Quartz flexible acceleration scale factor compensation method based on inverse proportional function model

Abstract

The invention provides a quartz flexible acceleration scale factor compensation method based on an inverse proportional function model, and the method comprises the steps: carrying out a test through employing a quartz flexible accelerometer, and obtaining an accurate scale factor and an accurate pulse number in each test; establishing an inverse proportion function model between the scale factor and the pulse number; establishing a cost function according to the inverse proportional function, substituting the accurate scale factor and pulse number obtained by the test, fitting an inverse proportional function model coefficient, and calculating a compensated scale factor based on the fitted inverse proportional function model coefficient and the pulse number measured in real time; and calculating zero offset based on the pulse number during zero acceleration input and the compensated scale factor, and substituting the compensated scale factor into an acceleration measurement formula to obtain an acceleration measurement formula after scale factor compensation in the task. According to the method, the measurement precision of the quartz flexible accelerometer can be remarkably improved, software engineering is easy and efficient to implement, and flexibility is high.

Description

Technical Field

[0001] The invention relates to a quartz flexible acceleration scale factor compensation method based on an inverse proportional function model, and belongs to the field of spacecraft navigation, guidance and control. Background Art

[0002] The main purpose of the quartz flexible accelerometer of the spacecraft GNC subsystem is to provide acceleration measurement information for the spacecraft platform. It is suitable for spacecraft with high-precision autonomous orbit control mission requirements (such as autonomous orbit transfer, game pursuit). The accelerometer circuit box converts the accelerometer output current signal into a pulse signal. After the host computer collects the accelerometer pulse signal, it calculates the acceleration measurement value based on the pulse signal, scale factor, zero bias, etc.:

[0003]

[0004] Where g0 = 9.8015 m / s 2 , |g0|=9.8015 dimensionless, G m Indicates the acceleration measurement output (unit: m / s 2 ), N is the number of pulses (unit ^), G0 is the accelerometer zero bias (unit g0), K is the scale factor (unit ^ / (s·g0)), and ΔT is the sampling period (unit s).

[0005] The output measurement accuracy of the quartz flexible accelerometer is mainly affected by factors such as temperature, scale factor, and zero bias. Even if the accelerometer has been calibrated on the ground, if it is not adjusted and suppressed in real time during use, it will seriously affect the orbit control accuracy. Therefore, it is necessary to design a real-time compensation algorithm. When the accelerometer cannot be accurately calibrated for each input acceleration value, the scale factor and zero bias of the accelerometer can be adjusted in real time using the limited calibrated accelerometer test data to reduce the measurement error of the accelerometer.

[0006] The published literature mainly considers the influence of environmental factors such as temperature and air pressure on the scale factor, and few literature considers the nonlinear relationship between the scale factor and the number of pulses of the accelerometer. In 2015, the paper "Research on the Calibration Algorithm of the Full-Scale Scale Factor Asymmetry of Accelerometer (Volume 2, Issue 1)" published in "Navigation Positioning and Timing" proposed a third-order polynomial model and its least squares calibration algorithm for the full-scale asymmetry problem of the scale factor; the patent "Deep neural network-based inertial measurement unit (IMU) sensor compensation method" (US20200311514A1) published in 2020 adopts an IMU compensation method based on a deep neural network. The model is complex and consumes a lot of computing resources. For the scale factor compensation measures of quartz flexible accelerometers, there are two relatively simple compensation methods: binary method and partition interpolation method. The binary method of the scale factor considers the scale factor to be two constant values ​​when the acceleration G>0 and G<0, but its disadvantage is low precision. The partition interpolation method can adapt to the changes in the number of pulses N in different intervals, but its disadvantage is that it occupies more onboard control computer resources. Summary of the invention

[0007] The technical problem solved by the present invention is: to overcome the deficiencies of the prior art and provide a quartz flexible acceleration scale factor compensation method based on an inverse proportional function model, so that the measurement accuracy of the accelerometer is improved and less control computer resources are occupied.

[0008] The technical solution of the present invention is: a quartz flexible acceleration scale factor compensation method based on an inverse proportional function model, comprising:

[0009] The test was carried out using a quartz flexible accelerometer to obtain the accurate scale factor and number of pulses in each test;

[0010] Considering the relationship between the scale factor and the pulse number of the quartz flexible accelerometer, an inverse proportional function model between the scale factor and the pulse number is established;

[0011] A cost function is established based on the inverse proportional function model, and the accurate scale factor and pulse number obtained from the quartz flexible accelerometer test are introduced to fit the model coefficient of the inverse proportional function to obtain the fitted inverse proportional function model;

[0012] Based on the pulse number at zero acceleration input and using the fitted inverse proportional function model, the scale factor after compensation at zero acceleration is calculated, and the zero bias is further calculated;

[0013] The compensated scale factor is calculated based on the real-time measured pulse number and by using the fitted inverse proportional function model; the compensated scale factor and zero bias are substituted into the acceleration measurement formula to obtain the acceleration measurement formula of the quartz flexible accelerometer after the scale factor is compensated in real-time measurement.

[0014] Preferably, the inverse proportional function model is:

[0015]

[0016] Where A, B, C are the inverse function model coefficients, K represents the scale factor, and N represents the number of pulses.

[0017] Preferably, when fitting the model coefficients of the inverse proportional function model, two situations, that is, the real acceleration is greater than 0 and that is less than 0, are considered, and the inverse proportional function model coefficients A, B, and C in the inverse proportional function model are fitted respectively.

[0018] Preferably, the cost function is specifically:

[0019]

[0020] Where is the cost value, K i is the scale factor in the quartz flexible accelerometer test, N i is the number of pulses in the quartz flexible accelerometer test, A, B, and C are the model coefficients of the inverse proportional function, i represents the number of tests, and n represents the total number of tests in which the input true acceleration is greater than or less than 0.

[0021] Preferably, the method for fitting the model coefficients A, B, C of the inverse proportional function model is:

[0022] Use the modified gradient descent method to iteratively update the values ​​of A, B, and C, and bring them into the cost function E = E (A, B, C, N i ,K i ) calculation, the iteration end condition is E <E end , E end is the index requirement, and i represents the number of tests.

[0023] Preferably, the modified gradient descent method is used to fit the inverse proportional function model coefficients A, B, and C. The specific method is:

[0024]

[0025] Where j = 1, 2, 3, ..., m, m represents the total number of iterations, 0 ≤ β < α < 1;

[0026]

[0027]

[0028] Among them, A j-1 , B j-1 , and C j-1 represent the coefficients of the inverse proportional function model obtained in the (j - 1)-th iteration, and E represents the cost function in the current iteration.

[0029] Preferably, the method for determining the initial value in the first iteration is as follows:

[0030]

[0031] Among them, A0, B0, and C0 represent the initial values of the given coefficients of the inverse proportional function model, and E represents the cost function in the current iteration.

[0032] Preferably, the initial value X0 of the coefficients of the inverse proportional function model is selected as follows:

[0033] Take

[0034] If K1 < A0, take Conversely, take

[0035] If N1 < 0, then C0 < 0, conversely C0 > 0;

[0036] Among them, K i is the scale factor in the test of the quartz flexure accelerometer, N i is the number of pulses in the test of the quartz flexure accelerometer, i represents the test number, i = 1, 2, 3,..., n, and n represents the total number of tests where the input true acceleration is greater than 0 or less than 0.

[0037] Preferably, the method for calculating the zero offset based on the number of pulses at zero acceleration input and the compensated scale factor is specifically as follows:

[0038] When the input true acceleration is 0, directly obtain the number of pulses N0 at this time from the reading of the quartz flexure accelerometer, and then combine the compensated scale factor calculated from the parameters of the inverse proportional function model corresponding to when the true acceleration is greater than 0 and the compensated scale factor calculated from the parameters of the inverse proportional function model corresponding to when the true acceleration is less than 0 to calculate the zero offset G0, and the formula is:

[0039]

[0040] In the formula, A + , B + , C + are the coefficients of the inverse proportional function model obtained by fitting the number of pulses and the scale factor when the input true acceleration is greater than 0, A- ,B - ,C - It is the inverse proportional function model coefficient obtained by fitting the pulse number and scale factor when the input true acceleration is less than 0.

[0041] Preferably, the measurement formula after scale factor compensation is:

[0042]

[0043] Where N0 represents the number of pulses when the input real acceleration is G=0, G0 is the zero bias, ΔT represents the sampling period, g0=9.8015m / s 2 , |g0|=9.8015 dimensionless, N represents the number of pulses, K + and K - The calculation method is:

[0044]

[0045] K + Indicates the scale factor after real-time compensation based on the real-time measured pulse number N and the fitted inverse proportional function when the real acceleration is greater than 0, K - It indicates the scale factor after real-time compensation based on the real-time measured pulse number N and the fitted inverse proportional function when the real acceleration is less than 0.

[0046] Compared with the prior art, the present invention has the following advantages:

[0047] (1) The present invention considers the influence of input acceleration on the scale factor, introduces an inverse proportional function model and a modified gradient descent algorithm, and effectively improves the measurement accuracy of the quartz flexible accelerometer compared with the binary method;

[0048] (2) Compared with the partition interpolation method, the control computer of the present invention no longer needs to bind a large number of prior values ​​of the scale factor, which makes the software implementation simple. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a flow chart of the scale factor compensation method of the quartz flexible accelerometer of the present invention;

[0050] Figure 2 It is a flow chart of the modified gradient descent algorithm of the present invention;

[0051] Figure 3 NK curve of the test sample of the embodiment of the present invention;

[0052] Figure 4 NK fitting curve of the test sample of the embodiment of the present invention. DETAILED DESCRIPTION

[0053] The present invention proposes a quartz flexible accelerometer scale factor compensation method based on an inverse proportional function model. The implementation process is as follows: Figure 1 The implementation of this method requires at least a quartz flexible accelerometer and a control computer in the loop. The quartz flexible accelerometer is sensitive to acceleration signals and outputs pulse signals, and the control computer collects the pulse signals and calculates acceleration measurement data based on the pulse signals.

[0054] The specific implementation steps are as follows:

[0055] (1)Reference Figure 1 Data collection can be obtained through ground tests, and the real acceleration G needs to be collected and input. i >0 and G i <0Data in both cases{N i , K i}, where i represents the number of trials (i = 1, 2, 3, ..., k), k represents the total number of trials, N i represents the number of pulses in the ith trial, K i represents the scale factor in the i-th trial. Then the sample data is divided into two groups, {N p , K p} and {N q , K q}, where {N p , K p} is the input real acceleration G p >0(p=1,2,3,…,n p ) when the sample data is obtained, N p G p The corresponding number of pulses, K p G p The corresponding scaling factor, {N q , K q} is the input real acceleration G q <0(q=1,2,3,…,n q ) when the sample data is obtained, N q G q The corresponding number of pulses, K q G q The corresponding scaling factor, n p +n q =k.

[0056] (2) Considering the relationship between the scale factor of the quartz flexible accelerometer and the output of the accelerometer, an inverse proportional function model between the scale factor K and the number of pulses N is established:

[0057]

[0058] Where A, B, C are the inverse function model coefficients, K represents the scale factor, and N represents the number of pulses. Based on the experimental data of step (1) {N p , K p} and {N q , K q}, and further establish the piecewise inverse proportional function model:

[0059]

[0060] Among them, A + ,B + ,C + Indicates the test data to be used {N p , K p}The inverse proportional function model coefficient obtained by fitting, A - ,B - ,C - Indicates the test data to be used {N q , K q}The coefficients of the inverse proportional function model fitted.

[0061] The coefficient A obtained by fitting - ,B - ,C - ,A + ,B + ,C + Substitute the inverse proportional function model of step (2) into the real-time measured pulse number N, and calculate the scale factor K after real-time compensation in different situations. + , K - , specifically:

[0062]

[0063] (3) The model coefficients A, B, and C of the inverse proportional function model are fitted by the modified gradient descent method to obtain the relationship between the scaling factor K and the number of pulses N.

[0064] The specific method is as follows:

[0065] Define the cost function Iteratively update A using modified gradient descent + ,B + ,C + After each iteration, it is brought into the cost function to calculate the cost value E + The iteration end condition is E + <E end1 , E end1 For indicator requirements.

[0066] Define the cost function Iteratively update A using modified gradient descent- , B - , C - The value of, which is substituted into the cost function after each iteration to calculate the cost value E - , and the iteration end condition is E - < E end2 , E end2 is the index requirement.

[0067] The modified gradient descent method is as Figure 2 shown, and the specific iteration formula is as follows:

[0068] X1 = X0 - αY + βM -1 Y

[0069]

[0070] where j = 1, 2, 3,..., m, m represents the total number of iterations, and 0 ≤ β < α < 1 are constant coefficients;

[0071]

[0072] Among them, A j-1 , B j-1 and C j-1 represent the coefficients of the inverse proportional function model obtained in the (j - 1)-th iteration, and E represents the coefficients A j-1 , B j-1 and C j-1 of the inverse proportional function model to be iteratively updated after the j-th iteration, which are substituted into to calculate the obtained cost value, where n = n p or n q .

[0073] In the initial state:

[0074]

[0075] 0 ≤ β < α < 1 are constant coefficients. When the correction factor β = 0, the above formula degenerates into the gradient descent algorithm.

[0076] The initial value X0 is selected as follows: Take If K1 < A0, take Otherwise, take B0 = 1ni = 1nKi - A0Ni; if N1 < 0, take C0 < 0, otherwise take C0 > 0.

[0077] In the modified gradient descent method, when fitting A - , B - , C - , take E = E - , n = n q ; when fitting A + , B+ ,C + When E=E + , n=n p .

[0078] (4) When the input real acceleration G = 0, the pulse number N0 when G = 0 can be directly obtained from the reading of the quartz flexible accelerometer, and then the compensated scale factor is calculated by combining the corresponding inverse proportional function model parameters when the real acceleration is greater than 0 And the compensated scale factor calculated by the inverse proportional function model parameters when the true acceleration is less than 0 Calculate the zero bias G0:

[0079]

[0080] in:

[0081]

[0082] Based on the inverse proportional function model obtained in step (2), the spacecraft performs real-time compensation of the accelerometer scale factor when performing autonomous orbit control missions on orbit. The compensation formula is as follows:

[0083]

[0084] Where N0 represents the number of pulses when the input real acceleration is G=0, G0 is the zero bias, ΔT represents the sampling period (unit s), g0=9.8015m / s 2 , |g0|=9.8015 dimensionless, N represents the number of pulses measured in real time (unit ^), K + and K - It represents the real-time compensated scale factor based on the real-time measured pulse number N:

[0085]

[0086] Example:

[0087] For a quartz flexible accelerometer, n=14 tests were conducted, and the NK curve of the test sample is as follows: Figure 3 As shown. The test samples are grouped, where n p =n q =7. Use the implementation step (2) to establish the inverse proportional function model, and use the implementation step (3) to respectively + ,B + ,C + and A - ,B - ,C - Perform curve fitting. p >0 when the test data (N p , Kp ), the initial values ​​A0=93785.96,B0=-28123.01,C0=100, take E end1 =910, α=0.003, β=0.0001, call the modified gradient descent algorithm for 9138 iterations to get A + =93825.84,B + =-30202.81,C + =259.64. For G q <0 when the test data (N q , K q ), the initial values ​​A0=94087.75,B0=-21021.54,C0=-100, take E end1 =60, α=0.003, β=0.0001, call the modified gradient descent algorithm for 132610 iterations to get A - =93825.84, B - =-30202.81, C - =259.64, NK fitting curve is as follows Figure 4 shown.

[0088] Take the sampling period ΔT = 1s. If the input acceleration is 0, the accelerometer output pulse N0 = 10, and the zero bias G0 = 1.06 × 10 -4 g0, the error measurement under full range after compensation is less than 2×10 -6 g0.

[0089] The contents not described in detail in the specification of the present invention belong to the prior art known to the professional and technical personnel in this field.

Claims

1. A quartz flexible acceleration scale factor compensation method based on an inverse proportional function model, characterized in that include: The test was carried out using a quartz flexible accelerometer to obtain the accurate scale factor and number of pulses in each test; Considering the relationship between the scale factor and the pulse number of the quartz flexible accelerometer, an inverse proportional function model between the scale factor and the pulse number is established; A cost function is established based on the inverse proportional function model, and the accurate scale factor and pulse number obtained from the quartz flexible accelerometer test are introduced to fit the model coefficient of the inverse proportional function to obtain the fitted inverse proportional function model; Based on the pulse number at zero acceleration input and using the fitted inverse proportional function model, the scale factor after compensation at zero acceleration is calculated, and the zero bias is further calculated; Calculating a compensated scale factor based on the real-time measured pulse number and using a fitted inverse proportional function model; Substituting the compensated scale factor and zero bias into the acceleration measurement formula, the acceleration measurement formula of the quartz flexible accelerometer after scale factor compensation in real-time measurement is obtained.

2. The quartz flexible acceleration scale factor compensation method based on the inverse proportional function model according to claim 1 is characterized in that: The inverse proportional function model is: Where A, B, C are the inverse function model coefficients, K represents the scale factor, and N represents the number of pulses.

3. The quartz flexible acceleration scale factor compensation method based on the inverse proportional function model according to claim 2 is characterized in that: When fitting the model coefficients of the inverse proportional function model, two situations, that is, the real acceleration is greater than 0 and that is less than 0, are considered, and the inverse proportional function model coefficients A, B, and C in the inverse proportional function model are fitted respectively.

4. The quartz flexible acceleration scale factor compensation method based on the inverse proportional function model according to claim 1 is characterized in that: The cost function is specifically: Where is the cost value, K i is the scale factor in the quartz flexible accelerometer test, N i is the number of pulses in the quartz flexible accelerometer test, A, B, and C are the model coefficients of the inverse proportional function, i represents the number of tests, and n represents the total number of tests in which the input true acceleration is greater than or less than 0.

5. The method for compensating the quartz flexible acceleration scale factor based on the inverse proportional function model according to claim 4, characterized in that: The method for fitting the model coefficients A, B, and C of the inverse proportional function model is: Use the modified gradient descent method to iteratively update the values ​​of A, B, and C, and bring them into the cost function E = E (A, B, C, N i ,K i ) calculation, the iteration end condition is E <E end , E end is the index requirement, and i represents the number of tests.

6. The quartz flexible acceleration scale factor compensation method based on the inverse proportional function model according to claim 5 is characterized in that: Use the modified gradient descent method to fit the inverse proportional function model coefficients A, B, and C. The specific method is: Where j = 1, 2, 3, ..., m, m represents the total number of iterations, 0 ≤ β < α < 1; Among them, A j-1 , B j-1 , and C j-1 represents the inverse proportional function model coefficient obtained in the j-1th iteration, and E represents the cost function in the current iteration.

7. The method for compensating the quartz flexible acceleration scale factor based on the inverse proportional function model according to claim 6, characterized in that: The method for determining the initial value in the first iteration is: Among them, A0, B0, and C0 represent the initial values ​​of the given inverse proportional function model coefficients, and E represents the cost function in the current iteration.

8. The quartz flexible acceleration scale factor compensation method based on the inverse proportional function model according to claim 7, characterized in that: The initial value X0 of the inverse proportional function model coefficient is selected as follows: Pick If K1 < A0, take Conversely, take If N1<0, then C0<0, otherwise C0>0; Among them, K i is the scale factor in the quartz flexible accelerometer test, N i is the number of pulses in the quartz flexible accelerometer test, i represents the number of tests, i=1,2,3,…,n, and n represents the total number of tests in which the input true acceleration is greater than 0 or less than 0.

9. The method for compensating the quartz flexible acceleration scale factor based on the inverse proportional function model according to claim 1, characterized in that: The method for calculating the zero bias based on the number of pulses at zero acceleration input and the compensated scale factor is as follows: When the input real acceleration is 0, the pulse number N0 is directly obtained from the reading of the quartz flexible accelerometer, and then the compensated scale factor is calculated by combining the inverse proportional function model parameters corresponding to the real acceleration greater than 0. And the compensated scale factor calculated by the inverse proportional function model parameters when the true acceleration is less than 0 Calculate the zero bias G0, the formula is: In the formula, A + ,B + ,C + A is the inverse function model coefficient obtained by fitting the number of pulses and the scale factor when the input true acceleration is greater than 0. - ,B - ,C - It is the inverse proportional function model coefficient obtained by fitting the pulse number and scale factor when the input true acceleration is less than 0.

10. The method for compensating the quartz flexible acceleration scale factor based on the inverse proportional function model according to claim 1, characterized in that: The measurement formula after scale factor compensation is: Where N0 represents the number of pulses when the input real acceleration is G=0, G0 is the zero bias, ΔT represents the sampling period, g0=9.8015m / s 2 , |g0|=9.8015 dimensionless, N represents the number of pulses, K + and K - The calculation method is: K + Indicates the scale factor after real-time compensation based on the real-time measured pulse number N and the fitted inverse proportional function when the real acceleration is greater than 0, K - It indicates the scale factor after real-time compensation based on the real-time measured pulse number N and the fitted inverse proportional function when the real acceleration is less than 0.

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