Anti-disturbance self-calibration method for inertial navigation equipment for navigation

Abstract

The present application relates to the field of ship navigation technology, and more particularly to a kind of anti-disturbance self-calibration method for inertial navigation equipment for navigation, comprising the following steps: obtaining the calculation speed by carrying out inertial calculation on inertial navigation original data, and obtaining the speed error by subtracting the reference speed from the calculation speed;The speed error containing disturbance speed is removed by real-time wavelet transform to remove the disturbance speed;The speed error processed by wavelet transform is used as the observation of Kalman filter, and the inertial navigation error parameter is obtained by using Kalman filter;The inertial navigation error parameter is fed back to the inertial calculation process;Repeat the above steps until the inertial navigation error parameter estimated by Kalman filter converges, and the calibration is completed.The present application solves the technical problem that the calibration method in the prior art cannot meet the long-time, high-precision calibration requirements under the conditions of mooring, anchoring and heading change.

Description

Technical Field

[0001] The present invention relates to the technical field of ship navigation, and in particular to an anti-disturbance self-calibration method for an inertial navigation device for navigation. Background Art

[0002] Calibration is a key technology in the field of inertial navigation systems and the foundation for their navigation solutions. Essentially, it's an error compensation technique. This involves establishing an accurate model of inertial component measurement errors and rationally designing experiments to stimulate the error sources of these components, enabling the determination of various error parameters. Ultimately, these calibration-derived error parameters are used to perform software compensation on the inertial navigation output, reducing the error. Calibration results directly impact inertial navigation accuracy.

[0003] Currently, commonly used calibration methods can be divided into discrete calibration methods and system-level calibration methods. The parameters to be calibrated are the zero bias, scale factor error, and installation error of the inertial component. Discrete calibration is performed by directly comparing the inertial sensor output with an external reference input. With the turntable leveled and aligned, its rotation is equivalent to the external reference input. The inertial navigation system is mounted on the turntable, and the true angular velocity and accelerometer on each axis of the inertial navigation coordinate system are known. Rotating the turntable is a process of constructing equations to solve for the parameters. The relationship between the inertial sensor output and the turntable input is used to determine the inertial component error coefficients, thereby completing the calibration. The principle of system-level calibration is to use the navigation parameter error as the observed quantity and utilize filtering methods to identify the inertial component error coefficients. This method, based on the principle of navigation error resolution, uses navigation error to estimate inertial component errors, independent of turntable accuracy. Therefore, it has been applied in actual production with good results.

[0004] Self-calibration in dynamic scenarios is typically performed in the field, where various disturbances have a significant impact and auxiliary equipment such as high-precision turntables are lacking. Discrete calibration methods are therefore difficult to adapt to such environments. Therefore, a system-level calibration approach is often used to address dynamic self-calibration. By designing a reasonable transposition path and using navigation errors to calculate device errors, the dependency on high-precision turntables is avoided. However, existing system-level calibration methods are unable to achieve high-precision calibration in dynamic scenarios with significant disturbances, making it difficult to meet the high-precision calibration requirements of long-duration, high-precision marine inertial navigation systems under mooring, anchoring, and heading conditions.

[0005] Existing technologies typically treat external disturbance velocities as observation noise in the Kalman filter, attempting to reduce their impact on inertial navigation calibration by adjusting the observation noise parameters. However, these technologies fail to effectively suppress the disturbance. Furthermore, in practice, external disturbance velocities have a fixed frequency and do not follow a Gaussian distribution, making it difficult to satisfy the Kalman filter's assumption that the observation noise is white. Consequently, this inevitably significantly impacts calibration accuracy. Other existing technologies employ simplified error parameter models designed for self-calibration, but these approaches have limited interference immunity.

[0006] In summary, there is an urgent need for a method that can meet the high-precision calibration requirements of long-duration and high-precision marine inertial navigation under mooring, anchoring and heading conditions to solve the problems existing in the existing technology. Summary of the Invention

[0007] The present invention aims to provide a method for anti-disturbance self-calibration of marine inertial navigation equipment to solve the technical problem that existing calibration methods are difficult to meet the requirements of long-term, high-precision calibration under mooring, anchoring and heading changes. The specific technical solution is as follows:

[0008] The present invention provides a method for anti-disturbance self-calibration of an inertial navigation device for navigation, comprising the following steps:

[0009] S1. Rotate the turntable of the marine inertial navigation device according to the calibration path to collect raw inertial navigation data;

[0010] S2. Perform inertial solution on the raw inertial navigation data to obtain a solution velocity, and subtract the reference velocity from the solution velocity to obtain a velocity error including the disturbance velocity;

[0011] S3, removing the disturbance velocity from the velocity error including the disturbance velocity by real-time wavelet transform;

[0012] S4, using the velocity error processed by wavelet transform as the Kalman filter observation quantity, and using Kalman filtering to obtain the inertial navigation error parameter;

[0013] S5. Feed the calculated inertial navigation error parameters back to the inertial solution process; S6. Repeat S2 to S5 until the inertial navigation error parameters estimated by the Kalman filter converge, completing the calibration of the inertial navigation error parameters.

[0014] A further improvement of the anti-disturbance self-calibration method for a marine inertial navigation device of the present invention is that, when removing the disturbance velocity from the velocity error including the disturbance velocity by real-time wavelet transform, the method includes the following steps:

[0015] Through the scale transformation and translation transformation of the wavelet decomposition calculation equation, the velocity error signal is transformed into wavelet coefficients of different scales and positions to obtain wavelet signals of different frequencies. The wavelet decomposition calculation equation is:

[0016]

[0017] Where x(t) is the finite input signal of velocity error; ψ * () is the complex conjugate of the mother wavelet basis function; * is the complex conjugate; a and b are transformation parameters; x(a,b) is the signal obtained after wavelet transformation; t is time; dt represents the time differential.

[0018] A further improvement of the anti-disturbance self-calibration method for marine inertial navigation equipment of the present invention is to filter the wavelet signal below the target frequency and reconstruct it to obtain a reconstructed velocity error signal, which is expressed as follows:

[0019]

[0020] ψ j,k (t) = 2 j / 2 ψ(2 j tk);

[0021] Among them, x r (t) is the reconstructed velocity error signal; ψ j,k (t) is the wavelet basis function, which is the kth wavelet basis function of the jth layer transformed from the mother wavelet basis function ψ(t); ψ(t) is the mother wavelet basis function; j is the jth layer transformed from the mother wavelet basis function; k is the kth wavelet basis function in this layer.

[0022] A further improvement of the anti-disturbance self-calibration method for a marine inertial navigation device of the present invention is that it further comprises:

[0023] The wavelet transform is used to eliminate the disturbance velocity of the reconstructed velocity error signal to obtain the velocity error, which includes the following steps:

[0024] Determine the basis function, and choose db4 wavelet as the basis function;

[0025] Determine the number of decomposition layers and the number of transformation layers K to satisfy the following formula:

[0026]

[0027] Among them, f c is the final low-frequency component obtained by wavelet transform; f s is the velocity solution frequency in actual calculation, K is the number of transformation layers;

[0028] Determine the width of the sliding window of the wavelet transform input data window;

[0029] Process the boundary data and extend the input data window to obtain the velocity error.

[0030] A further improvement of the anti-disturbance self-calibration method for a marine inertial navigation device of the present invention is that it further comprises:

[0031] When extending the input data window, the particle swarm optimization algorithm is used to extend the boundary data, including the following steps:

[0032] Cache the input velocity and construct a fitting function based on the characteristics of velocity error and disturbance velocity:

[0033]

[0034] Among them, h m 、p o 、L o and t o is the fitting coefficient to be determined; x is the independent variable of the velocity model; V predict is the predicted velocity output by the velocity model; M is the highest power of x in the fitting function; m is the mth power of the x polynomial in the fitting function and the corresponding mth fitting coefficient; N is the number of superimposed sine functions; o is the oth coefficient to be fitted in the sine function term;

[0035] The particle swarm optimization algorithm is used to fit the cache input speed and solve the fitting coefficient in the fitting function;

[0036] Splice the input speed and prediction speed to extend the data boundary.

[0037] A further improvement of the anti-disturbance self-calibration method for marine inertial navigation equipment of the present invention is that when solving the fitting coefficient in the fitting function, the particle group X composed of S particles is X={x1, x2, ... x s}, the speed and position of each particle change iteratively; in each iteration, the particle will record two optimal values: one is the optimal solution found by the particle itself; the other is the optimal solution currently found by the entire group; based on these two optimal values, the particle's speed and position are updated, and the optimal position obtained is the fitting coefficient. The update formula is as follows:

[0038] V q =ω*V q +e1r1(P best -P q )+e2r2(G best -P q );

[0039] P q =P q +V q ;

[0040] Among them, V q is the velocity of the qth particle; P q is the position of the qth particle; ω is the inertia weight coefficient; e1 and e2 are learning factors; r1 and r2 are random numbers; the value range is [0,1]; P best is the optimal position of the particle in its own history; G best is the optimal position for the entire group.

[0041] A further improvement of the anti-disturbance self-calibration method for a marine inertial navigation device of the present invention is that before obtaining the inertial navigation error parameters using the Kalman filter, an inertial device error model is determined. The inertial device error model includes an accelerometer error model. The accelerometer error model is expressed as follows:

[0042]

[0043] Among them, δa b is the output error of the accelerometer in the carrier coordinate system, a I is the input acceleration of the I-axis accelerometer, (I = x, y, z); K I is the accelerometer scale factor error of the I axis, (I = x, y, z); M IJ is the accelerometer installation error, (I, J = x, y, z and I ≠ J); λ I is the asymmetry error of the scale factor of the I axis, (I = x, y, z); is the accelerometer bias of the I axis, (I = x, y, z).

[0044] A further improvement of the anti-disturbance self-calibration method for marine inertial navigation equipment of the present invention is that the inertial device error model also includes a gyroscope error model, and the gyroscope error model is expressed as follows:

[0045]

[0046] Among them, δω b is the output error of the gyroscope in the carrier coordinate system, ω I is the angular velocity measured by the I-axis gyroscope, (I = x, y, z); S I is the gyro scale factor error of the I axis, (I = x, y, z); E IJ is the gyro installation error, (I, J = x, y, z and I ≠ J); ε I is the gyro bias of the I-axis, (I = x, y, z).

[0047] A further improvement of the anti-disturbance self-calibration method for marine inertial navigation equipment of the present invention is that after determining the inertial device error model, an inertial navigation error equation is established:

[0048]

[0049] Among them, the superscript n is the navigation coordinate system, b is the carrier coordinate system, e is the earth coordinate system, and i is the inertial coordinate system. is the differential of the position error of the inertial navigation in the navigation coordinate system, is the differential of the velocity error of the inertial navigation in the navigation coordinate system, is the differential of the attitude error of the inertial navigation in the navigation coordinate system, δr n is the position error of the inertial navigation in the navigation coordinate system, δV n is the velocity error of the inertial navigation in the navigation coordinate system, ψ n is the attitude error of the inertial navigation in the navigation coordinate system, is the projection of the rotational angular velocity of the navigation coordinate system relative to the earth coordinate system in the navigation coordinate system, is the projection of the angular velocity of the earth coordinate system relative to the inertial coordinate system in the navigation coordinate system, is the projection of the angular velocity of the navigation coordinate system relative to the inertial coordinate system in the navigation coordinate system, is the transformation matrix from the carrier coordinate system to the navigation coordinate system, that is, the attitude matrix, δa b is the output error of the accelerometer in the carrier coordinate system, δω b is the output error of the gyroscope in the carrier coordinate system, f n is the projection of the comparison in the navigation coordinate system.

[0050] A further improvement of the anti-disturbance self-calibration method for marine inertial navigation equipment of the present invention is that, when the inertial navigation error parameters are obtained by using Kalman filtering, a self-calibration filter is designed:

[0051] The standard form of the Kalman filter state equation is used: u is the noise of the system; the error model of the accelerometer and gyroscope is substituted into the inertial error equation to obtain the matrix form of the calibration model; the state variable of the model is X = [δr n ,δV n ,ψ n ,X g ,X a ] T , namely position error, velocity error, attitude error and device error of gyroscope and accelerometer. The state variables are as follows:

[0052] δr n =[δn N δn E δn D ] T

[0053] δV n =[δVN δV E δV D ] T

[0054] ψ n =[ψ N ψ E ψ D ] T

[0055] X g =[S x E yx S y E zy E xz S z ε x ε y ε z ] T

[0056]

[0057] Among them, δr n is the position error, δn N is the north position error, δn E Easting position error, δn D Ground position error; δV n is the velocity error, δV N is the north velocity error, δV E Eastward velocity error, δV D Ground velocity error; ψ n is the attitude error, ψ N is the north attitude error, ψ E is the eastward attitude error, ψ D is the ground attitude error; X g is the device error of the gyroscope, X a is the device error added to the table;

[0058] The coefficient matrix in the model is:

[0059]

[0060] The sub-matrices in F are:

[0061]

[0062] in, is the earth component of the projection of the angular velocity of the navigation coordinate system relative to the earth coordinate system in the navigation coordinate system, is the east component of the projection of the angular velocity of the navigation coordinate system relative to the earth coordinate system in the navigation coordinate system, is the north component of the projection of the angular velocity of the navigation coordinate system relative to the earth coordinate system in the navigation coordinate system, is the earth component of the projection of the angular velocity of the navigation coordinate system relative to the inertial coordinate system in the navigation coordinate system, is the earthward component of the projection of the angular velocity of the earth coordinate system relative to the inertial coordinate system in the navigation coordinate system, is the east component of the projection of the angular velocity of the earth coordinate system relative to the inertial coordinate system in the navigation coordinate system, is the north component of the projection of the angular velocity of the earth coordinate system relative to the inertial coordinate system in the navigation coordinate system, is the ground component of the projection of the specific force in the navigation coordinate system, is the east component of the projection of the specific force in the navigation coordinate system, is the north component of the projection of the specific force in the navigation coordinate system;

[0063]

[0064] in, is the transformation matrix from the carrier coordinate system to the navigation coordinate system, that is, the attitude matrix; c AB for The B-th component in the A-th row of the matrix has a value range of A (1, 2, 3) and a value range of B (1, 2, 3).

[0065]

[0066] in, It is the north component of the projection of the angular velocity of the navigation coordinate system relative to the inertial coordinate system in the navigation coordinate system.

[0067] The application of the technical solution of the present invention has the following beneficial effects:

[0068] The present invention discloses a method for anti-disturbance self-calibration of a marine inertial navigation device. The method utilizes wavelet transform to process signals, thereby achieving separation of signals of different frequencies while simultaneously providing low time delay, making it suitable for real-time inertial navigation self-calibration. Compared to low-pass filtering based on Fourier transform, the method has variable time-frequency resolution, providing relatively good frequency resolution for the low-frequency portion of the signal and relatively good time resolution for the high-frequency portion of the signal. The method utilizes wavelet transform to separate the disturbance velocity and velocity error, eliminates external disturbance velocity, minimizes the impact of introducing reference velocity error into filtered observation on calibration accuracy, and uses the velocity after disturbance elimination as the filtered observation. A Kalman filter is then established to achieve dynamic self-calibration of the dual-axis inertial navigation system. Compared to the prior art that typically treats the disturbance velocity as observation noise of the Kalman filter, the calibration accuracy of the present invention is greatly improved. Furthermore, to address the boundary signal distortion problem faced after wavelet transform, the present invention utilizes a particle swarm optimization algorithm to extend the input data window, thereby improving the boundary signal accuracy of the wavelet transform. Compared with the currently commonly used boundary extension methods such as constant extension, symmetric extension, and linear extension, the processing accuracy of the present invention is higher, thereby solving the technical problem that the calibration methods in the existing technology cannot achieve the high-precision calibration requirements of long-time and high-precision marine inertial navigation under mooring, anchoring and heading conditions.

[0069] In addition to the above-described objects, features and advantages, the present invention has other objects, features and advantages. The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings:

[0071] Figure 1 This is a flow chart of the anti-disturbance self-calibration method for marine inertial navigation equipment of the present invention;

[0072] Figure 2 This is a coordinate diagram comparing errors of different boundary extension methods for the anti-disturbance self-calibration method of the marine inertial navigation equipment of the present invention;

[0073] Figure 3 This is a comparative coordinate diagram of north velocity errors extracted by the anti-disturbance self-calibration method of the marine inertial navigation device of the present invention;

[0074] Figure 4 This is a comparative coordinate diagram of eastward velocity errors extracted by the anti-disturbance self-calibration method for marine inertial navigation equipment of the present invention;

[0075] Figure 5This is a comparative coordinate diagram of navigation results (latitude error) extracted by the anti-disturbance self-calibration method of the marine inertial navigation device of the present invention;

[0076] Figure 6 This is a comparative coordinate diagram of navigation results (northward velocity error) extracted by the anti-disturbance self-calibration method of the marine inertial navigation device of the present invention;

[0077] Figure 7 This is a comparative coordinate diagram of navigation results (longitude error) extracted by the anti-disturbance self-calibration method of the marine inertial navigation device of the present invention;

[0078] Figure 8 This is a comparative coordinate diagram of navigation results (eastward velocity error) extracted by the anti-disturbance self-calibration method of the marine inertial navigation device of the present invention. DETAILED DESCRIPTION

[0079] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0080] See also Figures 1 to 8 As shown, a method for anti-disturbance self-calibration of an inertial navigation device for navigation includes the following steps:

[0081] S1. Rotate the turntable of the marine inertial navigation device according to the calibration path to collect raw inertial navigation data;

[0082] S2. Perform inertial solution on the raw inertial navigation data to obtain a solution velocity, and subtract the reference velocity from the solution velocity to obtain a velocity error including the disturbance velocity;

[0083] S3, removing the disturbance velocity from the velocity error including the disturbance velocity by real-time wavelet transform;

[0084] S4, using the velocity error processed by wavelet transform as the Kalman filter observation quantity, and using Kalman filtering to obtain the inertial navigation error parameter;

[0085] S5, feeding back the calculated inertial navigation error parameters into the inertial solution process;

[0086] S6. Repeat S2 to S5 until the inertial navigation error parameters estimated by the Kalman filter converge, completing the calibration of the inertial navigation error parameters.

[0087] Specifically, the calibration path is the calibration path of position 18 in Table 1 as shown in the following table:

[0088] Table 118 Position Rotation Path

[0089]

[0090] In the table, in the 18-position rotation path, N represents north, E represents east, D represents earth, U represents sky, W represents west, and S represents south.

[0091] The relevant steps of inertial navigation solution can be found in Chapter 4 of Yan Gongmin's "Strapdown Inertial Navigation Algorithm and Integrated Navigation Principle" (Northwestern Polytechnical University Press).

[0092] The present invention can solve the calibration problem of inertial navigation in dynamic scenarios. In the moving state, the self-calibration of inertial navigation is seriously affected by the external disturbance speed, resulting in too low calibration accuracy and unable to meet the requirements of high-precision marine navigation. In order to solve this problem, the present invention proposes an anti-disturbance self-calibration method for laser gyro inertial navigation that can be applied to dynamic scenarios. The primary technical problem to be solved is to achieve the separation of the true value and the error value of the velocity observation quantity, that is, the separation of the external disturbance speed and the inertial navigation velocity error. The present invention is suitable for the self-calibration of laser gyro inertial navigation systems in dynamic scenarios and environments with severe velocity disturbances. Its typical application scenario is the self-calibration of high-precision and long-duration marine inertial navigation under mooring, anchoring or moving conditions.

[0093] To address the dynamic calibration problem of inertial navigation, the present invention adopts a system-level calibration method. The system-level calibration method is to perform inertial solution on the output of the inertial component, subtract it from the reference to obtain the navigation error, and use the Kalman filter method to calculate the error parameters and compensate for it.

[0094] The system-level calibration method links the inertial device error model with the navigation error equation to obtain the relationship between the navigation error result and the inertial device error.

[0095] Therefore, the inertial device error model should be determined first. The model includes scale factor error, installation error, scale factor asymmetry error, and zero bias. The inertial device error model includes the accelerometer error model and the gyroscope error model. The accelerometer error model is expressed as follows:

[0096]

[0097] Among them, δa b is the output error of the accelerometer in the carrier coordinate system, a I is the input acceleration of the I-axis accelerometer, (I = x, y, z); K I is the accelerometer scale factor error of the I axis, (I = x, y, z); M IJ is the accelerometer installation error, (I, J = x, y, z and I ≠ J); λ I is the asymmetry error of the scale factor of the I axis, (I = x, y, z); is the accelerometer bias of the I axis, (I = x, y, z).

[0098] The gyroscope error model is as follows:

[0099]

[0100] Among them, δω b is the output error of the gyroscope in the carrier coordinate system, ω I is the angular velocity measured by the I-axis gyroscope, (I = x, y, z); S I is the gyro scale factor error of the I axis, (I = x, y, z); E IJ is the gyro installation error, (I, J = x, y, z and I ≠ J); ε I is the gyro bias of the I-axis, (I = x, y, z).

[0101] In order to uniquely determine the carrier system, in this embodiment, the installation error variables of the three gyroscopes are set to zero, that is, the three axes of the gyroscope system are constrained within the plane of the carrier system.

[0102] Then establish the inertial navigation error equation, and estimate the inertial device error through the inertial navigation error. The relationship between the inertial navigation error and the inertial device error is reflected by the inertial navigation error equation, which is as follows:

[0103]

[0104] Among them, the superscript n is the navigation coordinate system, b is the carrier coordinate system, e is the earth coordinate system, and i is the inertial coordinate system. is the differential of the position error of the inertial navigation in the navigation coordinate system, is the differential of the velocity error of the inertial navigation in the navigation coordinate system, is the differential of the attitude error of the inertial navigation in the navigation coordinate system, δr n is the position error of the inertial navigation in the navigation coordinate system, δV n is the velocity error of the inertial navigation in the navigation coordinate system, ψ n is the attitude error of the inertial navigation in the navigation coordinate system, is the projection of the rotational angular velocity of the navigation coordinate system relative to the earth coordinate system in the navigation coordinate system, is the projection of the angular velocity of the earth coordinate system relative to the inertial coordinate system in the navigation coordinate system, is the projection of the angular velocity of the navigation coordinate system relative to the inertial coordinate system in the navigation coordinate system, is the transformation matrix from the carrier coordinate system to the navigation coordinate system, that is, the attitude matrix, δa b is the output error of the accelerometer in the carrier coordinate system, δω b is the output error of the gyroscope in the carrier coordinate system, f n is the projection of the comparison in the navigation coordinate system.

[0105] By substituting the output error model of the accelerometer in the carrier coordinate system and the output error model of the gyroscope in the carrier coordinate system into the above formula, the relationship between the navigation error and the inertial device error can be obtained.

[0106] System-level calibration involves externally rotating or maneuvering the carrier to excite inertial device errors, performing inertial navigation calculations, comparing the calculated results with reference results, and calculating error parameters using a specific algorithm. System-level calibration is primarily implemented in two ways. The first is an analytical approach. This approach first designs a specific motion translation rule and, based on this rule, derives the equation between navigation errors (such as position error and velocity error) and the IMU (Inertial Measurement Unit) error parameters to be calibrated. The navigation errors during the calibration process are then recorded, and the desired error parameters are estimated using a least-squares fit. The second is a filtering approach. This approach designs a Kalman filter based on the error equations of the strapdown inertial navigation system. The desired error parameters are selected as the Kalman filter state variables, and the navigation errors are measured as Kalman filter quantities. A specific motion translation rule is also designed to ensure that the desired error parameters are sufficiently excited. Finally, filtering is used to estimate the desired error parameters. The system-level fitting method requires calibration equipment and environment, while the system-level filtering method reduces the requirements for turntable accuracy, can establish complex models to improve system accuracy, and reduce calibration time. Therefore, the present invention adopts the filtering method to achieve system-level calibration.

[0107] The next step is to design a self-calibrating filter. The standard form of the Kalman filter state equation is used: u is the noise of the system; the error model of the accelerometer and gyroscope is substituted into the inertial error equation to obtain the matrix form of the calibration model; the state variable of the model is X = [δr n ,δV n ,ψ n ,X g ,X a ] T , namely position error, velocity error, attitude error and device error of gyroscope and accelerometer. The state variables are as follows:

[0108] δr n =[δn N δn E δn D ] T

[0109] δV n =[δV N δV E δV D ]T

[0110] ψ n =[ψ N ψ E ψ D ] T

[0111] X g =[S x E yx S y E zy E xz S z ε x ε y ε z ] T

[0112]

[0113] Where N is north, E is east, and D is ground direction; δr n is the position error, δn N is the north position error, δn E Easting position error, δn D Ground position error; δV n is the velocity error, δV N is the north velocity error, δV E Eastward velocity error, δV D Ground velocity error; ψ n is the attitude error, ψ N is the north attitude error, ψ E is the eastward attitude error, ψ D is the ground attitude error; X g is the device error of the gyroscope, X a is the device error added to the table; a I (I = x, y, z) is the input acceleration of the I-axis accelerometer, K I (I = x, y, z) is the accelerometer scale factor error of the I axis, M IJ (I, J = x, y, z and I ≠ J) is the accelerometer installation error, λ I (I = x, y, z) is the asymmetric error of the scale factor of the I axis, is the accelerometer bias of the I axis, ω I (I=x,y,z) is the angular velocity measured by the I-axis gyroscope, S I (I = x, y, z) is the gyro scale factor error of the I axis, E IJ (I, J = x, y, z and I ≠ J) is the gyro installation error, ε I(I = x, y, z) is the gyro bias of the I axis.

[0114] The coefficient matrix in the model is:

[0115]

[0116] The sub-matrices in F are:

[0117]

[0118] in, is the earth component of the projection of the angular velocity of the navigation coordinate system relative to the earth coordinate system in the navigation coordinate system, is the east component of the projection of the angular velocity of the navigation coordinate system relative to the earth coordinate system in the navigation coordinate system, is the north component of the projection of the angular velocity of the navigation coordinate system relative to the earth coordinate system in the navigation coordinate system, is the earth component of the projection of the angular velocity of the navigation coordinate system relative to the inertial coordinate system in the navigation coordinate system, is the earthward component of the projection of the angular velocity of the earth coordinate system relative to the inertial coordinate system in the navigation coordinate system, is the east component of the projection of the angular velocity of the earth coordinate system relative to the inertial coordinate system in the navigation coordinate system, is the north component of the projection of the angular velocity of the earth coordinate system relative to the inertial coordinate system in the navigation coordinate system, is the ground component of the projection of the specific force in the navigation coordinate system, is the east component of the projection of the specific force in the navigation coordinate system, is the north component of the projection of the specific force in the navigation coordinate system;

[0119]

[0120] in, is the transformation matrix from the carrier coordinate system to the navigation coordinate system, that is, the attitude matrix. AB for The B-th component in the A-th row of the matrix has a value range of A (1, 2, 3) and a value range of B (1, 2, 3).

[0121]

[0122] in, It is the north component of the projection of the angular velocity of the navigation coordinate system relative to the inertial coordinate system in the navigation coordinate system.

[0123] The next step is to design the system's measurement equation z = Hx + v, where z is the measured value of the observed quantity, H is the measurement system parameter, x is the system state, and v is the measurement noise.

[0124] Considering that it is difficult to obtain the absolute attitude of the inertial navigation under field conditions, speed is selected as the observation quantity, and the convergence rate of the error parameter is now faster. After the filter design is completed, the inertial navigation speed error is excited by the rotation of the mechanism, and the instrument error parameter can be identified using the measured speed error. When the carrier is in motion, the reference speed always has an error. In this way, when calculating the filter observation error, directly subtracting the reference speed will introduce the reference speed error into the filter observation, resulting in a reduction in calibration accuracy. Therefore, the present invention specifically proposes an anti-disturbance dynamic self-calibration scheme for this problem of low dynamic self-calibration accuracy. The anti-disturbance dynamic self-calibration method of the present invention is introduced in detail below, which can effectively reduce the error of the reference speed.

[0125] like Figure 1 As shown in the figure, the overall framework process of dynamic self-calibration is as follows: first, the output data of the inertial sensor is solved by inertial navigation to obtain the speed, the solved speed is subtracted from the reference speed to obtain the speed error, the external disturbance speed is eliminated by wavelet transform, the speed error after eliminating the disturbance is used as the observation quantity of Kalman filter, and then the error parameters are estimated, and the data after the correction of sensor error and navigation error are returned to the inertial navigation solution.

[0126] The principle of wavelet transform to eliminate disturbance velocity: It is known from the literature of existing technology that under the influence of waves, sea breeze, etc., ships will produce periodic angular motion and linear motion, with a frequency generally above 0.05Hz, while the inertial navigation velocity error is composed of the Shura period, Foucault period and Earth period. The frequency of these errors is much lower than the frequency of the disturbance motion at sea, so the inertial navigation velocity error and the disturbance motion can be distinguished from the spectrum. The traditional filtering method uses IIR filter (recursive filter) or FIR filter (finite length unit impulse response filter, also known as non-recursive filter) to eliminate the disturbance information. Such filters can filter out the disturbance motion brought by the outside world, but because the stop band cutoff frequency is too low, phase delay will inevitably be caused during filtering. For real-time systems such as calibration, serious delay will cause the Kalman filter to not converge. Therefore, the present invention uses wavelet transform to eliminate the disturbance information. The time delay caused by wavelet transform as filtering is low, which is suitable for the real-time process of inertial navigation self-calibration. The principle of wavelet transform is to decompose the signal by convolving it with a set of wavelet functions to obtain the time-frequency representation of the signal. Compared with the low-pass filtering based on Fourier transform, it has variable time-frequency resolution, which can have better frequency resolution for the low-frequency part of the signal and better time resolution for the high-frequency part of the signal.

[0127] For a finite velocity error input signal, the wavelet decomposition equation is:

[0128]

[0129] Where x(t) is the finite input signal of velocity error; ψ * () is the complex conjugate of the mother wavelet basis function; * is the complex conjugate; a and b are transformation parameters; x(a,b) is the signal obtained after wavelet transformation; x is the original signal; t is time; dt is the time differential.

[0130] Through the above transformation, the signal can be transformed into wavelet coefficients of different scales and positions through the scale transformation and translation transformation of the wavelet function, and a series of wavelets of different frequencies can be obtained. The wavelets below 0.05Hz can be screened out and then reconstructed to obtain the processed signal. Its expression is as follows:

[0131]

[0132] ψ j,k (t) = 2 j / 2 ψ(2 j tk);

[0133] Among them, x r (t) is the reconstructed velocity error signal; x(t) is the finite input signal of velocity error; ψ j,k (t) is the kth wavelet basis function of the jth layer transformed from the mother wavelet basis function ψ(t); ψ is the mother wavelet basis function; j is the jth layer transformed from the mother wavelet basis function; k is the kth wavelet basis function in this layer, and t is time;.

[0134] During the calibration process, the basic principle of extracting the speed error is to transform the speed signal into a wavelet signal with multiple frequencies through the above-mentioned wavelet transform. The frequency of the disturbance speed is higher than 0.05Hz, and the frequency of the speed error is much lower than 0.05Hz. The high-frequency wavelet coefficients are set to zero using the hard threshold method, and the wavelet is reconstructed to obtain the speed error after removing the disturbance speed. The following is the specific process of eliminating the disturbance speed by wavelet transform:

[0135] First, determine the basis function: the db4 wavelet is selected as the basis function. The db4 wavelet function has compact support in the time domain and good smoothness. It can effectively remove noise from the signal and is computationally simple and efficient.

[0136] The second step is to determine the number of decomposition layers: During the wavelet transform process, each transformation will produce a new low-frequency component that is half of the previous low-frequency component. In order to distinguish the disturbance velocity from the velocity error, the final low-frequency component f c It should be lower than the frequency of the disturbance velocity. In actual calculation, the velocity solution frequency is fs =250Hz, the frequency of the disturbance speed is above 0.05Hz, the number of transformation layers K satisfies the following formula, and the minimum number of transformation layers is calculated to be K=12.

[0137]

[0138] Among them, f c is the final low-frequency component obtained by wavelet transform; f s is the velocity solution frequency in actual calculation, K is the number of transformation layers;

[0139] The third step is to determine the width of the sliding window: Wavelet transforms require real-time calculations, so an appropriate window length is required. After repeated adjustments, a window length of 200 seconds was chosen.

[0140] Finally, the boundary data is processed. One problem faced after wavelet transform is boundary signal distortion. This is due to insufficient data at the boundary, resulting in large errors at the boundary of the reconstructed signal. The present invention extends the input data window to improve the accuracy of the wavelet transform boundary signal. The essence of boundary extension is to increase the observed amount of boundary information, thereby improving accuracy. Currently, common boundary extension methods include constant extension, symmetric extension, and linear extension. These methods are quite effective for processing regularly periodic signals, but the processing accuracy is still insufficient. Therefore, the present invention uses a particle swarm optimization algorithm to extend the boundary data.

[0141] The velocity of the inertial navigation system on the sea surface exhibits the following characteristics: the velocity error exhibits long-period oscillations without sudden changes; the disturbance velocity exhibits short-period oscillations. Based on the above characteristics, the following velocity model is constructed:

[0142]

[0143] Among them, h m 、p o 、L o and t o is the fitting coefficient to be determined; x is the independent variable of the velocity model; V predict is the predicted speed output by the speed model; M is the highest power of x in the fitting function; m is the mth power of the x polynomial in the fitting function and the corresponding mth fitting coefficient; N is the number of superimposed sine functions, that is, a total of N+1 sine terms are added; o is the oth coefficient to be fitted in the sine function term;

[0144] The polynomial part in the above formula is mainly used to fit the trend term in the window velocity, and the order of the polynomial should not be too high; the trigonometric function part is used to fit the disturbance velocity, which is related to the characteristics of the external disturbance velocity. The commonly used method to solve the coefficients in the above formula is the nonlinear least squares method, but it is easy to fall into the local optimal solution. Therefore, the particle swarm optimization algorithm (PSO algorithm) adopted in the present invention is simple to implement, and it is solved by searching, which has more opportunities to solve the global optimal solution and improves the fitting accuracy. The particle swarm optimization algorithm (PSO algorithm) simulates the foraging process of birds in nature, iteratively selects particles with high fitness, and completes the optimization process. The particle swarm composed of S particles X = {x1, x2, ... x s}, the velocity V of each particle i and position P i Iterative changes. In each iteration, the particle will record two optimal values: one is the optimal solution P found by the particle itself best ; The other is the optimal solution G currently found by the entire group best Based on these two optimal values, the particle speed and position are updated until the termination condition is met, that is, the maximum number of iterations is reached or the optimal position searched by the particle swarm so far meets the predetermined minimum adaptation threshold. The particle swarm stops updating and the optimal position found is the fitting coefficient. The update formula is as follows:

[0145] V q =ω*V q +e1r1(P best -P q )+e2r2(G best -P q );

[0146] P q =P q +V q ;

[0147] Among them, V q is the velocity of the qth particle; P q is the position of the qth particle; ω is the inertia weight coefficient; e1 and e2 are learning factors; r1 and r2 are random numbers; the value range is [0,1]; P best is the optimal position of the particle in its own history; G best is the optimal position for the entire group.

[0148] The particle swarm optimization algorithm is used to fit the cached input speed and solve the fitting coefficient in the fitting function; the input speed and the predicted speed are spliced ​​to extend the data boundary.

[0149] The core concept of the PSO-based boundary extension algorithm constructed in this paper is to predict future speeds based on the current cached speed, and then combine the future speed with the current cached speed to obtain data for extending the boundary. This PSO-based boundary extension method is used to address the problem of boundary signal distortion after wavelet transform. Wavelet transform can be used to remove disturbance information, obtain Kalman filter observations, and perform filtering calculations to obtain calibration parameters.

[0150] To address the problem of significant time delay caused by the design of low-pass filters to separate the disturbance velocity and velocity error in traditional IIR and FIR filters, a more advanced technology uses a zero-phase-shift low-pass filter to process the resolved velocity. By performing zero-phase filtering on the velocity output of a certain type of inertial navigation system in a moored state, it can be seen that the velocity error using zero-phase filtering has essentially no phase delay, ensuring that the inertial navigation system can complete the self-calibration task without relying on external input. In contrast, the present invention addresses the time delay caused by traditional filters by using a wavelet transform to process the velocity. The time delay caused by the wavelet transform used as a filter is very low, making it suitable for real-time inertial navigation self-calibration.

[0151] From the theoretical analysis and comparison, it can be seen that the wavelet transform used in the present invention has the following advantages compared with the zero-phase shift filter:

[0152] ① Multi-resolution analysis capability: The wavelet transform has the ability to perform multi-resolution analysis, decomposing signals at different scales. This capability gives the wavelet transform an advantage in processing non-stationary signals and allows it to better describe the signal's local characteristics. In contrast, while zero-phase-shift filtering can eliminate phase distortion, it may not be as flexible as the wavelet transform in multi-resolution analysis.

[0153] ② Fast Algorithm: The wavelet transform is a fast algorithm that can complete signal processing in a relatively short time. Compared with the Fourier transform, the wavelet transform is faster when processing non-stationary and nonlinear signals. Although zero-phase shift filtering can reduce the amount of computation in some cases through optimization algorithms, its overall speed may still be slower than that of the wavelet transform.

[0154] ③ Sparse representation and storage space savings: The wavelet transform uses a sparse representation method, meaning only a few coefficients need to be retained. This representation method can significantly reduce storage space and computation time, and facilitates operations such as compression, noise reduction, and feature extraction. However, zero-phase shift filtering may require saving the entire signal sequence and its filtering results during processing, so it may not be as storage-efficient as the wavelet transform.

[0155] ④ Denoising and Robustness: The wavelet transform is robust to noise and interference. While noise and interference are unavoidable in signal processing, the wavelet transform can reduce their impact through methods such as filtering and thresholding, and can better extract signal features. While zero-phase-shift filtering can also suppress noise to a certain extent, its denoising effectiveness may be affected by factors such as filter design and parameter tuning.

[0156] 5. Flexibility in basis selection: Wavelet transforms can use different wavelet basis functions to process different types of signals, such as Haar wavelets (the simplest wavelet basis function) and Daubechies wavelets (a type of wavelet function). This flexibility in basis selection enables wavelet transforms to better adapt to different application scenarios and signal characteristics. In contrast, zero-phase shift filtering may be relatively fixed in terms of filter design and selection, lacking this flexibility.

[0157] ⑥ Suitable for sudden changes in signals: For sudden changes in signals (such as edges and spikes), the wavelet transform can maintain a high resolution at the sudden change point, thereby more accurately describing the local characteristics of the signal. In contrast, although zero-phase shift filtering can eliminate phase distortion, it may not provide the same level of detailed information as the wavelet transform when processing sudden changes in signals.

[0158] From the perspective of technical effects, the results of the respective simulation verifications show that the present invention has higher calibration accuracy than the best existing technology in the second aspect. The simulation verification results are as follows:

[0159] Table 2 Gyro error calibration simulation results of the present invention

[0160]

[0161]

[0162] Table 3 Simulation results of gyro error calibration using current technology

[0163] Error parameters True value Calibration method <![CDATA[ε x (° / h)]]> 0.3 0.2866 <![CDATA[ε y (° / h)]]> 0.4 0.3996 <![CDATA[ε z (° / h)]]> 0.5 0.4992 <![CDATA[S x (ppm)]]> 70 81.4253 <![CDATA[S y (ppm)]]> 90 87.5992 <![CDATA[S z (ppm)]]> 90 94.6076 <![CDATA[E xz (office)]]> 145 148.5973 <![CDATA[E yx (office)]]> 242 246.8443 <![CDATA[E zy (office)]]> 242 249.3901

[0164] Table 4 Error calibration results of the present invention

[0165]

[0166]

[0167] Table 5 Simulation results of current technology plus table error calibration

[0168]

[0169] In the table, S I(I = x, y, z) is the gyro scale factor error of the I axis, E IJ (I, J = x, y, z and I ≠ J) is the gyro installation error, ε I (I=x,y,z) is the gyro bias of axis I. K I (I = x, y, z) is the accelerometer scale factor error of the I axis, M IJ (I, J = x, y, z and I ≠ J) is the accelerometer installation error, λ I (I = x, y, z) is the asymmetric error of the scale factor of the I axis, is the accelerometer bias of the I axis.

[0170] The comparison of simulation results shows that the gyroscope bias estimation accuracy obtained by the existing technology is better than 0.015° / h, the scale factor estimation accuracy is better than 5ppm, the installation error estimation accuracy is better than 7.2722urad, the accelerometer bias estimation accuracy is better than 5ug, the scale factor estimation accuracy is better than 2ppm, and the accelerometer asymmetric error estimation accuracy is better than 2×10 -3 ppm. The gyroscope zero bias estimation accuracy obtained by the calibration of the present invention is better than 0.003° / h, the scale factor estimation accuracy is better than 0.598ppm, the installation error estimation accuracy is better than 1.724urad, the accelerometer zero bias estimation accuracy is better than 0.708ug, the scale factor estimation accuracy is better than 0.126ppm, and the accelerometer asymmetric error estimation accuracy is better than 0.691ppm. The data obtained from the simulation results show that the calibration accuracy achieved by the technical solution proposed by the present invention is higher than that of the existing technology.

[0171] Simulation analysis and experimental testing:

[0172] (1) Simulation analysis:

[0173] ①Simulation analysis verifies the effectiveness of the disturbance velocity elimination method based on wavelet transform:

[0174] First, in order to verify the effectiveness of the disturbance velocity elimination method in this paper, the following simulation is performed: the input signal consists of sinusoidal signals with frequencies of 0.001Hz and 0.08Hz, both with amplitudes of 1m / s, sampling frequency of 250Hz, and signal duration of 200s. Here, the 0.001Hz signal is regarded as an ideal signal, and the 0.08Hz signal is regarded as a disturbance signal. The input signal is processed using the method of the present invention, and compared with the currently commonly used constant extension method, symmetric extension method, and linear extension method, and the signal error after wavelet transformation is calculated. In order to compare the changes before and after extension, only the right side of the input signal is extended during the simulation. Figure 2It can be seen that compared with other traditional data continuation methods, the continuation method of the present invention has the highest accuracy, with an error of 1.7% after wavelet transformation, which is more than 10% higher than other methods. The fitted boundary continuation method is then applied to inertial navigation velocity. Figure 2 In the table, No extension means no extension, With extension means extension, Constant extension means constant extension, Symmetric extension means symmetric extension, Linear extension means linear extension, PSO extension means particle swarm optimization algorithm extension, the horizontal axis is time in seconds, and the vertical axis is error.

[0175] During the error extraction process, the effectiveness of the wavelet transform method based on the extension of the particle swarm optimization algorithm proposed in the present invention is verified. The simulation process is as follows: a. Generate inertial raw data containing a 0.08Hz disturbance velocity, and the disturbance velocity amplitude in the carrier coordinate system b is 0.5m / s; b. Perform inertial solution on the raw data to obtain the solution velocity; c. Use the wavelet transform method proposed in the present invention to eliminate the disturbance velocity and obtain the velocity after the disturbance is removed. During the simulation process, the carrier performs periodic linear motion in situ, and the velocity error can be obtained by removing the actual disturbance velocity. The simulation results are as follows. Figure 3 and Figure 4 As shown in the figure, the solved speed is composed of the oscillating disturbance speed and the speed error of the trend change. After being removed by wavelet transform, the eastward disturbance speed is reduced by 97% and the northward disturbance speed is reduced by 95%. The algorithm can extract the speed error more accurately and solve it in real time. Figure 3 The horizontal axis is time, in seconds; the vertical axis is the north velocity error, in m / s; Velocity is the velocity; and Velocity after wavelet transform is the velocity after wavelet transform. Figure 4 The horizontal axis is time, in seconds; the vertical axis is the eastward velocity error, in m / s.

[0176] ② Dynamic base state calibration simulation:

[0177] A dynamic base state calibration simulation is designed to explore the effect of the anti-disturbance calibration method proposed in this invention on inertial navigation calibration under navigation state. The following simulation conditions are set:

[0178] a. The carrier has periodic angular motion, and the amplitude of the shaking angle is A θs is 3°, and the frequency is 0.08Hz;

[0179] b. The carrier is in the dynamic base state and is heading east at a constant speed. The speed is V cs At the same time, the carrier has periodic linear motion with amplitude Acs The velocity is 0.3m / s and the frequency is 0.08Hz. The periodic linear motion is used to simulate the disturbance speed of the carrier during navigation.

[0180] c. The inertial guidance error parameters added during the simulation are shown in Table 6, and the calibration path is shown in Table 1;

[0181] d. When performing filtering estimation, the initial value of each error term is 0.

[0182] Table 6 Gyro error calibration results

[0183] Error parameters True value Anti-disturbance calibration method No-disturbance elimination method <![CDATA[ε x (° / h)]]> 0.01 0.0097 0.0341 <![CDATA[ε y (° / h)]]> 0.01 0.0096 0.0328 <![CDATA[ε z (° / h)]]> 0.01 0.0098 -0.0113 <![CDATA[S x (ppm)]]> 100 99.518 105.939 <![CDATA[S y (ppm)]]> 100 99.442 110.561 <![CDATA[S z (ppm)]]> 100 99.402 88.933 <![CDATA[E xz (office)]]> 100 101.724 99.091 <![CDATA[E yx (office)]]> 100 99.980 117.028 <![CDATA[E zy (office)]]> 100 99.083 83.323

[0184] Table 7 Calibration results of table error

[0185]

[0186] The simulation lasted 7200 seconds. During the simulation, the inertial navigation system was first aligned for 60 seconds. Then the vehicle accelerated eastward to 5 m / s for 100 seconds, maintained a constant speed, and then self-calibrated. The final calibration results are shown in Tables 6 and 7. I (I = x, y, z) is the gyro scale factor error of the I axis, E IJ (I, J = x, y, z and I ≠ J) is the gyro installation error, ε I (I=x,y,z) is the gyro bias of axis I. K I (I = x, y, z) is the accelerometer scale factor error of the I axis, M IJ (I, J = x, y, z and I ≠ J) is the accelerometer installation error, λ I (I = x, y, z) is the asymmetric error of the scale factor of the I axis, is the accelerometer bias of the I axis.

[0187] As can be seen from Tables 6 and 7, when external disturbance velocity is present and disturbance velocity elimination is not performed, calibration accuracy is significantly reduced. After disturbance velocity elimination, calibration accuracy is significantly improved. The algorithm proposed in this invention can achieve inertial navigation calibration under a moving base. This disturbance velocity elimination method is effective and can significantly improve calibration accuracy.

[0188] (2) Experimental testing

[0189] ① Dynamic base state calibration test

[0190] We conducted a ship navigation calibration test to verify the performance of the proposed anti-disturbance calibration algorithm under a motion base. The dual-axis inertial navigation system was placed on the ship. During the inertial navigation alignment, the ship was in a moored state. After the alignment was completed, self-calibration was performed and the ship sailed away from the port. The test process is as follows:

[0191] a. Power on the inertial navigation system and return the dual-axis inertial navigation turntable to zero;

[0192] b. The inertial navigation system performs coarse alignment, which takes 120 seconds, and the ship is moored at the pier;

[0193] c. The inertial navigation system performs fine alignment, which takes 180 seconds, and the ship is moored at the dock;

[0194] d. The inertial navigation system performs self-calibration at 10500s while the ship is sailing.

[0195] Table 8 INS performance indicators

[0196]

[0197] The accuracy of the calibrated inertial navigation device is shown in Table 8. The dual-axis inertial navigation device was loaded on the ship and the calibration test was carried out in the navigation state. The total navigation time was 10500s and the maximum navigation speed was 4.6m / s. Before the navigation, the inertial navigation device was aligned and then entered the calibration state. The test conditions during the calibration process are as follows:

[0198] a. The carrier is in a dynamic base state, and the disturbance velocity comes from the periodic linear velocity of the ship during navigation and the velocity caused by the arm error;

[0199] b. The carrier position and reference velocity are provided by GPS (GPS position accuracy 5m, velocity accuracy 0.1m / s), with a frequency of 1Hz. The GPS position is used to correct the position calculated by the inertial navigation in real time.

[0200] c. The dual-axis inertial navigation system rotates according to the calibration path in Table 1;

[0201] d. The initial values ​​of all error terms estimated by the filter are 0.

[0202] To make fuller use of the collected raw data, multiple rounds of iteration were used to improve the calibration accuracy. After four iterations, the error parameters stabilized. The results of the navigation calibration were compared with those of the static base, as shown in Tables 9 and 10.

[0203] Table 9 Gyro error calibration results in navigation state

[0204] Error parameters Navigation calibration Static base calibration deviation <![CDATA[ε x (° / h)]]> -0.0329 -0.0363 0.0034 <![CDATA[ε y (° / h)]]> -0.0111 -0.0056 -0.0055 <![CDATA[ε z (° / h)]]> 0.0316 0.02519 0.0065 <![CDATA[S x (ppm)]]> -42.266 -39.234 -3.032 <![CDATA[S y (ppm)]]> -230.573 -230.704 0.131 <![CDATA[S z (ppm)]]> -236.307 -238.321 2.014 <![CDATA[E xz (office)]]> -1378.007 -1384.555 6.548 <![CDATA[E yx (office)]]> 535.288 536.323 -1.035 <![CDATA[E zy (office)]]> 392.172 401.061 -8.889

[0205] Table 10 Calibration results of navigation status plus table error

[0206]

[0207] Compared with the calibration results obtained under a static base, the estimated gyro bias under navigation conditions is 0.007° / h, the gyro scale error is 3.1ppm, and the gyro installation error is 8.9urad. The estimated bias using a table is 20.4ug, the scale error is 5.3ppm, the installation error is 9.4urad, and the scale asymmetry is 6ppm. This demonstrates that the proposed calibration scheme can effectively implement inertial navigation self-calibration under navigation conditions and achieve effective estimation of all parameters.

[0208] ② Navigation experiment verification

[0209] To verify the accuracy of the motion base calibration results, we conducted inertial navigation experiments using the same inertial navigation system. The calibrated error parameters were written into the program for post-processing, with the same set of raw data being processed. The inertial navigation operating mode was dual-axis rotation modulation, employing a 16-step rotation scheme. The specific experimental steps are as follows:

[0210] a. Write the inertial navigation error parameters calibrated by different methods under different navigation conditions into the program;

[0211] b. Binding the initial position of the inertial navigation;

[0212] c. Enter the coarse alignment mode, the coarse alignment time is 240s;

[0213] d. Enter the fine alignment mode, the fine alignment time is 2400s;

[0214] e. Enter the dual-axis rotation modulation mode for inertial navigation, total time 10 hours.

[0215] The inertial navigation error parameters calibrated by the method of the present invention in the dynamic base state and the inertial navigation error parameters calibrated by the non-disturbance suppression method in the dynamic base state are solved and compared. The navigation results are shown in Table 11. Figures 5 to 8 shown.

[0216] Table 11 Navigation results of different calibration algorithms

[0217]

[0218] From Table 11 and Figures 5 to 8 It can be seen that the latitude error corresponding to the inertial navigation error calibrated by the calibration algorithm proposed in the present invention in the navigation state is 0.2651n mile, and the longitude error is 0.2852n mile. Compared with the traditional method, the navigation position accuracy and speed accuracy are significantly improved, indicating that the calibration algorithm proposed in the present invention can achieve relatively accurate calibration in the navigation state.

[0219] Figure 5The horizontal axis is time, in hours; the vertical axis is latitude error, in n mile. The blue line in the coordinate axis is the traditional method, and the red line in the coordinate axis is the method of the present invention. Figure 6 The horizontal axis is time, in hours; the vertical axis is north velocity error, in n mile. The blue line in the coordinate axis is the traditional method, and the red line in the coordinate axis is the method of the present invention. Figure 7 The horizontal axis is time, in hours; the vertical axis is longitude error, in n mile. The blue line in the coordinate axis is the traditional method, and the red line in the coordinate axis is the method of the present invention. Figure 8 The horizontal axis is time, in hours; the vertical axis is eastward velocity error, in n mile. The blue line in the coordinate axis is the traditional method, and the red line in the coordinate axis is the method of the present invention.

[0220] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A method for anti-disturbance self-calibration of an inertial navigation device for navigation, characterized in that: The process includes the following steps: S1. Rotate the turntable of the marine inertial navigation device according to the calibration path to collect raw inertial navigation data; S2. Perform inertial solution on the raw inertial navigation data to obtain a solution velocity, and subtract the reference velocity from the solution velocity to obtain a velocity error including the disturbance velocity; S3, removing the disturbance velocity from the velocity error including the disturbance velocity by real-time wavelet transform; S4, using the velocity error processed by wavelet transform as the Kalman filter observation quantity, and using Kalman filtering to obtain the inertial navigation error parameter; S5, feeding back the calculated inertial navigation error parameters into the inertial solution process; S6. Repeat S2 to S5 until the inertial navigation error parameters estimated by the Kalman filter converge, completing the calibration of the inertial navigation error parameters. The wavelet transform is used to eliminate the disturbance velocity of the reconstructed velocity error signal to obtain the velocity error, which includes the following steps: Determine the basis function, and choose db4 wavelet as the basis function; Determine the number of decomposition layers and the number of transformation layers K to satisfy the following formula: Among them, f c is the final low-frequency component obtained by wavelet transform; f s is the velocity solution frequency in actual calculation, K is the number of transformation layers; Determine the width of the sliding window of the wavelet transform input data window; Process the boundary data and extend the input data window to obtain the velocity error; When extending the input data window, the particle swarm optimization algorithm is used to extend the boundary data, including the following steps: Cache the input velocity and construct a fitting function based on the characteristics of velocity error and disturbance velocity: Among them, h m 、p o 、L o and t o is the fitting coefficient to be determined; x is the independent variable of the velocity model; V predict is the predicted velocity output by the velocity model; M is the highest power of x in the fitting function; m is the mth power of the x polynomial in the fitting function and the corresponding mth fitting coefficient; N is the number of superimposed sine functions; o is the oth coefficient to be fitted in the sine function term; The particle swarm optimization algorithm is used to fit the cache input speed and solve the fitting coefficient in the fitting function; Splice the input speed and prediction speed to extend the data boundary.

2. The anti-disturbance self-calibration method for marine inertial navigation equipment according to claim 1, characterized in that: When removing the disturbance velocity from the velocity error including the disturbance velocity by real-time wavelet transform, the following steps are included: Through the scale transformation and translation transformation of the wavelet decomposition calculation equation, the velocity error signal is transformed into wavelet coefficients of different scales and positions to obtain wavelet signals of different frequencies. The wavelet decomposition calculation equation is: Where x(t) is the finite input signal of velocity error; ψ * () is the complex conjugate of the mother wavelet basis function; * is the complex conjugate; a and b are transformation parameters; x(a,b) is the signal obtained after wavelet transformation; t is time; dt is the time differential.

3. The anti-disturbance self-calibration method for a marine inertial navigation device according to claim 2, characterized in that: Also includes: The wavelet signal below the target frequency is filtered and reconstructed to obtain the reconstructed velocity error signal, which is expressed as follows: ψ j,k (t)=2 j / 2 ψ(2 j tk); Among them, x r (t) is the reconstructed velocity error signal; ψ j,k (t) is the wavelet basis function, which is the kth wavelet basis function of the jth layer transformed from the mother wavelet basis function ψ(t); ψ(t) is the mother wavelet basis function; j is the jth layer transformed from the mother wavelet basis function; k is the kth wavelet basis function in this layer.

4. The anti-disturbance self-calibration method for a marine inertial navigation device according to claim 3, characterized in that: When solving the fitting coefficients in the fitting function, the speed and position of each particle in the particle swarm composed of multiple particles change iteratively. In each iteration, the particle will record two optimal values: one is the optimal solution found by the particle itself; the other is the optimal solution currently found by the entire swarm. The particle speed and position are updated based on these two optimal values. The optimal position obtained is the fitting coefficient. The update formula is as follows: V q =ω*V q +e1r1(P best -P q )+e2r2(G best -P q ); P q =P q +V q ; Among them, V q is the velocity of the qth particle; P q is the position of the qth particle; ω is the inertia weight coefficient; e1 and e2 are learning factors; r1 and r2 are random numbers; the value range is [0,1]; P best is the optimal position of the particle in its own history; G best is the optimal position for the entire group.

5. The anti-disturbance self-calibration method for marine inertial navigation equipment according to claim 1, characterized in that: Before using Kalman filtering to obtain inertial navigation error parameters, the inertial device error model is determined. The inertial device error model includes the accelerometer error model. The accelerometer error model is expressed as follows: Among them, δa b is the output error of the accelerometer in the carrier coordinate system, a I is the input acceleration of the I-axis accelerometer, (I = x, y, z); K I is the accelerometer scale factor error of the I axis, (I = x, y, z); M IJ is the accelerometer installation error, (I, J = x, y, z and I ≠ J); λ I is the asymmetry error of the scale factor of the I axis, (I = x, y, z); is the accelerometer bias of the I axis, (I = x, y, z).

6. The anti-disturbance self-calibration method for marine inertial navigation equipment according to claim 5, characterized in that: The inertial device error model also includes a gyroscope error model, which is expressed as follows: Among them, δω b is the output error of the gyroscope in the carrier coordinate system, ω I is the angular velocity measured by the I-axis gyroscope, (I = x, y, z); S I is the gyro scale factor error of the I axis, (I = x, y, z); E IJ is the gyro installation error, (I, J = x, y, z and I ≠ J); ε I is the gyro bias of the I-axis, (I = x, y, z).

7. The anti-disturbance self-calibration method for a marine inertial navigation device according to claim 6, characterized in that: After determining the inertial device error model, the inertial guidance error equation is established: Among them, the superscript n is the navigation coordinate system, b is the carrier coordinate system, e is the earth coordinate system, and i is the inertial coordinate system. is the differential of the position error of the inertial navigation in the navigation coordinate system, is the differential of the velocity error of the inertial navigation in the navigation coordinate system, is the differential of the attitude error of the inertial navigation in the navigation coordinate system, δr n is the position error of the inertial navigation in the navigation coordinate system, δV n is the velocity error of the inertial navigation in the navigation coordinate system, ψ n is the attitude error of the inertial navigation in the navigation coordinate system, is the projection of the rotational angular velocity of the navigation coordinate system relative to the earth coordinate system in the navigation coordinate system, is the projection of the angular velocity of the earth coordinate system relative to the inertial coordinate system in the navigation coordinate system, is the projection of the angular velocity of the navigation coordinate system relative to the inertial coordinate system in the navigation coordinate system, is the transformation matrix from the carrier coordinate system to the navigation coordinate system, that is, the attitude matrix, δa b is the output error of the accelerometer in the carrier coordinate system, δω b is the output error of the gyroscope in the carrier coordinate system, f n is the projection of the comparison in the navigation coordinate system.

8. The anti-disturbance self-calibration method for marine inertial navigation equipment according to claim 7, characterized in that: When using Kalman filtering to obtain inertial navigation error parameters, a self-calibrated filter is designed: The standard form of the Kalman filter state equation is used: u is the noise of the system; the error model of the accelerometer and gyroscope is substituted into the inertial error equation to obtain the matrix form of the calibration model; the state variable of the model is X = [δr n ,δV n ,ψ n ,X g ,X a ] T , namely position error, velocity error, attitude error and device error of gyroscope and accelerometer. The state variables are as follows: δr n =[δn N δn E δn D ] T δV n =[δV N δV E δV D ] T ψ n =[ψ N ψ E ψ D ] T X g =[S x E yx S y E zy E xz S z e x e y e z ] T Among them, δr n is the position error, δn N is the north position error, δn E Easting position error, δn D Ground position error; δV n is the velocity error, δV N is the north velocity error, δV E Eastward velocity error, δV D Ground velocity error; ψ n is the attitude error, ψ N is the north attitude error, ψ E is the eastward attitude error, ψ D is the ground attitude error; X g is the device error of the gyroscope, X a is the device error added to the table; The coefficient matrix in the model is: The sub-matrices in F are: in, is the earth component of the projection of the angular velocity of the navigation coordinate system relative to the earth coordinate system in the navigation coordinate system, is the east component of the projection of the angular velocity of the navigation coordinate system relative to the earth coordinate system in the navigation coordinate system, is the north component of the projection of the angular velocity of the navigation coordinate system relative to the earth coordinate system in the navigation coordinate system, is the earth component of the projection of the angular velocity of the navigation coordinate system relative to the inertial coordinate system in the navigation coordinate system, is the earthward component of the projection of the angular velocity of the earth coordinate system relative to the inertial coordinate system in the navigation coordinate system, is the east component of the projection of the angular velocity of the earth coordinate system relative to the inertial coordinate system in the navigation coordinate system, is the north component of the projection of the angular velocity of the earth coordinate system relative to the inertial coordinate system in the navigation coordinate system, is the ground component of the projection of the specific force in the navigation coordinate system, is the east component of the projection of the specific force in the navigation coordinate system, is the north component of the projection of the specific force in the navigation coordinate system; in, is the transformation matrix from the carrier coordinate system to the navigation coordinate system, that is, the attitude matrix, c AB for The B-th component in the A-th row of the matrix has a value range of A (1, 2, 3) and a value range of B (1, 2, 3). in, It is the north component of the projection of the angular velocity of the navigation coordinate system relative to the inertial coordinate system in the navigation coordinate system.

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