A method for establishing a horizontal attitude reference of a three-axis turntable based on inertial navigation

Abstract

The present invention relates to a method for establishing a horizontal attitude reference of a three-axis turntable based on inertial navigation, which includes 1) definition of a reference coordinate system; 2) calibration of the horizontal installation error angles of the turntable: designing a turntable rotation scheme, and obtaining the horizontal installation error angles dP and dR of the turntable and the installation error angle dh between the inertial navigation and the turntable heading through the change of the turntable heading error err_h at different turntable positions. By utilizing the characteristics that the inertial navigation can output a high-precision heading to maintain the attitude and the three-axis turntable can achieve high-precision three-dimensional rotation, the present invention reasonably designs the turntable rotation scheme, decouples the relevant installation error angles by using the change of the turntable heading error caused by the installation error angles between different rotations, and calculates the horizontal installation error angles dP and dR of the turntable and the installation error angle dh between the inertial navigation and the turntable heading, so as to realize the calibration of the horizontal installation error of the three-axis turntable.

Description

Technical Field

[0001] The present invention belongs to the technical field of inertial navigation, and particularly relates to a method for establishing a horizontal attitude reference of a three-axis turntable based on inertial navigation. Background Technique

[0002] A high-precision three-axis turntable is equipped with high-precision angle measuring elements and control mechanisms, and can be used to simulate the attitude changes during the movement of a carrier. It is a high-precision attitude reference for verifying and evaluating the inertial navigation attitude accuracy. The high-precision three-axis turntable consists of components such as an outer frame, a middle frame, and an inner frame. Among them, the outer frame makes a heading movement around the z-axis, the middle frame makes a pitch movement around the y-axis, and the inner frame makes a roll movement around the x-axis. During the test, the inertial navigation is fixedly installed on the inner frame of the turntable.

[0003] When the three-axis turntable is installed, the turntable zeroing coordinate system formed by the outer frame (z-axis), the middle frame (y-axis), and the inner frame (x-axis) when the three axes of the turntable are all at zero position can be aligned with the navigation coordinate system (such as the "north-east-up" geographic coordinate system). At this time, after calibrating the installation error between the inertial navigation and the turntable, the three-axis rotation angles of the turntable can be directly used as the reference values of the three-dimensional attitude angles of the inertial navigation. However, in actual operation, it is impossible for the turntable zeroing coordinate system to be completely aligned with the navigation coordinate system, that is, there is a small-angle installation error between the turntable zeroing coordinate system and the navigation coordinate system. The horizontal component of this installation error will cause additional errors when the pitch angle is relatively large, directly affecting the accuracy of using the turntable rotation angle as the attitude reference. Therefore, it is necessary to design a method for establishing a horizontal attitude reference for a three-axis turntable.

[0004] In the currently published literature, most of the research on turntable errors is focused on the analysis and compensation of the turntable's own errors: Yang Huahui et al. analyzed and compared the principles and methods of several calibration techniques for the angular position errors of the turntable itself; Li Zhongming et al. proposed a high-precision angular dividing turntable and its error correction method; Jiang Dengming et al. analyzed, modeled, and compensated for the angular position errors caused by the encoder installation eccentricity and inclination rotation errors generated during the turntable assembly process; Qu Zhiyong et al. summarized a total of 27 geometric motion errors of the three-axis turntable according to the structural characteristics of the three-axis turntable; Jia Jianyuan et al. proposed a method for identifying the error parameters of the axis system of a one-azimuth pitch two-axis turntable by using the measurement data of an electronic level and a kinematic model; Chen Yi et al. proposed a three-dimensional turntable system angle error correction algorithm, and obtained the distance and angular offset between the antenna rotation center of the radar system and the turntable rotation center by using the high tracking accuracy of the radar.

[0005] The research on the method for establishing the initial attitude reference of the turntable is mainly based on the field of radar simulation applications. Guo Fusheng et al. established a theodolite / total station three-dimensional intelligent measurement system in a darkroom, and used a non-contact measurement mode and a geometric fitting data processing system to calibrate the zero position reference of the turntable; Liu Qingbo et al. observed the targets installed at the shaft ends of the inner and middle rings of the turntable through a theodolite to determine the initial attitude reference of the three-axis turntable. The above methods are mainly based on precision measuring instruments such as total stations and theodolites, and the operation is relatively complex. Summary of the Invention

[0006] The purpose of the present invention is to overcome the deficiencies of the prior art, and provide a method for establishing the horizontal attitude reference of a three-axis turntable based on inertial navigation. By making full use of the characteristics that inertial navigation can output high-precision heading and maintain attitude, and the three-axis turntable can achieve high-precision three-dimensional rotation, a reasonable turntable rotation scheme is designed. By using the change of the turntable heading error caused by the installation error angle between different rotations, the relevant installation error angles are decoupled, and the horizontal installation error angle of the turntable is calculated, so as to realize the establishment of the horizontal attitude reference of the three-axis turntable.

[0007] The present invention solves its technical problems through the following technical solutions:

[0008] A method for establishing the horizontal attitude reference of a three-axis turntable based on inertial navigation, the method includes the following steps:

[0009] (1) Definition of the reference coordinate system: Define the following coordinate systems:

[0010] 1) The reference coordinate system is the n system: The east-north-up geographic coordinate system n is used as the reference coordinate system. That is, the x-axis and y-axis of the n system are located in the local horizontal plane, the x-axis points east, the y-axis points north, and the z-axis points up along the local vertical line;

[0011] 2) The inertial navigation carrier coordinate system is the b system: The right-front-up coordinate system is used as the carrier coordinate system. That is, the x-axis of the b system is along the transverse axis of the carrier to the right, the y-axis is along the longitudinal axis forward, and the z-axis is along the normal axis up;

[0012] 3) The turntable zeroing coordinate system is the a0 system: The turntable zeroing coordinate system a0 is the coordinate system when the three axes of the turntable are all in the zero position. Its z-axis points up along the azimuth axis of the turntable, the x-axis is consistent with the direction of the middle frame axis of the turntable, and the y-axis is consistent with the direction of the inner frame axis of the turntable. The three coordinate axes form a right-handed coordinate system.

[0013] 4) The turntable coordinate system is the a system: The turntable coordinate system a is obtained by rotating the turntable zeroing coordinate system. The specific calculation formula is

[0014]

[0015] Among them, is the attitude transformation matrix between the turntable coordinate system and the turntable zeroing coordinate system, H zt, P zt , R zt are the angles of the outer frame, middle frame, and inner frame of the turntable respectively;

[0016] Define the attitude transformation relationship between the turntable zeroing coordinate system and the reference coordinate system as:

[0017]

[0018] Among them, is the attitude transformation matrix between the turntable zeroing coordinate system and the reference coordinate system, and dH, dP, and dR are the heading installation error angle, pitch installation error angle, and roll installation error angle between the turntable zeroing coordinate system and the reference coordinate system respectively;

[0019] Define the attitude transformation relationship between the inertial navigation carrier coordinate system and the turntable coordinate system as:

[0020]

[0021] Among them, is the attitude transformation matrix between the inertial navigation carrier coordinate system and the turntable coordinate system, and dh, dp, and dr are the heading installation error angle, pitch installation error angle, and roll installation error angle between the inertial navigation carrier coordinate system and the turntable coordinate system respectively;

[0022] The relationship between the reference coordinate system, the turntable zeroing coordinate system, the turntable coordinate system, and the inertial navigation carrier coordinate system can be expressed by the following formula:

[0023]

[0024] Among them, is the attitude transformation matrix between the reference coordinate system and the inertial navigation carrier coordinate system, which can be represented by the inertial navigation attitude angles H ins , P ins , R ins ;

[0025] (2) Calibration of the turntable horizontal installation error angle:

[0026] 1) The turntable is stationary at position 0, the zeroing position. After the inertial navigation completes power-on alignment and records the heading value of the inertial navigation alignment result , the inertial navigation switches to the navigation state;

[0027] 2) The turntable rotates to position 1: After the outer frame is at 0° - the middle frame is at 60° - the inner frame is at 0° and then stops, record the heading value output by the inertial navigation

[0028] 3) The turntable rotates to position 2: After the outer frame is at 90° - the middle frame is at 0° - the inner frame is at 0° and then stops, the inertial navigation switches to realignment. After recording the heading value of the inertial navigation alignment result , the inertial navigation switches to the navigation state;

[0029] 4) The turntable rotates to position 3: After the outer frame is at 90°, the middle frame is at 60°, and the inner frame is at 0° and then stops, record the heading value output by the inertial navigation

[0030] 5) The turntable rotates to position 4: After the outer frame is at 180°, the middle frame is at 0°, and the inner frame is at 0° and then stops, the inertial navigation enters re-alignment, record the heading value of the inertial navigation alignment result After that, the inertial navigation enters the navigation state;

[0031] 6) The turntable rotates to position 5: After the outer frame is at 180°, the middle frame is at 60°, and the inner frame is at 0° and then stops, record the heading value output by the inertial navigation

[0032] 7) The turntable rotates to position 6: After the outer frame is at 270°, the middle frame is at 0°, and the inner frame is at 0° and then stops, the inertial navigation enters re-alignment, record the heading value of the inertial navigation alignment result After that, the inertial navigation enters the navigation state;

[0033] 8) The turntable rotates to position 7: After the outer frame is at 270°, the middle frame is at 60°, and the inner frame is at 0° and then stops, record the heading value output by the inertial navigation The inertial navigation is powered off;

[0034] 9) Use the heading differences between the tilt positions and horizontal positions of the inertial navigation at each azimuth recorded in steps 1)-8)

[0035]

[0036] 10) Calculate the horizontal installation errors dP, dR of the turntable and the heading installation error angle dh of the turntable using the intermediate variables calculated in step 9). The specific calculation method is as follows:

[0037]

[0038] Among them, the units of dR, dP, and dh are the same as the unit of the recorded inertial navigation heading.

[0039] Moreover, it also includes the verification of the calibration result of the horizontal installation error of the turntable in step 3). The verification method steps are as follows:

[0040] 1) The turntable stops at position 0: The zeroing position, the inertial navigation completes power-on alignment, record the heading value of the inertial navigation alignment result After that, the inertial navigation enters the navigation state;

[0041] 2) Keep the outer and inner frames of the turntable stationary, and the middle frame stops at four positions of 15°, 30°, 45°, and 60° respectively, and record the heading values output by the inertial navigation respectively

[0042] 3) The turntable rotates to position 1: the outer frame is at 90° - the middle frame is at 0° - the inner frame is at 0°, then it stops. The inertial navigation system enters the re-alignment process, and the heading value of the inertial navigation alignment result is recorded. After that, the inertial navigation system enters the navigation state;

[0043] 4) The outer and inner frames of the turntable remain stationary, and the middle frame stops at four positions of 15°, 30°, 45°, and 60° respectively. The heading values output by the inertial navigation are recorded respectively. and

[0044] 5) The turntable rotates to position 2: the outer frame is at 180° - the middle frame is at 0° - the inner frame is at 0°, then it stops. The inertial navigation system enters the re-alignment process, and the heading value of the inertial navigation alignment result is recorded. After that, the inertial navigation system enters the navigation state;

[0045] 6) The outer and inner frames of the turntable remain stationary, and the middle frame stops at four positions of 15°, 30°, 45°, and 60° respectively. The heading values output by the inertial navigation are recorded respectively. and

[0046] 7) The turntable rotates to position 3: the outer frame is at 270° - the middle frame is at 0° - the inner frame is at 0°, then it stops. The inertial navigation system enters the re-alignment process, and the heading value of the inertial navigation alignment result is recorded. After that, the inertial navigation system enters the navigation state;

[0047] 8) The outer and inner frames of the turntable remain stationary, and the middle frame stops at four positions of 15°, 30°, 45°, and 60° respectively. The heading values output by the inertial navigation are recorded respectively. and

[0048] 9) Calculate the calculated turntable headings at 20 positions in steps 1) - 8) according to formulas (1) - (4). When calculating, dp, dr, and dH are all taken as 0, and they are respectively recorded as where P1(0°, 90°, 180°, 270°) is the angle of the outer frame of the turntable, and P2(0°, 15°, 30°, 45°, 60°) is the angle of the middle frame of the turntable;

[0049] 10) Calculate the heading differences at 20 positions respectively and the maximum heading difference at all positions The calculation formula is as shown below. If then this calibration is considered valid

[0050]

[0051] The advantages and beneficial effects of the present invention are:

[0052] 1. The method for establishing the horizontal attitude reference of a three-axis turntable based on inertial navigation makes full use of the characteristics that inertial navigation can output high-precision heading to maintain attitude and the three-axis turntable can achieve high-precision three-dimensional rotation, and completes the quantitative analysis of the heading errors under different outer frame angles and different middle frame angles for the horizontal installation error angles dP and dR of the turntable and the heading installation error angle dh between the inertial navigation and the turntable. On this basis, a reasonable turntable rotation scheme is designed, and by using the change of the turntable heading error caused by the installation error angles between different rotations, the relevant installation error angles are decoupled, and the horizontal installation error angles dP and dR of the turntable and the heading installation error angle dh between the inertial navigation and the turntable are calculated, so as to realize the calibration of the horizontal installation error of the three-axis turntable. Description of the Drawings

[0053] Figure 1 It is the heading error curve under different outer frame angles when dR = 0.1 mil;

[0054] Figure 2 It is the heading error curve under different outer frame angles when dP = 0.1 mil;

[0055] Figure 3 It is the heading error curve under different outer frame angles when dh = 0.1 mil. Detailed Embodiment

[0056] The present invention will be further described in detail below through specific embodiments. The following embodiments are only descriptive and not restrictive, and the protection scope of the present invention cannot be limited thereby.

[0057] A method for establishing the horizontal attitude reference of a three-axis turntable based on inertial navigation, the method comprising the following steps:

[0058] 1. Definition of the reference coordinate system: For the convenience of description, the following coordinate systems are defined:

[0059] 1) Reference coordinate system (n system)

[0060] In this article, the east-north-up geographic coordinate system (n system) is used as the reference coordinate system, that is, the x-axis and y-axis of the n system are located in the local horizontal plane, the x-axis points east, the y-axis points north, and the z-axis points up along the local vertical line.

[0061] 2) Inertial navigation carrier coordinate system (b system)

[0062] In this article, the right-front-up coordinate system is used as the carrier coordinate system, that is, the x-axis of the b system is along the transverse axis of the carrier to the right, the y-axis is along the longitudinal axis forward, and the z-axis is along the normal axis upward.

[0063] 3) The turntable zeroing coordinate system is the a0 system: The turntable zeroing coordinate system a0 is the coordinate system when all three axes of the turntable are in the zero position. Its z-axis points up along the azimuth axis of the turntable, the x-axis is consistent with the middle frame axis of the turntable, the y-axis is consistent with the inner frame axis of the turntable, and the three coordinate axes form a right-handed coordinate system.

[0064] 4) The turntable coordinate system is the a - system: The turntable coordinate system a is obtained by rotating the turntable zero - return coordinate system. The specific calculation formula is

[0065]

[0066] where is the attitude transformation matrix between the turntable coordinate system and the turntable zero - return coordinate system, and H zt , P zt , R zt are the angles of the outer frame, middle frame, and inner frame of the turntable respectively;

[0067] When the three - axis turntable is initially installed, after the initial adjustment by the manufacturer, the installation error angle between the turntable zero - return coordinate system and the reference coordinate system can be considered as a small angle. Therefore, the attitude transformation relationship between the turntable zero - return coordinate system and the reference coordinate system is defined as:

[0068]

[0069] where is the attitude transformation matrix between the turntable zero - return coordinate system and the reference coordinate system, and dH, dP, dR are the heading installation error angle, pitch installation error angle, and roll installation error angle between the turntable zero - return coordinate system and the reference coordinate system respectively. Among them, dP and dR are the horizontal installation errors of the turntable that need to be calibrated in this article.

[0070] When the inertial navigation is installed on the turntable, since the designed installation transition plate can ensure that the installation error angle between the inertial navigation carrier coordinate system and the turntable coordinate system is a small angle. Therefore, the attitude transformation relationship between the inertial navigation carrier coordinate system and the turntable coordinate system is defined as:

[0071]

[0072] where is the attitude transformation matrix between the inertial navigation carrier coordinate system and the turntable coordinate system, and dh, dp, dr are the heading installation error angle, pitch installation error angle, and roll installation error angle between the inertial navigation carrier coordinate system and the turntable coordinate system respectively;

[0073] The relationship between the reference coordinate system, the turntable zero - return coordinate system, the turntable coordinate system, and the inertial navigation carrier coordinate system can be expressed by the following formula:

[0074]

[0075] where is the attitude transformation matrix between the reference coordinate system and the inertial navigation carrier coordinate system, which can be expressed by the inertial navigation attitude angles H ins , P ins , R ins .

[0076] As can be seen from the above analysis, the installation error angles dH, dP, dR between the turntable zeroing coordinate system and the reference coordinate system, and the installation error angles dh, dp, dr between the inertial navigation coordinate system and the turntable coordinate system are all unknowns, and there is a certain coupling relationship among the above six installation error angles. This paper makes full use of the characteristics that inertial navigation can output high-precision heading to maintain attitude and the three-axis turntable can achieve high-precision three-dimensional rotation, reasonably designs the turntable rotation scheme, and decouples the relevant installation error angles by using the change of the turntable heading error caused by the installation error angles between different rotations, and calculates the horizontal installation error angles dP, dR of the turntable and the heading installation error angle dh between the inertial navigation and the turntable, so as to realize the calibration of the horizontal installation error of the three-axis turntable.

[0077] 2. Calibration of the horizontal installation error angle of the turntable

[0078] From the attitude conversion relationship between the reference coordinate system, the turntable zeroing coordinate system, the turntable coordinate system, and the inertial navigation carrier coordinate system analyzed above, combined with theoretical derivation and simulation analysis, it can be seen that when the other two axes of the turntable do not move and only rotate around the pitch axis (the middle frame), only the horizontal installation error angles dP, dR of the turntable and the heading installation error angle dh between the inertial navigation and the turntable will cause the outer frame rotation angle H of the turntable zt relative to the true inertial navigation heading H ins of the heading error err_h. The influence of the horizontal installation error angles dP, dR of the turntable and the heading installation error angle dh between the inertial navigation and the turntable on err_h is as Figures 1 - 3 shown.

[0079] From Figures 1 - 3 it can be seen that the error err_h caused by the heading installation error angle dh between the inertial navigation and the turntable is independent of the position of the outer frame of the turntable, while the errors err_h caused by the horizontal installation error angles dP, dR of the turntable are related to the position of the outer frame of the turntable. Therefore, the above principle can be used to design the turntable rotation scheme, and the horizontal installation error angles dP, dR of the turntable and the heading installation error angle dh between the inertial navigation and the turntable can be obtained through the change of the turntable heading error err_h under different turntable positions. The specific calibration steps are as follows:

[0080] 1) The turntable is stationary at position 0 (zeroing position), the inertial navigation completes power-on alignment, records the heading value of the inertial navigation alignment result and then the inertial navigation enters the navigation state;

[0081] 2) The turntable rotates to position 1 (outer frame 0° - middle frame 60° - inner frame 0°) and then stops, records the heading value output by the inertial navigation

[0082] 3) The turntable rotates to position 2 (outer frame 90° - middle frame 0° - inner frame 0°) and then stops, the inertial navigation enters re-alignment, records the heading value of the inertial navigation alignment result After that, the inertial navigation system enters the navigation state;

[0083] 4) After the turntable rotates to position 3 (outer frame 90° - middle frame 60° - inner frame 0°) and stops, record the heading value output by the inertial navigation system

[0084] 5) After the turntable rotates to position 4 (outer frame 180° - middle frame 0° - inner frame 0°) and stops, the inertial navigation system enters re-alignment, and record the heading value of the inertial navigation alignment result After that, the inertial navigation system enters the navigation state;

[0085] 6) After the turntable rotates to position 5 (outer frame 180° - middle frame 60° - inner frame 0°) and stops, record the heading value output by the inertial navigation system

[0086] 7) After the turntable rotates to position 6 (outer frame 270° - middle frame 0° - inner frame 0°) and stops, the inertial navigation system enters re-alignment, and record the heading value of the inertial navigation alignment result After that, the inertial navigation system enters the navigation state;

[0087] 8) After the turntable rotates to position 7 (outer frame 270° - middle frame 60° - inner frame 0°) and stops, record the heading value output by the inertial navigation system The inertial navigation system is powered off;

[0088] 9) Use the heading differences of the inertial navigation system at different azimuths of the tilt position and the horizontal position recorded in the steps

[0089]

[0090] 10) Calculate the horizontal installation errors dP, dR of the turntable and the heading installation error angle dh of the turntable using the intermediate variables calculated in step 9). The specific calculation method is as follows:

[0091]

[0092] Among them, the units of dR, dP, and dh are the same as the unit of the recorded inertial navigation heading.

[0093] 3. Verification of the calibration result of the horizontal installation error of the turntable

[0094] After completing the calibration of the horizontal installation error angle of the turntable, verify whether the calibration result meets the accuracy requirements through the verification method of the calibration result of the horizontal installation error of the turntable. The specific verification method steps are as follows:

[0095] 1) The turntable stops at position 0 (zeroing position), the inertial navigation system completes power-on alignment, and record the heading value of the inertial navigation alignment result After that, the inertial navigation system enters the navigation state;

[0096] 2) The outer and inner frames of the turntable remain stationary, and the middle frame is stationary at four positions of 15°, 30°, 45°, and 60° respectively. Record the heading values output by the inertial navigation system respectively. and

[0097] 3) After the turntable rotates to position 1 (outer frame 90° - middle frame 0° - inner frame 0°) and stops, the inertial navigation system enters re-alignment, and record the heading value of the inertial navigation alignment result. After that, the inertial navigation system enters the navigation state;

[0098] 4) The outer and inner frames of the turntable remain stationary, and the middle frame is stationary at four positions of 15°, 30°, 45°, and 60° respectively. Record the heading values output by the inertial navigation system respectively. and

[0099] 5) After the turntable rotates to position 2 (outer frame 180° - middle frame 0° - inner frame 0°) and stops, the inertial navigation system enters re-alignment, and record the heading value of the inertial navigation alignment result. After that, the inertial navigation system enters the navigation state;

[0100] 6) The outer and inner frames of the turntable remain stationary, and the middle frame is stationary at four positions of 15°, 30°, 45°, and 60° respectively. Record the heading values output by the inertial navigation system respectively. and

[0101] 7) After the turntable rotates to position 3 (outer frame 270° - middle frame 0° - inner frame 0°) and stops, the inertial navigation system enters re-alignment, and record the heading value of the inertial navigation alignment result. After that, the inertial navigation system enters the navigation state;

[0102] 8) The outer and inner frames of the turntable remain stationary, and the middle frame is stationary at four positions of 15°, 30°, 45°, and 60° respectively. Record the heading values output by the inertial navigation system respectively. and

[0103] 9) Calculate the calculated turntable headings at 20 positions in steps 1) - 8) according to equations (1) - (4) (when calculating, dp, dr, and dH are all taken as 0), and record them respectively as where P1(0°, 90°, 180°, 270°) is the angle of the outer frame of the turntable, and P2(0°, 15°, 30°, 45°, 60°) is the angle of the middle frame of the turntable;

[0104] 10) Calculate the heading differences at 20 positions respectively and the maximum heading difference at all positions The calculation formula is shown as follows. If Then it is considered that this calibration is valid.

[0105]

[0106] Although the embodiments and drawings of the present invention are disclosed for illustrative purposes, those skilled in the art can understand that various substitutions, changes, and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the content disclosed in the embodiments and drawings.

Claims

1. A method for establishing a horizontal attitude reference of a three-axis turntable based on inertial navigation, characterized in that: The method includes the following steps: (1) Definition of the reference coordinate system: Define the following coordinate systems: 1) The reference coordinate system is the n-system: The east-north-up geographic coordinate system n-system is used as the reference coordinate system. That is, the x-axis and y-axis of the n-system are located in the local horizontal plane, the x-axis points east, the y-axis points north, and the z-axis points up along the local vertical line; 2) The inertial navigation carrier coordinate system is the b-system: The right-front-up coordinate system is used as the carrier coordinate system. That is, the x-axis of the b-system is along the transverse axis of the carrier to the right, the y-axis is along the longitudinal axis forward, and the z-axis is along the normal axis up; 3) The turntable zeroing coordinate system is the a0-system: The turntable zeroing coordinate system a0-system is the coordinate system when all three axes of the turntable are in the zero position. Its z-axis points up along the azimuth axis of the turntable, the x-axis is in the same direction as the middle frame axis of the turntable, the y-axis is in the same direction as the inner frame axis of the turntable, and the three coordinate axes form a right-handed coordinate system; 4) The turntable coordinate system is the a-system: The turntable coordinate system a is obtained by rotating the turntable zeroing coordinate system. The specific calculation formula is Among them, is the attitude transformation matrix between the turntable coordinate system and the turntable zeroing coordinate system, H zt , P zt , R zt are the angles of the outer frame, middle frame, and inner frame of the turntable respectively; Define the attitude conversion relationship between the turntable zeroing coordinate system and the reference coordinate system as: Among them, is the attitude transformation matrix between the turntable zeroing coordinate system and the reference coordinate system, and dH, dP, and dR are the heading installation error angle, pitch installation error angle, and roll installation error angle between the turntable zeroing coordinate system and the reference coordinate system, respectively; Define the attitude conversion relationship between the inertial navigation carrier coordinate system and the turntable coordinate system as: Among them, is the attitude transformation matrix between the inertial navigation carrier coordinate system and the turntable coordinate system, and dh, dp, and dr are respectively the heading installation error angle, pitch installation error angle, and roll installation error angle between the inertial navigation carrier coordinate system and the turntable coordinate system; The relationship between the reference coordinate system, the turntable zeroing coordinate system, the turntable coordinate system, and the inertial navigation carrier coordinate system can be expressed by the following formula: Among them, is the attitude transformation matrix between the reference coordinate system and the inertial navigation carrier coordinate system, which can be represented by the inertial navigation attitude angles H ins , P ins , R ins ; (2) Calibration of the turntable horizontal installation error angle: 1) The turntable is stationary at position 0, the zeroing position. The inertial navigation system completes power-on alignment, records the heading value of the inertial navigation alignment result, and then the inertial navigation system enters the navigation state; 2) The turntable rotates to position 1: the outer frame is at 0°, the middle frame is at 60°, and the inner frame is at 0° and then stops. Record the heading value output by the inertial navigation system. 3) The turntable rotates to position 2: After the outer frame is at 90°, the middle frame is at 0°, and the inner frame is at 0° and then stops, the inertial navigation system enters the re-alignment process, and the heading value of the inertial navigation alignment result is recorded. After that, the inertial navigation system enters the navigation state; 4) The turntable rotates to position 3: after the outer frame is at 90°, the middle frame is at 60°, and the inner frame is at 0° and then stops, record the heading value output by the inertial navigation 5) The turntable rotates to position 4: After the outer frame is at 180°, the middle frame is at 0°, and the inner frame is at 0°, it stops, and the inertial navigation enters the re-alignment process, recording the heading value of the inertial navigation alignment result. After that, the inertial navigation enters the navigation state; 6) The turntable rotates to position 5: After the outer frame rotates 180°, the middle frame rotates 60°, and the inner frame rotates 0° and then stops, record the heading value output by the inertial navigation 7) The turntable rotates to position 6: After the outer frame is at 270°, the middle frame is at 0°, and the inner frame is at 0° and then stops, the inertial navigation system switches to re-alignment, and records the heading value of the inertial navigation alignment result. After that, the inertial navigation system switches to the navigation state; 8) The turntable rotates to position 7: After the outer frame is at 270°, the middle frame is at 60°, and the inner frame is at 0° and then stops, record the heading value output by the inertial navigation system. Turn off the inertial navigation system; 9) Use the course differences between the inclined positions and the horizontal positions at each azimuth of the inertial navigation recorded in steps 1)-8) 10) Calculate the turntable horizontal installation errors dP, dR, and the turntable heading installation error angle dh using the intermediate variables calculated in step 9). The specific calculation method is as follows: Among them, the units of dR, dP, and dh are the same as the unit of the recorded inertial navigation heading.

2. The method for establishing a horizontal attitude reference of an inertial navigation-based three-axis turntable according to claim 1, characterized in that: It also includes step 3) Verification of the calibration result of the turntable horizontal installation error. The verification method steps are: 1) The turntable is stationary at position 0: the zeroing position. The inertial navigation system completes power-on alignment, records the heading value of the inertial navigation alignment result, and then the inertial navigation system enters the navigation state; 2) The outer frame and inner frame of the turntable remain stationary, and the middle frame is stationary at four positions of 15°, 30°, 45° and 60° respectively, and the heading values output by the inertial navigation are recorded respectively. and 3) The turntable rotates to position 1: After the outer frame is at 90°, the middle frame is at 0°, and the inner frame is at 0° and then stops, the inertial navigation system enters the re-alignment process, and the heading value of the inertial navigation alignment result is recorded. After that, the inertial navigation system enters the navigation state; 4) The outer frame and inner frame of the turntable remain stationary, and the middle frame is stationary at four positions of 15°, 30°, 45° and 60° respectively, and the heading values output by the inertial navigation are recorded respectively. and 5) The turntable rotates to position 2: After the outer frame is at 180°, the middle frame is at 0°, and the inner frame is at 0°, it stops, and the inertial navigation system enters the re-alignment process, and the heading value of the inertial navigation alignment result is recorded. After that, the inertial navigation system enters the navigation state; 6) The outer frame and inner frame of the turntable remain stationary, and the middle frame is stationary at four positions of 15°, 30°, 45° and 60° respectively, and the heading values output by the inertial navigation are recorded respectively. and 7) The turntable rotates to position 3: After the outer frame is at 270°, the middle frame is at 0°, and the inner frame is at 0° and then stops, the inertial navigation system enters the re-alignment process, and the heading value of the inertial navigation alignment result is recorded. After that, the inertial navigation system enters the navigation state; 8) The outer frame and inner frame of the turntable remain stationary, and the middle frame is stationary at four positions of 15°, 30°, 45° and 60° respectively, and the heading values output by the inertial navigation are recorded respectively. and 9) Calculate the computed turntable headings at a total of 20 positions in steps 1)-8) according to equations (1)-(4). When calculating, dp, dr, and dH are all taken as 0, and they are respectively denoted as where P1(0°, 90°, 180°, 270°) is the angle of the turntable outer frame, and P2(0°, 15°, 30°, 45°, 60°) is the angle of the turntable middle frame; 10) Calculate the course differences at 20 positions respectively and the maximum course difference at all positions The calculation formula is as follows. If then this calibration is considered valid

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