A heading effect error calibration and compensation method for an inertial measurement unit

Abstract

The application discloses a heading effect error calibration and compensation method of an inertial measurement unit, and is based on a calibration system composed of a single-axis turntable, a transfer tool, an optical assembly and a sighting device. After the system-related devices are installed in place, the sighting device performs optical sighting on the optical assembly, and the heading angle of the optical assembly is obtained. In combination with the spatial geometric transmission relationship of the optical assembly, the transfer tool and the inertial measurement unit, the heading angle optical sighting value of the inertial measurement unit is indirectly obtained. Through high-precision angle position control of the single-axis turntable around the sky axis, self-alignment of the inertial measurement unit at any position in the full heading range is realized, and a difference value is obtained by subtracting the heading angle optical sighting value, which is used for parameter estimation of a compensation model. Finally, the compensation model is embedded in the inertial measurement unit, and compensation of the self-alignment result is realized. The application has the advantages of simple operation process, high execution efficiency, low cost and small calculation amount.

Description

Technical Field

[0001] This invention relates to the field of inertial navigation, and in particular to a method for calibrating and compensating for heading effect errors in inertial measurement units. Background Technology

[0002] Inertial navigation systems (INS) use built-in gyroscopes and accelerometers to sense the angular velocity and linear acceleration of the carrier. Through multiple integrations, they can obtain the carrier's position, velocity, and attitude. This process requires no external intervention, radiates low energy, and possesses strong stealth and adaptability, making it widely used in aerospace, precision surveying, and other fields. INS achieving navigation-level accuracy often also perform self-alignment, using its own inertial sensor data to analyze the carrier's angle relative to north. The accuracy of self-alignment directly affects the accuracy of subsequent integration calculations, and errors cannot be eliminated by the INS itself. Therefore, self-alignment technology has become a research hotspot in inertial navigation. The accuracy of self-alignment is affected by many factors, with heading effect being one of them. Heading effect refers to the different north-finding accuracies that occur when self-aligning at different heading angles. Factors affecting accuracy include geomagnetic distribution, uneven temperature fields, servo interference torque, mechanical vibration, etc., making it a nonlinear model with high uncertainty and many factors. Although the causes of heading effect are complex and varied, and it is impossible to completely eliminate heading effect error through a single model, multiple studies have shown that the influence of heading effect at the same heading position has high repeatability. Furthermore, relevant research indicates that the influence of heading effect and heading position exhibit a trigonometric function relationship. Therefore, the self-alignment results of the product across the entire heading range can be corrected by introducing an external high-precision north-finding data source, and the obtained empirical values ​​can be used to correct the product's self-alignment output, thereby reducing the impact of heading effect error.

[0003] The paper "Calibration and Compensation of Heading Effect in Optical Inertial Navigation Platform" discloses three methods for calibrating and compensating for heading effect: a rotational shell calibration method using a turntable, a rotational shell calibration method using a heading sensor, and a heading precession calibration method using control commands. The essence of these methods is that when the heading effect reaches equilibrium, the drift of the three-axis gyroscope at the current heading position due to the heading effect can be extracted using the three-axis command angular velocity within the platform. Exciting multiple heading positions allows for the calibration of the drift of multiple three-axis gyroscopes. Compensating the gyroscope data with the calibrated drift improves the self-alignment accuracy of the system across the entire heading range. This method achieves the calibration and compensation of heading effect error without the need for an external heading reference, reducing the error by almost an order of magnitude after calibration and compensation. However, this method relies on the platform's tracking characteristics to eliminate the need for an external heading reference, making it unsuitable for strapdown inertial measurement systems. Furthermore, achieving heading effect stability requires a considerable amount of time, which, for multi-position calibration, means waiting for the heading effect to stabilize, failing to meet the efficiency requirements of streamlined production.

[0004] The paper "A Calibration Method for Strapdown Gyrocompass Based on Heading Error" discloses a calibration and compensation method for the heading effect of an inertial measurement unit (IMU). Through theoretical derivation, the relationship between the heading error of the strapdown compass alignment and gyro drift is obtained. In the specific implementation, the IMU is fixed on a turntable, and data from the gyroscope and accelerometer are collected at different angular positions. The heading error is fitted to obtain a constant value for the gyro drift error, and finally, the gyroscope output is corrected, improving heading accuracy. However, this method does not fully disclose the method of fixing the IMU on the turntable or the method of obtaining the heading reference. Furthermore, the method is based on an ideal gyrocompass alignment method, and the final error compensation term is the constant drift of the gyroscope. Therefore, it is not suitable for addressing the error effects caused by changing factors such as temperature fields and geomagnetic fields encountered in engineering implementation. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a method for calibrating and compensating for the heading effect error of an inertial measurement unit, thereby improving the absolute accuracy of the inertial measurement unit across the entire heading range, while also meeting the requirements of assembly line production for the efficiency of compensation tests.

[0006] The technical solution of this invention is: a method for calibrating and compensating for heading effect errors in inertial measurement units, comprising the following steps:

[0007] S1. Construct a calibration system, including a single-axis turntable, a transfer fixture, an optical component, and an aiming device; the single-axis turntable rotates around the axial axis and has a plane C; the transfer fixture is fixed on the single-axis turntable and has a plane B perpendicular to plane C; the optical component is fixed on the transfer fixture and has a plane D parallel to plane B;

[0008] S2. Adjust the calibration system to ensure that the perpendicularity of plane C to plane B and the parallelism of plane B to plane D are within the required threshold range.

[0009] S3. Implement error calibration and compensation. The heading reference plane on the outer surface of the inertial measurement unit (IMU) under test is aligned and fixed with plane B. The optical component's plane D is optically aligned using an aiming device to obtain its heading angle. Based on the spatial geometric transfer relationship between the optical component, the adapter, and the IMU, the heading angle of the IMU is indirectly obtained. By controlling the angular position of the single-axis turntable around the azimuth axis, the IMU is self-aligned within the entire heading range. The difference between this self-alignment and the heading angle optical value is calculated, and the compensation model is parameter-estimated to obtain the compensation model. The compensation model is then embedded within the IMU to compensate for the self-alignment heading result of the IMU.

[0010] Furthermore, by controlling the angular position of the single-axis turntable around the azimuth axis, performing inertial measurement unit self-alignment across the entire heading range, and calculating the difference between the inertial measurement unit and the heading angle optical aiming value, parameter estimation is performed on the compensation model to obtain the compensation model. Specific steps include:

[0011] Set the total number of rotational tests to a constant N, and the number of rotational tests to a variable k, and assign the value of k to 0;

[0012] S31. Calculate the target position angle α of the single-axis turntable. k :

[0013]

[0014] In the formula, α is the current angle of the single-axis turntable;

[0015] S32. Control the single-axis rotary table to rotate to the target position angle α. k ;

[0016] S33, the inertial measurement unit performs self-alignment, and the heading result is β. k ;

[0017] S34. Increment the value of variable k by 1;

[0018] S35. If the value of variable k is equal to N, proceed to step S36; otherwise, return to step S31.

[0019] S36. Fitting the compensation model:

[0020] Calculate vector P1:

[0021]

[0022] Calculate vector P2:

[0023]

[0024] Calculate vector X:

[0025]

[0026] In the formula, P1(n) represents the nth element in vector P1, and P2(n) represents the nth element in vector P2;

[0027] Calculate vector Y:

[0028]

[0029] Calculate vector A:

[0030]

[0031] The compensation model is obtained as follows:

[0032] f(θ)=A1+A2·cos(θ)+A3·cos 2 (θ)+A4·cos 3 (θ)+·sin(θ)+A6·sin 3 (θ).

[0033] Furthermore, a compensation model is embedded within the inertial measurement unit (IMU) to compensate for the IMU's self-alignment heading results. The specific method is as follows:

[0034] The inertial measurement unit's self-alignment heading result is β. k ;

[0035] The output of the inertial measurement unit is the compensated result.

[0036]

[0037] Furthermore, the calibration system is debugged, and the specific steps include:

[0038] S21. Perform mechanical leveling on the single-axis turntable so that plane C is parallel to the horizontal plane;

[0039] S22. Fix the adapter tooling on the plane C of the single-axis rotary table;

[0040] S23. If the perpendicularity between plane B and plane C exceeds the set threshold, proceed to step S24; otherwise, proceed to step S25.

[0041] S24. Fine-tune the plane on the adapter fixture that is fixed to the single-axis rotary table, and return to step S22;

[0042] S25. Secure the optical components to the adapter fixture;

[0043] S26. If the parallelism between plane B and the aiming plane D of the optical component exceeds a set threshold, proceed to step S25; otherwise, proceed to step S28.

[0044] S27. Adjust the installation position of the optical components and the adapter fixture, and return to step S25;

[0045] S28. Debugging complete.

[0046] Furthermore, during the error calibration and compensation process in step S3, the calibration system is periodically calibrated. If the calibration is successful, the error calibration and compensation process continues; if the calibration fails, the calibration system is re-adjusted.

[0047] Furthermore, the calibration system should be calibrated periodically, specifically in the following manner:

[0048] In step S2, after the perpendicularity between plane C and plane B and the parallelism between plane B and plane D have been adjusted to the required threshold range, the single-axis turntable is operated to rotate to angle α, and the aiming device is operated to perform optical aiming on the optical component plane D to obtain the optical aiming heading angle γ of plane B.

[0049] When the calibration system needs to be calibrated, operate the single-axis turntable to rotate it to angle α, operate the aiming device to perform optical aiming on the optical component plane D, and obtain the optical aiming heading angle γ1 of plane B;

[0050] If |γ-γ1| is greater than the set threshold, the calibration judgment fails; otherwise, the calibration judgment succeeds.

[0051] The present invention also provides a calibration system for the aforementioned method of calibrating and compensating heading effect error in inertial measurement units, comprising:

[0052] A single-axis turntable, which rotates around a axial axis and has a plane C;

[0053] The adapter fixture is fixed on a single-axis rotary table and has a plane B perpendicular to plane C;

[0054] An optical component, fixed to an adapter fixture, has a plane D parallel to plane B;

[0055] The aiming device is used to perform optical aiming on the plane D of the optical component to obtain the heading angle of the optical component. Based on the spatial geometric transfer relationship between the optical component, the adapter, and the inertial measurement unit, the heading angle optical aiming value of the inertial measurement unit is indirectly obtained.

[0056] Furthermore, the upper surface of plane C of the single-axis turntable has an installation interface for fixing the adapter tooling; the adapter tooling has a shape interface, which can be used to fix the inertial measurement unit and optical components, and can be fixed on plane C of the single-axis turntable.

[0057] Furthermore, the single-axis turntable adopts, but is not limited to, an electrically controlled turntable or an indexing plate; the optical components adopt, but are not limited to, plane mirrors or prisms; and the aiming equipment adopts, but is not limited to, a gyro theodolite or a combination of a north-finding instrument and a theodolite.

[0058] The advantages of this invention compared to existing technologies are as follows: This invention only requires optical aiming at a single heading angle position to obtain the heading angle at any heading angle position across the entire heading, and the compensation model has a small computational load, which can be embedded into the inertial measurement unit to improve the heading accuracy of self-alignment. Compared with other disclosed methods, this invention has a simple operation process, high execution efficiency, and low cost, making it suitable for assembly line production. Attached Figure Description

[0059] Figure 1 This is a schematic diagram of the calibration system of the present invention;

[0060] Figure 2 This is a flowchart of the method of the present invention;

[0061] Figure 3 This is a flowchart of the debugging phase of the method of the present invention;

[0062] Figure 4 This is a flowchart illustrating the implementation stages of the method of the present invention;

[0063] Figure 5 This is a flowchart of the calibration stage of the method of the present invention. Detailed Implementation

[0064] To better understand the technical solution of the present invention, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0065] The method proposed in this invention is implemented through the calibration system proposed in this invention, and the system composition is shown in the figure below. Figure 1 As shown, it mainly consists of a single-axis turntable (such as an electrically controlled turntable, indexing plate, or other equipment capable of high-precision rotation along the axial axis), a transition fixture (the shape of the transition fixture is determined based on the fixing method of the object being measured and the reserved installation interface of the single-axis turntable), optical components (such as plane mirrors, prisms, etc.), and aiming equipment (such as a combination of a gyrotheodolite or a north-finding instrument and a theodolite, etc.). Specific requirements include: the single-axis turntable rotates around the axial axis and has a plane C; the transition fixture is fixed on the single-axis turntable and has a plane B perpendicular to plane C, plane B being a high-precision machining surface of the transition fixture; the optical components are fixed on the transition fixture and have a plane D parallel to plane B, plane D being the aiming plane of the optical components. The upper surface of the single-axis turntable plane C has an installation interface for fixing the adapter fixture; the adapter fixture has sufficient rigidity and its external interface can be used to fix the inertial measurement unit and optical components, and can be fixed on the single-axis turntable plane C; the outer surface of the inertial measurement unit, which is the object being measured, is machined with a high-precision plane A, which serves as the heading reference plane.

[0066] This method is executed in three stages, such as Figure 2 As shown, initial use requires a debugging phase, followed by the implementation phase. During implementation, the system periodically transitions to a calibration phase. Successful calibration allows continued implementation; failure results in a return to the debugging phase. In the implementation phase, the aiming device performs optical aiming on the optical components to obtain their heading angle. This is then combined with the spatial geometric transfer relationship between the optical components, adapter fixture, and inertial measurement unit (IMU) assembly to indirectly obtain the heading angle of the IMU assembly. High-precision angular position control around the azimuth axis using a single-axis turntable enables self-alignment of the IMU assembly at any position within the entire heading range. The difference between this self-alignment and the heading angle is calculated and used for parameter estimation in the compensation model. Finally, a compensation model is embedded within the IMU assembly to compensate for the self-alignment results.

[0067] The specific implementation process is as follows:

[0068] (1) Entering the debugging stage, please refer to Figure 3 ;

[0069] (2) Perform mechanical leveling on the single-axis turntable so that plane C is parallel to the horizontal plane;

[0070] (3) Fix the adapter tooling on the plane C of the single-axis rotary table;

[0071] (4) If the perpendicularity between plane B and plane C exceeds the threshold A1 (A1 is an empirical value obtained based on precision decomposition), proceed to step (5); otherwise, proceed to step (6).

[0072] (5) Repair the plane on the adapter fixture that is fixed to the single-axis rotary table, and proceed to step (3);

[0073] (6) Fix the optical components onto the adapter fixture;

[0074] (7) If the parallelism between plane B and the aiming plane D of the optical component exceeds the threshold A2 (A2 is an empirical value obtained based on the accuracy decomposition), proceed to step (8); otherwise, proceed to step (9).

[0075] (8) Adjust the installation position of the optical components and the adapter, and proceed to step (6);

[0076] (9) Operate the single-axis turntable to rotate it to angle α;

[0077] (10) Operate the aiming device to perform optical aiming on the plane D of the optical component;

[0078] (11) Obtain the aiming heading angle γ of plane B (plane D);

[0079] (12) Entering the implementation stage, you can refer to Figure 4 ;

[0080] (13) After the plane A of the inertial measurement unit is in place with the plane B of the transfer fixture, fix the inertial measurement unit on the transfer fixture.

[0081] (14) Let N be the constant for the total number of rotation tests and k be the variable for counting rotation tests, and assign it a value of 0;

[0082] (15) Calculate the target position angle α of the single-axis turntable. k :

[0083]

[0084] (16) Control the single-axis turntable to rotate to the target position angle α k ;

[0085] (17) The inertial measurement unit performs self-alignment, and the heading result is β. k ;

[0086] (18) Increment the value of variable k by 1;

[0087] (19) If the value of variable k is equal to N, proceed to step (20); otherwise, proceed to step (15).

[0088] (20) The compensation model is obtained by least squares fitting:

[0089] (20.1) Calculate vector P1:

[0090]

[0091] (20.2) Calculate vector P2:

[0092]

[0093] (20.3) Calculate vector X:

[0094]

[0095] (20.4) Calculate vector Y:

[0096]

[0097] (20.5) Calculate vector A:

[0098]

[0099] (20.6) The expression for the compensation model function is obtained:

[0100] f(θ)=A1+A2·cos(θ)+A3·cos 2(θ)+A4·cos 3 (θ)++A5·sin(θ)+A6·sin 3 (θ)

[0101] (21) Embed the compensation model into the inertial measurement unit;

[0102] (21.1) The self-alignment heading result of the inertial measurement unit is β. k ;

[0103] (21.2) The output of the inertial measurement unit is the compensated result.

[0104]

[0105] (22) If the calibration stage has been reached, proceed to step (23); otherwise, proceed to step (1). Please refer to the instructions. Figure 5 ;

[0106] (23) Operate the single-axis turntable to rotate it to angle α;

[0107] (24) Operate the aiming device to perform optical aiming on the plane D of the optical component;

[0108] (25) Obtain the aiming heading angle γ1 of plane B (plane D);

[0109] (26) If |γ-γ1| is greater than the threshold A3 (A3 is an empirical value obtained based on precision decomposition), proceed to step (27); otherwise proceed to step (28).

[0110] (27) The calibration decision failed, proceed to step (1);

[0111] (28) The calibration was successful. Proceed to step (12).

[0112] It is understood that this invention has been described through embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of this invention. Furthermore, under the teachings of this invention, these features and embodiments can be modified to adapt to specific circumstances without departing from the spirit and scope of this invention. Therefore, this invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are protected by this invention.

[0113] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for calibrating and compensating for heading effect error in an inertial measurement unit, characterized in that, Includes the following steps: S1. Construct a calibration system, including a single-axis turntable, a transfer fixture, optical components, and aiming equipment; the single-axis turntable rotates around the celestial axis and has a plane C; Transfer The fixture is fixed on a single-axis rotary table and has a plane B perpendicular to plane C; the optical component is fixed on the adapter fixture and has a plane D parallel to plane B. S2. Adjust the calibration system to ensure that the perpendicularity of plane C to plane B and the parallelism of plane B to plane D are within the required threshold range. S3. Implement error calibration and compensation. The heading reference plane on the outer surface of the inertial measurement unit (IMU) under test is aligned and fixed with plane B. The plane D of the optical component is optically aligned using an aiming device to obtain the heading angle of the optical component. Based on the spatial geometric transfer relationship between the optical component, the adapter fixture, and the IMU, the heading angle optical alignment value of the IMU is indirectly obtained. By controlling the angular position of the single-axis turntable around the azimuth axis, the IMU is self-aligned within the entire heading range. The difference between this self-alignment and the heading angle optical alignment value is calculated, and the parameters of the compensation model are estimated to obtain the compensation model. The compensation model is then embedded within the IMU to compensate for the self-alignment heading result of the IMU. The process involves controlling the angular position of a single-axis turntable around the azimuth axis, performing inertial measurement unit self-alignment across the entire heading range, and calculating the difference between this position and the heading angle optical aiming value to estimate the parameters of the compensation model, thus obtaining the compensation model. Specific steps include: Set the total number of rotational tests to a constant N, and the number of rotational tests to a variable k, and assign the value of k to 0; S31. Calculate the target position angle α of the single-axis turntable. k : α k =(α +k× )%360 In the formula, α is the current angle of the single-axis turntable; S32. Control the single-axis rotary table to rotate to the target position angle α. k ; S33, the inertial measurement unit performs self-alignment, and the heading result is β. k ; S34. Increment the value of variable k by 1; S35. If the value of variable k is equal to N, proceed to step S36; otherwise, return to step S31. S36. Fitting the compensation model: Calculate vector P1: P1 = Calculate vector P2: P2 = Calculate vector X: In the formula, This represents the Nth element in vector P1. This represents the Nth element in vector P2; Calculate vector Y: Y = Calculate vector A: A = The compensation model is obtained as follows: 。 2. The method for calibrating and compensating for heading effect error of inertial measurement units according to claim 1, characterized in that: A compensation model is embedded within the inertial measurement unit (IMU) to compensate for the IMU's self-alignment heading results. The specific method is as follows: The inertial measurement unit's self-alignment heading result is ; The output of the inertial measurement unit is the compensated result. : 。 3. The method for calibrating and compensating for heading effect error of inertial measurement units according to claim 1, characterized in that: The calibration system needs to be debugged. The specific steps include: S21. Perform mechanical leveling on the single-axis turntable so that plane C is parallel to the horizontal plane; S22. Fix the adapter tooling on the plane C of the single-axis rotary table; S23. If the perpendicularity between plane B and plane C exceeds the set threshold, proceed to step S24; otherwise, proceed to step S25. S24. Fine-tune the plane on the adapter fixture that is fixed to the single-axis rotary table, and return to step S22; S25. Secure the optical components to the adapter fixture; S26. If the parallelism between plane B and the aiming plane D of the optical component exceeds a set threshold, proceed to step S25; otherwise, proceed to step S28. S27. Adjust the installation position of the optical components and the adapter fixture, and return to step S25; S28. Debugging complete.

4. The method for calibrating and compensating for heading effect error of inertial measurement units according to claim 1, characterized in that: During the error calibration and compensation process in step S3, the calibration system is periodically calibrated. If the calibration is successful, the error calibration and compensation process continues. If the calibration fails, the calibration system is re-adjusted.

5. The method for calibrating and compensating for heading effect error of inertial measurement unit according to claim 3, characterized in that: The calibration system should be calibrated regularly, specifically in the following ways: In step S2, after the perpendicularity between plane C and plane B and the parallelism between plane B and plane D have been adjusted to the required threshold range, the single-axis turntable is operated to rotate to angle α, and the aiming device is operated to perform optical aiming on the optical component plane D to obtain the optical aiming heading angle γ of plane B. When the calibration system needs to be calibrated, operate the single-axis turntable to rotate it to angle α, operate the aiming device to perform optical aiming on the optical component plane D, and obtain the optical aiming heading angle γ1 of plane B; If |γ If γ1 is greater than the set threshold, the calibration decision fails; otherwise, the calibration decision succeeds.

6. A calibration system for the heading effect error calibration and compensation method of the inertial measurement unit as described in claim 1, characterized in that, include: A single-axis turntable, which rotates around a axial axis and has a plane C; The adapter fixture is fixed on a single-axis rotary table and has a plane B perpendicular to plane C; An optical component, fixed to an adapter fixture, has a plane D parallel to plane B; The aiming device is used to perform optical aiming on the plane D of the optical component to obtain the heading angle of the optical component. Based on the spatial geometric transfer relationship between the optical component, the adapter, and the inertial measurement unit, the heading angle optical aiming value of the inertial measurement unit is indirectly obtained.

7. The calibration system according to claim 6, characterized in that: The upper surface of plane C of the single-axis rotary table has an installation interface for fixing the adapter tooling; the adapter tooling has a shape interface, which can be used to fix the inertial measurement unit and optical components, and can be fixed on plane C of the single-axis rotary table.

8. The calibration system according to claim 6, characterized in that: The single-axis turntable uses, but is not limited to, an electrically controlled turntable or an indexing plate; the optical components use, but are not limited to, plane mirrors or prisms; and the aiming equipment uses, but is not limited to, a gyro theodolite or a combination of a north finder and a theodolite.

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