High-precision inertial platform nine-position autonomous calibration method

Abstract

This invention discloses a high-precision nine-position autonomous calibration method for an inertial platform, belonging to the field of inertial navigation technology. Specifically, it includes the following steps: S1: analyzing the installation error of the gyroscope; S2: analyzing the installation error of the accelerometer; S3: constructing a static error model of the inertial platform system; S4: based on the static error model of the inertial platform system in step S3, constructing a nine-position mathematical model for error coefficient calibration; S5: performing calibration calculations on the nine-position mathematical model for error coefficient calibration in step S4. Based on the characteristics of inertial platform installation errors, this invention analyzes the error model of the platform system considering installation errors, and the proposed calibration method can calibrate both the platform error coefficients and installation errors. Experimental verification shows that this calibration method has good stability and repeatability, and can relax the installation requirements of inertial instruments, ensuring the stability of installation accuracy and improving the accuracy of inertial instruments.

Description

Technical Field

[0001] This invention relates to the field of inertial navigation technology, and in particular to a high-precision inertial platform nine-position autonomous calibration method. Background Technology

[0002] Inertial navigation plays a crucial role in modern navigation systems. The errors of the instruments in an inertial navigation system determine the accuracy of the system; therefore, error compensation for inertial instruments is necessary, especially for high-precision inertial platforms, where error compensation for accelerometers and gyroscopes is particularly important.

[0003] Currently, research on the autonomous calibration of inertial platform error coefficients mainly focuses on the calibration of gyroscope and accelerometer error coefficients, with relatively little research on the calibration of instrument installation errors. Multi-position calibration methods are a widely used approach. In 1995, Liu Xihe et al. of the Beijing Institute of Automatic Control proposed a multi-position self-calibration method for platform parameters. However, this method did not analyze the calibration accuracy of the parameters, nor did it effectively excite the quadratic and cross terms in the model. In 2000, Yang Lixi et al. of the Beijing Institute of Control Instruments systematically described the "three-self" technology and development trends of typical American inertial platforms, providing guidance for domestic research on self-calibration and self-alignment technologies. Furthermore, Yang Lixi et al. proposed a sixteen-position self-calibration method for inertial platforms, which can calibrate 42 parameters of the platform's inertial navigation system. In 2003, Xu Zhigang et al. of the Beijing Institute of Automation Control Equipment proposed a nine-position calibration method capable of calibrating the installation error of accelerometers with an accuracy of 1–3 arcminutes. Xu Junhui et al. from the Second Artillery Engineering Academy also proposed a nine-position autonomous calibration method to calibrate the main parameters of gyroscopes and accelerometers, but it did not calibrate all installation error angles. Xiao Zhenglin et al. from the Second Artillery Engineering Academy proposed a twelve-position calibration method in 2005, which can calibrate the installation error angles of accelerometers. Yang Huabo from the National University of Defense Technology improved Yang Lixi's sixteen-position method in 2006, which can improve the calibration accuracy of the inertial platform and effectively calibrate the key parameters of the inertial platform. Wang Junshan et al. from the Second Artillery Engineering Academy proposed a seven-position self-calibration method for inertial platforms in 2010, which can complete calibration within 40 minutes, a relatively short calibration time with certain practical value. Zhou Wen et al. from Harbin Engineering University analyzed the observability of six-position and sixteen-position calibration methods in 2013 and conducted simulation verification.

[0004] Currently, domestic scholars' research on error modeling and parameter calibration of inertial navigation systems is mostly limited to theoretical analysis and simulation verification. Further efforts are needed in areas such as the study of error mechanisms of inertial devices, improvement of error models, research on identification methods, and experimental design. Summary of the Invention

[0005] To address the aforementioned problems, this invention aims to provide a high-precision inertial platform nine-position autonomous calibration method that combines the structural characteristics of inertial platforms, offers good stability and repeatability, and takes into account installation errors.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A high-precision inertial platform nine-position autonomous calibration method, characterized by the following steps:

[0008] S1: Analyze the installation error of the gyroscope;

[0009] S2: Analyze the installation error of the accelerometer;

[0010] S3: Construct a static error model for the inertial platform system;

[0011] S4: Based on the static error model of the inertial platform system in step S3, construct a nine-position mathematical model for error coefficient calibration;

[0012] S5: Perform calibration and solution calculations on the nine-position mathematical model for calibrating the error coefficients in step S4.

[0013] Furthermore, the specific operation of step S1 includes the following steps:

[0014] S101: Let E be the mounting coordinate system of the three gyroscopes, x, y, and z. x E y and E z The installation error angle of the x-gyroscope is E. xx E xy and E xz Analyzing the installation relationship between the x-gyroscope and the inertial platform, the installation error matrix of the x-gyroscope is:

[0015]

[0016] S102: Analyze the installation relationship between the Y-gyroscope and Z-gyroscope and the inertial platform, and obtain the installation error matrices of the Y-gyroscope and Z-gyroscope.

[0017] S103: Rotational angular velocity based on the inertial platform body Projection on the x-axis of the gyroscope The installation error angle E of the x-gyroscope xx E xy and E xz Simplified to E xx and E xz Similarly, the installation error angle of the y-gyroscope can be simplified to E.yx and E yz The installation error angle of the z-gyroscope is simplified to E. zy and E zx .

[0018] Furthermore, the specific operation of step S2 includes the following steps:

[0019] S201: Let K be the installation coordinate system of the three accelerometers (x, y, z). x K y and K z The installation error angle of the x-accelerometer is K. xx K xy and K xz Analyzing the installation relationship between the x-accelerometer and the inertial platform, the installation error matrix of the x-accelerometer is:

[0020]

[0021] S202: Analyze the installation relationship between the y-accelerometer and z-accelerometer and the inertial platform, and obtain the installation error matrices of the y-accelerometer and z-accelerometer.

[0022] S203: Since only the specific force acting on the sensitive axis of the accelerometer affects the output of the accelerometer, the installation error angle of the x-accelerometer is simplified to K. xy and K xz The installation error angle of the y-accelerometer is simplified to K. yx and K yz The installation error angle of the z-accelerometer is simplified to K. zy and K zx .

[0023] Furthermore, the specific operation of step S3 includes the following steps:

[0024] S301: Construct a static error model ω for the gyroscope considering quadratic terms. g And the accelerometer output model Z considering quadratic terms a ;

[0025] S302: Without considering the quadratic term error coefficient, construct an output model of the inertial platform system that takes into account installation errors, including the error model Z of the gyroscope. g (Z gx Z gy Z gz Error model Z of accelerometer a (Z ax Z ay Z az ).

[0026] Furthermore, the specific operation of step S4 includes the following steps:

[0027] S401: Construct a mathematical model for error coefficient calibration.

[0028] Z = HX + ε

[0029] The least squares solution of this mathematical model For the least squares estimate of the state variable X;

[0030] In the formula, Z is the observation vector, representing the output of the gyroscope and accelerometer at different calibration positions; H is the measurement matrix; X is the state variable, which is a column vector composed of error coefficients and installation errors; ε is the system measurement noise, assumed to be zero-mean Gaussian white noise.

[0031] S402: Define the information matrix

[0032] M = H T H

[0033] The condition number of the information matrix is ​​defined as

[0034]

[0035] In the formula, λ1 and λ n These are the maximum and minimum singular values ​​of the measurement matrix H;

[0036] S403: For the X-axis gyroscope, when using nine-position calibration, the measurement matrix H is...

[0037]

[0038] At this time, the information matrix M is

[0039]

[0040] In the formula, i = 1, 2, ... 9,

[0041] h i =[1 -sinγ i g0 -cosα i cosγ i g0 cosα i cosγ i g0 cosα i sin(λ0-γ i )ω ie sinα i sin(λ0-γ i )ω ie ].

[0042] Furthermore, in step S5, the calibration calculation of the error coefficient nine-position mathematical model includes accelerometer parameter calculation and calibration, and inertial platform drift calculation and calibration.

[0043] Furthermore, the accelerometer parameter calculation and calibration process includes the following steps:

[0044] S501a: Initialize Position = 0;

[0045] S502a: Determine the projection of linear velocity increments onto the local geographic coordinate system using navigation algorithms;

[0046] S503a: Determine the projection of the uncompensated accelerometer error onto the local geographic coordinate system, as well as the velocity component ignored at t=0, and calculate the transition parameters using the least squares algorithm;

[0047] S504a: Determine the accelerometer error and the alignment error of the platform's XYZ coordinate system relative to the horizontal plane, calculate the estimated uncompensated accelerometer parameters, and the estimated alignment error of the inertial platform's XYZ relative to the horizontal plane.

[0048] S505a: Corrects accelerometer parameters, matrix C gm (0) and the velocity component at t=0;

[0049] S506a: Determine whether Position = 9 is true. If it is true, use the corrected accelerometer parameters as the solution result. If it is not true, repeat steps S502a to S505a until Position = 9 is true.

[0050] Furthermore, the inertial platform drift calculation and calibration operation includes the following steps:

[0051] S501b: Use the functional coarse alignment algorithm to determine the matrix at each position of the platform at t=0, and initialize Position=0;

[0052] S502b: Uses navigation algorithms to determine linear velocity increments relative to the horizontal axis and rotation about the vertical axis of the local geographic coordinate system;

[0053] S503b: Determine the uncompensated platform drift relative to the local geographic coordinate system and the alignment error of the platform XYZ relative to the horizontal plane;

[0054] S504b: Determine platform drift and orientation alignment XYZ error, and output the estimated value of uncompensated platform drift and the estimated value of platform orientation alignment error;

[0055] S505b: Correcting platform drift and matrix C using an iterative algorithm gp (0);

[0056] S506b: Determine whether Position = 9 is true. If it is true, use the corrected platform drift parameter as the solution result. If it is not true, repeat steps S502b to S505b until Position = 9 is true.

[0057] The beneficial effects of this invention are:

[0058] This invention addresses the problem of error coefficient calibration for high-precision inertial platform systems. Combining the structural characteristics of inertial platforms with practical engineering considerations, it proposes a nine-position autonomous calibration method for high-precision inertial platforms. Based on the characteristics of inertial platform installation errors, it analyzes the error model of the platform system considering installation errors. The proposed calibration method can calibrate both the platform error coefficients and installation errors. Experimental verification shows that this calibration method has good stability and repeatability, and it can relax the installation requirements for inertial instruments, ensuring the stability of installation accuracy and improving the accuracy of inertial instruments. It possesses certain theoretical and engineering application value. Attached Figure Description

[0059] Figure 1 This is a schematic diagram showing the installation relationship of the x-gyroscope in this invention.

[0060] Figure 2 This is a schematic diagram showing the installation relationship of the x-accelerometer in this invention.

[0061] Figure 3 This is a flowchart of the accelerometer parameter calculation process in this invention.

[0062] Figure 4 This is a flowchart of the platform drift calculation process in this invention. Detailed Implementation

[0063] To enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0064] A high-precision inertial platform nine-position autonomous calibration method includes the following steps:

[0065] S1: Analyze the installation error of the gyroscope;

[0066] The gyroscopes and accelerometers mounted on the inertial platform each have their own coordinate systems. The rotation between the two coordinate systems can be represented by three Euler angles. That is, the installation error of each instrument relative to the platform coordinate system can be represented by three Euler angles. The analysis of the installation error of the gyroscope includes the following steps.

[0067] S101: Let E be the mounting coordinate system of the three gyroscopes, x, y, and z. x E y and Ez The installation error angle of the x-gyroscope is E. xx E xy and E xz The installation relationship between the x-gyroscope and the inertial platform was analyzed, and the installation relationship is shown in the attached figure. Figure 1 As shown, the installation error matrix of the x-gyroscope is calibrated as follows:

[0068]

[0069] S102: The installation relationship between the Y-gyroscope and the Z-gyroscope and the inertial platform is analyzed. Similarly, the installation error matrices of the Y-gyroscope and the Z-gyroscope can be obtained as follows:

[0070]

[0071]

[0072] In the formula, E yx E yy E yz E represents the installation error angle of the y-gyroscope. zx E zy and E zz The installation error angle of the z-gyroscope;

[0073] S103: Based on the analysis results of step S101, the rotational angular velocity of the inertial platform body. The projections of the x-gyroscope onto each axis are:

[0074]

[0075] For the x-gyroscope, the most important thing is Projection onto the x-axis of the gyroscope The projection onto the x-axis of the gyroscope is specifically represented as: Therefore, the installation error angle E of the x-gyroscope xx E xy and E xz Simplified to E xx and E xz ;

[0076] S104: Based on the operation in step S103, simplify the installation error angle of the y gyroscope to E. yx and E yz The installation error angle of the z-gyroscope is simplified to E. zy and E zx .

[0077] Furthermore, S2: Analyze the installation error of the accelerometer;

[0078] Similar to gyroscopes, the installation error of each accelerometer is also represented by three Euler angles.

[0079] Specifically, S201: The installation coordinate systems of the three accelerometers, x, y, and z, are respectively denoted as K. x K y and K z The installation error angle of the x-accelerometer is K. xx K xy and K xz The installation relationship between the x-accelerometer and the inertial platform is analyzed, as shown in the attached figure. Figure 2 As shown, the installation error matrix of the x-accelerometer is calibrated as follows:

[0080]

[0081] S202: The installation relationship between the y-accelerometer and z-accelerometer and the inertial platform is analyzed. Similarly, the installation error matrices of the y-accelerometer and z-accelerometer can be obtained as follows:

[0082]

[0083]

[0084] In the formula, K yx K yy K yz K is the installation error angle of the y-accelerometer. zx K zy and K zz The installation error angle of the z-accelerometer;

[0085] S203: Since only the specific force acting on the sensitive axis of the accelerometer affects the output of the accelerometer, the installation error angle of the x-accelerometer is simplified to K. xy and K xz Similarly, the installation error angle of the y-accelerometer can be simplified to K. yx and K yz The installation error angle of the z-accelerometer is simplified to K. zy and K zx .

[0086] Furthermore, S3: Construct a static error model for the inertial platform system;

[0087] Specifically, S301: Construct the static error model of the inertial instrument; considering quadratic terms, the static error model of the gyroscope is as follows:

[0088]

[0089] In the formula, ω g k represents the static error of the gyroscope.g0 For gyroscope constant drift, k g1i (i = 1, 2, 3) are the error coefficients of the first-order term of the gyroscope, k g2i (i = 1, 2, 3, 4) are the quadratic error coefficients of the gyroscope, a gi a go a gs These are the specific forces on the gyroscope's input shaft, output shaft, and rotor shaft, respectively.

[0090] When considering quadratic terms, the accelerometer output model is as follows:

[0091]

[0092] In the formula, Z a k represents the output error of the accelerometer. a0 It is the accelerometer zero bias, k a11 It is the proportional error coefficient of the accelerometer; k a2i (i = 1, 2, 3) are the second-order error coefficients of the accelerometer; a ai a a0 a ap These represent the specific forces on the input shaft, output shaft, and self-oscillation shaft of the accelerometer, respectively.

[0093] S302: Construct an output model of the inertial platform system that takes into account installation errors;

[0094] Assuming the geographic coordinate system is the Northeast-Sky coordinate system, in the multi-position tumbling experiment, the inertial platform rotates by an angle α around the platform axis and by an angle γ around the outer ring axis. The transformation matrix between the geographic coordinate system and the platform coordinate system is:

[0095]

[0096] Considering the installation error matrices of the accelerometer and gyroscope, projecting the components of Earth's gravitational acceleration and rotational angular velocity in the platform coordinate system onto the coordinate systems of the accelerometer and gyroscope, we obtain the observation expressions for the gyroscope and accelerometer as follows:

[0097]

[0098]

[0099]

[0100]

[0101]

[0102]

[0103] In the formula, Zgx Z gy Z gz For the observations of the gyroscope, Z ax Z ay Z az For the observations of the accelerometer; g 0 represents the local gravitational acceleration; ω ie λ is the Earth's rotational angular velocity; λ0 is the local latitude; e gx e gy e gz e represents the random error of the gyroscope. ax e ay e az The above formula represents the random error of the accelerometer; there are a total of 48 error coefficients. Among them, there are 24 error coefficients for the gyroscope, 15 error coefficients for the accelerometer, 6 error coefficients for the gyroscope installation, and 3 error coefficients for the accelerometer installation.

[0104] Since gravitational acceleration is the input quantity when performing multi-position calibration in a gravitational field, it cannot fully excite the quadratic error coefficient. Therefore, in engineering applications, the quadratic error coefficient is generally not calibrated to simplify the error model. Thus, without considering the quadratic error coefficient, the error model of the gyroscope and accelerometer can be further simplified to...

[0105] Z gx =k g0x -k g11x sinγg0-k g12x cosαcosγg0+k g13x sinαcosγg0+ω ie cos(γ-λ0)+E zx cosαsin(λ0-γ)ω ie +E yx sinαsin(λ0-γ)ω ie

[0106] Z gy =k g0y -k g11y cosαcosγg0-k g12y sinγg0-k g13y sinαcosγg0+ω ie cosαsin(λ0-γ)+E zy sinαsin(γ-λ0)ω ie -E xy cos(γ-λ0)ω ie

[0107] Z gz =k g0z +k g11zsinαcosγg0-k g12z sinγg0-k g13z cosαcosγg0-ω ie sinαsin(γ-λ0)+E yz cos(λ0-γ)ω ie -E xz cosαcos(γ-λ0)ω ie (13)

[0108] Z ax =k a0x -k a11x sinγg0-sinγg0

[0109] Z ay =k a0y -k a11y cosαcosγg0+sinγg0+K yx sinαcosγg0

[0110] Z az =k a0z +k a11z sinαcosγg0-K zx sinγg0+K zy cosαcosγg0 (14).

[0111] Furthermore, S4: Based on the static error model of the inertial platform system in step S3, construct a nine-position mathematical model for error coefficient calibration;

[0112] In self-calibration technology, to improve accuracy, it is necessary to perfect the error model of the platform and its instruments as much as possible. However, a more perfect model with more error items inevitably increases the number of measurement positions to be calibrated, thus lengthening the calibration time. One of the important indicators of self-calibration is to shorten the reaction time; therefore, the time used for calibration is generally strictly limited. Under this constraint, the error model used for calibration cannot be too complex or perfect; it needs to be appropriately simplified to shorten the calibration time. Therefore, the self-calibration of inertial platforms requires the selection of an appropriate model and reasonable measurement positions.

[0113] In multi-position calibration of a platform system, the mechanical arrangement (position selection) determines the number of calibrable error coefficients and the calibration accuracy. When the system is observable, all error coefficients can be estimated. The calibration accuracy is affected by the observability of the error coefficients; the higher the observability of the error coefficients, the higher the calibration accuracy; conversely, the lower the observability, the lower the calibration accuracy.

[0114] In engineering, the rotation range of the inner ring axis of the inertial platform is limited and cannot rotate 360°. If the calibration position is not chosen reasonably, some error coefficients may not be excited and cannot be observed. Therefore, it is necessary to consider the actual structural characteristics of the platform and choose a reasonable calibration position to improve the observability of the error coefficients to be calibrated.

[0115] Specifically, S401: Constructing the mathematical model for error coefficient calibration is as follows:

[0116] Z = HX + ε (15)

[0117] In the formula, Z is the observation vector, representing the output of the gyroscope and accelerometer at different calibration positions; H is the measurement matrix; X is the state variable, a column vector composed of error coefficients and installation errors; ε is the system measurement noise, assumed to be zero-mean Gaussian white noise; the least squares solution of this mathematical model... For the least squares estimate of the state variable X;

[0118] S402: Define the information matrix

[0119] M = H T H (16)

[0120] When the information M is invertible, all components of the state variable can be estimated, and the system is fully observable. When a certain eigenvalue of the information matrix M is small, the condition number of the information matrix will be relatively large, and the accuracy of least squares estimation will be very poor.

[0121] The condition number of the information matrix is ​​defined as

[0122]

[0123] In the formula, λ1 and λ n These are the maximum and minimum singular values ​​of the measurement matrix H;

[0124] S403: For the X-axis gyroscope, when using nine-position calibration, the measurement matrix H is...

[0125]

[0126] At this time, the information matrix M is

[0127]

[0128] In the formula, i = 1, 2, ... 9,

[0129] h i =[1 -sinγ i g0 -cosα i cosγ i g0 cosα i cosγi g0 cosα i sin(λ0-γ i )ω ie sinα i sin(λ0-γ i )ω ie ].

[0130] Based on the frame structure characteristics of the inertial platform, and after comprehensively analyzing the error model, calibration time requirements, and limitations of certain conditions in practice, a nine-position combined calibration scheme was designed. The nine-position model is shown in Table 1 below.

[0131] Table 1. Nine-position model

[0132] Location 1 2 3 4 5 6 7 8 9 α 0° 0° -90° -90° 0° 90° 90° 180° 180° γ 0° -90° -90° -180° -180° -90° -90° -90° 0°

[0133] All coefficients are observable only when the information matrix M is a full-rank matrix. When M is a full-rank matrix, the smaller the condition number of the measurement matrix H, the higher the estimation accuracy of the error coefficients. Analysis shows that, based on the nine-position calibration model given in Table 3, the rank of the information matrix M is 6, and the condition number is 2.43 × 10⁻⁶. 5 This satisfies the observability condition for the error coefficient.

[0134] Furthermore, S5: Perform calibration and calculation on the error coefficient calibration nine-position mathematical model in step S4.

[0135] Based on the nine-position calibration model proposed in step S4, step S5 proposes an inertial platform nine-position self-calibration algorithm to separate the error coefficients of the platform system and perform calibration on the nine-position model. The calibration algorithm mainly consists of an accelerometer parameter calculation algorithm and a platform drift calculation algorithm. Specifically...

[0136] Accelerometer parameter calculation and calibration mainly includes four steps: navigation algorithm, algorithm for calculating transient parameters, algorithm for calculating required parameters, and correction algorithm. The accelerometer parameter calculation process is attached. Figure 3 As shown, it includes the following steps:

[0137] S501a: Initialize Position = 0;

[0138] S502a: Determines the projection of linear velocity increments onto the local geographic coordinate system using navigation algorithms; accelerometer data for the platform at each location is...

[0139] b xk (j) b yk (j) b zk (j) (j=1,...,9;k=1,...,N)

[0140] In the formula, N is the total number of sensor data sampling points at each location; b xk (j) b yk (j) b zk (j) This represents the accelerometer data at the j-th position and k-th step size of the platform;

[0141] The platform's frame sensor data at each location is

[0142]

[0143] In the formula, and These represent the angle sensor data at the j-th position and k-th step size of the platform, respectively;

[0144] The projection of the linear velocity increment at each location of the output platform onto the local geographic coordinate system is:

[0145] V xgk (j) V ygk (j) V zgk (j) (j=1,...,9;k=1,...,N)

[0146]

[0147] In the formula, V xgk (j) V ygk (j) V zgk (j) This represents the projection of the linear velocity increment at each location on the platform onto the local geographic coordinate system; C gpk The matrix to be operated on is represented; Δt represents the sensor sampling step size.

[0148]

[0149] Among them, f xk f yk f zk Indicates the specific force value; Δ nx Δ ny Δ nz This indicates the nonlinearity error of the scaling factor;

[0150] S503a: Determine the projection of the uncompensated accelerometer error onto the local geographic coordinate system, and the velocity component neglected at t=0; determine the projection of the uncompensated phase accelerometer error onto the local geographic coordinate system as...

[0151] Δxg (j) Δ yg (j) Δ zg (j) (j = 1, ..., 9)

[0152] The velocity components of the inertial platform at each position at t=0 that are neglected are:

[0153]

[0154] The transition parameters are calculated using the least squares algorithm.

[0155]

[0156]

[0157]

[0158]

[0159]

[0160]

[0161] In the formula, Δ xg (j) , Δ yg (j) These represent the projections of the accelerometer error onto the local geographic coordinate system; These represent the projections of the platform's linear velocity components at each location onto the local geographic coordinate system.

[0162] S504a: Determine the accelerometer error and the alignment error of the platform's XYZ coordinate system relative to the horizontal plane; the estimated uncompensated accelerometer parameters are as follows:

[0163]

[0164]

[0165]

[0166]

[0167]

[0168]

[0169] Alignment error estimate of inertial platform XYZ relative to the horizontal plane They are respectively

[0170]

[0171]

[0172] In the formula, This indicates that the accelerometer has zero bias. Indicates the accelerometer installation error angle; Δ xg Δ zg This represents the projection of the uncompensated accelerometer error onto the local geographic coordinate system. Indicates alignment error;

[0173] S505a: Corrects accelerometer parameters, matrix C gm (0) and the velocity component at t=0; the parameters for calibrating the accelerometer are:

[0174]

[0175]

[0176]

[0177] S506a: Determine whether Position = 9 is true. If it is true, use the corrected accelerometer parameters as the solution result. If it is not true, repeat steps S502a to S505a until Position = 9 is true.

[0178] The algorithm for determining inertial platform drift mainly includes five steps: coarse alignment algorithm, navigation algorithm, algorithm for calculating transition parameters, algorithm for calculating required parameters, and correction algorithm. A flowchart of the inertial platform drift calculation is attached. Figure 4 As shown, the specific steps include:

[0179] S501b: Uses a functional coarse alignment algorithm to determine the matrix C at each position of the platform at t=0. gp (0), C gp (j) (0) = C gm (0)C mp0 (j) (j = 1, ..., 9), initialize Position = 0;

[0180] in, These represent the data from the frame corner sensors at the initial moment of the sensor data acquisition cycle at each position of the platform.

[0181] S502b: Utilizes a navigation algorithm to determine the linear velocity increment relative to the horizontal axis and the rotation about the vertical axis of the local geographic coordinate system; outputs the linear velocity increment of the platform at each position relative to the horizontal axis of the local geographic coordinate system and the rotation angle about the vertical axis.

[0182] V xgk (j) V zgk (j) (j=1,...,9;k=1,...,N)

[0183] The output platform rotates around the vertical axis (Y) at each position. g The rotation of ) results in an uncompensated platform drift of θ. k (j) (j=1,...,9;k=1,...,N);

[0184] S503b: Determine the uncompensated platform drift relative to the local geographic coordinate system and the alignment error of the platform XYZ relative to the horizontal plane; the projection of the uncompensated platform drift onto the local geographic coordinate system and the alignment error relative to the horizontal plane at each location are...

[0185]

[0186]

[0187]

[0188]

[0189]

[0190]

[0191] In the formula, Represents velocity components; Indicates the alignment error angle; ω zg ω xg V represents the drift angular velocity; xgk V zgk These represent linear velocity increments; P x =A x -1 P z =A z -1 ,in,

[0192]

[0193]

[0194] In the formula, S1(N)=N(N+1) / 2, S2(N)=N(N+1)(2N+1) / 6, S3(N)=N 2 (N+1) 2 / 4, S4(N)=N(N+1)(2N+1)(3N 2 +3N-1) / 30;

[0195] S504b: Determines platform drift and orientation alignment XYZ error, and outputs an estimate of the uncompensated platform drift.

[0196]

[0197] And the estimation of platform orientation alignment error

[0198] S505b: Correcting platform drift and matrix C using an iterative algorithm gp (0);

[0199] Platform drift correction includes

[0200]

[0201]

[0202]

[0203]

[0204]

[0205] Correcting the horizontal component of the platform's velocity vector at each position at t=0

[0206]

[0207] Correct the matrix C of the platform at each position gp (0)(j=1,…,9);

[0208]

[0209] In the formula,

[0210]

[0211] in,

[0212] S506b: Determine whether Position = 9 is true. If it is true, use the corrected platform drift parameter as the solution result. If it is not true, repeat steps S502b to S505b until Position = 9 is true.

[0213] Experimental verification

[0214] The calibration test process is as follows: At each position, the three axes are locked, with the horizontal axis locked within the horizontal plane. After stabilization, the three-axis locking is released, and data acquisition from the accelerometer and platform frame angle outputs begins. Once data acquisition is complete, torque is applied to the corresponding gyroscopes according to the calibrated positions, causing the platform to precess to the next position, completing data acquisition. By processing the data acquired at each position, the parameters requiring platform calibration can be obtained. The test process mainly consists of three steps:

[0215] Step 1: Install the platform on the fixed base. The outer ring shaft (Zm) is located in the horizontal plane, facing south. When the angle of the outer ring shaft is zero, the inner ring shaft is located in the horizontal plane, facing east. Heat the platform for 20 minutes, start the platform and stabilize it for 30 minutes.

[0216] Step 2: With the platform started once, referring to the nine-position model in step S4, the platform is flipped to the nine specified positions relative to the local geographic coordinate system. The platform torque device is disconnected, and accelerometer and frame angle data are collected with a sampling period of 100ms. The test time for each position is 5 minutes.

[0217] Step 3: Process the collected data and separate the various error coefficients of the platform system.

[0218] Based on the nine-position model in step S4, experimental verification was carried out, and the calibration algorithm in step S5 was used to separate the various error coefficients of the platform system.

[0219] Test results

[0220] Using the self-calibration algorithm in step S5, the calibration results of the accelerometers (Jx, Jy, Jz) in the three tests are shown in Table 2 below, and the calibration results of the gyroscopes (Tx, Ty, Tz) are shown in Table 3 below.

[0221] Table 2. Accelerometer Error Coefficient Calibration Results

[0222] Error coefficient first The second The third <![CDATA[k a0x (m / s 2 )]]> 0.07066 0.07071 0.07070 <![CDATA[k a11x (m / s 2 / g0)]]> 0.000169 0.000169 0.000168 <![CDATA[k a0y (m / s 2 )]]> -0.04507 -0.04507 -0.04514 <![CDATA[k a11y (m / s 2 / g0)]]> 0.000156 0.000156 0.000155 <![CDATA[k a0z (m / s 2 )]]> 0.06676 0.06667 0.06686 <![CDATA[k a11z (m / s 2 / g0)]]> 0.000171 0.000171 0.000171 <![CDATA[K yx (″)]]> 15.65 16.25 16.56 <![CDATA[K zx (″)]]> -22.84 -19.98 -16.88 <![CDATA[K zy (″)]]> -61.63 -61.99 -63.29

[0223] Table 3. Calibration results of gyroscope error coefficients

[0224] Error coefficient first The second The third <![CDATA[k g0x (deg / h)]]> -0.147101 -0.162348 -0.180750 <![CDATA[k g11x (you / h / g0)]]> 2.420342 2.434714 2.390731 <![CDATA[k g12x (you / h / g0)]]> 0.012752 0.013027 0.012896 <![CDATA[k g13x (you / h / g0)]]> -1.539847 -1.547516 -1.561006 <![CDATA[k g0y (deg / h)]]> 0.142265 0.155567 0.170062 <![CDATA[k g11y (you / h / g0)]]> 0.004945 0.004701 0.009200 <![CDATA[k g12y (you / h / g0)]]> -0.023471 -0.076497 0.007664 <![CDATA[k g13y (you / h / g0)]]> 1.650751 1.650948 1.710207 <![CDATA[k g0z (deg / h)]]> -0.224229 -0.216826 -0.271068 <![CDATA[k g11z (you / h / g0)]]> -1.389895 -1.389908 -1.348096 <![CDATA[k g12z (you / h / g0)]]> -0.007113 -0.002477 -0.002668 <![CDATA[k g13z (you / h / g0)]]> -0.069316 0.013188 -0.049599

[0225] Experiments show that the error coefficient of the nine-position self-calibration method has good stability and repeatability, indicating that the nine-position self-calibration scheme proposed in this invention, which combines the structural characteristics of the inertial platform and other practical engineering problems, is feasible.

[0226] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A high-precision inertial platform nine-position autonomous calibration method, characterized in that, Includes the following steps, S1: Analyze the installation error of the gyroscope; S2: Analyze the installation error of the accelerometer; S3: Construct a static error model for the inertial platform system; S4: Based on the static error model of the inertial platform system in step S3, construct a nine-position mathematical model for error coefficient calibration; S5: Perform calibration calculation on the error coefficient calibration nine-position mathematical model in step S4; the calibration calculation includes accelerometer parameter calculation and calibration and inertial platform drift calculation and calibration; Step S4 specifically includes the following steps: S401: Construct a mathematical model for error coefficient calibration. ； The least squares solution of this mathematical model For the least squares estimate of the state variable X; In the formula, Z is the observation vector, representing the output of the gyroscope and accelerometer at different calibration positions; H is the measurement matrix; and X is the state variable, which is a column vector composed of error coefficients and installation errors. For the system measurement noise, it is assumed to be zero-mean Gaussian white noise; S402: Define the information matrix ； The condition number of the information matrix is ​​defined as ； In the formula, , These are the maximum and minimum singular values ​​of the measurement matrix H; S403: For the x-gyroscope, when using nine-position calibration, the measurement matrix H is... ； At this time, the information matrix M is ； In the formula, i = 1, 2, ..., 9. ， For local gravitational acceleration, The latitude is the local latitude. This is the Earth's rotational angular velocity.

2. The high-precision inertial platform nine-position autonomous calibration method according to claim 1, characterized in that, Step S1 includes the following steps: S101: The mounting coordinate systems of the three gyroscopes, x, y, and z, are respectively denoted as... , and The installation error angle of the x-gyroscope is... , and Analyzing the installation relationship between the x-gyroscope and the inertial platform, the installation error matrix of the x-gyroscope is: ； S102: Analyze the installation relationship between the Y-gyroscope and Z-gyroscope and the inertial platform, and obtain the installation error matrices of the Y-gyroscope and Z-gyroscope. , ; S103: Rotational angular velocity based on the inertial platform body Projection on the x-axis of the gyroscope The installation error angle of the x-gyroscope , and Simplified to and Similarly, the installation error angle of the y-gyroscope can be simplified to... and The installation error angle of the z-gyroscope is simplified to... and .

3. The high-precision inertial platform nine-position autonomous calibration method according to claim 2, characterized in that, Step S2 includes the following steps: S201: The installation coordinate systems of the three accelerometers, x, y, and z, are respectively denoted as... , and The installation error angle of the x-accelerometer is... , and Analyzing the installation relationship between the x-accelerometer and the inertial platform, the installation error matrix of the x-accelerometer is: ； S202: Analyze the installation relationship between the y-accelerometer and z-accelerometer and the inertial platform, and obtain the installation error matrices of the y-accelerometer and z-accelerometer. , ; S203: Since only the specific force acting on the sensitive axis of the accelerometer affects the output of the accelerometer, the installation error angle of the x-accelerometer is simplified to... and The installation error angle of the y-accelerometer is simplified to... and ; The installation error angle of the z-accelerometer is simplified to: and .

4. The high-precision inertial platform nine-position autonomous calibration method according to claim 2, characterized in that, Step S3 includes the following steps: S301: Construct a static error model for the gyroscope considering quadratic terms. And the accelerometer output model considering quadratic terms ; S302: Without considering the quadratic term error coefficient, construct an output model of the inertial platform system that takes into account installation errors, including the error model Z of the gyroscope. g (Z gx Z gy Z gz Error model Z of accelerometer a (Z ax Z ay Z az ).

5. The high-precision inertial platform nine-position autonomous calibration method according to claim 4, characterized in that, The accelerometer parameter calculation and calibration process includes the following steps: S501a: Initialize Position=0; S502a: Determine the projection of linear velocity increments onto the local geographic coordinate system using navigation algorithms; S503a: Determine the projection of the uncompensated accelerometer error onto the local geographic coordinate system, as well as the velocity component ignored at t=0, and calculate the transition parameters using the least squares algorithm; S504a: Determine the accelerometer error and the alignment error of the platform's XYZ coordinate system relative to the horizontal plane, calculate the estimated uncompensated accelerometer parameters, and the estimated alignment error of the inertial platform's XYZ relative to the horizontal plane. S505a: Corrects accelerometer parameters and matrix And the velocity component at t=0; S506a: Determine whether Position=9 is true. If it is true, use the corrected accelerometer parameters as the solution result. If it is not true, repeat steps S502a to S505a until Position=9 is true.

6. The high-precision inertial platform nine-position autonomous calibration method according to claim 4, characterized in that, The inertial platform drift calculation and calibration operation includes the following steps: S501b: Use the functional coarse alignment algorithm to determine the matrix at each position of the platform at t=0, and initialize Position=0; S502b: Uses navigation algorithms to determine linear velocity increments relative to the horizontal axis and rotation about the vertical axis of the local geographic coordinate system; S503b: Determine the uncompensated platform drift relative to the local geographic coordinate system and the alignment error of the platform XYZ relative to the horizontal plane; S504b: Determine platform drift and orientation alignment XYZ error, and output the estimated value of uncompensated platform drift and the estimated value of platform orientation alignment error; S505b: Correcting platform drift and matrix using iterative algorithms ; S506b: Determine whether Position=9 is true. If it is true, use the corrected platform drift parameter as the solution result. If it is not true, repeat steps S502b to S505b until Position=9 is true.

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