A circumferential temperature compensation calibration method for a digital accelerometer

Abstract

The application discloses a kind of circumferential temperature compensation calibration methods of digital accelerometer, by circumferential multi-position temperature pull practice, make full use of the temperature characteristics of each position in the circumference of accelerometer to solve each temperature compensation parameter of temperature compensation calibration model, further utilize intelligent optimization algorithm to optimize each temperature compensation parameter nonlinear temperature compensation model, finally obtain the nonlinear temperature compensation model coefficient of accelerometer scale factor, zero offset, turntable initial error angle, and then realize the temperature compensation and calibration of accelerometer.The method of the application can simultaneously calibrate and calibrate the digital accelerometer, and the temperature compensation and calibration parameter model makes full use of the temperature characteristics of each position in the circumference.Finally, the intelligent optimization algorithm is applied to the optimization of the temperature compensation and calibration parameter nonlinear temperature compensation model, and the temperature compensation and calibration model parameters of the high-precision accelerometer can be obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of digital accelerometer temperature compensation (hereinafter referred to as "temperature compensation" for short) and calibration, and particularly relates to a circumferential temperature compensation calibration method for a digital accelerometer. BACKGROUND

[0002] Digital quartz flexible accelerometers are widely used in the fields of aerospace and oil exploration at present due to their high precision, small size, high stability and other characteristics. The precision of the accelerometers directly affects the attitude, speed and positioning precision of a navigation system. However, the precision of the accelerometers is adversely affected by environmental temperature, vibration, magnetic field, air pressure and the like, especially the environmental temperature. Therefore, the scale factor and zero offset error of the accelerometers are compensated with high precision before the accelerometers are actually applied.

[0003] In the traditional temperature compensation method for quartz flexible accelerometers, a turntable with a temperature control function is often used, and the method of first calibration and then temperature compensation using an error model, or first temperature compensation and then turntable calibration, is adopted. Both of the two methods separate the calibration and the temperature compensation, do not simultaneously consider the temperature drift errors of the zero offset and the scale factor, and do not consider the error angle of the temperature control turntable itself. Therefore, the precision of the accelerometer is still improved greatly after the traditional method is used for temperature compensation.

[0004] The patent specification with the publication number CN 109142792 A discloses a quartz flexible accelerometer temperature error calibration compensation method. The output and temperature data of the accelerometer are obtained by performing eight-position calibration on the quartz flexible accelerometer at room temperature and performing multiple variable temperature experiments on the quartz flexible accelerometer in a temperature chamber. Then, the function relationship between the output and the temperature of the quartz flexible accelerometer is obtained by using an accelerometer temperature model. Then, n-1 sets of differential data results are obtained by using the backstepping method and the term-by-term difference processing. Finally, the function of the scale factor with respect to the temperature is obtained by using the robust regression estimation method, and then the function of the zero offset with respect to the temperature is obtained. Finally, the temperature error calibration compensation model of the output of the quartz flexible accelerometer is obtained. The above patent technical solution does not involve the initial error angle of the turntable, and the data used for solving is discrete according to the temperature. Compared with the continuous domain data, the precision of the discrete domain data of the patent technology is poor.

[0005] In addition, the patent specification with the publication number CN 113670336 A discloses a method for determining the scale factor temperature coefficient compensation characteristics of a quartz flexible accelerometer, which also does not involve the initial error angle of the turntable.

[0006] In order to meet the development needs of high-precision navigation equipment in recent years, the related precision index requirements of the quartz flexible accelerometer are also getting higher and higher. Therefore, it is necessary to propose a higher-precision accelerometer temperature compensation and calibration method considering the error angle of the turntable itself. SUMMARY

[0007] In view of the above technical problems and deficiencies in the art, the present application provides a circumferential temperature compensation and calibration method for a digital accelerometer, which can simultaneously perform synchronous temperature compensation and calibration for the digital accelerometer, and the temperature compensation and calibration parameter model fully utilizes the temperature characteristics of each position in the circumference. Finally, an intelligent optimization algorithm is applied to optimize the nonlinear temperature compensation model of the temperature compensation and calibration parameters, so as to obtain a high-precision temperature compensation and calibration model parameter for the accelerometer. The present application has been successfully applied to a digital quartz flexible accelerometer, and is suitable for high-precision temperature compensation and calibration of various accelerometers that meet the temperature compensation and calibration model of the digital quartz flexible accelerometer.

[0008] The specific technical solutions are as follows:

[0009] A circumferential temperature compensation and calibration method for a digital accelerometer, which fully utilizes the temperature characteristics of each position in the circumference of the accelerometer to solve each temperature compensation parameter of the temperature compensation and calibration model, and further optimizes the nonlinear temperature compensation model of each temperature compensation parameter by using an intelligent optimization algorithm, so as to obtain the nonlinear temperature compensation model coefficients of the accelerometer scale factor, zero offset, and initial error angle of the turntable, and then realize the temperature compensation and calibration of the accelerometer.

[0010] The circumferential temperature compensation and calibration method for the digital accelerometer specifically includes the following steps:

[0011] Step 1: Constructing an acceleration output temperature related model of the accelerometer, and establishing a solving model of each temperature compensation parameter in the temperature compensation and calibration model;

[0012] Step 2: Using a high-precision turntable and a controllable oven to perform a temperature pull test at multiple positions in the circumference of the accelerometer;

[0013] Step 3: Substituting the temperature pull test data into the solving model in Step 1 to establish a nonlinear temperature compensation model of each temperature compensation parameter;

[0014] Step 4: Using an intelligent optimization algorithm to perform online intelligent optimization on each temperature compensation parameter, with the error sum of squares of the measured and calculated data as the fitness function;

[0015] Step 5: When the intelligent optimization algorithm meets the termination condition, the population individual corresponding to the minimum value of the fitness function is the nonlinear temperature compensation model coefficient of each temperature compensation parameter, which is substituted into the nonlinear temperature compensation model of each temperature compensation parameter established in Step 3, and this model is further substituted into the acceleration output temperature related model established in Step 1, so as to complete the temperature compensation and calibration of the accelerometer.

[0016] The temperature compensation model fully utilizes the temperature characteristics of the accelerometer at each position in the circumference, and also considers the error term of the turntable itself during temperature compensation calibration, and can realize high-precision synchronous temperature compensation and calibration.

[0017] In step one, the constructed acceleration output temperature correlation model contains a scale factor, a zero offset, and an initial error angle of the turntable, and is expressed by a formula as follows:

[0018] a(θ,T)=K(T)*(N(θ,T)-b(T))=g*sin(θ+α)

[0019] θ is the input angle of the turntable during calibration, T is the temperature, and α is the initial error angle of the turntable, and g is the gravitational acceleration;

[0020] a(θ,T) is the measured acceleration related to the input angle of the turntable and the temperature;

[0021] K(T) is a scale factor related to the temperature;

[0022] b(T) is a zero offset related to the temperature;

[0023] N(θ,T) is the measured value of the accelerometer related to the input angle of the turntable and the temperature.

[0024] In step one, N(θ,T) is the actual measured value of the accelerometer before temperature compensation calibration, and after compensation of the zero offset b(T) and the scale factor K(T), the actual measured acceleration a(θ,T) can be obtained, which can also be expressed by the gravitational acceleration component g*sin(θ+α).

[0025] In step one, the temperature characteristics of the accelerometer at each position in the circumference are not consistent in actual application, so a circumference measurement temperature compensation calibration model is established by considering the circumference measurement method, and the temperature characteristics of the accelerometer at each position in the circumference are fully utilized. The test is usually carried out by the method of measuring the symmetrical angles in the circumference, θ takes 0°, 45°, 90°, 135°, 180°, 225°, 270° and 315°, i.e. eight position measurement method, and then the temperature compensation calibration model is obtained from step one as follows:

[0026]

[0027] The corresponding solving model of each temperature compensation parameter can be further simplified as follows:

[0028]

[0029] In step two, the high-precision turntable has high angle resolution and supports program control, the controllable oven supports high and low temperature range of the accelerometer, and the temperature range of the accelerometer can be programmed to set the temperature range curve, and the high-precision turntable is fixed in the controllable oven.

[0030] The accelerometer is fixed on the high-precision rotary table, a temperature pull curve is set, the rotary table is rotated to a 0° position, temperature pull is performed, and acceleration output data N(0°, T) are collected. After the temperature pull at the 0° position is completed, the rotary table is rotated to another position for temperature pull until temperature pull at eight positions is completed, and the acceleration measurement data N(θ, T) of each position can be obtained.

[0031] Preferably, in step two:

[0032] The temperature pull range of the accelerometer is -40℃ to 60℃.

[0033] The temperature pull curve is set as follows: after power-on normal temperature 30℃ is set and kept for half an hour, a temperature rising rate of 1℃ / min is set, the temperature is raised to 60℃, and kept for half an hour; then a temperature falling rate of -1℃ / min is set, the temperature is lowered to -40℃, and kept for half an hour; finally, a temperature rising rate of 1℃ / min is set, the temperature is raised to normal temperature 30℃, and kept for half an hour.

[0034] In step three, the temperature pull accelerometer test data N(θ, T) of each position in step two are substituted into the temperature compensation parameter solving model established in step one, and the temperature compensation parameter data changing with temperature can be obtained. Further, the non-linear temperature compensation model is modeled, that is, the accelerometer temperature compensation calibration problem is converted into a non-linear model coefficient optimization problem, and the non-linear temperature compensation model corresponding to each temperature compensation parameter is as follows:

[0035]

[0036] b0, b1, b2, b3, and b4 are zero bias temperature compensation model coefficients.

[0037] k0, k1, k2, k3, and k4 are scale factor temperature compensation model coefficients.

[0038] α0, α1, α2, α3, and α4 are rotary table initial error angle temperature compensation model coefficients.

[0039] In the temperature compensation model, tanα(T) can be regarded as a measurement error term caused by the rotary table. Thus, the accelerometer temperature compensation calibration is converted into solving the above non-linear model coefficient optimization problem according to the measurement data in step two.

[0040] In step four, in order to obtain the optimal coefficient of the non-linear temperature compensation model corresponding to the temperature compensation calibration parameters in step three, according to the temperature pull data of each temperature compensation parameter in steps one and two, the intelligent optimization algorithm is used, the error sum of squares of the measurement solving data and the fitting data is used as the fitness function, the above temperature compensation model coefficients are used as the optimization objects, and the non-linear temperature compensation model coefficients of each temperature compensation parameter in step three are optimized. The fitness function is expressed as:

[0041]

[0042] u(k) is the temperature compensation parameter data solved in step three according to the data solved in steps one and two;

[0043] y(k) is the data fitted by the above-mentioned nonlinear temperature compensation model corresponding to the temperature compensation parameter.

[0044] In step five, the parameter intelligent optimization is ended when the fitness function value in the intelligent optimization algorithm in step four meets the specified error precision or the population iteration number reaches the specified value.

[0045] The intelligent optimization algorithm described in the application can be a genetic algorithm, an immune algorithm, a particle swarm algorithm, an ant colony algorithm, a simulated annealing algorithm, etc.

[0046] Compared with the prior art, the application has the beneficial effects of:

[0047] 1. The accelerometer temperature compensation and calibration method proposed in the application combines the temperature characteristics of multiple positions in the circumference of a high-precision turntable, establishes a temperature compensation model combined with accelerometer temperature compensation and calibration, introduces the error angle of the turntable itself into the temperature compensation and calibration model, and solves the fusion model of each temperature compensation parameter under eight-position measurement of the accelerometer, so that higher-precision temperature compensation and calibration can be realized compared with traditional methods.

[0048] 2. The accelerometer temperature compensation and calibration method proposed in the application adopts an intelligent optimization algorithm, takes the error sum of squares between model fitting data and accelerometer measurement fusion data as a fitness function, can high-precision fit the temperature compensation model of scale factors and zero offset coefficients, greatly improves the efficiency of model identification, and realizes high-precision temperature compensation of the accelerometer.

[0049] 3. The accelerometer temperature compensation and calibration method proposed in the application is suitable for high-precision temperature compensation of various accelerometers, and the solving method proposed fully utilizes the temperature characteristics of each position of the accelerometer and adopts an intelligent optimization algorithm for model solving, so that the precision and efficiency of accelerometer temperature compensation and calibration can be greatly improved. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 It is a flowchart of a digital accelerometer circumferential temperature compensation and calibration method described in the specific embodiment of the application.

[0051] Figure 2 It is a temperature setting schematic diagram of an accelerometer temperature pull test in the specific embodiment of the application.

[0052] Figure 3 It is a model identification flowchart of a temperature compensation parameter intelligent algorithm in the specific embodiment of the application.

[0053] Figure 4This is a comparison chart of accelerometer zero-bias test data and identification curve in a specific embodiment of the present invention.

[0054] Figure 5 This is a comparison chart of accelerometer scaling factor test data and identification curve in a specific embodiment of the present invention.

[0055] Figure 6 This is a comparison chart of the test data and identification curve of the accelerometer turntable error angle tangent in a specific embodiment of the present invention.

[0056] Figure 7 This is a test diagram of the accelerometer's full-temperature range output after overall temperature compensation in a specific embodiment of the present invention. Detailed Implementation

[0057] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0058] like Figure 1 As shown, the present invention provides a method for circumferential temperature compensation calibration of a digital accelerometer, which specifically includes the following steps:

[0059] Step 1: Construct a temperature-dependent model for the accelerometer's acceleration output and establish a solution model for each temperature compensation parameter in the temperature compensation calibration model;

[0060] Step 2: Use a high-precision turntable and a controllable temperature chamber to conduct temperature testing at multiple locations within the circumference of the accelerometer.

[0061] Step 3: Substitute the temperature data from the temperature training into the mathematical model from Step 1 to establish a nonlinear temperature-related model optimization problem for each temperature compensation parameter.

[0062] Step 4: Using an intelligent optimization algorithm, with the sum of squared errors as the fitness function, perform online intelligent optimization of each temperature compensation parameter;

[0063] Step 5: Once the intelligent optimization algorithm meets the termination condition, the parameters corresponding to the optimal individual in the population are the optimal temperature compensation model coefficients of the temperature-related model for each temperature compensation parameter.

[0064] In step one, the constructed acceleration output temperature-dependent model includes the scaling factor, zero bias, and turntable initial error angle, expressed by the formula:

[0065] a(θ,T)=K(T)*(N(θ,T)-b(T))=g*sin(θ+α)

[0066] θ is the input angle of the turntable during calibration, T is the temperature, α is the initial error angle of the turntable, and g is the acceleration due to gravity.

[0067] a(0, T) is the measured acceleration related to input angle and temperature;

[0068] K(T) is the scale factor related to temperature;

[0069] b(T) is the zero offset related to temperature;

[0070] N(0, T) is the accelerometer measurement value related to turntable input angle and temperature.

[0071] In step one, N(0, T) is the actual measurement value of the accelerometer before temperature compensation calibration, and the actual measurement acceleration a(0, T) can be obtained after the zero offset b(T) and the scale factor K(T) compensation. Since only ±1g acceleration can be applied in the direction of the turntable, a(0, T) can also be expressed as g*sin(0+α).

[0072] In step one, the temperature characteristics of the accelerometer at each position in the circumference are inconsistent in actual application, so the circumferential measurement method is considered to establish a circumferential measurement temperature compensation calibration model, and the temperature characteristics of the accelerometer at each position in the circumference are fully utilized. The method of measuring at symmetrical angles in the circumference is usually used for testing. In this patent, both the characteristics of each position in the circumference and the reduction of measurement positions are considered to improve the temperature compensation efficiency. Eight positions are measured at 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°, i.e., eight position measurement method. Then, according to step one, the temperature compensation calibration model is:

[0073]

[0074] Further simplification can solve the calculation model corresponding to each temperature compensation parameter:

[0075]

[0076] In actual application, in order to fully integrate the temperature characteristics of the accelerometer at each position, the more the circumferential positions are measured, the better the characteristics are integrated, and the higher the accuracy of the accelerometer after temperature compensation is. Therefore, different multi-position measurement methods can be selected according to actual conditions.

[0077] In step two, the high-precision turntable and the temperature-controlled box are used to carry out multi-position temperature pull test of the accelerometer in the circle. The high-precision turntable needs to have high angle resolution and support program control, the temperature-controlled box needs to support high and low temperature range pull test of the accelerometer, and the temperature pull test curve can be programmed, and the high-precision turntable needs to be fixed in the temperature-controlled box. The accelerometer is fixed on the turntable, the temperature pull test curve is set, the turntable is rotated to 0° position, the temperature pull test is carried out, and the acceleration output data N(0°, T) are collected. After the temperature pull test at 0° position is completed, the turntable is rotated to another position for temperature pull test until the temperature pull test at eight positions is completed, and the measurement data N(θ, T) of the accelerometer at each position are obtained.

[0078] In step two, as shown in Figure 2 , the temperature pull test range of the accelerometer is -40℃ to 60℃, the temperature curve is set to normal temperature 30℃ after power-on for half an hour, then the temperature is raised to 60℃ at a rate of 1℃ / min, and kept for half an hour, then the temperature is lowered to -40℃ at a rate of -1℃ / min, and kept for half an hour, and finally the temperature is raised to normal temperature 30℃ at a rate of 1℃ / min, and kept for half an hour.

[0079] In step three, as shown in Figure 3 , the test data N(θ, T) of the accelerometer at each position in step two are substituted into the solving model of each temperature compensation parameter established in step one, and the data of each temperature compensation parameter changing with temperature are obtained, and further, the nonlinear temperature compensation model of each temperature compensation parameter is modeled, that is, the accelerometer temperature compensation calibration problem is converted into a nonlinear model coefficient optimization problem, and the nonlinear temperature compensation model corresponding to each temperature compensation parameter is:

[0080]

[0081] In the formula:

[0082] b0, b1, b2, b3, b4 are zero bias temperature compensation model coefficients;

[0083] k0, k1, k2, k3, k4 are scale factor temperature compensation model coefficients;

[0084] α0, α1, α2, α3, α4 are error angle temperature compensation model coefficients;

[0085] In this temperature compensation model, tanα(T) can be regarded as a measurement error term caused by the turntable, and thus the accelerometer temperature compensation calibration is converted into solving the above nonlinear model coefficient optimization problem according to the measurement data in step two.

[0086] In step three, the established nonlinear temperature compensation model of each temperature compensation parameter uses conventional temperature, temperature square, temperature rate of change and temperature rate of change square as nonlinear related variables. Considering the model identification efficiency, the order is only taken to the square term here. The higher the actual nonlinear model order is, the stronger the nonlinear fitting capability is, but the corresponding identification complexity increases, and the model order needs to be selected comprehensively.

[0087] In step four, as shown in Figure 3 , to obtain the optimal coefficients of the nonlinear temperature compensation model corresponding to the temperature compensation calibration parameters in step three, according to the temperature pull test data of each temperature compensation parameter in step two, an intelligent optimization algorithm is used, the sum of squares of errors between the measured data and the fitting data is used as the fitness function, and the coefficients of the above-mentioned temperature compensation model are used as the optimization objects. The fitness function is expressed as:

[0088]

[0089] u(k) is the pull test data of each temperature compensation parameter solved in step three;

[0090] y(k) is the data fitted by the above-mentioned model corresponding to the temperature compensation parameter.

[0091] In step five, as shown in Figure 3 , when the fitness function value in the intelligent optimization algorithm in step four meets the specified error precision or the population iteration number reaches the specified value, the parameter intelligent optimization is ended. At this time, the population individual corresponding to the minimum fitness value is the optimal coefficient of the nonlinear temperature compensation model corresponding to the temperature compensation parameter.

[0092] The intelligent optimization algorithm used in this embodiment is a symbiotic organism intelligent algorithm containing multiple screening mechanisms, which has strong global search and local convergence capabilities. In this embodiment, the parameter intelligent optimization is ended when the population iteration number reaches the specified value 200. The finally fitted zero offset temperature compensation model coefficients are b0=57.51561837, b1=-0.00133424, b2=0.00001515, b3=0.00045457, b4=0.00022559; the scale factor coefficients are k0=-0.00331441, k1=0.00000044, k2=-0.000000005, k3=-0.00000041, k4=-0.00000021; the error angle temperature compensation model coefficients are a0=0.10960531, a1=-0.00000169, a2=-0.00000001, a3=-0.00000597, a4=-0.00000298.

[0093] As shown in Figure 4 , Figure 5 , Figure 6As shown, the wavy curve represents the original data of the accelerometer test zero offset and scale factor and error angle tangent value, and the smooth curve represents the temperature related curve obtained by the above intelligent optimization algorithm model recognition. As can be seen from the figure, the zero offset and scale factor data obtained after the fusion of the multi-position measurement data have good temperature correlation, and the intelligent optimization algorithm can efficiently identify the obtained curve to realize high-precision temperature compensation of the accelerometer as a whole.

[0094] In step five, after obtaining the optimal nonlinear temperature compensation model coefficients of each temperature compensation parameter, the coefficients are substituted into the nonlinear temperature related model of each temperature compensation parameter established in step three, and the model is further substituted into the acceleration output model established in step one to complete the temperature compensation and calibration of the accelerometer. At the same time, the temperature compensation model fully utilizes the temperature characteristics of the accelerometer at each position in the circle, and also considers the error term of the turntable itself parameters during temperature compensation and calibration, so that high-precision synchronous temperature compensation and calibration can be realized.

[0095] As Figure 7 As shown is the full-temperature-range output test diagram of the accelerometer after the above temperature compensation step. As can be seen from the figure, the method fully considers the temperature characteristics of the accelerometer at each position, and the temperature compensation greatly reduces the temperature correlation of the accelerometer output and greatly improves the accuracy, further proving the effectiveness of the proposed method for temperature compensation and calibration of the accelerometer.

[0096] In addition, it should be understood that, after reading the above description of the present application, those skilled in the art can make various modifications or modifications to the present application, and these equivalent forms also fall within the scope defined by the appended claims of the present application.

Claims

1. A method for circumferential temperature compensation calibration of a digital accelerometer, characterized in that, By conducting temperature testing at multiple positions around the circumference, the temperature characteristics of each position within the accelerometer's circumference are fully utilized to solve for the temperature compensation parameters of the temperature compensation calibration model. Furthermore, intelligent optimization algorithms are used to optimize the nonlinear temperature compensation model for each temperature compensation parameter. Finally, the nonlinear temperature compensation model coefficients for the accelerometer's scaling factor, zero bias, and turntable initial error angle are obtained, thereby realizing the temperature compensation and calibration of the accelerometer. The circular temperature compensation calibration method for the digital accelerometer specifically includes the following steps: Step 1: Construct a temperature-dependent model for the accelerometer's acceleration output and establish a solution model for each temperature compensation parameter in the temperature compensation calibration model; Step 2: Use a high-precision turntable and a controllable temperature chamber to conduct temperature testing at multiple locations within the circumference of the accelerometer. Step 3: Substitute the temperature data from the temperature simulation into the solution model from Step 1 to establish a nonlinear temperature compensation model for each temperature compensation parameter. Step 4: Using intelligent optimization algorithms, the sum of squared errors between the measured and fitted data is used as the fitness function to perform online intelligent optimization of each temperature compensation parameter; Step 5: Once the intelligent optimization algorithm meets the termination condition, the population individual corresponding to the minimum value of the fitness function is the nonlinear temperature compensation model coefficient of each temperature compensation parameter. Substitute it into the nonlinear temperature compensation model of each temperature compensation parameter established in Step 3, and further substitute this model into the acceleration output temperature correlation model established in Step 1 to complete the temperature compensation and calibration of the accelerometer. In step one, the constructed acceleration output temperature-dependent model includes the scaling factor, zero bias, and turntable initial error angle, expressed by the formula: a(θ,T)=K(T)*(N(θ,T)-b(T))=g*sin(θ+α) θ is the input angle of the turntable during calibration, T is the temperature, α is the initial error angle of the turntable, and g is the acceleration due to gravity. a(θ,T) is the measured acceleration related to the input angle and temperature of the turntable; K(T) is a temperature-dependent scaling factor; b(T) is the temperature-dependent zero bias; N(θ,T) is the accelerometer measurement value related to the input angle and temperature of the turntable; In step three, the accelerometer test data N(θ,T) from each location temperature training in step two are substituted into the temperature compensation parameter calculation model established in step one to obtain the temperature compensation parameter variation data with temperature. Further, a nonlinear temperature compensation model is built for each temperature compensation parameter, transforming the accelerometer temperature compensation calibration problem into a nonlinear model coefficient optimization problem. The nonlinear temperature compensation model corresponding to each temperature compensation parameter is as follows: in: b0, b1, b2, b3, and b4 are the coefficients of the zero-partial temperature compensation model; k0, k1, k2, k3, and k4 are scaling factors and temperature-compensated model coefficients; α0, α1, α2, α3, and α4 are the coefficients of the turntable initial error angular temperature compensation model.

2. The method for circumferential temperature compensation calibration of a digital accelerometer according to claim 1, characterized in that, In step one, a circumferential temperature-compensated calibration model is established using a circumferential measurement method. This fully utilizes the temperature characteristics of the accelerometer at various positions within the circle and employs a symmetrical angle measurement method within the circle. θ is taken as eight angles: 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°, i.e., an eight-position measurement method. Therefore, from step one, the temperature-compensated calibration model is as follows: The solution model for each temperature compensation parameter can be further simplified as follows:

3. The method for circumferential temperature compensation calibration of a digital accelerometer according to claim 2, characterized in that, In step two, the high-precision turntable has high angular resolution and supports programmable control, the controllable temperature chamber supports high and low temperature range training of accelerometers, and the temperature training curve can be programmed. The high-precision turntable is fixed inside the controllable temperature chamber. An accelerometer is fixed on the high-precision turntable. A temperature training curve is set, and the turntable is rotated to the 0° position to conduct a temperature training. At the same time, acceleration output data N(0°,T) is collected. After the temperature training at the 0° position is completed, the turntable is rotated to another position to conduct a temperature training until all eight positions are completed. Then, the accelerometer measurement data N(θ,T) at each position can be obtained.

4. The method for circumferential temperature compensation calibration of a digital accelerometer according to claim 3, characterized in that, In step two: The accelerometer temperature range is -40℃ to 60℃; The temperature testing curve is set to power on at 30℃ and hold for half an hour, then set the heating rate to 1℃ / min to heat up to 60℃ and hold for half an hour, then set the cooling rate to -1℃ / min to cool down to -40℃ and hold for half an hour, and finally set the heating rate to 1℃ / min to heat up to 30℃ and hold for half an hour.

5. The method for circumferential temperature compensation calibration of a digital accelerometer according to claim 1, characterized in that, In step four, to obtain the optimal coefficients of the nonlinear temperature compensation model corresponding to the temperature compensation calibration parameters in step three, based on the temperature training data of each temperature compensation parameter in steps one and two, an intelligent optimization algorithm is used. The fitness function is the sum of squared errors between the measured and fitted data. The coefficients of each temperature compensation model are taken as the objects to be optimized. The nonlinear temperature compensation model coefficients of each temperature compensation parameter in step three are optimized respectively. The fitness function is expressed as: u(k) represents the training data of each temperature compensation parameter obtained in step three based on steps one and two; y(k) represents the data fitted by the above nonlinear temperature compensation model for the corresponding temperature compensation parameters.

6. The method for circumferential temperature compensation calibration of a digital accelerometer according to claim 1, characterized in that, In step five, the intelligent parameter optimization ends when the fitness function value in the intelligent optimization algorithm in step four meets the specified error precision or the number of population iterations reaches the specified value.

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