A method for six-position temperature compensation calibration of accelerometers in a strapdown inertial navigation system

Abstract

This invention provides a six-position temperature-compensated calibration method for accelerometers in a strapdown inertial navigation system (SINS), belonging to the field of inertial navigation technology. The specific steps are as follows: The SINS is calibrated for a short time at different temperatures on a dual-axis temperature-controlled turntable without a mounting reference. The accelerometer zero bias, scale coefficient, and installation error at different temperatures are estimated using the least squares method. A cubic polynomial model is established relating the accelerometer zero bias, scale coefficient, and installation error to the actual temperature. The initial temperature scale coefficient is obtained by fitting the curve. Then, six-position calibration is performed on a turntable with a mounting reference to obtain a transformation matrix. The final temperature compensation coefficient is obtained from the transformation matrix and applied to the SINS to reduce the impact of temperature on the accelerometer output. This invention features short accelerometer data acquisition time, high reliability, and ease of operation. It is a method for improving accelerometer output accuracy through accelerometer compensation calibration.

Description

Technical Field

[0001] This invention belongs to the field of inertial navigation technology, specifically relating to a six-position temperature compensation calibration method for accelerometers in a strapdown inertial navigation system. Background Technology

[0002] Accelerometers, as crucial sensing devices in strapdown inertial navigation systems (INS), measure the acceleration of the system and obtain vital navigation information such as velocity and position through integration. Accelerometer temperature compensation is a necessary step to improve the accuracy of the INS, directly impacting the final navigation calculation accuracy and being one of the compensation techniques that determines the performance of the INS. Traditional methods involve placing the strapdown INS in a temperature chamber to collect accelerometer data at different temperatures for compensation. This method only reduces the temperature-dependent zero-point output of the triaxial accelerometer but cannot reduce the drift caused by temperature-induced errors in the accelerometer scale coefficients and installation errors, resulting in poor compensation under dynamic conditions. Furthermore, the newly adopted eight-position, ten-position, and nineteen-position system-level temperature compensation calibration methods suffer from excessively long data acquisition times. In practical applications, even the shortest eight-position system-level temperature compensation calibration requires at least 40 minutes of data acquisition at each temperature point. During these 40 minutes, the triaxial accelerometer output continuously changes with temperature, resulting in zero bias, scale coefficients, and installation errors not being calculated within the same temperature range, leading to inaccurate compensation results. Meanwhile, the system-level temperature compensation calibration involves multiple rotation positions and requires rotating the dual-axis temperature control turntable in a specific sequence, making the rotation positions difficult to identify and prone to errors during manual operation. Therefore, in actual production and delivery, it is necessary to design an accelerometer compensation method with short data acquisition time, high compensation model reliability, and ease of operation to improve the compensation effect. Summary of the Invention

[0003] The technical problem solved by this invention is to provide a six-position temperature-compensated calibration method for accelerometers in a strapdown inertial navigation system. The purpose of this invention is to design an accelerometer temperature-compensated calibration method with short data acquisition time, high reliability of the compensation model, and easy operation to obtain the accelerometer temperature scale coefficient, thereby compensating for and reducing the influence of temperature on the accelerometer output of the strapdown inertial navigation system.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] A method for six-position temperature-compensated calibration of accelerometers in a strapdown inertial navigation system includes the following steps:

[0006] Step 1): Establish an accelerometer calibration model for the strapdown inertial navigation system;

[0007] Step 2): Install the strapdown inertial navigation system in a dual-axis temperature-controlled turntable without an installation reference, and connect the test cable and test equipment;

[0008] Step 3): Rotate the dual-axis temperature-controlled turntable to perform short-time six-position accelerometer calibration on the strapdown inertial navigation system at different temperatures;

[0009] Step 4): Convert the accelerometer calibration model using the formula. The accelerometer zero bias, scale coefficient, and installation error, a total of 12 calibration parameters, were calculated using the least squares matrix method at different temperatures.

[0010] Step 5): Establish cubic polynomial models of zero bias, calibration coefficient, and installation error with accelerometer output temperature respectively. Obtain the coefficients of the cubic polynomial in the model, i.e. the initial temperature scale coefficients, by fitting the curve regression equation and writing them into the strapdown inertial navigation system.

[0011] Step 6): At room temperature, install the inertial navigation system on a dual-axis turntable with an installation reference and perform six-position calibration to obtain the transformation matrix between the dual-axis turntable and the dual-axis temperature control turntable. Use the transformation matrix to transform the initial temperature scale coefficients to the turntable with the installation reference, and then write the final solved temperature scale coefficients into the strapdown inertial navigation system to reduce the influence of temperature on the accelerometer output of the strapdown inertial navigation system.

[0012] In step 1) above, the accelerometer calibration model of the strapdown inertial navigation system is as follows:

[0013]

[0014] in, , , ,

[0015] in:

[0016] — Triaxial accelerometer coupling matrix, —Triaxial accelerometer scale coefficients, (i≠j) — Installation error of the triaxial accelerometer;

[0017] — Triaxial accelerometer zero bias error;

[0018] —Actual output value of the triaxial accelerometer;

[0019] —Theoretical value of triaxial accelerometer.

[0020] In step 3) above, the six-position accelerometer calibration process is as follows: Rotate the dual-axis temperature-controlled turntable to position the strapdown inertial navigation system at the six positions shown in Table 1 below. There is no requirement for the rotation order. Accelerometer output data is collected for 20 seconds at each position, and the average value is calculated to obtain the actual output value of the accelerometer at the current position. After the data collection was completed, the actual output values ​​of the accelerometers at six locations were obtained. Its theoretical acceleration is ;

[0021] .

[0022] In step 4) above, the accelerometer calibration model is transformed using a formula. The specific process of determining the accelerometer's zero bias, calibration coefficient, and installation error using the least squares matrix method is as follows:

[0023] right Transpose on both sides:

[0024]

[0025]

[0026] Right now:

[0027] The actual output values ​​of the six accelerometers in step 3) Substituting into the above equation, we get:

[0028]

[0029] remember:

[0030]

[0031] in:

[0032] , ,

[0033] Based on the matrix form of the least squares method, we obtain The estimated value for:

[0034]

[0035] The accelerometer zero bias at the current temperature is calculated. Scale coefficient Installation error ;

[0036] Set the temperature of the temperature-controlled turntable chamber to -40℃, -20℃, 0℃, 20℃, 40℃, and 60℃ respectively, and operate according to steps 1) to 3) respectively. Calculate the accelerometer zero bias at different chamber temperatures. Scale coefficient Installation error .

[0037] In step 5) above, zero bias is established respectively. Scale coefficient Installation error The cubic polynomial model of the 12 parameters and their corresponding actual accelerometer temperatures is as follows:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050] in i=1, 2…12 are the coefficients of the cubic polynomial, namely the 48 temperature scale coefficients required for the temperature compensation calibration of the accelerometer in the strapdown inertial navigation system. For X-axis accelerometer temperature, For Y-axis accelerometer temperature, Temperature of the Z-axis accelerometer;

[0051] Using the corresponding temperature as the independent variable and 12 parameters such as accelerometer zero point, scale coefficient, and installation error as the dependent variable, a cubic curve is fitted to obtain the regression equation of the fitted curve. The coefficients of the regression equation are the 48 initial temperature scale coefficients. The 48 temperature scale coefficients are written into the strapdown inertial navigation system. At this point, the temperature compensation calibration on the dual-axis temperature control turntable has been completed, and the strapdown inertial navigation system outputs the accelerometer data after the initial temperature scale.

[0052] In step 6) above, at room temperature, the inertial navigation system is installed on a dual-axis turntable with an installation reference. A level is used for calibration, ensuring the X-axis of the strapdown inertial navigation system points north. The turntable is rotated at six positions as shown in Table 1. After each position is stable, accelerometer output data is collected for 20 seconds. Accelerometer calibration is then completed according to step 3), yielding the coupling matrix. and zero offset ; This is the conversion matrix between a dual-axis temperature control turntable and a dual-axis turntable;

[0053] ,

[0054] Substitute into the accelerometer output model Zhongde:

[0055]

[0056]

[0057] Then the scale coefficient after installation reference transformation Right now:

[0058]

[0059] Then, the zero offset of the accelerator after the installation reference transformation Right now:

[0060]

[0061] Adjust scale coefficients , .

[0062] Advantages of this invention compared to existing technologies:

[0063] 1. This solution addresses the shortcomings of traditional temperature compensation methods, the excessively long data acquisition time, inaccurate compensation effects, and complex operation processes in new system-level temperature compensation calibration. It proposes a temperature compensation calibration method for accelerometers in strapdown inertial navigation systems with short data acquisition time, high reliability of the compensation model, and ease of operation. This method aims to compensate for and reduce the impact of temperature on the accelerometer output of strapdown inertial navigation systems and is also applicable to other strapdown inertial navigation systems.

[0064] 2. The total accelerometer data acquisition time and turntable rotation time at each temperature point in this scheme are less than 5 minutes;

[0065] 3. This scheme converts the acceleration calibration model into Ax=b, and calculates 12 calibration parameters for each temperature point, including accelerometer zero bias, scale coefficient, and installation error, using the least squares method.

[0066] 4. This scheme designs a cubic polynomial compensation model for 12 calibration parameters (accelerometer zero bias, scale coefficient, installation error, etc.) and temperature. The temperature scale coefficient is obtained by fitting a regression equation to the fitted curve. The correlation coefficient R of the fitted curve is... 2 The model has a high degree of fit (≈1), making it reliable and suitable for the entire temperature range of strapdown inertial navigation systems.

[0067] 5. This solution designs a reference conversion method to transfer the compensated accelerometer temperature scale coefficient from a dual-axis temperature control turntable without an installation reference to a dual-axis turntable with an installation reference, thus obtaining the final temperature scale coefficient, which does not depend on the accuracy of the temperature control turntable. Attached Figure Description

[0068] Figure 1 This is a flowchart of the present invention;

[0069] Figure 2 The accelerometer temperature-compensated fitting curve in this embodiment of the invention. Figure 1 ;

[0070] Figure 3 The accelerometer temperature-compensated fitting curve in this embodiment of the invention. Figure 2 ;

[0071] Figure 4 The accelerometer temperature-compensated fitting curve in this embodiment of the invention. Figure 3 ;

[0072] Figure 5 The accelerometer temperature-compensated fitting curve in this embodiment of the invention. Figure 4 ;

[0073] Figure 6 The accelerometer temperature-compensated fitting curve in this embodiment of the invention. Figure 5 ;

[0074] Figure 7 The accelerometer temperature-compensated fitting curve in this embodiment of the invention. Figure 6 ;

[0075] Figure 8 The accelerometer temperature-compensated fitting curve in this embodiment of the invention. Figure 7 ;

[0076] Figure 9 The accelerometer temperature-compensated fitting curve in this embodiment of the invention. Figure 8 ;

[0077] Figure 10 The accelerometer temperature-compensated fitting curve in this embodiment of the invention. Figure 9 ;

[0078] Figure 11 The accelerometer temperature-compensated fitting curve in this embodiment of the invention. Figure 10 ;

[0079] Figure 12 The accelerometer temperature-compensated fitting curve in this embodiment of the invention. Figure 10 one;

[0080] Figure 13 The accelerometer temperature-compensated fitting curve in this embodiment of the invention. Figure 10 two;

[0081] Figure 14 This is an external view of the strapdown inertial navigation system used in this embodiment of the invention;

[0082] Figure 15 This invention provides a comparison of the output compensation of accelerometers on each axis before and after different temperatures in an embodiment of the invention. Figure 1 ;

[0083] Figure 16 This invention provides a comparison of the output compensation of accelerometers on each axis before and after different temperatures in an embodiment of the invention. Figure 2 ;

[0084] Figure 17 This invention provides a comparison of the output compensation of accelerometers on each axis before and after different temperatures in an embodiment of the invention. Figure 3 ;

[0085] Figure 18 This invention provides a comparison of the output compensation of accelerometers on each axis before and after different temperatures in an embodiment of the invention. Figure 4 ;

[0086] Figure 19 This invention provides a comparison of the output compensation of accelerometers on each axis before and after different temperatures in an embodiment of the invention. Figure 5 ;

[0087] Figure 20 This invention provides a comparison of the output compensation of accelerometers on each axis before and after different temperatures in an embodiment of the invention. Figure 6 . Detailed Implementation

[0088] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0089] Please see Figure 1-20 The embodiments of the present invention are described in detail below.

[0090] A method for six-position temperature-compensated calibration of accelerometers in a strapdown inertial navigation system. The flowchart of this invention is shown below. Figure 1 .

[0091] Step 1): Establish the accelerometer calibration model for the strapdown inertial navigation system as follows:

[0092]

[0093] in, , , ,

[0094] Step 2): Fix the strapdown inertial navigation system in a dual-axis temperature-controlled turntable without an installation reference using the mounting clamp, connect the test cable and test equipment, and keep it at temperatures of -40℃, -20℃, 0℃, 20℃, 40℃ and 60℃ for no less than 4 hours in sequence;

[0095] Step 3): Power on the strapdown inertial navigation system and rotate the dual-axis temperature-controlled turntable to position the system at the six locations shown in Table 1. There is no specific rotation order. Collect accelerometer output data for 20 seconds at each location and calculate the average value. The final result is the actual accelerometer output data for the six locations. ;

[0096]

[0097] The theoretical accelerometer output value at six positions is

[0098]

[0099] Step 4): Convert the accelerometer calibration model using the formula. The accelerometer zero bias, scale coefficient, and installation error are obtained in matrix form using the least squares method.

[0100] right Transpose on both sides:

[0101]

[0102]

[0103] Right now:

[0104] The actual output value of the accelerometer in step 3) Substituting into the above equation, we get:

[0105]

[0106] remember:

[0107]

[0108] in:

[0109] , ,

[0110] Based on the matrix form of the least squares method, we obtain The estimated value for:

[0111]

[0112] The accelerometer zero bias at -40℃ was calculated. Coupling matrix .

[0113]

[0114]

[0115] Set the temperature of the temperature control turntable chamber to -20℃, 0℃, 20℃, 40℃, and 60℃ respectively. Follow steps 1) to 3) respectively to calculate the accelerometer zero bias, scale coefficient, and installation error at different chamber temperatures, as shown in Table 2.

[0116]

[0117] Step 5): Using the corresponding temperature as the independent variable and 12 parameters (zero point, scale coefficient, installation error, etc.) as the dependent variables, fit 12 curves respectively, and list the regression equations and correlation coefficients. See attached image. Figures 2 to 13 Correlation coefficient R 2 The values ​​range from 0.9788 to 0.9997, indicating a high degree of fit and reliable model. The regression equation is as follows:

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130] The 48 temperature scale coefficients can be directly solved using the regression equation. (i=1, 2…12) See Table 3. Write the 48 temperature scale coefficients into the strapdown inertial navigation system. At this point, the temperature compensation calibration on the dual-axis temperature control turntable has been completed.

[0131] Step 6): At room temperature, install the inertial navigation system on a dual-axis turntable with a mounting reference. Use a level to calibrate the system, ensuring the X-axis of the strapdown inertial navigation system points north. Rotate the turntable according to the six positions in Table 1. After the turntable stabilizes at each position, collect accelerometer output data for 20 seconds. Complete one accelerometer calibration as per Step 3) to obtain the coupling matrix. and zero offset . This is the conversion matrix between a dual-axis temperature control rotary table and a dual-axis rotary table. This represents the zero-point deviation between the dual-axis temperature control rotary table and the dual-axis rotary table.

[0132]

[0133] Substitute into the accelerometer output model Zhongde:

[0134]

[0135]

[0136] Then the scale coefficient after the reference transformation Right now:

[0137]

[0138] Then the zero bias of the accelerator after the reference transformation Right now:

[0139]

[0140] The 48 temperature scale coefficients were treated as 12 points according to their corresponding calibration parameters. Substituting into the above equation yields a new and The converted temperature scale coefficients are shown in Table 4.

[0141]

[0142] In summary, this invention provides an accelerometer temperature compensation calibration method with short data acquisition time, high reliability of the compensation model, and easy operation to obtain the accelerometer temperature scale coefficient, thereby compensating for and reducing the impact of temperature on the accelerometer output of a strapdown inertial navigation system.

[0143] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention, and no reference numerals in the claims should be construed as limiting the scope of the claims.

[0144] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A six-position temperature compensation calibration method for accelerometers in a strapdown inertial navigation system, characterized by: The method comprises the following steps: Step 1): establishing an accelerometer calibration model of a strapdown inertial navigation system; Step 2): installing the strapdown inertial navigation system in a two-axis temperature-controlled turntable without installation reference, connecting test cables and test equipment; Step 3): rotating the two-axis temperature-controlled turntable, and performing short-time six-position accelerometer calibration of the strapdown inertial navigation system at different temperatures; Step 4): converting the accelerometer calibration model by formula Form, through the least square method of matrix form calculation to find different temperature accelerometer zero offset, scale factor, installation error of 12 calibration parameters; Step 5): respectively establishing a third-order polynomial model of zero offset, scale factor and installation error and accelerometer output temperature, obtaining the coefficients of the third-order polynomial in the model, i.e. initial temperature scale coefficients, through a fitting curve regression equation, and writing the initial temperature scale coefficients into the strapdown inertial navigation system; Step 6): at normal temperature, installing the inertial navigation system on a two-axis turntable with installation reference, performing six-position calibration, obtaining a conversion matrix of the two-axis turntable and the two-axis temperature-controlled turntable, converting the initial temperature scale coefficients to the two-axis turntable with installation reference by using the conversion matrix, obtaining final temperature scale coefficients to be solved, and compensating and writing into the strapdown inertial navigation system to reduce the influence of temperature on accelerometer output of the strapdown inertial navigation system; In step 1) above, the accelerometer calibration model of the strapdown inertial navigation system is: wherein , , , Wherein: — triaxial accelerometer coupling matrix, — triaxial accelerometer scale factor, (i≠j) — triaxial accelerometer mounting error; - tri-axial accelerometer zero offset error; - the actual output value of the three-axis accelerometer; - a three-axis accelerometer theoretical value; In the above step 4), the accelerometer calibration model is converted by a formula The specific process of finding the accelerometer zero offset, scale factor, and installation error in matrix form by least squares method is as follows: On Both sides transpose: That is, The actual output values of the six groups of accelerometers in step 3) are brought into the above formula to obtain: ​ Let: Wherein: ， ， The estimate of in matrix form according to the least squares method is ​ accelerometer zero offset calculated for current temperature , scale factor , mounting error ; The temperature of the temperature control turntable temperature box is set to be -40℃, -20℃, 0℃, 20℃, 40℃ and 60℃ in sequence, and the accelerometer zero offset under different temperature box temperatures is calculated according to the steps 1) to 3) , scale factor , installation error .

2. The six-position temperature compensation calibration method for accelerometers of a SINS according to claim 1, wherein: In the above step 3), the six-position accelerometer calibration process: rotate the double-axis temperature control turntable to make the strapdown inertial navigation system be located at the six positions shown in Table 1 below, without rotation sequence requirement, collect the accelerometer output data for 20s at each position, and calculate the average value to obtain the actual output value of the three-axis accelerometer at the current position After the collection is completed, the actual output values of the accelerometers at the six positions are obtained , and the theoretical accelerations are ; 。 3. The six-position temperature compensation calibration method for accelerometers of a SINS according to claim 2, wherein: In the above step 5), the accelerometer zero offset is established respectively , the scale factor , the installation error A total of 12 parameters correspond to the actual accelerometer temperature cubic polynomial model: wherein , i = 1, 2…12 are cubic polynomial coefficients, i.e. 48 temperature coefficients to be solved in the accelerometer temperature compensation calibration of the SINS, is the temperature of the X-axis accelerometer, is the temperature of the Y-axis accelerometer, is the temperature of the Z-axis accelerometer; Taking corresponding temperature as independent variable and 12 parameters of accelerometer zero offset, scale factor and installation error as dependent variable, fitting a third-order curve, obtaining a regression equation of the fitting curve, and the regression equation coefficients are 48 initial temperature scale coefficients; Writing the 48 temperature scale coefficients into the strapdown inertial navigation system, and at this time, the temperature compensation calibration on the two-axis temperature-controlled turntable has been completed, and the accelerometer data of the strapdown inertial navigation system after initial temperature scale is output.

4. The six-position temperature compensation calibration method for accelerometers of a SINS according to claim 3, characterized in that: In step 6) above, at normal temperature, the inertial navigation system is installed on a two-axis turntable with installation reference, a level is used for leveling, the X-axis of the strapdown inertial navigation system points to the north, the turntable is rotated according to the six positions shown in Table 1, and accelerometer output data is collected for 20s after the turntable is stable at each position; According to step 3), complete an accelerometer calibration to obtain a coupling matrix and an accelerometer zero offset ; is a conversion matrix between the two-axis temperature-controlled turntable and the two-axis turntable. ， Substituting into the accelerometer output model Y = 0.5 * (1 - 0.5) = 0.25 Then the scale factor after installation reference transformation That is: then the mounting reference transformed accelerometer bias i.e. Arrange the scale factor , .

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