Small-angle calibration method and device for inertial navigation system and storage medium

Abstract

The application relates to the technical field of navigation, in particular to a small-angle calibration method and device for an inertial navigation system and a storage medium. The application calibrates accelerometers and gyroscopes in the inertial navigation system by using a multi-position calibration method, can be completed in a short period, and obtains a calibration result with low precision. Then, the installation error calibration and the scale factor error calibration of the gyroscopes are carried out by using a small-angle rotation mode, the calibration precision of the gyroscopes is further improved, the requirements of automatic calibration by rotation are met, and finally, the inertial navigation system is calibrated at the system level to obtain a calibration result with high precision. The technical problem that the calibration method in the prior art cannot realize high-precision calibration in a short period is solved.

Description

Technical Field

[0001] This application relates to the field of navigation technology, and in particular to a method, device and storage medium for small-angle calibration of an inertial navigation system. Background Technology

[0002] Laser gyroscopes offer high measurement accuracy and low engineering difficulty, outperforming existing fiber optic gyroscopes by two to three orders of magnitude. With the engineering application of laser gyroscopes, it is necessary to integrate three laser gyroscopes and an accelerometer to form a laser gyro inertial navigation system (INS). Traditional calibration methods mainly fall into two categories: one is a multi-position calibration method based on Earth's rotation, characterized by simplicity and short calibration cycles but low accuracy; the other is a high-order Kalman filter calibration method based on a strapdown INS error model, i.e., a system-level calibration method, characterized by precise modeling and high calibration accuracy, but also by complexity and long calibration cycles. Existing calibration methods cannot achieve high-precision calibration within a short period. Summary of the Invention

[0003] This application provides a small-angle calibration method for inertial navigation systems, which solves the technical problem that existing technologies cannot achieve high-precision calibration within a short period of time.

[0004] To achieve the above objectives, the technical solutions adopted in the embodiments of this application are as follows:

[0005] In a first aspect embodiment, this application provides a small-angle calibration method for an inertial navigation system, comprising:

[0006] S1. Perform multi-position calibration on the accelerometer in the inertial navigation system to obtain the coarse calibration result of the accelerometer;

[0007] S2. Perform multi-position calibration on the gyroscope in the inertial navigation system to obtain the coarse calibration result of the gyroscope;

[0008] S3. Use a small angular velocity rotation method to calibrate the installation error and scale factor error of the gyroscope, thereby improving the calibration accuracy of the gyroscope;

[0009] S4. Perform system-level calibration on the inertial navigation system to obtain high-precision calibration results.

[0010] This application first uses a multi-position calibration method to calibrate the accelerometer and gyroscope, which can be completed in a short period of time and yields calibration results with lower accuracy. Then, a small angular velocity rotation method is used to calibrate the installation error and scale factor error, further improving the calibration accuracy of the gyroscope to meet the requirements of automatic calibration for statistical rotation. Finally, a system-level calibration is performed on the inertial navigation system to obtain high-precision calibration results, solving the technical problem that existing calibration methods cannot achieve high-precision calibration in a short period of time.

[0011] In some embodiments, the process of calibrating the accelerometer at multiple positions includes:

[0012] S11. Zero the outer frame shaft, middle frame shaft and inner frame shaft of the turntable, rotate the middle frame shaft, take several first angles during the rotation, and collect the output of the accelerometer and the output of the turntable at each first angle;

[0013] S12. Zero the outer frame shaft, middle frame shaft and inner frame shaft of the turntable, rotate the outer frame shaft to a first preset angle, rotate the middle frame shaft, take several first angles during the rotation, and collect the output of the accelerometer and the output of the turntable at each first angle;

[0014] S13. Substitute the output of the accelerometer and the output of the turntable into the accelerometer installation error model to calculate the calibration parameters of the accelerometer, and then obtain the zero bias, scaling factor and installation error of the accelerometer.

[0015] In some embodiments, the expression for the accelerometer installation error model is as follows:

[0016]

[0017] Among them, KA x KA y KA z The calibration parameters for the accelerometer are: XA i for

[0018] [1 sinβ*g -cosβsinγ* g cosβcosγ*g] T β and γ are the angles of the middle frame axis and the inner frame axis, respectively; A ix A iy A iz The output of the accelerometer.

[0019] In some embodiments, the process of performing multi-position calibration on the gyroscope includes:

[0020] S21. Zero the outer frame axis, middle frame axis and inner frame axis of the turntable, rotate the middle frame axis, take several second angles during the rotation, and collect the output of the gyroscope and the output of the turntable at each second angle;

[0021] S22. Zero the outer frame axis, middle frame axis and inner frame axis of the turntable, rotate the outer frame axis to the second preset angle, rotate the middle frame axis, take several second angles during the rotation, and collect the output of the gyroscope and the output of the turntable at each second angle;

[0022] S23. Substitute the output of the gyroscope and the output of the turntable into the gyroscope installation error model to calculate the calibration parameters of the gyroscope, and then obtain the zero bias, scaling factor and installation error of the gyroscope.

[0023] In some embodiments, the expression for the gyroscope installation error model is as follows:

[0024]

[0025] Among them, KG x KG y KG z The calibration parameters for the gyroscope are: XG i for G represents the Earth's rotational angular velocity, L represents the latitude of the calibration location, and α, β, and γ represent the angles of the outer frame axis, the middle frame axis, and the inner frame axis, respectively. ix G iy G iz This is the output of the gyroscope.

[0026] In some embodiments, the process of calibrating the gyroscope installation error and the scale factor error using a small angular velocity rotation method includes:

[0027] S31. Zero the outer frame axis, middle frame axis, and inner frame axis of the turntable, rotate the outer frame axis at a preset angular velocity, and record the output of the turntable and the output of the gyroscope when the outer frame axis rotates from the first position to the second position; zero the outer frame axis, middle frame axis, and inner frame axis, rotate the outer frame axis in the opposite direction at the preset angular velocity, and record the output of the turntable and the output of the gyroscope when the outer frame axis rotates from the second position to the first position;

[0028] S32. Zero the outer frame axis, middle frame axis, and inner frame axis of the turntable, rotate the middle frame axis at a preset angular velocity, and record the output of the turntable and the output of the gyroscope when the middle frame axis rotates from the third position to the fourth position; zero the outer frame axis, middle frame axis, and inner frame axis, rotate the middle frame axis in the opposite direction at the preset angular velocity, and record the output of the turntable and the output of the gyroscope when the middle frame axis rotates from the fourth position to the third position;

[0029] S33. Zero the outer frame axis, middle frame axis, and inner frame axis of the turntable, rotate the inner frame axis at a preset angular velocity, and record the output of the turntable and the output of the gyroscope when the inner frame axis rotates from the fifth position to the sixth position; zero the outer frame axis, middle frame axis, and inner frame axis, rotate the inner frame axis in the opposite direction at the preset angular velocity, and record the output of the turntable and the output of the gyroscope when the inner frame axis rotates from the sixth position to the fifth position;

[0030] S34. Substitute the output of the turntable and the output of the gyroscope into the calculation formulas for the gyroscope scaling factor and installation error matrix to obtain the gyroscope scaling factor and installation error matrix.

[0031] In some embodiments, the expressions for calculating the gyroscope scaling factor and installation error matrix are as follows:

[0032]

[0033] in, G ij (i = 1, 2, 3; j = x, y, z) represents the output of the gyroscope when the outer frame axis, the middle frame axis, and the inner frame axis are rotated, G ij ′, (i = 1, 2, 3; j = x, y, z) are the outputs of the gyroscope when the outer frame axis, the middle frame axis, and the inner frame axis are rotated in reverse.

[0034] In some implementations, the system-level calibration process includes:

[0035] S41. Establish scaling factor error and installation error models for the accelerometer and the gyroscope, respectively;

[0036] S42. Establish the error equations for the inertial navigation system;

[0037] S43. The position error, velocity error, attitude error, scale factor error, and installation error are calculated by the inertial navigation system as filtered state variables, and the state equation is established.

[0038] S44. Using the difference between the position information calculated by the inertial navigation system and the position information provided by GPS as the measurement of the filter, establish the measurement equation;

[0039] S45. Based on step S43, perform a further prediction;

[0040] S46. Based on the measurement results of step S44, the prediction results of the first step are corrected to obtain the optimal state estimation results and the calibration is completed.

[0041] In a second aspect of the embodiment, this application provides a small-angle calibration device for an inertial navigation system, comprising:

[0042] Accelerometer multi-position calibration module, used to perform multi-position calibration of accelerometers in inertial navigation systems;

[0043] A gyroscope multi-position calibration module is used to perform multi-position calibration of the gyroscope in the inertial navigation system.

[0044] The small-angle rotation calibration module is used to calibrate the installation error and scale factor error of the gyroscope using a small angular velocity rotation method.

[0045] The system-level calibration module is used to perform system-level calibration on the inertial navigation system.

[0046] In a third aspect embodiment, this application provides a storage medium comprising: at least one instruction that, when executed, implements the method as described in any of the preceding claims.

[0047] Additional aspects and advantages of embodiments of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of embodiments of this application. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] The methods, systems, and / or procedures shown in the accompanying drawings will be further described with reference to exemplary embodiments. These exemplary embodiments will be described in detail with reference to the drawings. These exemplary embodiments are non-limiting exemplary embodiments, wherein example figures represent similar mechanisms in the various views of the drawings.

[0050] Figure 1 This is a flowchart of a small-angle calibration method for an inertial navigation system in one embodiment;

[0051] Figure 2 This is a flowchart of multi-position calibration of an accelerometer in one embodiment;

[0052] Figure 3 This is a flowchart of multi-position calibration of a gyroscope in one embodiment;

[0053] Figure 4 This is a flowchart of an embodiment using a small angular velocity rotation method to calibrate installation error and scale factor error;

[0054] Figure 5This is a flowchart of system-level calibration in one embodiment;

[0055] Figure 6 This is a schematic diagram of a small-angle rotation calibration path during system-level calibration in one embodiment. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0057] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0058] In the description of this invention, it should be noted that the terms "first," "second," etc., are used only for distinguishing descriptions and should not be construed as indicating or implying relative importance.

[0059] The coordinate system used in this application is defined as follows:

[0060] Navigation reference coordinate system (t-system): The origin of the coordinate system is located at the latitude and longitude position, the x-axis points east, the y-axis points north, and the z-axis points to the sky.

[0061] Inertial platform coordinate system (p-frame): The actual coordinate system obtained by inertial navigation based on attitude calculation, tracking, and reproduction of the navigation reference coordinate system.

[0062] Inertial navigation calculation coordinate system (C system): The northeast-sky coordinate system is determined based on the latitude and longitude calculated by inertial navigation. The origin is at the calculated latitude and longitude position, the x-axis points east, the y-axis points north, and the z-axis points to the sky.

[0063] Carrier coordinate system (b system): A reference coordinate system fixed on the carrier, with the x-axis along the right side of the carrier, the y-axis pointing forward of the carrier, and the z-axis pointing to the top of the carrier.

[0064] Initial inertial coordinate system of the carrier (b0 system): It coincides with the carrier coordinate system at the initial moment and is relatively stationary with respect to the inertial coordinate system.

[0065] A high-precision three-axis turntable provides the rotation. At the turntable's zero position, the carrier coordinate system and the geographic coordinate system coincide. During rotation, the turntable's attitude is determined by the rotation angles of its outer, middle, and inner axes, and the turntable angles can be accurately output. The matrix (attitude transformation matrix) of the turntable's three axis rotation angles is described as follows:

[0066]

[0067] Wherein, α is the turntable angular position reading around the outer frame axis, that is, the azimuth angle reading, ranging from 0° to 360°; β is the turntable angular position reading around the middle frame axis, that is, the pitch angle reading, ranging from 0° to 360°; γ is the turntable angular position reading around the inner frame axis, that is, the roll angle reading, ranging from 0° to 360°.

[0068] During calibration, the inertial navigation system is installed on the turntable surface in one go, and the carrier coordinate system is defined to coincide with the turntable coordinate system. Therefore, the carrier's attitude angle can be directly obtained using the turntable readings, which can be used as the reference value for calculating the angular velocity and acceleration during the calibration process.

[0069] Please see Figure 1 In a first aspect embodiment, this application provides a small-angle calibration method for an inertial navigation system, comprising:

[0070] S1. Perform multi-position calibration of the accelerometers in the inertial navigation system.

[0071] Please see Figure 2 In some implementations, the process of calibrating the accelerometer at multiple positions includes:

[0072] S11. Zero the outer frame shaft, middle frame shaft and inner frame shaft of the turntable, rotate the middle frame shaft, take several first angles during the rotation, and collect the output of the accelerometer and the output of the turntable at each first angle.

[0073] In some specific implementations, the sixteen-position method can be used for multi-position calibration of the accelerometer. Eight first angles can be taken when rotating the middle frame shaft, for example, β = -45°, -35°, -25°, -10°, 0°, 10°, 35°, and 45°. The middle frame shaft is stopped for 120 seconds at each angle, and then the output of the accelerometer and the output of the turntable are collected. Here, the output value of the turntable is the sum of β.

[0074] S12. Zero the outer frame shaft, middle frame shaft and inner frame shaft of the turntable, rotate the outer frame shaft to the first preset angle, rotate the middle frame shaft at the first preset angular velocity, take several first angles during the rotation, and collect the output of the accelerometer and the output of the turntable at each first angle.

[0075] In some specific implementations, the first preset angle can be selected as α = 90°. When calibrating using the sixteen-position method, after rotating the outer frame shaft to 90°, when rotating the middle frame shaft, select the same eight first angles as in S11, and pause for 120 seconds when the middle frame shaft rotates to each angle, and collect the output of the accelerometer and the turntable.

[0076] S13. Substitute the output of the accelerometer and the output of the turntable into the accelerometer installation error model to calculate the calibration parameters of the accelerometer, and then obtain the zero bias, scaling factor and installation error of the accelerometer.

[0077] The accelerometer installation error model was obtained through the following process:

[0078] The output value of the accelerometer can be expressed as

[0079] A=A0+KAf b ...Equation 2

[0080] In the formula, A = [A x A y A z ] T The count value output by the accelerometer; A0 = [A 0x A 0y A 0z ] T This is the zero-bias output of the accelerometer; f is the inverse matrix of the accelerometer's scaling factor and installation error coefficient matrix; b This represents the true value of acceleration along the sensitive axis of the accelerometer.

[0081] When the pitch angle is β and the roll angle is γ, f b The relationship with the attitude angle can be expressed as:

[0082]

[0083] Equation 2 can then be expressed as:

[0084]

[0085] In steps S11 and S12, the output value of the accelerometer at the i-th first angle is denoted as

[0086] A ix A iy A iz , convert [1 sinβ*g -cosβsinγ*g cosβcosγ*g] T Let it be denoted as XAi, then equation 2.5 can be expressed as:

[0087]

[0088] In the formula, KA x For [A] 0x KA xx KA xy KA xz ] T KA y For [A] 0y KA yx KA yy KA yz ] T KA z For [A] 0z KA zx KA zy KA zz ] T .

[0089] According to Equation 5, the expression for the accelerometer installation error model is:

[0090]

[0091] The maximum value of i in the formula is the number of positions selected during calibration. For example, when using the sixteen-position method, i = 1, 2, ..., 16.

[0092] The least squares method is used to solve for KA. x KA y KA z This allows us to obtain the accelerometer's zero bias, scale factor, and installation error.

[0093] S2. Perform multi-position calibration of the gyroscope in the inertial navigation system.

[0094] Please see Figure 3 In some implementations, the process of multi-position calibration of the gyroscope includes:

[0095] S21. Zero the outer frame axis, middle frame axis and inner frame axis of the turntable, rotate the middle frame axis, and take several second angles during the rotation. Collect the output of the gyroscope and the output of the turntable at each second angle.

[0096] In some specific implementations, the sixteen-position method can be used for multi-position calibration of the gyroscope. Eight second angles can be taken when the middle frame axis is rotated, such as β = -45°, -35°, -25°, -10°, 0°, 10°, 35°, and 45°. The middle frame axis is stopped for 120 seconds when it is rotated to each angle, and then the output of the accelerometer and the turntable are collected.

[0097] S22. Zero the outer frame axis, middle frame axis and inner frame axis of the turntable, rotate the outer frame axis to the second preset angle, rotate the middle frame axis, take several second angles during the rotation, and collect the output of the gyroscope and the output of the turntable at each second angle.

[0098] In some specific implementations, the second preset angle can be selected as α = 90°. When calibrating using the sixteen-position method, after rotating the outer frame shaft to 90°, when rotating the middle frame shaft, select the same eight second angles as in S21, and pause for 120 seconds when the middle frame shaft rotates to each angle, and collect the output of the accelerometer and the turntable.

[0099] S23. Substitute the output of the gyroscope and the output of the turntable into the gyroscope installation error model to calculate the calibration parameters of the gyroscope, and then obtain the zero bias, scaling factor and installation error of the gyroscope.

[0100] The gyroscope installation error model was obtained through the following process:

[0101] The gyroscope is calibrated using a multi-position calibration method under static Earth rotation conditions. The equation for the sensitive angular velocity of the gyroscope is:

[0102] G=G0+KGω b ...Form 7

[0103] Where G = [G x G y G z ] T This is the output of the gyroscope; G0 = [G 0x G 0y G 0z ] T To achieve zero drift of the gyroscope; ω is the inverse matrix of the gyroscope's scaling factor and installation error coefficient matrix; b This represents the true value of the angular velocity along the sensitive axis of the gyroscope.

[0104] When the pitch angle β, roll angle γ, and azimuth angle are α in the i-th test:

[0105]

[0106] In the formula, L is the Earth's rotational angular velocity, and L is the local latitude.

[0107] Equation 7 can then be expressed as:

[0108]

[0109] In steps S21 and S22, the output value of the gyroscope at the i-th second angle is denoted as G. ix G iyG iz ,Will Noted as XG i Then equation 9 can be expressed as:

[0110]

[0111] In the formula, KA x For [A] 0x KA xx KA xy KA xz ] T KA y For [A] 0y KA yx KA yy KA yz ] T KA z For [A] 0z KA zx KA zy KA zz ] T .

[0112] According to Equation 10, the expression for the gyroscope installation error model is:

[0113]

[0114] In Equation 11, the maximum value of i is the number of positions selected during calibration. For example, when using the sixteen-position method, i = 1, 2, ..., 16.

[0115] The least squares method was used to calculate KG. x KG y KG z This allows us to obtain the gyroscope's zero bias, scaling factor, and installation error.

[0116] S3. Use a small angular velocity rotation method to calibrate the gyroscope installation error and scale factor error.

[0117] It should be noted that because the Earth's rotational angular velocity is too small, the installation error accuracy of the gyroscope calibrated at multiple positions does not meet the usage requirements. Therefore, it is necessary to use a small angular velocity rotation method to further calibrate the installation error and scaling factor error of the gyroscope.

[0118] Please see Figure 4 In some implementations, the process of calibrating gyroscope installation errors and scaling factor errors using a small angular velocity rotation method includes:

[0119] S31. Zero the outer frame axis, middle frame axis, and inner frame axis of the turntable, rotate the outer frame axis at a preset angular velocity, and record the output of the turntable and the output of the gyroscope when the outer frame axis rotates from the first position to the second position; zero the outer frame axis, middle frame axis, and inner frame axis, rotate the outer frame axis in the opposite direction at a preset angular velocity, and record the output of the turntable and the output of the gyroscope when the outer frame axis rotates from the second position to the first position.

[0120] In some specific implementations, the first position and the second position can be selected as -45° and 45° respectively. The preset angular velocity ω should be within the region where the gyroscope has good linearity, and the deformation of the damper caused by rotation should not be too large. Preferably, ω is 5° / s.

[0121] S32. Zero the outer frame axis, middle frame axis, and inner frame axis of the turntable, rotate the middle frame axis at a preset angular velocity, and record the output of the turntable and the output of the gyroscope when the middle frame axis rotates from the third position to the fourth position; zero the outer frame axis, middle frame axis, and inner frame axis, rotate the middle frame axis in the opposite direction at a preset angular velocity, and record the output of the turntable and the output of the gyroscope when the middle frame axis rotates from the fourth position to the third position.

[0122] In some specific implementations, the third position and the fourth position can be selected as -45° and 45°, respectively.

[0123] S33. Zero the outer frame axis, middle frame axis, and inner frame axis of the turntable. Rotate the inner frame axis at a preset angular velocity and record the output of the turntable and the output of the gyroscope when the inner frame axis rotates from the fifth position to the sixth position. Zero the outer frame axis, middle frame axis, and inner frame axis and rotate the inner frame axis in the opposite direction at a preset angular velocity. Record the output of the turntable and the output of the gyroscope when the inner frame axis rotates from the sixth position to the fifth position.

[0124] In some specific implementations, the fifth and sixth positions can be selected as -45° and 45°, respectively.

[0125] S34. Substitute the output of the turntable and the output of the gyroscope into the calculation formulas for the gyroscope scaling factor and installation error matrix to obtain the gyroscope scaling factor and installation error matrix.

[0126] The formulas for calculating the gyroscope scaling factor and installation error matrix are obtained through the following process:

[0127] The output value of a gyroscope can be expressed as

[0128]

[0129] During the calibration process, data is recorded starting before rotation begins, and recording stops again after a period of time when rotation has ceased. Then, a data point of the same length is extracted from the recorded data, thus obtaining... The rotation process of the three axes has the following relationship:

[0130]

[0131] In the formula, G ij (i = 1, 2, 3; j = x, y, z) are the output values ​​of the gyroscopes during the uniform clockwise rotation from -45° to 45° around the outer, middle, and inner frame axes, respectively; G ij ′, (i=1,2,3; j=x,y,z) are the output values ​​of the gyroscopes during the process of rotating uniformly clockwise from 45° to -45° around the outer, middle, and inner frame axes, respectively.

[0132] remember for The expressions for the formulas for calculating the gyroscope scaling factor and installation error matrix are as follows:

[0133]

[0134] Calculated using the least squares method The accurate gyroscope scaling factor and installation error matrix are obtained.

[0135] S4. Perform system-level calibration on the inertial navigation system.

[0136] Specifically, the inertial navigation system first initiates alignment, then performs system-level calibration. During system-level calibration, a small-angle rotation calibration path is used, as shown in the calibration path below. Figure 6 As shown, a turntable is used to provide rotational conditions to excite the scaling factor error and installation error of the inertial navigation system, and the installation error and scaling factor error of the inertial navigation system are estimated by Kalman filtering based on the position information provided by the satellite equipment.

[0137] Please see Figure 5 In some implementations, the system-level calibration process includes:

[0138] S41. Establish models for the scaling factor error and installation error of accelerometers and gyroscopes.

[0139] The scaling factor error and installation error model of the accelerometer are shown in the following formula:

[0140]

[0141] [δK A ]=diag[δK Ax ,δK Ay ,δK Az ]

[0142]

[0143] Wherein, δK A δA and δA represent the accelerometer's scale coefficient error and installation error angle, respectively.

[0144] The scaling factor error and installation error model of the gyroscope are shown in the following formula:

[0145]

[0146] [δK G ]=diag[δK Gx ,δK Gy ,δK Gz ]

[0147]

[0148] Where, δK G δG represents the gyroscope's calibration coefficient error and installation error angle, respectively.

[0149] S42. Establish the error equations for the inertial navigation system.

[0150] Before small-angle calibration, the constant zero bias of the gyroscope and accelerometer has been accurately compensated, so the constant zero bias of the gyroscope and accelerometer is not considered as a state variable of the Kalman filter. Therefore, the Kalman filter here selects the system error term, scaling factor error, and installation error as 25 dimensions of state variables, as detailed below:

[0151] X = [φ E φ N φ U δV E δV N δλ δL δK Gx δG xy δG xz δG yx δK Gy δG yz δG zx δG zy δK Gz δK Ax δA xy δA xz δA yx δK Ay δA yz δA zx δA zy δK Az ] T ...Form 17

[0152] The established error equation is as follows:

[0153] Attitude error equation:

[0154]

[0155]

[0156]

[0157] Velocity error equation:

[0158]

[0159]

[0160] Position error equation:

[0161]

[0162]

[0163] S43. The position error, velocity error, attitude error, scale factor error, and installation error are calculated by the inertial navigation system as filtered state variables, and the state equation is established.

[0164] The vector representation of the state equation established in step S42 is as follows:

[0165]

[0166] In the formula, X is the state variable. Let A be the derivative of the state variable, A be the system matrix, and W be the noise matrix.

[0167]

[0168]

[0169]

[0170]

[0171]

[0172]

[0173]

[0174]

[0175]

[0176] In the formula, C ij (i = 1, 2, 3; j = 1, 2, 3) are the elements of the attitude transformation matrix in Equation 1.

[0177] S44. The difference between the position information calculated by the inertial navigation system and the position information provided by the satellite navigation system is used as the measurement of the filter, and the measurement equation is established.

[0178] High-precision location information is obtained through external devices such as GPS. Therefore, the location error can be selected as the observation vector of the Kalman filter, and the specific measurement equation is as follows:

[0179] Z = HX + V... Equation 23

[0180] In the formula, Z represents the measurement quantity, H represents the measurement matrix, and V represents the measurement noise.

[0181] Where Z = [δλ δL] T ...Formula 24

[0182]

[0183] In Equation 24: δλ is the longitude error between the inertial navigation system and the satellite navigation system, and δL is the latitude error between the inertial navigation system and the satellite navigation system.

[0184] S45. Based on step S43, perform a further prediction.

[0185] State prediction is performed using the state equations established by S43: X k+1 / k =Φ k+1,k X k ...Form 25

[0186] Update the predicted mean square value in one step:

[0187] Update filter gain:

[0188] In the formula, Φ k+1,k Q is a discretized representation of the state transition matrix. k For the system noise level, Γ k R is the noise driving matrix. k+1 To measure the noise level.

[0189] S46. Based on the measurement results of step S44, correct the prediction results of the first step to obtain the optimal state estimation results and complete the calibration.

[0190] Optimal estimation using measurement information from S44

[0191] X k+1 =X k+1,k +K k+1 (Z k+1 -H k+1 X k+1 / k Equation 28

[0192] Update the variance matrix of the estimation error: P k+1 =P k+1,k -K k+1 H k+1 P k+1 / k ...Form 29

[0193] In one embodiment of the second aspect, this application provides a small-angle calibration device for an inertial navigation system, including an accelerometer multi-position calibration module, a gyroscope multi-position calibration module, a small-angle rotation calibration module, and a system-level calibration module. The accelerometer multi-position calibration module is used to perform multi-position calibration of the accelerometer. The gyroscope multi-position calibration module is used to perform multi-position calibration of the gyroscope. The small-angle rotation calibration module is used to perform installation error calibration and scale factor error calibration using a small angular velocity rotation method. The system-level calibration module is used to perform system-level calibration.

[0194] In a third aspect of the embodiment, this application provides a storage medium including at least one instruction that, when executed, implements the small-angle calibration method for an inertial navigation system as described above.

[0195] Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of this application, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for small-angle calibration of an inertial navigation system, characterized in that, include: S1. Perform multi-position calibration on the accelerometer in the inertial navigation system to obtain the coarse calibration result of the accelerometer; S2. Perform multi-position calibration on the gyroscope in the inertial navigation system to obtain the coarse calibration result of the gyroscope; S3. Use a small angular velocity rotation method to calibrate the installation error and scale factor error of the gyroscope, thereby improving the calibration accuracy of the gyroscope; S4. Perform system-level calibration on the inertial navigation system to obtain high-precision calibration results; The process of calibrating the accelerometer at multiple positions includes: S11. Zero the outer frame shaft, middle frame shaft and inner frame shaft of the turntable, rotate the middle frame shaft, take several first angles during the rotation, and collect the output of the accelerometer and the output of the turntable at each first angle; S12. Zero the outer frame shaft, middle frame shaft and inner frame shaft of the turntable, rotate the outer frame shaft to a first preset angle, rotate the middle frame shaft, take several first angles during the rotation, and collect the output of the accelerometer and the output of the turntable at each first angle; S13. Substitute the output of the accelerometer and the output of the turntable into the accelerometer installation error model to calculate the calibration parameters of the accelerometer, and then obtain the zero bias, scale factor and installation error of the accelerometer. The process of performing multi-position calibration on the gyroscope includes: S21. Zero the outer frame axis, middle frame axis and inner frame axis of the turntable, rotate the middle frame axis, take several second angles during the rotation, and collect the output of the gyroscope and the output of the turntable at each second angle; S22. Zero the outer frame axis, middle frame axis and inner frame axis of the turntable, rotate the outer frame axis to the second preset angle, rotate the middle frame axis, take several second angles during the rotation, and collect the output of the gyroscope and the output of the turntable at each second angle; S23. Substitute the output of the gyroscope and the output of the turntable into the gyroscope installation error model to calculate the calibration parameters of the gyroscope, and then obtain the zero bias, scaling factor and installation error of the gyroscope; The expression for the gyroscope installation error model is as follows: ； in, These are the calibration parameters of the gyroscope; for , Where is the Earth's rotational angular velocity, and L is the latitude of the calibration location. , and These are the angles of the outer frame axis, the middle frame axis, and the inner frame axis, respectively. This is the output of the gyroscope.

2. The small-angle calibration method for an inertial navigation system as described in claim 1, characterized in that, The expression for the accelerometer installation error model is as follows: ； in, These are the calibration parameters for the accelerometer; for , and These are the angles of the middle frame axis and the inner frame axis, respectively; The output of the accelerometer.

3. The small-angle calibration method for an inertial navigation system as described in claim 1, characterized in that, The process of calibrating the gyroscope installation error and the scale factor error using a small angular velocity rotation method includes: S31. Zero the outer frame axis, middle frame axis, and inner frame axis of the turntable, rotate the outer frame axis at a preset angular velocity, and record the output of the turntable and the output of the gyroscope when the outer frame axis rotates from the first position to the second position; zero the outer frame axis, middle frame axis, and inner frame axis, rotate the outer frame axis in the opposite direction at the preset angular velocity, and record the output of the turntable and the output of the gyroscope when the outer frame axis rotates from the second position to the first position; S32. Zero the outer frame axis, middle frame axis, and inner frame axis of the turntable, rotate the middle frame axis at a preset angular velocity, and record the output of the turntable and the output of the gyroscope when the middle frame axis rotates from the third position to the fourth position; zero the outer frame axis, middle frame axis, and inner frame axis, rotate the middle frame axis in the opposite direction at the preset angular velocity, and record the output of the turntable and the output of the gyroscope when the middle frame axis rotates from the fourth position to the third position; S33. Zero the outer frame axis, middle frame axis, and inner frame axis of the turntable, rotate the inner frame axis at a preset angular velocity, and record the output of the turntable and the output of the gyroscope when the inner frame axis rotates from the fifth position to the sixth position; zero the outer frame axis, middle frame axis, and inner frame axis, rotate the inner frame axis in the opposite direction at the preset angular velocity, and record the output of the turntable and the output of the gyroscope when the inner frame axis rotates from the sixth position to the fifth position; S34. Substitute the output of the turntable and the output of the gyroscope into the calculation formulas for the gyroscope scaling factor and installation error matrix to obtain the gyroscope scaling factor and installation error matrix.

4. The small-angle calibration method for an inertial navigation system as described in claim 3, characterized in that, The expressions for the calculation formulas of the gyroscope scaling factor and the installation error matrix are as follows: ； in, = , The output of the gyroscope when the outer frame axis, the middle frame axis, and the inner frame axis are rotated. The output of the gyroscope when the outer frame axis, the middle frame axis, and the inner frame axis are rotated in reverse.

5. The small-angle calibration method for an inertial navigation system as described in claim 1, characterized in that, The system-level calibration process includes: S41. Establish scaling factor error and installation error models for the accelerometer and the gyroscope, respectively; S42. Establish the error equations for the inertial navigation system; S43. The position error, velocity error, attitude error, scale factor error, and installation error are calculated by the inertial navigation system as filtered state variables, and the state equation is established. S44. Using the difference between the position information calculated by the inertial navigation system and the position information provided by GPS as the measurement of the filter, establish the measurement equation; S45. Based on step S43, perform a further prediction; S46. Based on the measurement results of step S44, the prediction results of the first step are corrected to obtain the optimal state estimation results and the calibration is completed.

6. A small-angle calibration device for an inertial navigation system, applied to the small-angle calibration method for an inertial navigation system as described in any one of claims 1 to 5, characterized in that, include: Accelerometer multi-position calibration module, used to perform multi-position calibration of accelerometers in inertial navigation systems; A gyroscope multi-position calibration module is used to perform multi-position calibration of the gyroscope in the inertial navigation system. The small-angle rotation calibration module is used to calibrate the installation error and scale factor error of the gyroscope using a small angular velocity rotation method. The system-level calibration module is used to perform system-level calibration on the inertial navigation system.

7. A storage medium, characterized in that, The storage medium includes at least one instruction that, when executed, implements the method as described in any one of claims 1 to 5.

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