis self-calibration method proposed in this invention is as follows: Figure 1 As shown.

[0082] To demonstrate the feasibility of this invention, a simulation experiment was conducted. During the experiment, two HRGs oscillated together, and the applied angular velocity changed over time as follows: Figure 2As shown. The zero-bias instability of both HRGs is set to 0.1° / h, and the random walk is... Both HRG virtual rotational angular velocities are Ω0 = 12° / s; simultaneously, it is assumed that due to environmental changes and other factors, the azimuth angle θ of the HRG's damping axis will vary. τ It changes slowly over time.

[0083] The Kalman filter period is set to 200Hz. The initial values ​​of the mean square error matrix of the state estimation are set as shown in equation (24), where diag represents the diagonal matrix:

[0084]

[0085] The system noise covariance matrix is ​​set as shown in equation (25):

[0086] Q = diag[0 0 0 0 0 (5×10 -4 ° / h) 2 (5×10 -4 ° / h) 2 (5×10 -4 ° / h) 2 (5×10 -4 ° / h) 2 (25)

[0087] The observation noise covariance matrix is ​​set as shown in equation (26):

[0088] R = diag[(5×10 -4 °) 2 (26)

[0089] Error calibration is performed using the method proposed in this invention. The intermediate parameter a is used during the calibration process. A and a B The estimated value is as follows Figure 3 and Figure 4 As shown; b A and b B The estimated value is as follows Figure 5 and Figure 6 As shown; it can be seen that although the true values ​​of a and b in the two HRGs change slowly over time, the estimated values ​​basically fluctuate around the true values, indicating that this method has the ability to calibrate and compensate in real time; the angular rate errors of the HRGs before and after compensation are as follows. Figure 7 As shown, it can be observed that this method has a significant suppressive effect on damping mismatch error and can effectively improve the measurement accuracy of HRG.

Claims

1. A dual-gyroscope self-calibration method applicable to rate integral hemispherical resonator gyroscopes, characterized in that, This method consists of the following steps: S1 mounts two identical rate integral HRGs on the base, ensuring their sensing axes are parallel. The two HRGs are then connected to the control circuit, which outputs the following data to the calculation module. The two rate integral HRGs are named HRG_A and HRG_B respectively: The azimuth angle of the harmonic oscillator mode at time k in HRG_A The azimuth angle of the harmonic oscillator mode at time k in HRG_B The subscript k indicates the value of the corresponding variable at time k; the superscripts A and B indicate that the corresponding variable is a parameter of HRG_A or HRG_B, respectively. S2 controls both rate integrals HRG to perform virtual rotation at a constant rate Ω0; S3 establishes the continuous-time Kalman filter error equation: In the rate integral HRG, considering only the error caused by damping mismatch and neglecting random noise, the azimuth angle θ of the harmonic oscillator mode shape can be described by the following differential equation: Where G is the angular gain in rate integral mode; Ω is the angular rate applied to the gyroscope from the outside; Δ(1 / τ)=1 / τ1-1 / τ2 is the anisotropic damping coefficient, where τ1 and τ2 are the decay times of the main mode and secondary mode of the harmonic oscillator, respectively; This indicates taking the derivative with respect to θ; θ τ The azimuth angle of the damping axis; By performing an identity transformation on equation (1), we can obtain equation (2): The intermediate variables a and b are represented as follows: For HRG_A and HRG_B, respectively: Subtracting equation (4) and equation (5) yields: Continuous-time Kalman filter error equation: in, As an intermediate variable, it represents and The difference; δa A and δb A They represent a respectively A and b A rate of change; δa B and δb B They represent a respectively B and b B The rate of change; further, the continuous-time Kalman filter error equation in fractional form can be obtained: S4 establishes a Kalman filter: S4.1 Define the state vector X of the Kalman filter system at time k. k as follows: In equation (9), each variable is the value of the corresponding variable in S3 at time k; The formula for one-step state prediction using the S4.2 Kalman filter is as follows: in X represents the state variable at time k-1. k-1 The estimated value; Φ represents the one-step prediction of the state variable from time k-1 to time k; k / k-1 The state transition matrix from time k-1 to time k is: In equation (11), I is the identity matrix, T is the sampling interval, and F k-1 Let F be the value of the continuous-time state transition matrix F of the Kalman filter at time k-1; from equation (8), we know that: S4.3 One-step prediction mean square error matrix P of the state from time k-1 to time k k / k-1 The calculation formula is as follows: In equation (13), P k-1 The mean square error matrix for the one-step prediction of the state at time k-1 is represented; Q is the system noise covariance matrix. S4.4 Filter gain K at time k k The calculation formula is as follows: K k =P k / k-1 H T (HP k / k-1 H T +R) -1 (14) In equation (14), H is the measurement matrix: H＝[1 0 0 0 0 0 0 0 0] (15) In equation (14), R is the observation noise covariance matrix; State quantity estimates at time S4.5 k The calculation formula is as follows: In equation (16), Z k For the observations at time k: S4.6 The mean square error matrix P of the state estimation at time k k The calculation formula is as follows: S5 performs HRG damping mismatch error parameter estimation and compensation: S5.1 Initialize the timer by setting k = 0; S5.2 sequentially executes S4.2-S4.6 to perform one round of Kalman filtering parameter estimation, obtaining the state vector X at time k. k The estimated value Pick The second element in The estimated value Pick The third element in The estimated value Pick The 4th element in The estimated value Pick The 5th element in The estimated value S5.3 If k≥1, compensate for the HRG damping mismatch error: S5.3.1 Calculate the angular increments of HRG_A and HRG_B from time k-1 to time k before compensation. and S5.3.2 Calculate the angular increments of HRG_A and HRG_B from time k-1 to time k after compensation. and S5.4 take and The mean value is used as the output of the dual gyroscope system at time k. S5.5 Let k = k + 1; S5.6 executes S5.2-S5.5 repeatedly until the current measurement ends, then exits the loop.

2. The dual-gyroscope self-calibration method for rate-integrating hemispherical resonator gyroscopes according to claim 1, characterized in that: Set the state variable X at time k-1 k-1 The estimated value The initial value at k=0 is 0 1×9 This represents a 1×9 zero matrix.

3. The dual-gyroscope self-calibration method for rate integral hemispherical resonator gyroscopes according to claim 1, characterized in that: Set the mean square error matrix P for the one-step prediction of the state at time k-1. k-1 The initial value at k=0 is P. 0-1 , P 0-1 The specific value is determined by the actual performance of the gyroscope and engineering experience.

4. The dual-gyroscope self-calibration method for rate integral hemispherical resonator gyroscopes according to claim 1, characterized in that: The specific value of the system noise covariance matrix Q is obtained from the actual performance of the gyroscope and engineering experience.

5. The dual-gyroscope self-calibration method for rate integral hemispherical resonator gyroscopes according to claim 1, characterized in that: The specific value of the observation noise covariance matrix R is obtained from the actual performance of the gyroscope and engineering experience.

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