CN115435768A - Hemispherical resonant gyroscope temperature modeling compensation method based on real-time sliding window - Google Patents
Hemispherical resonant gyroscope temperature modeling compensation method based on real-time sliding window Download PDFInfo
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Abstract
The invention provides a hemispherical resonator gyro temperature modeling compensation method based on a real-time sliding window, which comprises the following steps: step 1: acquiring 431# hemispherical resonant gyroscope output signal data; 2: analyzing and selecting independent variables based on multiple output characteristics of the gyroscope; 3: intercepting data by using a real-time sliding window, establishing a prediction model based on data in the window, and predicting the output value of the gyroscope at the next moment; 4: sliding the time window forward by one step, judging whether the newly-entered window data is normal data, if not, replacing the newly-entered window data with a predicted value, and then establishing a prediction model; if the new window data are normal data, a prediction model is directly established based on the data in the window; 5: calculating the sensitive angular velocity of the 431# hemispherical resonant gyroscope based on the prediction data; 6: and (3) verifying the temperature modeling compensation method of the real-time sliding window by taking the zero-bias stability of the gyroscope as a standard.
Description
Technical Field
The invention belongs to the technical field of inertial instruments, and particularly relates to a hemispherical resonant gyroscope temperature modeling compensation method based on a real-time sliding window.
Background
A Hemispherical Resonator Gyro (HRG) is a high-precision Gyro with inertial navigation level performance in a coriolis type vibration Gyro, and the random drift can reach 10 °/hr level and the service life is as long as 15 years. The method has the advantages of high measurement precision, high stability, high reliability, long service life and the like, and has wide application prospect in the fields of aviation, aerospace, missile weapons and the like.
However, due to the limitation of the current production process, the output of the hemispherical resonator gyroscope has the following problems: (1) The repeatability is poor, namely the correlation between the gyroscope output and the state of the gyroscope during starting is large, but the output regularity of the gyroscope started for multiple times is poor; (2) After the gyroscope is started, the internal temperature of the gyroscope has certain amplitude change due to circuit work and harmonic oscillator vibration, and accordingly the measurement precision of the gyroscope is reduced.
In order to improve the measurement accuracy of the hemispherical resonant gyroscope, how to reduce the influence of temperature change on the hemispherical resonant gyroscope is a problem to be solved urgently at present.
Disclosure of Invention
Aiming at the existing problems, the defect of poor output repeatability of the hemispherical resonator gyroscope is considered, the real-time sliding window temperature compensation model with output characteristic self-adaptability is established, the model is essentially a time-varying polynomial compensation model, and a fitting model can be adaptively changed according to the change of the gyroscope output, so that the prediction model can track the change characteristics of the gyroscope output in real time, and a better temperature compensation effect is achieved.
The core thought of the invention is as follows: intercepting gyroscope output data by using a time window, fitting the input and output relation in the time window, and predicting gyroscope output at the next moment based on a fitting model; the time window slides forward by one step, the gyro output at the next moment is brought into the time window, whether the gyro output is a normal value or not is judged, if not, a predicted value is used for replacing the abnormal output, and if so, the measured value is directly brought into the time window; fitting a gyro measurement angular velocity to every 2500 (corresponding to 100 s) data based on a predicted value and a least square method; and subtracting the predicted value from the real value of the angle of the rotary table frame to obtain the prediction error of the angle of the rotary table frame, and calculating the rotation angle measurement error of the gyroscope and the zero offset stability of the gyroscope according to the prediction error.
The technical solution for realizing the purpose of the invention is as follows:
a hemispherical resonator gyro temperature modeling compensation method based on a real-time sliding window is characterized by comprising the following steps:
step 1: collecting a plurality of groups of test output signal data of the hemispherical resonator gyroscope;
step 2: analyzing and selecting independent variables of a gyro temperature error model based on the output signals of the hemispherical resonant gyro and the shape characteristics of a two-dimensional plane of the resonant frequency;
and step 3: according to the selected independent variable, using a real-time sliding window to intercept data, establishing a prediction model based on the data in the time window, and predicting the frame angle of the rotary table at the next moment;
and 4, step 4: sliding the time window forward by one step, judging whether the newly entered window data is normal data, if not, replacing the newly entered window data with a predicted value, and then establishing a prediction model; if the new window data are normal data, a prediction model is directly established based on the data in the current time window;
and 5: calculating the sensitive angular velocity of the hemispherical resonator gyro based on the prediction data;
and 6: and (5) verifying the compensation effect by taking the zero-bias stability of the gyroscope as a standard.
Further, the specific operation steps of step 1 include:
step 1.1: installing a hemispherical resonance gyroscope on a rotary table loop of an inertia platform, wherein a gyroscope input shaft is installed in a vertical direction, a gyroscope output shaft and the other shaft are installed in a horizontal direction and in the same horizontal plane, and a stable loop of the inertia platform is not electrified to work;
step 1.2: setting the sampling frequency to be 0.04Hz, and collecting the rotation angle of the frame of the rotary table, the standing wave angle of the gyroscope and the resonant frequency of the gyroscope at the moment of electrification of the gyroscope;
step 1.3: and (3) repeatedly executing the steps 1.1-1.2 for 6 times to perform 6 groups of tests, wherein the interval between the two tests is at least 24h, the data acquisition time of a single test is at least 6h, and finally 6 groups of test data are obtained, and each group of test data comprises a rotating platform frame angle, a gyro standing wave angle and a gyro resonance frequency.
Further, the specific operation steps of step 2 include:
step 2.1: obtaining a rotating table frame angle-resonant frequency diagram of 6 groups of experiments by taking the resonant frequency f as an independent variable and the rotating table frame angle y as a dependent variable;
step 2.2: determining the independent variable of a gyro temperature error model according to the shape of a turntable frame angle-resonance frequency diagram as
Where Δ f is the resonant frequency gradient.
Further, the specific operation steps of step 3 include:
step 3.1: using a time window with the length of 10 to intercept the rotation angle of the rotary table frame and the resonance frequency of the gyroscope, and calculating the independent variable based on the resonance frequency
Step 3.2: rotating the corner y and independent variable of the rotary table frame by using a second-order model based on data in a time window
The relation between the two is regressed to obtain a regression relation formula as follows:
in the formula: a is 1 、a 2 、a 3 Is a coefficient of a first order term 11 Is a coefficient of a quadratic term 12 、a 13 Is the coupling term coefficient;
step 3.3: predicting a rotary table frame angle y (t + 1) at the next moment based on the formula (1) and a resonant frequency f (t + 1) acquired at the next moment, wherein the rotary table frame angle at the next moment is obtained as follows:
in the formula:
is the corner of the rotating platform frame at the next moment.
Further, the specific operation steps of step 4 include:
step 4.1: sliding the time window forward for 1 step to enable the angle y (t + 1) of the rotary table frame at the next moment to be included in the current time window;
step 4.2: setting a gyro output variation threshold value delta y, taking y (t + 1) as abnormal output when y (t + 1) -y (t) is more than or equal to delta y, and using a predicted value at the moment
Replacing y (t + 1), returning to the step 3 for fitting and predicting, and outputting a predicted value; and when y (t + 1) -y (t) < delta y, taking y (t + 1) as normal output, directly returning to the step 3 for fitting and prediction, and outputting a predicted value.
Further, the specific operation steps of step 5 include:
based on the predicted value obtained in the step 4.2, performing first-order linear fitting on every 2500 data, and fitting by using a least square method, wherein the obtained fitting slope is the angular velocity sensitive to the gyroscope:
Ω＝(X T X) -1 XY (3)
in the formula: omega is the output angular velocity of the gyroscope obtained by fitting,
is a matrix constructed from the sampling times,
is a matrix constructed from the predicted values of the gantry frame angles.
Further, the specific operation steps of step 6 include:
step 6.1: subtracting the predicted value from the actually acquired output value of the frame angle of the rotary table to obtain a prediction error of the frame angle of the rotary table;
step 6.2: obtaining a gyro measurement angular velocity error corresponding to the prediction error according to the formula (3);
step 6.3: calculating a standard deviation for each 36 angular velocity errors by using a time window with the length of 36 and the step length of 1 to obtain the zero-offset stability of the gyroscope at the moment;
step 6.4: sliding the time window forward for 1 step, and repeating the step 6.3 and the step 6.4 until all data are calculated, so as to obtain a zero offset stability change rule of the hemispherical resonator gyroscope;
step 6.5: and comparing the zero offset stability change rule of the obtained hemispherical resonator gyroscope with the zero offset stability change rule obtained by a polynomial-based compensation method, and verifying the compensation effect.
Compared with the prior art, the method has the following beneficial effects:
the invention adopts a real-time sliding window temperature modeling compensation method, and the method can adaptively track the continuously changing output rule of the gyroscope, thereby realizing high-precision prediction and compensation of gyroscope output. Firstly, intercepting data by using a time window with the length of 10, carrying out input-output model regression based on the data in the window, and predicting the gyro output at the next moment based on the regression model; then, the time window slides forward by one step, if the output value at the next moment is a normal value, the time window is directly included in the time window, if the output value is an abnormal value, the abnormal value is replaced by a predicted value, and the replaced predicted value is included in the time window; model regression and prediction are performed based on the data within the time window, and the forward rolling is performed until the gyro is powered off. The temperature compensation model based on the real-time sliding window is a time-varying polynomial model in nature, and can adaptively track the system output rule changing in real time, so that the measurement precision of the hemispherical resonant gyroscope is effectively improved.
Drawings
FIG. 1 is a flow chart of a real-time sliding window based temperature modeling compensation method;
FIG. 2 is a schematic view of a hemispherical resonator gyroscope installation;
FIGS. 3 (a) - (f) are graphs showing the variation of the angle of the frame of 6 sets of the turret versus the resonant frequency;
FIGS. 4 (a) - (f) are diagrams of compensated gyro measured angular velocities;
fig. 5 (a) - (f) show compensated gyro zero bias stability.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the following further describes the technical solution of the present invention with reference to the drawings and the embodiments.
The invention provides a hemispherical resonant gyroscope temperature modeling compensation method based on a real-time sliding window, the working process of which is shown as the attached figure 1, and the method specifically comprises the following steps:
step 1: collecting gyro output signal data
Step 1.1: installing a No. 431 gyroscope on a turntable loop of an inertial platform, wherein a stable loop of the inertial platform is not electrified to work; wherein the gyro input shaft is mounted in the vertical direction for sensing the vertical component of the local ground speed, and the gyro output shaft and the other shaft are mounted in the horizontal plane, as shown in fig. 2;
step 1.2: setting the sampling frequency to be 0.04Hz, and starting to acquire data at the moment of electrification of the gyroscope, wherein the acquisition parameters comprise the rotation angle of a rotary table frame, the standing wave angle of the gyroscope and the resonant frequency of the gyroscope;
step 1.3: and 6 times of tests are carried out according to the gyro mounting and data acquisition method, each test is at least 24h apart, and the data acquisition time of a single test is at least 6h. Analysis of the raw data shows that: (1) The gyro has an output drifting process in a starting stage, which is caused by temperature change caused by starting the gyro; and (2) the output of the gyroscope has a 'burr' phenomenon.
Step 2: analysis and selection of independent variable based on multiple output characteristics of 431# gyroscope
Step 2.1: according to the published prior art, the hemispherical resonant gyroscope has extremely strong linear relationship between the internal temperature T and the resonant frequency f, so that the resonant frequency f is used for replacing the temperature T as a basic independent variable to establish a gyroscope temperature error model;
step 2.2: by taking the resonant frequency as an independent variable and the angle of the rotating table frame as a dependent variable, drawing a graph of the angle y-the resonant frequency f of the rotating table frame of 6 groups of experiments, as shown in the attached figure 3;
step 2.3: analyzing 6 groups of corner-resonance frequency graphs of the rotating platform frame can know that: (1) The repeatability of 6 times of output is poor, which means that a unified turntable corner-resonant frequency model is difficult to establish; (2) The input and output relation of the gyroscope is time-varying, and a time-invariant model is difficult to use to obtain a good compensation effect; (3) A one-to-many mapping relation exists between the rotation angle y of the rotary table and the resonant frequency f, so that the mapping relation between the rotation angle y of the rotary table and the resonant frequency f cannot be established by only depending on one variable of the resonant frequency; (4) In addition to the graph (b), there are regions of "opposite sign" shape in the remaining graphs, and therefore it is considered that
As an independent variable; (5) Based on the resonance frequency f, the difference quantity Δ f may also be considered as an argument. Combining the above analysis, the final selected temperature model independent variable is
And the method is used for constructing a new gyro temperature error model.
And 3, step 3: the method comprises the following specific operation steps of intercepting data by using a real-time sliding window, establishing a prediction model based on data in the window, and predicting the output value of a gyroscope at the next moment:
step 3.1: using a time window with the length of 10 to intercept the rotation angle of the rotary table frame and the resonance frequency of the gyroscope, and calculating the independent variable based on the resonance frequency
Step 3.2: rotating the corner y and independent variable of the rotary table frame by using a second-order model based on data in a time window
The relationship between the two is regressed to obtain a new gyro temperature error model:
in the formula: a is 1 、a 2 、a 3 Is a coefficient of a first order term 11 Is a coefficient of a quadratic term 12 、a 13 Is the coupling term coefficient.
Step 3.3: predicting the angle y (t + 1) of the rotary table frame at the next moment based on the model obtained by fitting in the step 3.2 and the resonance frequency f (t + 1) acquired at the next moment, wherein the prediction is as follows:
in the formula:
is the corner of the rotating platform frame at the next moment.
And 4, step 4: sliding the time window forward by one step, judging whether the newly-entered window data is normal data, if not, replacing the newly-entered window data with a predicted value, and then establishing a prediction model; if the new window data are normal data, a prediction model is directly established based on the data in the window, and the method comprises the following specific steps:
step 4.1: sliding the time window forwards for 1 step, and bringing the angle y (t + 1) of the rotary table frame at the next moment into the time window;
step 4.2: considering that the output of the 431# hemispherical resonator gyro has a burr problem, whether the output of the gyro is abnormal or not needs to be judged. Setting a gyro output variation threshold value delta y =0.01, regarding y (t + 1) as abnormal output when y (t + 1) -y (t) ≧ delta y, and using the method
Replacing y (t + 1), then returning to the step 3, and carrying out fitting and prediction according to the formulas (1) - (2); and when y (t + 1) -y (t) < delta y, regarding y (t + 1) as a normal output, and directly returning to the step 3 for fitting and prediction.
And 5: based on the prediction data, calculating the sensitive angular speed of the 431# hemispherical resonant gyro, which comprises the following specific steps:
based on the predicted data, performing first-order linear fitting on 2500 data (namely 100 s), wherein the fitting slope is the sensitive angular velocity of the gyroscope, and the fitting slope is obtained by using a least square method as follows:
Ω＝(X T X) -1 XY (3)
in the formula: omega is the output angular velocity of the gyroscope obtained by fitting,
is a matrix constructed from the sampling times,
is a matrix constructed from the predicted values of the turret frame angles.
Step 6: the method for verifying the temperature modeling compensation of the real-time sliding window by taking the zero-offset stability of the gyroscope as a standard comprises the following specific steps:
step 6.1: subtracting the predicted value from the output value of the angle of the rotary table frame to obtain the predicted error of the angle of the rotary table frame;
step 6.2: obtaining a gyro measurement angular velocity error corresponding to the prediction error according to the least square method in the step 5, as shown in fig. 4;
step 6.3: calculating a standard deviation according to a root mean square error formula in the prior art by using a time window with the length of 36 and the step length of 1 and every 36 (corresponding to 1h data) angular speed errors in a windowing manner to obtain the gyro zero-offset stability at the moment;
step 6.4: the time window slides forwards for 1 datum, the step 6.3 and the step 6.4 are repeated until all the data are calculated, the zero offset stability of the gyro at each moment is obtained, a graph 5 is drawn according to the zero offset stability, and the change rule of the zero offset stability of the 431# hemispherical resonant gyro can be obtained according to the graph 5: the smaller the zero offset stability is, the higher the gyro measurement precision is. In the field of gyros, zero bias stability is an extremely important index for evaluating the measurement accuracy of the gyros. And the zero-bias stability is used for subsequent gyro measurement precision evaluation.
Examples
To further verify the effect of the system, the comparison result obtained by comparing the method of the present invention with the compensation method based on polynomial equation is shown in fig. 5. From the compensation effect given in fig. 5, after the temperature modeling compensation based on the real-time sliding window, the gyro zero-offset stability can be rapidly converged to the range of 10-3, and the compensation precision is far higher than that of the compensation method based on the polynomial, because the real-time sliding window method can track the change of the gyro output characteristic in real time, and the polynomial is a fixed and time-invariant model and is difficult to adapt to the real-time changing gyro output characteristic. Therefore, the temperature modeling compensation method based on the real-time sliding window has higher precision.
Those not described in detail in this specification are within the skill of the art. Although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that various changes in the embodiments and modifications of the invention can be made, and equivalents of some features of the invention can be substituted, and any changes, equivalents, improvements and the like, which fall within the spirit and principle of the invention, are intended to be included within the scope of the invention.
Claims (7)
1. A hemispherical resonator gyro temperature modeling compensation method based on a real-time sliding window is characterized by comprising the following steps:
step 1: collecting a plurality of groups of test output signal data of the hemispherical resonator gyroscope;
step 2: analyzing and selecting independent variables of a gyro temperature error model based on the output signals of the hemispherical resonant gyro and the shape characteristics of a two-dimensional plane of the resonant frequency;
and step 3: intercepting data by using a real-time sliding window according to the selected independent variable, establishing a prediction model based on the data in the time window, and predicting the frame angle of the rotary table at the next moment;
and 4, step 4: sliding the time window forward by one step, judging whether the newly entered window data is normal data, if not, replacing the newly entered window data with a predicted value, and then establishing a prediction model; if the new window data are normal data, a prediction model is directly established based on the data in the current time window;
and 5: calculating the sensitive angular velocity of the hemispherical resonator gyroscope based on the prediction data;
step 6: and (5) verifying the compensation effect by taking the zero-bias stability of the gyroscope as a standard.
2. The real-time sliding window based hemispherical resonator gyroscope temperature modeling compensation method according to claim 1, wherein the specific operation steps of step 1 comprise:
step 1.1: installing a hemispherical resonance gyroscope on a rotary table loop of an inertia platform, wherein a gyroscope input shaft is installed in a vertical direction, a gyroscope output shaft and the other shaft are installed in a horizontal direction and in the same horizontal plane, and a stable loop of the inertia platform is not electrified to work;
step 1.2: setting the sampling frequency to be 0.04Hz, and collecting the rotation angle of the frame of the rotary table, the standing wave angle of the gyroscope and the resonant frequency of the gyroscope at the electrification moment of the gyroscope;
step 1.3: and (3) repeatedly executing the steps 1.1-1.2 for 6 times to perform 6 groups of tests, wherein the interval between the two tests is at least 24h, the data acquisition time of a single test is at least 6h, and finally 6 groups of test data are obtained, and each group of test data comprises a rotating platform frame angle, a gyro standing wave angle and a gyro resonance frequency.
3. The real-time sliding window based hemispherical resonator gyroscope temperature modeling compensation method according to claim 1, wherein the specific operation steps of step 2 comprise:
step 2.1: obtaining a rotating table frame angle-resonant frequency diagram of 6 groups of experiments by taking the resonant frequency f as an independent variable and the rotating table frame angle y as a dependent variable;
step 2.2: determining the independent variable of a gyro temperature error model according to the shape of a turntable frame angle-resonance frequency diagram as
Where Δ f is the resonant frequency gradient.
4. The real-time sliding window based hemispherical resonator gyroscope temperature modeling compensation method according to claim 1, wherein the specific operation steps of step 3 include:
step 3.1: using a time window with the length of 10 to intercept the rotation angle of the rotary table frame and the resonance frequency of the gyroscope, and calculating the independent variable based on the resonance frequency
Step 3.2: rotating the corner y and independent variable of the rotary table frame by using a second-order model based on data in a time window
The relation between the two is regressed to obtain a regression relation formula as follows:
in the formula: a is 1 、a 2 、a 3 Is a coefficient of a first order term 11 Is a coefficient of a quadratic term 12 、a 13 Is the coupling term coefficient;
step 3.3: predicting the angle y (t + 1) of the rotary table frame at the next moment based on the formula (1) and the resonance frequency f (t + 1) acquired at the next moment, and acquiring the angle of the rotary table frame at the next moment as follows:
in the formula:
is the corner of the rotating platform frame at the next moment.
5. The real-time sliding window based hemispherical resonator gyroscope temperature modeling compensation method according to claim 2, characterized in that the specific operation steps of step 4 include:
step 4.1: sliding the time window forward for 1 step to enable the angle y (t + 1) of the rotary table frame at the next moment to be contained in the current time window;
and 4.2: setting a gyro output variation threshold value delta y, taking y (t + 1) as abnormal output when y (t + 1) -y (t) is more than or equal to delta y, and using a predicted value at the moment
Replacing y (t + 1), returning to the step 3 for fitting and predicting, and outputting a predicted value; and when y (t + 1) -y (t) < delta y, taking y (t + 1) as normal output, directly returning to the step 3 for fitting and prediction, and outputting a predicted value.
6. The real-time sliding window based hemispherical resonator gyroscope temperature modeling compensation method according to claim 5, characterized in that, the specific operation steps of step 5 include:
based on the predicted value obtained in the step 4.2, performing first-order linear fitting on every 2500 data, and fitting by using a least square method, wherein the obtained fitting slope is the angular velocity sensitive to the gyroscope:
Ω＝(X T X) -1 XY (3)
in the formula: omega is the output angular velocity of the gyroscope obtained by fitting,
is a matrix constructed from the sampling times,
is a matrix constructed from the predicted values of the turret frame angles.
7. The real-time sliding window based hemispherical resonator gyroscope temperature modeling compensation method according to claim 6, wherein the specific operation steps of step 6 include:
step 6.1: subtracting the predicted value from the actually acquired output value of the frame angle of the rotary table to obtain a prediction error of the frame angle of the rotary table;
step 6.2: obtaining a gyro measurement angular velocity error corresponding to the prediction error according to the formula (3);
step 6.3: calculating a standard deviation for each 36 angular velocity errors by using a time window with the length of 36 and the step length of 1 to obtain the zero offset stability of the gyroscope at the moment;
step 6.4: sliding the time window forward for 1 step, and repeating the step 6.3 and the step 6.4 until all data are calculated, so as to obtain a zero offset stability change rule of the hemispherical resonator gyroscope;
step 6.5: and comparing the zero offset stability change rule of the obtained hemispherical resonator gyroscope with the zero offset stability change rule obtained by a polynomial-based compensation method, and verifying the compensation effect.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116608890A (en) * | 2023-07-21 | 2023-08-18 | 中国船舶集团有限公司第七〇七研究所 | Scale error compensation method of full-angle mode hemispherical resonator gyroscope |
| CN117109566A (en) * | 2023-08-23 | 2023-11-24 | 长春航盛艾思科电子有限公司 | IMU temperature compensation method based on piecewise polynomial fitting |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116608890A (en) * | 2023-07-21 | 2023-08-18 | 中国船舶集团有限公司第七〇七研究所 | Scale error compensation method of full-angle mode hemispherical resonator gyroscope |
| CN116608890B (en) * | 2023-07-21 | 2023-10-13 | 中国船舶集团有限公司第七〇七研究所 | Scale error compensation method of full-angle mode hemispherical resonator gyroscope |
| CN117109566A (en) * | 2023-08-23 | 2023-11-24 | 长春航盛艾思科电子有限公司 | IMU temperature compensation method based on piecewise polynomial fitting |
| CN117109566B (en) * | 2023-08-23 | 2024-01-23 | 长春航盛艾思科电子有限公司 | IMU temperature compensation method based on piecewise polynomial fitting |
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