A low-precision gyroscope-assisted rate integral hemispherical resonator gyroscope self-calibration method

Abstract

This invention belongs to the field of inertial navigation technology, specifically relating to a low-precision gyroscope-assisted self-calibration method for a rate integral hemispherical resonator (HRG), applicable to various applications of the HRG. This invention uses a low-precision gyroscope coaxial with the HRG for assistance, and employs a Kalman filter method to estimate and compensate for the damping mismatch error of the HRG in real time, thus achieving self-calibration of the HRG. The final output (ω′) HRG ) k The accuracy is higher than the original accuracy of the rate integral HRG, and also higher than the measurement accuracy of the auxiliary gyroscope. This invention achieves real-time calibration and compensation of the damping mismatch error parameter of the HRG without excessively increasing the size and cost by using a low-precision gyroscope as an aid. This significantly reduces the impact of the damping mismatch error on the accuracy of the HRG, can accurately calibrate the damping mismatch error parameter of the HRG under dynamic conditions, can significantly reduce the impact of environmental changes on the compensation effect, and improve the environmental adaptability of the HRG.

Description

Technical Field

[0001] This invention relates to the field of inertial navigation technology, specifically to a low-precision gyroscope-assisted self-calibration method for a rate integral hemispherical resonant gyroscope (HRG), applicable to various applications of rate integral HRGs. Background Technology

[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 mitigate the impact of environmental factors such as temperature changes on the rate integral HRG while suppressing damping mismatch errors, this invention proposes a low-precision gyroscope-assisted self-calibration method for the rate integral HRG. This method uses another low-precision auxiliary gyroscope coaxial with the rate integral HRG (note that this gyroscope itself does not have damping mismatch errors; the gyroscope that can be used includes, but is not limited to, laser gyroscopes, fiber optic gyroscopes, or micromechanical gyroscopes) to provide an external angular velocity reference. This allows for real-time estimation of the internal physical parameters of the rate integral HRG, achieving real-time compensation for the damping mismatch error and effectively improving the measurement accuracy of the rate integral HRG.

[0007] The technical solution adopted in this invention is: a self-calibration method for a low-precision gyroscope-assisted rate integral hemispherical resonator gyroscope, which consists of the following steps:

[0008] S1 mounts the rate integral gyroscope (HRG) and the auxiliary gyroscope on the base, making the sensitive axes of the two gyroscopes parallel to each other. Both are then connected to the control circuit, causing it to output the following data to the calculation module:

[0009] The output data of HRG includes: the azimuth angle θ of the harmonic oscillator mode shape at time k. k ;

[0010] 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;

[0011] The output data of the auxiliary gyroscope includes: the external angular velocity reference at time k. It should be noted that the auxiliary gyroscope used here has relatively low precision. There will inevitably be a certain difference between the actual angular velocity and the external environment.

[0012] In the above explanation, the subscript k indicates the value of the corresponding variable at time k, and the same applies below.

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

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

[0015] In 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 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; Δ(1 / τ) = 1 / τ1 - 1 / τ2 is the anisotropic damping coefficient, where τ1 and τ2 are the decay times of the primary and secondary modes of the harmonic oscillator, respectively; θ is the azimuth angle of the harmonic oscillator mode shape. 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), if another coaxial auxiliary gyroscope is used to provide a reference for the angular rate Ω applied to the gyroscope from the outside, then only a and b are unknowns in the equation. In this case, Kalman filtering can be used to estimate the intermediate variables a and b in real time, achieving the same result as real-time estimation of Δ(1 / τ) and θ. τ Same effect.

[0023] For the auxiliary gyroscope, since there is no damping mismatch error, its output external angular velocity reference Ω is considered. ref The true angular velocity Ω and the constant zero bias B ref The sum, ignoring random noise, gives:

[0024] Ω ref =Ω-B ref (4)

[0025] From equations (2) and (4), we can obtain:

[0026]

[0027] On the other hand, 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; since B ref There is basically no change, and it is believed that B ref The derivative with respect to time is 0. From the above analysis, the error equation for continuous-time Kalman filtering can be obtained:

[0028]

[0029] a′ represents the rate of change of intermediate variable a, and b′ represents the rate of change of intermediate variable b;

[0030] Further, the continuous-time Kalman filter error equation can be expressed in fractional form:

[0031]

[0032] S4 establishes a Kalman filter.

[0033] S4.1 Define the state vector X of the Kalman filter system at time k. k as follows:

[0034] X k =[θ k a k b k a′ k b k 'B k ref ] T (8)

[0035] Among them, a k and b k Let a and b represent the values ​​of intermediate variables a and b at time k, respectively; a′ k and b k ′ represent the values ​​of the rates of change of a and b at time k, respectively; This represents the value of the constant zero bias of the auxiliary gyroscope at time k.

[0036] The formula for one-step state prediction using the S4.2 Kalman filter is as follows:

[0037]

[0038] 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 1×6 Represents a 1×6 zero matrix; Φ represents the one-step prediction of the state variable from time k-1 to time k; k / k-1The state transition matrix from time k-1 to time k is:

[0039]

[0040] In equation (10), 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 (7), we know that:

[0041]

[0042] In equation (9), U k The control matrix at time k is shown in equation (12):

[0043]

[0044] Where u k The value of the continuous-time control matrix u at time k can be obtained from equation (7):

[0045]

[0046] 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:

[0047]

[0048] In equation (14), P k-1 This represents the mean square error matrix for the 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.

[0049] S4.4 Filter gain K at time k k The calculation formula is as follows:

[0050] K k =P k / k-1 H T HP k / k-1 H T +R) -1 (15)

[0051] In equation (15), H is the measurement matrix:

[0052] H = [1 0 0 0 00] (16)

[0053] In equation (15), R is the observation noise covariance matrix, and its specific value is obtained from the actual performance of the gyroscope and engineering experience.

[0054] State quantity estimates at time S4.5 k The calculation formula is as follows:

[0055]

[0056] In equation (17), Z k For the observations at time k:

[0057] Z k =θ k (18)

[0058] S4.6 The mean square error matrix P of the state estimation at time k k The calculation formula is as follows:

[0059]

[0060] S5 performs HRG damping mismatch error parameter estimation and compensation:

[0061] S5.1 Initialize the timer by setting k = 0;

[0062] 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 is a k The estimated value Pick The third element in is b k The estimated value

[0063]

[0064] S5.3 If k≥1, compensate for the HRG damping mismatch error:

[0065] S5.3.1 Calculate the angular increment (ω) of HRG from time k-1 to time k before compensation. HRG ) k :

[0066]

[0067] S5.3.2 Calculate the angular increment (ω′) of HRG from time k-1 to time k after compensation. HRG ) k :

[0068]

[0069] Use (ω′) HRG ) k As the angular increment output of HRG at time k.

[0070] S5.4 Let k = k + 1;

[0071] S5.5 executes S5.2-S5.4 repeatedly until the current measurement is completed, then exits the loop.

[0072] This invention uses a low-precision gyroscope coaxial with the rate integral gyroscope (HRG) for assistance, and employs the Kalman filtering method to estimate and compensate for the damping mismatch error of the HRG in real time, thus achieving self-calibration of the HRG. The final output (ω′) HRG ) k Its accuracy is higher than the original accuracy of the rate integral HRG, and also higher than the measurement accuracy of the auxiliary gyroscope.

[0073] The present invention has the following technical effects:

[0074] 1. This invention achieves real-time calibration and compensation of the damping mismatch error parameters of the HRG without excessively increasing the size and cost by using a low-precision gyroscope as an aid, thus significantly reducing the impact of damping mismatch error on the accuracy of the HRG.

[0075] 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.

[0076] 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

[0077] Figure 1 The self-calibration method proposed in this invention: implementation process

[0078] Figure 2 Graph showing the change of applied external angular rate over time

[0079] Figure 3 : Estimated value of intermediate parameter a

[0080] Figure 4 The estimated value of the intermediate parameter b

[0081] Figure 5 Angular rate error of HRG before and after compensation Detailed Implementation

[0082] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

[0083] 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.

[0084] 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.

[0085] To demonstrate the feasibility of this invention, a simulation experiment was conducted. During the experiment, HRG and RLG oscillated together, and the applied angular velocity changed over time as follows: Figure 2 As shown in Table 1, the performance parameters of HRG and RLG are set; the virtual rotational angular rate of HRG Ω0 = 3° / s; and it is assumed that due to environmental changes, the azimuth angle θ of the damping axis of HRG will change. τ It changes slowly over time.

[0086] Table 1 Performance parameters of HRG and RLG

[0087]

[0088] 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 (22), where diag represents a diagonal matrix:

[0089] P 0-1 =diag[(1°)] 2 (0.1° / h) 2 (0.1° / h) 2 (0.001° / h 2 ) 2 (0.001°h 2 ) 2 (1° / h) 2 ](twenty two)

[0090] The system noise covariance matrix is ​​set as shown in equation (23):

[0091] Q = diag[(1×10 -10 °) 2 0 0 (5×10 -6 ° / h) 2 (5×10 -6 ° / h) 2 0] (23)

[0092] The observation noise covariance matrix is ​​set as shown in equation (24):

[0093] R = diag[(2×10 -6 °) 2] (twenty four)

[0094] Error calibration is performed using the method proposed in this invention. The estimated values ​​of intermediate parameters a and b during the calibration process are as follows: Figure 3 and Figure 4 As shown, although the true values ​​of a and b change slowly over time, the estimated values ​​fluctuate around the true values, indicating that this method has the ability to calibrate and compensate in real time; the angular rate error of HRG before and after compensation is as follows: Figure 4 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 self-calibration method for a low-precision gyroscope-assisted rate integral hemispherical resonator gyroscope, characterized in that, This method consists of the following steps: S1 mounts the rate integral (HRG) and auxiliary gyroscope on the base, ensuring that the sensitive axes of the two gyroscopes are parallel to each other. Simultaneously, it connects both to the control circuit, causing it to output the following data to the calculation module: The output data of HRG includes: the azimuth angle θ of the harmonic oscillator mode shape at time k. k , represents the angle between the mode shape of the harmonic oscillator at time k and the x-axis electrode in the HRG; The output data of the auxiliary gyroscope includes: the external angular velocity reference at time k. The subscript k indicates the value of the corresponding variable at time k; S2 controls HRG to perform a virtual rotation at a constant rate Ω0; S3: Establish the continuous-time Kalman filter error equation: In 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; Δ(1 / τ) = 1 / τ1 - 1 / τ2 is the anisotropic damping coefficient, where τ1 and τ2 are the decay times of the primary and secondary modes of the harmonic oscillator, respectively; θ is the azimuth angle of the harmonic oscillator mode shape. 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 the auxiliary gyroscope, consider its output external angular velocity reference Ω. ref The true angular velocity Ω and the constant zero bias B ref The sum, ignoring random noise, gives: Oh ref =Ω-B ref (4) From equations (2) and (4), we can obtain: Continuous-time Kalman filter error equation: a′ represents the rate of change of intermediate variable a, and b′ represents the rate of change of intermediate variable b; Further, the continuous-time Kalman filter error equation can be expressed in fractional form: S4 establishes a Kalman filter. S4.1 Define the state vector X of the Kalman filter system at time k. k as follows: X k =[θ k a k b k a′ k b′ k B k ref ] T (8) Among them, a k and b k Let a and b represent the values ​​of intermediate variables a and b at time k, respectively; a′ k and b′ k Let a and b represent the values ​​of their rates of change at time k, respectively. This represents the value of the constant zero bias of the auxiliary gyroscope 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 (10), 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 (7), we know that: In equation (9), U k The control matrix at time k is shown in equation (12): Where u k The value of the continuous-time control matrix u at time k can be obtained from equation (7): u=[G(Ω ref +Ω0) 0 0 0 0 0] T (13) 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 (14), 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 (15) In equation (15), H is the measurement matrix: H＝[1 0 0 0 0 0] (16) In equation (15), R is the observation noise covariance matrix; State quantity estimates at time S4.5 k The calculation formula is as follows: In equation (17), Z k For the observations at time k: WITH k =θ k (18) S4.6 The mean square error matrix P of the state estimation at time k k The calculation formula is as follows: P k =(I-K k H)P k / k-1 (I-K k H) T +K k RK k T ; (19) 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 is a k The estimated value Pick The third element in is b k The estimated value S5.3 If k≥1, compensate for the HRG damping mismatch error: S5.3.1 Calculate the angular increment (ω) of HRG from time k-1 to time k before compensation. HRG ) k : S5.3.2 Calculate the angular increment (ω′) of HRG from time k-1 to time k after compensation. HRG ) k : Use (ω′) HRG ) k As the angular increment output of HRG at time k; S5.4 Let k = k + 1; S5.5 executes S5.2-S5.4 repeatedly until the current measurement is completed, then exits the loop.

2. The low-precision gyroscope-assisted rate integral hemispherical resonator gyroscope self-calibration method 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 1×6 This represents a 1×6 zero matrix.

3. The low-precision gyroscope-assisted rate integral hemispherical resonator gyroscope self-calibration method according to claim 1, characterized in that: Set the state at time k-1 and the one-step prediction mean square error matrix P. k-1 The initial value when 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 low-precision gyroscope-assisted rate integral hemispherical resonator gyroscope self-calibration method 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 low-precision gyroscope-assisted rate integral hemispherical resonator gyroscope self-calibration method 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.

6. The low-precision gyroscope-assisted rate integral hemispherical resonator gyroscope self-calibration method according to any one of claims 1 to 5, characterized in that: The low-precision auxiliary gyroscope is a laser gyroscope, fiber optic gyroscope, or micromechanical gyroscope, and the gyroscope itself does not have damping mismatch error.

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