A three-axis gyroscope successive start error fast calibration method based on compass alignment error characteristics

Abstract

A kind of three-axis gyro successive start error fast calibration method based on compass alignment error characteristics is used to calibrate the successive start error of low-precision three-axis gyro in field quickly.The method is based on the characteristics of compass alignment heading error, and the relationship between the successive start error of each axis, compass control loop parameters and compass alignment heading angle error, to estimate the successive start error of three-axis gyro step by step.Firstly, collect and store the output data of inertial navigation system gyroscope and accelerometer at initial position, and perform compass alignment, record the alignment results;Then change the compass control loop parameters, and estimate the Z-axis gyro successive start error using the alignment results before and after changing the parameters;After compensating the Z-axis gyro successive start error, get the alignment results at initial position, then use the turntable to generate 90° and 180° angular position, and perform compass alignment at 90° and 180° respectively;Finally, combine the alignment results at three positions to establish equations, and solve the X and Y-axis gyro successive start error to realize the calibration of three-axis gyro successive start error.

Description

Technical Field

[0001] This invention relates to a rapid calibration method for successive start-up errors of a three-axis gyroscope based on the characteristics of compass alignment error. It belongs to the field of inertial navigation and can be used for rapid field calibration of medium- and low-precision gyroscopes. It is particularly suitable for short-term application scenarios where external information is scarce and a rapid response is required. Background Technology

[0002] Inertial navigation systems (INS) that calculate the velocity and position of a vehicle using gyroscope and accelerometer sensor signals are independent of external information. They are autonomous navigation and orientation systems capable of outputting all navigation parameters, characterized by smooth signals and high short-term accuracy. They play an irreplaceable role in navigation and positioning of various vehicles in the sea, land, air, and space domains. The gyroscope is the core component of an INS and a significant factor limiting its performance and cost. Countries worldwide invest heavily in the development of high-performance gyroscopes for high-precision applications, developing high-precision fiber optic gyroscopes, laser gyroscopes, and electrostatic gyroscopes, coupled with rotation modulation algorithms, to achieve high-precision navigation over long distances and endurance. However, in medium- and low-precision systems, gyroscopes are unstable due to limitations in materials, manufacturing processes, and processing systems, exhibiting successive startup errors, primarily manifested as changes in zero bias after each startup. This is more pronounced in MEMS gyroscopes, where the zero bias differs after each startup and fluctuates significantly, reaching the order of degrees per second. Compared to successive startup errors, the zero-bias error of a MEMS gyroscope during operation after startup is a slow, random process with little change in the constant value portion.

[0003] Meanwhile, traditional multi-source data fusion methods based on Kalman filtering require measurement information and often need to be combined with certain carrier maneuvering strategies to complete gyroscope error estimation. In short-term application scenarios where external information is scarce and rapid response is required, a fast and simple calibration method is necessary. Therefore, considering the characteristics of low-to-medium precision gyroscope application scenarios, this invention utilizes the successive startup error calibration compensation of low-to-medium precision three-axis gyroscopes to improve the initial alignment and navigation positioning accuracy of inertial navigation systems, which is of great significance. Summary of the Invention

[0004] The purpose of this invention is to address scenarios where external reference information is scarce and rapid response is required. Based on the study of the characteristics of compass alignment error, this invention estimates the successive start-up error of a three-axis gyroscope step by step by adjusting the parameters of the compass control loop and the system orientation, thereby achieving rapid calibration of the successive start-up error of a medium-to-low precision three-axis gyroscope.

[0005] The technical solution of this invention is as follows: By analyzing the characteristics of the compass heading angle alignment error, an expression for the compass heading angle alignment error is derived. Furthermore, the successive startup of the three-axis gyroscope is decoupled from the compass heading angle alignment error expression, and a rapid calibration method for the successive startup error of the three-axis gyroscope based on the characteristics of the compass alignment error is proposed. This method is characterized by first adjusting the compass control loop parameters to separate and estimate the successive startup error of the gyroscope's Z-axis; based on compensating for the Z-axis successive startup error, a system of equations is established using the turntable rotation azimuth, with the successive startup errors of the X and Y axes as unknowns; the successive startup errors of the gyroscope's X and Y axes are estimated by solving the system of equations. This method is simple and effective, enabling rapid calibration of the successive startup error of the three-axis gyroscope.

[0006] The rapid calibration method for successive startup errors of a three-axis gyroscope based on compass alignment error characteristics includes the following steps:

[0007] (1) Acquire and store the initial position gyroscope and accelerometer outputs online, and perform compass alignment;

[0008] (2) Adjust the parameters of the compass control loop, complete the compass alignment again, and estimate the successive start error of the Z-axis gyroscope;

[0009] (3) After compensating for the successive start-up error of the Z-axis gyroscope, perform compass alignment again and record the alignment result at this time;

[0010] (4) Use a turntable to generate 90° and 180° angular positions. Perform compass alignment at the positions 90° and 180° relative to the initial position. Combine the obtained compass alignment results with the initial position alignment results to establish equations and solve them to obtain the successive start errors of the X and Y axis gyroscopes.

[0011] The principle of this invention: The compass alignment method is a precision alignment method based on the inertial navigation error equation and the compass effect. Even after the compass horizontal alignment loop is completed, a misalignment angle φ still exists in the heading angle. U This will make the eastward axis sensitive to the heading misalignment angle φ. U The relevant angular velocity component of Earth's rotation φ U ω ie Therefore, the horizontal control loop will cause the eastward axis to rotate, resulting in a tilt of the northward axis. The northward accelerometer will then be sensitive to the gravitational acceleration component. After horizontal alignment, the heading misalignment angle φ U This connects the celestial axis and the northward horizontal loop, creating a certain coupling relationship between the two axes, which is known as the compass effect.

[0012] When there is a heading misalignment angle φ U At that time, due to the compass effect, the northward component of gravitational acceleration in the navigation system This will change, which will further lead to northbound velocity errors in the navigation system. A change has occurred. Utilizing the northbound velocity error. and heading misalignment angle φ U The coupling relationship between them, designing appropriate control loops and parameters (K) U1 K U2 K U3 and K U4 This allows the heading misalignment angle to gradually decrease, thus obtaining a heading angle ψ that does not diverge over time.

[0013] Based on the fundamental principles of compass alignment and Mason's formula, the heading misalignment angle φ can be calculated. U Frequency domain equation φ U (s) is:

[0014]

[0015] In equation (1), K(s), Δ * (s) are respectively

[0016]

[0017]

[0018] Substituting equations (2) and (3) into equation (1), we can obtain the compass heading angle alignment error Δψ as follows:

[0019]

[0020] In equation (4), ε E ε U These are the equivalent gyroscope zero biases for eastward and upward directions, respectively, expressed under the navigation system. When the IMU is installed in a "right-front-upward" configuration, ε is present. E =ε x cosψ-ε y sinψ, ε U =ε z , where ε x ε y ε z The gyroscope is zero biased under the load system. Therefore, equation (4) can be written as

[0021]

[0022] As can be seen from the above formula, the compass alignment error is affected by the local latitude L and the Earth's radius R. e Earth's rotational angular velocity ω ie X, Y, and Z axis gyroscope errors and compass loop control parameters K U2 K U3 K U4 Impact. Among them, L and Re ω ie It is a constant. In addition, the heading angle alignment error is also coupled with the heading angle ψ itself. Based on the analysis of the coupling relationship between the variables in equation (5) under different working conditions and different directions, this paper proposes a step-by-step estimation method for the Z-axis gyroscope error and the X and Y-axis gyroscope errors based on the compass alignment error.

[0023] As can be seen from equation (5), the first term is related to the zero bias of the X and Y axis gyroscopes and the heading angle, while the second term is related to the zero bias of the Z axis gyroscope and the compass parameters. Under the same initial state, the first term... None of the variables in the middle change. Therefore, the second term is adjusted. Control parameter K U2 K U3 K U4 This will lead to different heading errors. When K is adjusted separately... U2 K U3 K U4 For K' U2 K' U3 K' U4 At that time, the heading error Δψ' is expressed as:

[0024]

[0025] Subtracting equation (5) from equation (6) yields:

[0026]

[0027] Therefore, the Z-axis gyroscope error ε z It can be represented as:

[0028]

[0029] In equation (7), Δψ-Δψ' is the calculated difference between the alignment results before and after adjusting the control parameters, and is a measurable value. As shown in equation (8), with the initial state unchanged, based on the control parameters before and after adjustment, and the alignment results before and after adjusting the control parameters, the successive start-up error ε of the Z-axis gyroscope can be estimated. z .

[0030] From equation (5), it can be seen that the compensation in Δψ is due to ε z After the resulting heading error, the heading error is only related to the errors ε of the X and Y axis gyroscopes. x ε y It is related to the true heading angle ψ, and the heading error Δψ at this time xy It can be represented as:

[0031]

[0032] Since the X and Y axis gyroscope errors after startup are a random process that changes slowly over time, they can be considered constant in the short term. Therefore, based on equation (9), the successive startup errors of the X and Y axis gyroscopes can be calculated from multiple sets of input and output data aligned with the compass at different azimuth angles.

[0033] From equation (9), we can see that there are a total of ψ and ε. x , ε y Three unknowns require solving three equations simultaneously. Since the equations are nonlinear equations about the unknown ψ, solving the three equations simultaneously may result in multiple solutions. However, for ψ, there exist cosψ = ​​-cos(ψ + 180) and sinψ = -sin(ψ + 180). Adding the equation obtained after rotating the indexing mechanism by 180° to the equation at the initial position cancels out the nonlinear terms related to ψ. Therefore, to facilitate solving the equations, this paper establishes equations at three positions: 0°, 90°, and 180°, obtaining the heading angle errors at the three positions as shown in equations (10)(11)(12):

[0034]

[0035]

[0036]

[0037] Where ψ is the true value of the initial position heading angle, Δψ xyi (i = 0, 90, 180) represents the heading angle error of the compass alignment at an inversion position of i°, ψ xyi (i = 0, 90, 180) represents the heading angle obtained by compass alignment at a rotation position of i°. By combining equations (10), (11), and (12), the unknowns ψ and ε can be obtained. x , ε y The value of .

[0038] Adding equation (10) to equation (12) yields the true value of the initial position heading angle ψ. The calculated result is as follows:

[0039]

[0040] Substituting equation (13) into equations (10) and (11), we can immediately obtain the result that only relates to ε. x ε y The relevant linear equations are used to estimate the successive start-up errors ε of the X and Y axis gyroscopes. x ε y .

[0041] In summary, this allows for the rapid calibration of the successive start-up error of a three-axis gyroscope.

[0042] The advantages of this invention compared to the prior art are:

[0043] (1) It does not require external multi-source sensor information, has a short preparation time, and is more suitable for scenarios that require rapid response.

[0044] (2) Based on the characteristic expression of the compass alignment error, the successive start-up error of the three-axis gyroscope is decoupled step by step, and then the parameter and orientation are changed to calibrate it. Attached Figure Description

[0045] Figure 1 This is a flowchart of the rapid calibration method for successive start-up errors of a three-axis gyroscope based on the characteristics of compass alignment error, according to the present invention. Detailed implementation method:

[0046] Figure 1 The flowchart of the rapid calibration method for successive start-up errors of a three-axis gyroscope based on the characteristics of compass alignment error of the present invention is as follows:

[0047] (1) Acquire and store the initial position gyroscope and accelerometer outputs online, and perform compass alignment;

[0048] (2) Adjust the compass control circuit parameters, complete the compass alignment again, and calibrate the successive start error of the Z-axis gyroscope;

[0049] (3) After compensating for the successive start-up error of the Z-axis gyroscope, perform compass alignment again and record the alignment result at this time;

[0050] (4) Use a turntable to generate 90° and 180° angular positions. Perform compass alignment at the positions 90° and 180° relative to the initial position. Combine the obtained compass alignment results with the initial position alignment results to establish equations and solve them to obtain the successive start errors of the X and Y axis gyroscopes.

[0051] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A method for rapid calibration of successive start-up errors of a three-axis gyroscope based on the characteristics of compass alignment error, characterized in that... Includes the following steps: (1) Acquire and store the initial position gyroscope and accelerometer outputs online, and perform compass alignment; record the heading angle alignment error. ; (2) Adjust the parameters in the compass control circuit for Complete the compass alignment again and record the heading angle alignment error. And calibrate the successive start error of the Z-axis gyroscope: in, The radius of the Earth; (3) After compensating for the successive start-up error of the Z-axis gyroscope, perform compass alignment again and record the alignment error at this time; (4) Using a turntable to generate 90° and 180° angular positions, perform compass alignment at positions rotated to 0°, 90°, and 180° relative to the initial position, and record the compass alignment heading angle errors at the three positions as follows: Determine them according to the following three formulas respectively: in, This is the Earth's rotational angular velocity; The latitude is the local latitude. joint and The true value of the heading angle at the initial position is obtained. : Then Substitution and From the equations, the successive start errors of the X and Y axis gyroscopes can be obtained by solving them simultaneously. .

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