A self-calibration method for inner bar arm of non-concentric three-axis hybrid inertial navigation accelerometer

Abstract

The application discloses a non-concentric three-axis hybrid inertial navigation accelerometer inner lever arm self-calibration method, first, the three-axis hybrid inertial navigation system is powered on and preheated; second, the three-axis hybrid inertial navigation system control frame rotates according to the designed rotation scheme, and the original data of the gyro and the accelerometer are recorded; finally, the original data is processed, the system error parameters are estimated by using Kalman filtering, and compensation is made. The application provides a non-concentric three-axis hybrid inertial navigation system accelerometer inner lever arm error self-calibration method, the rotation mechanism of the three-axis hybrid inertial navigation system is used to realize the self-calibration of the accelerometer inner lever arm error, the machine does not need to be disassembled, and the engineering practicability is high; the method is a system-level calibration, and can calibrate various system error parameters including the inner lever arm length at the same time; the calibration process considers the problem that the frame rotation centers of the three-axis hybrid inertial navigation do not coincide, and has important significance for improving the output precision of the inertial navigation system.

Description

Technical Field

[0001] This invention belongs to the technical field of error calibration of the internal arm of a triaxial hybrid inertial navigation system accelerometer, specifically relating to a self-calibration method for the internal arm of a non-concentric triaxial hybrid inertial navigation accelerometer. Background Technology

[0002] Inertial navigation systems rely on inertial sensors to measure the specific force and angular velocity of the carrier, and then calculate the information required for navigation based on this. They offer advantages such as high accuracy in short time intervals, full autonomy, and strong anti-interference capabilities. However, the installation of inertial sensors is limited by physical conditions; accelerometers in three directions cannot be aligned with the rotation center of the inertial measurement unit. When angular velocity is input, the accelerometers become sensitive to the resulting acceleration, known as the inner arm error. This error is related to the input angular velocity, angular acceleration, and the position vector from the rotation center to the accelerometer.

[0003] Triaxial hybrid inertial navigation systems (INS) combine the characteristics of platform-based, strapdown, and rotary INS. By isolating the angular motion of the carrier through a platform and suppressing errors through rotational modulation, they can significantly improve system self-alignment and navigation accuracy while maintaining the same level of inertial device precision. This represents a cost-effective and innovative approach to INS. However, because rotational modulation results in a continuous angular velocity input, the impact of inner arm errors on navigation accuracy becomes more severe. Furthermore, in practical triaxial hybrid INS systems, limitations imposed by the actual installation location prevent the complete coincidence of the rotation centers of the three frames. Instead, the inner frame and middle frame, and the middle frame and outer frame each share a common rotation center—a non-concentric triaxial hybrid INS system—a point not addressed in existing research. Therefore, researching calibration methods for accelerometer inner arm errors in cases where the rotation centers of the three frames are not coincident has significant theoretical and engineering application value for triaxial hybrid INS. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a self-calibration method for the inner arm of a non-concentric triaxial hybrid inertial navigation accelerometer, enabling simple and rapid self-calibration and compensation of the inner arm error in a non-concentric triaxial hybrid inertial navigation system. This method utilizes the built-in rotation mechanism of the triaxial hybrid inertial navigation system to self-calibrate the inner arm error of the accelerometer under non-concentric frame conditions, without disassembling the system, thus possessing strong engineering practicality. This method is a system-level calibration, capable of simultaneously calibrating inertial device zero bias, scale factor error, installation angle, and inner arm error. The calibration process considers the issue of non-coincidence of the frame rotation centers in the triaxial hybrid inertial navigation system, resulting in high calibration accuracy, which is of great significance for improving the velocity output accuracy of the inertial navigation system.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A self-calibration method for the inner arm of a non-concentric triaxial hybrid inertial accelerometer includes the following steps:

[0007] Step 1: Control the three frames of the triaxial hybrid inertial navigation system to rotate at varying angular velocities according to the designed accelerometer internal arm error self-calibration rotation scheme, thereby exciting the error parameters, including the 12 accelerometer internal arm parameters, and simultaneously recording the raw data of the gyroscope and accelerometer; the three frames include an inner frame, a middle frame, and an outer frame;

[0008] Step 2: Process the raw data from the gyroscope and accelerometer, calculate the navigation error, and use the Kalman filter model with the frame rotation angle, velocity error and position error as the observations to obtain the estimation result of the internal lever error of the accelerometer.

[0009] Step 3: Perform error compensation on the estimation results of the accelerometer inner arm error in Step 2 to obtain the compensated output of the accelerometer.

[0010] The advantages of this invention compared to the prior art are as follows:

[0011] (1) The self-calibration method for the inner arm error of the accelerometer in a hybrid inertial navigation system with a non-concentric three-axis frame proposed in this invention is a system-level calibration. Using the Kalman filter model, it can simultaneously perform unbiased estimation of the zero bias of the inertial device, the scale factor error, the installation bias angle, and the inner arm error.

[0012] (2) The present invention utilizes the rotation structure inherent in the inertial navigation system to design a self-calibration rotation scheme, which does not require external facilities such as turntables, does not require disassembly, and has a simple calibration process.

[0013] (3) The present invention uses a rotation scheme with variable angular velocity, which can effectively excite the inner arm error and separate various error parameters.

[0014] (4) In view of the problem that the rotation centers of the three-axis hybrid inertial navigation system frame do not coincide, the present invention calibrates the length of the inner rod arm of the three accelerometers relative to the two rotation centers. The calibration accuracy of the inner rod arm error is high, and the relative error of the estimated value is less than 1%. Attached Figure Description

[0015] Figure 1 A flowchart illustrating the self-calibration method for the error of the inner arm of the accelerometer in the non-concentric triaxial hybrid inertial navigation system of the present invention;

[0016] Figure 2 A schematic diagram showing that the rotation centers of a three-axis hybrid inertial navigation system do not coincide.

[0017] Figure 3A schematic diagram defining the internal lever error of the accelerometer in a triaxial hybrid inertial navigation system is shown. Figure (a) is a three-dimensional coordinate decomposition diagram of the accelerometer in the x-direction relative to the two rotation centers O1 and O2, Figure (b) is a three-dimensional coordinate decomposition diagram of the accelerometer in the y-direction relative to the two rotation centers O1 and O2, and Figure (c) is a three-dimensional coordinate decomposition diagram of the accelerometer in the z-direction relative to the two rotation centers O1 and O2.

[0018] Figure 4 This is a schematic diagram of the rotating frame structure of a three-axis hybrid inertial navigation system according to a specific embodiment of the present invention, wherein 1 is the inner frame, 2 is the middle frame, and 3 is the outer frame, and the system can rotate around three axes;

[0019] Figure 5 This is a schematic diagram of the self-calibration rotation scheme for the internal arm error of the accelerometer in a non-concentric triaxial hybrid inertial navigation system. The top figure shows the rotation angles of the three frames, and the bottom figure shows the angular velocities of the three frames.

[0020] Figure 6 The simulation results show the self-calibration method for the internal link error of the accelerometer in a non-concentric triaxial hybrid inertial navigation system. The four sub-figures in the first row are... r xy r xz The filtering results, the four sub-images in the second row are respectively r yy r yz The filtering results, the four sub-images in the third row are respectively r zy r zz The filtering results. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0022] like Figure 1 As shown, the self-calibration method for the inner arm of the non-concentric triaxial hybrid inertial accelerometer of the present invention includes the following steps:

[0023] Step 1: Power on and preheat the triaxial hybrid inertial navigation system;

[0024] Step 2: Control the three-axis hybrid inertial navigation system to rotate according to the designed self-calibration rotation scheme of the accelerometer internal arm error, and record the original data of the gyroscope and accelerometer at the same time;

[0025] Step 3: Process the raw data, calculate the navigation error, estimate the inner arm length using Kalman filtering, and compensate for the inner arm error.

[0026] like Figure 2 As shown, in this invention, O1 is defined as the rotation center of the inner frame and the middle frame, O1z1 coincides with the rotation axis of the inner frame, O1x1 coincides with the rotation axis of the middle frame, and O1y1 is determined by the right-hand rule. O2 is defined as the rotation center of the middle frame and the outer frame, O2x2 coincides with the rotation axis of the middle frame, that is, O1 and O2 are collinear on the rotation axis of the middle frame, O2y2 coincides with the rotation axis of the outer frame, and O2z2 is determined by the right-hand rule. x O y O z These are the centers of mass of the three accelerometers.

[0027] The accelerometer arms in the x, y, and z directions relative to the inner rod of O1 are respectively... The accelerometer arms relative to O2 in the x, y, and z directions are respectively...

[0028] O1 to O x position vector Perform a three-dimensional coordinate decomposition in the O1x1y1z1 coordinate system, with components r in the x, y, and z directions respectively. x1x1 r x1y1 r x1z1 O1 to O y position vector Perform a three-dimensional coordinate decomposition in the O1x1y1z1 coordinate system, with components r in the x, y, and z directions respectively. y1x1 r y1y1 r y1z1 O1 to O z position vector Perform a three-dimensional coordinate decomposition in the O1x1y1z1 coordinate system, with components r in the x, y, and z directions respectively. z1x1 r z1y1 r z1z1 O2 to O x position vector Perform a three-dimensional coordinate decomposition in the O2x2y2z2 coordinate system, with components r in the x, y, and z directions respectively. x2x2 r x2y2 r x2z2 O2 to O y position vector A three-dimensional coordinate decomposition is performed in the O2x2y2z2 coordinate system, with the components in the x, y, and z directions being F. y2x2 r y2y2 r y2z2 O1 to O z position vector Perform a three-dimensional coordinate decomposition in the O2x2yxz2 coordinate system, with components r in the x, y, and z directions respectively. z2x2 r z2y2 r z2z2 .

[0029] Based on geometric relationships, the two sets of inner rod arms differ only in their x-direction components, while their y and z-direction components are equal. Therefore, they are redefined as follows:

[0030]

[0031]

[0032]

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[0035]

[0036] like Figure 2 , Figure 3 As shown, the inner arms of the accelerometer in the x-direction relative to O1 and O2 are respectively The inner arms of the y-axis accelerometer relative to O1 and O2 are respectively The z-axis accelerometer's inner arms relative to O1 and O2 are respectively

[0037] like Figure 4 As shown, the rotating frame structure of the triaxial hybrid inertial navigation system in this invention consists of an inner frame 1, a middle frame 2, and an outer frame 3, and the system can rotate around three axes.

[0038] like Figure 5 As shown, the accelerometer internal lever arm error self-calibration rotation scheme of the present invention includes 8 steps:

[0039] Step 1: First, return the three frames of the triaxial hybrid inertial navigation system to their zero positions, and set the inner frame 1 and the middle frame 2 to operate at periods of 120s and maximum values, respectively. The angular velocity in sine and cosine form rotates for a duration of 240s;

[0040] Step 2: The outer frame 3 rotates at an angular velocity of 6° / s for 15 seconds;

[0041] Step 3, inner frame 1 and middle frame 2 are set to a period of 120 seconds and a maximum value, respectively. The angular velocity in sine and cosine form rotates for a duration of 240s;

[0042] Step 4: The outer frame 3 rotates at an angular velocity of -6° / s for 15 seconds;

[0043] Step 5, outer frame 3 and middle frame 2 are set to a period of 120 seconds and a maximum value, respectively. The angular velocity in sine and cosine form rotates for a duration of 240s;

[0044] Step 6: Inner frame 1 rotates at an angular velocity of 6° / s for 15 seconds;

[0045] Step 7, outer frame 3 and middle frame 2 are set to a period of 120s and a maximum value, respectively. The angular velocity in sine and cosine form rotates for a duration of 240s;

[0046] Step 8: The outer frame 3 rotates at an angular velocity of -6° / s for 15 seconds.

[0047] The total duration is 17 minutes. Steps 1 to 4 excite the inner arm error relative to the common rotation center O1 of the inner frame 1 and the middle frame 2. Steps 5 to 8 excite the inner arm error relative to the common rotation center O2 of the middle frame 2 and the outer frame 3.

[0048] The process of estimating the error of the inner arm of the accelerometer using a Kalman filter model with frame rotation angle, velocity error, and position error as observations is as follows:

[0049] The Kalman filter model takes the frame rotation angle, velocity error and position error in three directions as observations. Based on the error model of the inertial navigation system under the static base, a 42-dimensional system state equation is established. The state variables are frame rotation angle, velocity error, position error, inertial device zero bias, scale factor error, installation bias angle and inner arm error, totaling 42 dimensions.

[0050] The Kalman filter model is as follows:

[0051]

[0052] Z = HX + V(8)

[0053] Where F represents the state matrix and X is the state vector. Z is the differential of the state vector, H is the observation vector, W and V are the measurement matrix, and W and V are the state noise and measurement noise, respectively, both of which are white noise.

[0054]

[0055] Where, φ E φ N φ UδV represents the frame rotation angle. E δV N δV U The values ​​represent the eastward, northward, and celestial velocity errors, respectively; δL, δλ, and δh represent the latitude, longitude, and altitude position errors, respectively; ε x ε y ε z This indicates gyroscope drift. K indicates zero bias of the accelerometer. gx K gy K gz K represents the gyroscope scaling factor error. ax K ay K az Expressed as the accelerometer scale factor error, S gxz S gxy S gyz S gyx S gzy S gzx S represents the gyroscope mounting angle. ayz S azy S azx Indicates the installation offset angle of the accelerometer. r zy r zz This represents 12 internal lever parameters;

[0056] The state matrix F can be written in the form of a block matrix:

[0057] F = [F M F N (10)

[0058]

[0059]

[0060]

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[0062]

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[0064]

[0065]

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

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[0075]

[0076] Where, ω ie Let L be the Earth's angular velocity of rotation, L be the local latitude, R be the Earth's radius, and g be the local gravitational acceleration. Let ω be the transformation matrix from the inertial measurement coordinate system (s-frame) to the navigation coordinate system (n-frame). x ω y ω z These represent the angular velocities of the frame rotation in the inertial measurement coordinate system. These are the angular accelerations of the frame rotation in the inertial measurement coordinate system, f0. x f y f z These are the accelerations input in the inertial measurement coordinate system; F1-F 15 F M F N For intermediate parameters;

[0077] The observable Z in the Kalman filter model includes velocity and position errors in three directions:

[0078] Z = [δV] E δV N δV U δL δλ δh] T (29)

[0079] The superscript T indicates transpose;

[0080] The measurement matrix H is:

[0081] H = [0 6×3 I 6×6 0 6×30 ] 6×39 (30)

[0082] Based on the fundamental equations of the Kalman filter model, Kalman filtering is performed to obtain an estimated value for the inner arm length.

[0083] The compensation scheme for the inner rod arm error is to subtract the additional acceleration caused by the inner rod arm from the accelerometer output, as shown in the following expression:

[0084]

[0085]

[0086]

[0087] in, These are the x, y, and z accelerometer outputs before error compensation for the inner arm. These are the x, y, and z accelerometer outputs after error compensation for the inner arm.

[0088] Table 1 shows the results of singular value decomposition (SVD) of the state variables of the inner arm based on piecewise linear time-invariant system theory (PWCS), i.e., the observability of the state variables of the inner arm. The larger the singular value, the higher the observability of the state variables.

[0089] Table 2 shows the simulation results of the self-calibration of the internal lever error of the accelerometer in a non-concentric triaxial hybrid inertial navigation system. The initial position was set to (40°N, 116°E), the gyroscope drift was 0.02° / h, and the gyroscope angle was set to random walk. Accelerometer zero bias 50μg, accelerometer random walk The scaling factor error for both the gyroscope and accelerometer is 20 ppm. The gyroscope mounting angle is 10″, and the accelerometer mounting angle is 20″. The relative error of the estimated inner rod length is less than 1%.

[0090] Table 1

[0091]

[0092] Table 2

[0093]

[0094] like Figure 6 As shown in the simulation results using the self-calibration method for accelerometer inner arm error proposed in this invention, the state variables of the inner arm length can all enter the 5% error band in about 4 minutes, and the relative errors of the estimated values ​​are all less than 1%, which proves the reliability of the self-calibration method for accelerometer inner arm error of non-concentric triaxial hybrid inertial navigation system proposed in this invention.

[0095] The parts of this invention not disclosed in detail are well-known technologies in the field.

[0096] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of the present invention are protected.

Claims

1. A self-calibration method for the inner arm of a non-concentric triaxial hybrid inertial accelerometer, characterized in that, Includes the following steps: Step 1: Control the three frames of the triaxial hybrid inertial navigation system to rotate at varying angular velocities according to the designed self-calibration rotation scheme of the accelerometer internal arm errors, thereby exciting the error parameters including the errors of the 12 accelerometer internal arms, and simultaneously recording the raw data of the gyroscope and accelerometer; the three frames include an inner frame, a middle frame, and an outer frame; Step 2: Process the raw data from the gyroscope and accelerometer to calculate navigation errors. Using a Kalman filter model with frame rotation angle, velocity error, and position error as observations, obtain the estimated results of the accelerometer inner arm error, including: The Kalman filter model takes the frame rotation angle, velocity error and position error in three directions as the observations. Based on the error model of the inertial navigation system under the static base, a 42-dimensional system state equation is established. The state variables are frame rotation angle, velocity error, position error, inertial device zero bias, scale factor error, installation bias angle and inner arm error. The Kalman filter model is as follows: （1） （2） in, Represents the state matrix, For state vectors, The derivative of the state vector, For the observation vector, For the measurement matrix, and These represent state noise and measurement noise, respectively, both of which are white noise. ； ； ； （3） in, , , Indicates the rotation angle of the frame. , , Indicates the speed errors in the east, north, and sky directions. , , Indicates the positional error of latitude, longitude, and altitude. , , This indicates gyroscope drift. , , This indicates that the accelerometer has zero bias. , , This indicates the gyroscope scale factor error. , , This is expressed as the accelerometer scale factor error. , , , , , Indicates the gyroscope's installation angle. , , Indicates the installation offset angle of the accelerometer. , , , , , , , , , , , This represents 12 internal lever parameters; The state matrix Written in block matrix form: （4） （5） （6） （7） （8） （9） （10） （11） （12） （13） （14） （15） （15） （17） （18） （19） （20） （21） （22） in, The angular velocity of Earth's rotation. The latitude is the local latitude. For the Earth's radius, For local gravitational acceleration, This is the transformation matrix from the inertial measurement coordinate system to the navigation coordinate system. The inertial measurement coordinate system is... Navigation system Tie, , , These represent the angular velocities of the frame rotation in the inertial measurement coordinate system. , , These represent the angular accelerations of the frame rotation in the inertial measurement coordinate system. , , These are the accelerations input in the inertial measurement coordinate system, respectively. - , , For intermediate parameters; Observations of the Kalman filter model Includes velocity and position errors in three directions: （23） Measurement matrix for: （24） Based on the basic equations of the Kalman filter model, Kalman filtering is performed to obtain the estimated value of the inner arm. Step 3: Perform error compensation on the estimation results of the accelerometer inner arm error in Step 2 to obtain the compensated output of the accelerometer.

2. The self-calibration method for the inner arm of a non-concentric triaxial hybrid inertial accelerometer according to claim 1, characterized in that: In step 1, the self-calibration rotation scheme for the error of the accelerometer inner arm is specifically divided into the following 8 steps: Step (1) First, return the three frames of the triaxial hybrid inertial navigation system to their zero positions. The gyroscope points to the sky; the inner frame and middle frame are set to rotate at a period of 120 seconds and a maximum value, respectively. The inner frame and the middle frame rotate at angular velocities in the form of sine and cosine for 240 seconds. Then the inner frame and the middle frame stop rotating at the same time, and at this time the inner frame and the middle frame return to the zero position. Step (2) The outer frame rotates at an angular velocity of 6° / s for 15 seconds. The gyroscope points to the ground; Step (3) The inner frame and middle frame are set with a period of 120s and a maximum value, respectively. The inner frame and the middle frame rotate at angular velocities in the form of sine and cosine for 240 seconds. Then the inner frame and the middle frame stop rotating at the same time, and at this time the inner frame and the middle frame return to the zero position. Step (4) Outline with Rotate at an angular velocity of 6° / s for 15 seconds, at which point the outer frame returns to its zero position; Step (5) The outer frame and the middle frame are set with a period of 120 seconds and a maximum value, respectively. The outer frame and the middle frame rotate at angular velocities in the form of sine and cosine for 240 seconds. Then the outer frame and the middle frame stop rotating at the same time, and at this time the outer frame and the middle frame return to the zero position. Step (6) The inner frame rotates at an angular velocity of 6° / s for 15 seconds. The gyroscope points to the ground; Step (7) The outer frame and the middle frame are set with a period of 120 seconds and a maximum value, respectively. The outer frame and the middle frame rotate at angular velocities in the form of sine and cosine for 240 seconds. Then the outer frame and the middle frame stop rotating at the same time, and at this time the outer frame and the middle frame return to the zero position. Step (8) Outline with Rotate at an angular velocity of 6° / s for 15 seconds, at which point the outer frame returns to its zero position.

3. The self-calibration method for the inner arm of a non-concentric triaxial hybrid inertial accelerometer according to claim 2, characterized in that: In step 3, the error compensation method is to subtract the acceleration error caused by the inner rod arm from the accelerometer output, as shown in the following expression: （25） （26） （27） in, , , These are the inner arm error compensation before and after. , , accelerometer output, , , These are the inner arm error compensation results. , , Accelerometer output.

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