A transfer alignment method based on FBG+second-order Markov

Abstract

The present invention is a transfer alignment method based on FBG+second-order Markov to solve the influence of wing flexible deformation on transfer alignment accuracy. The present invention divides the transfer alignment method into three parts: one is to model the wing flexural deformation, and select the measurement method of using FBG strain quadratic fitting along the direction of maximum deformation - the x direction of the carrier, and select the second-order Markov in the empirical modeling method for compensation along the direction of smaller deformation - the y and z directions of the carrier; the second is to process the change in angular velocity of the sub-node caused by the wing deformation, and decouple the motion of the carrier body from the dynamic deformation of the wing; the third is to process the change in the lever arm caused by the wing deformation, and establish a dynamic lever arm model. The present invention not only takes into account the various influences caused by the wing flexural deformation, but also improves the measurement accuracy of the deformation angle while reducing the filter dimension through the combined modeling of FBG and second-order Markov, and finally improves the accuracy and speed of transfer alignment.

Description

Technical Field

[0001] The invention belongs to the technical field of inertial navigation, and in particular is a transfer alignment method based on FBG+second-order Markov. Background Art

[0002] At present, the airborne earth observation system is an important means for military mapping and reconnaissance, land and resources monitoring, environmental degradation research, and solving problems such as frequent natural disasters. The accuracy and speed of transfer alignment directly affect the overall imaging accuracy of the airborne earth observation system, so how to achieve fast and accurate transfer alignment has very important theoretical research significance and engineering application value.

[0003] Since the carrier in the airborne distributed inertial measurement system has large and violent maneuverability, the dynamic lever effect and elastic deformation of the carrier in the transfer alignment will have a great impact, so the complex flexural deformation of the wing will lead to inaccurate information transmission between the master and sub-nodes. Therefore, the transfer alignment research based on the wing deformation model is very necessary. Summary of the invention

[0004] In order to solve the above technical problems, the present invention proposes a transfer alignment method based on FBG+second-order Markov, establishes a wing deformation model based on FBG+second-order Markov, and establishes a master-sub transfer alignment model by combining the matching method of "attitude+velocity+angular velocity". This design solves the accuracy problem of the existing FBG measurement of one-dimensional strain-assisted inertial measurement of flexible wings, and uses second-order Markov to compensate for the deformation angles with smaller deformation in the other two directions. The combined modeling of FBG and second-order Markov improves the measurement accuracy of the deformation angle while reducing the filter dimension, and finally improves the accuracy and speed of transfer alignment.

[0005] A transfer alignment method based on FBG+second-order Markov includes a demonstration and verification of a wing demonstration and verification platform, a main IMU, a sub-IMU, and a FBG. The specific steps are as follows:

[0006] (1) Use FBG and second-order Markov to model the wing deflection, derive the formula for measuring the wing deflection angle using FBG, derive the second-order Markov model of deflection, and establish a wing deformation model based on FBG + second-order Markov;

[0007] In the step (1), the formula for measuring the wing deflection angle by FBG and the second-order Markov model of deflection are derived, and a wing deformation model based on FBG+second-order Markov is established, which is as follows:

[0008] Considering the complex flight conditions and the need for temperature compensation and layout design of surface-mounted FBGs during actual flight, when operating FBGs to measure the wing deflection angle, the high aspect ratio wing is regarded as an Euler-Bernoulli model. The wavelength change ΔW at any point x′ in the x direction on the wing is F(x) The relationship between the deformation angle θ is as follows:

[0009]

[0010] Among them, P c is the photoelastic coefficient, W F(x) are the central wavelength at point x′, a is the thickness of the cantilever beam, and l is the length of the cantilever beam;

[0011] Considering the filtering order and filtering effect, the empirical modeling method uses the second-order Markov model to simulate the flexural deformation, which is specifically expressed as follows:

[0012]

[0013] in, θ, ω are deformation angle and angular velocity respectively, w is the excitation noise, τ is the correlation time, from which the deformation angle expression at any point y′, z′ on the wing in the y and z directions is obtained;

[0014] (2) The coupling angle model is derived using the wing deformation model based on FBG + second-order Markov in step (1); in step (2), the coupling angle model is derived in combination with the wing deformation model based on FBG + second-order Markov, as follows: In the geocentric inertial coordinate system, the angular velocity of the subnode is:

[0015]

[0016] in, Represents the direction cosine matrix from the master node to the child node in the ideal state, μ is the sum of the installation error angle and deformation angle between the master and child nodes, Represents the angular velocity of the master node in the master node coordinate system relative to the geocentric inertial coordinate system;

[0017] In actual flight conditions, wing deflection will also cause angular velocity ω θ , the angular velocity of the same child node in the ideal situation is in different directions, and there is a certain angle, so it is necessary to decouple the motion of the carrier body and the dynamic deformation of the wing, and the coupling angle The specific expressions are as follows:

[0018]

[0019] Among them, N coefficient matrix, is the first-order derivative of the deformation angle;

[0020] (3) establishing a dynamic lever arm model, combining the FBG-based wing deformation model of step (1) and the coupling angle model of step (2) for derivation;

[0021] (4) Combine the models established in the above three steps to establish the "posture + velocity + angular velocity" master-sub transfer alignment model.

[0022] As a further improvement of the present invention, in step (3), the wing deformation model based on FBG+second-order Markov in step (1) and the coupling angle model in step (2) are combined to derive and establish a dynamic lever arm model, specifically as follows: Assuming that the lever arm is a cantilever beam model, through the principle of trigonometric geometry and ignoring the quadratic minimum term, the lever arm length r is:

[0023]

[0024] Where r0 is the length of the initial arm of the master and child node system, and r0 = [x0 y0 z0] T ,θ x ,θ y ,θ z are the deformation angles in three directions,

[0025] Taking the coupling angle into account, the arm length is expressed as:

[0026]

[0027] The dynamic lever arms are:

[0028]

[0029] As a further improvement of the present invention, in step (4), the “posture+speed+angular velocity” master-sub transfer alignment model is established in combination with the models established in the above three steps. The specific process is as follows:

[0030] The deformation angle, coupling angle and dynamic lever arm in the y and z directions of the wing obtained by the second-order Markov model are expanded into state quantities for estimation and compensation, and the deformation angle in the x direction of the wing obtained by FBG quadratic fitting is used to compensate the two attitude measurements;

[0031] The state equation is:

[0032]

[0033] Among them, A is the state transfer matrix, B is the system noise distribution matrix, w is the system noise, and X is the state variable, which can be expressed as:

[0034]

[0035] in, is the misalignment angle of the sub-INS platform, δv is the speed difference between the main and sub-nodes, ε b is the zero drift of the child node gyroscope measurement, Δ b The zero drift of the sub-node accelerometer measurement, ρ0 is the initial installation error angle of the main and sub-nodes;

[0036] The state transfer matrix is:

[0037]

[0038] in, is the antisymmetric matrix of the rotation of the navigation system relative to the inertial system, is the transformation matrix between the subsystem ideal coordinate system and the navigation coordinate system, is the rotation angular velocity of the Earth-centered Earth-fixed coordinate system relative to the Earth-centered inertial coordinate system in the navigation coordinate system, is the rotation angular velocity of the navigation coordinate system relative to the Earth-centered Earth-fixed coordinate system in the navigation coordinate system, [A] 3×2 That is, the last two columns of matrix A, and the remaining parameters are expressed as:

[0039]

[0040] The measurement equation is:

[0041] Y=HX+V

[0042] Where V is the system noise, H is the measurement matrix, Including attitude difference Y a , speed difference Y v , angular velocity difference Y ω , the corrected attitude measurement Y a =[δψ δθ δγ] T It is expressed as:

[0043]

[0044]

[0045] Among them, B m (ij) The element of the i-th row and j-th column in the direction cosine matrix from the main system carrier coordinate system to the navigation coordinate system; the measurement matrix is ​​expressed as:

[0046]

[0047] in, is the symmetric form of the angular velocity of the main system relative to the geocentric inertial coordinate system, for The last two columns in the matrix are the y and z directions, and some parameter expressions are as follows:

[0048]

[0049] Beneficial effects:

[0050] Compared with the prior art, the present invention first uses a method combining FBG with a second-order Markov to compensate for the deformation angle, solving the accuracy problem of the existing FBG measurement of flexible wing one-dimensional strain-assisted inertial measurement and the problem that the order of the empirical modeling method is too high, resulting in a slow transfer alignment speed. Secondly, the coupling angle and lever arm model caused by wing deformation are derived based on the FBG+second-order Markov wing model, and are estimated and compensated as the state quantity of the filter, further improving the reliability of the transfer alignment model. Finally, the "attitude+velocity+angular velocity" matching method that can better estimate the installation error angle and flexural deformation is selected to derive the transfer alignment model. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 This is a flow chart of the transfer alignment method based on FBG+second-order Markov of the present invention;

[0052] Figure 2 Schematic diagram of the airborne transfer alignment experiment;

[0053] Figure 3 Schematic diagram of the angular velocity relationship between the main and sub nodes;

[0054] Figure 4 Schematic diagram of the dynamic lever arm changing along the y-axis. DETAILED DESCRIPTION

[0055] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments:

[0056] like Figure 1 and Figure 2 As shown, the present invention implements a FBG+second-order Markov transfer alignment method, uses a method combining FBG with second-order Markov to compensate for the deformation angle, and establishes a coupling angle and lever arm model on this basis; the deformation angle, coupling angle and dynamic lever arm of the wing in the y and z directions obtained by the second-order Markov model are used as state variables, and the flexural deformation angle measured by FBG is used to correct the measurement of attitude error. The master-sub transfer alignment model is established by using the "attitude+velocity+angular velocity" matching method, and a detailed analysis is given below:

[0057] Step 1: Use FBG and second-order Markov to model the wing deflection deformation, derive the formula for measuring the wing deflection deformation angle with FBG, derive the second-order Markov model of deflection deformation, and establish a wing deformation model based on FBG + second-order Markov.

[0058] First, the formula for measuring the wing deflection angle by FBG is derived. Through the analysis of the wing structure and aerodynamic characteristics, it can be concluded that the main force direction of the wing is along the wingspan direction. In order to more effectively study the wing deformation characteristics, the large aspect ratio wing is regarded as an Euler-Bernoulli model.

[0059] The deflection value and bending moment at the end of the beam can be expressed as:

[0060]

[0061] Among them, γ is the deflection value, F is the load, EI is the stiffness, b is the cantilever beam length, and M is the bending moment.

[0062] The relationship between stress and bending moment can be expressed as:

[0063]

[0064] Where W is stress, W is the bending section modulus, a is the thickness of the cantilever beam, and I is the moment of inertia.

[0065] The strain can be expressed as:

[0066]

[0067] Among them, P c is the photoelastic coefficient, W F(x) is the central wavelength at point x′, ΔW F(x) is the wavelength change at point x′.

[0068] According to the above formula, the wavelength change ΔW at any point x′ in the x direction on the wing is F(x) The relationship between the deformation angle θ is as follows:

[0069]

[0070] Among them, P c is the photoelastic coefficient, W F(x) are the central wavelength at point x′, a is the thickness of the cantilever beam, and l is the length of the cantilever beam;

[0071] Considering the filtering order and filtering effect, the empirical modeling method uses the second-order Markov model to simulate the flexural deformation, which is specifically expressed as follows:

[0072]

[0073] in, θ, ω are deformation angle and angular velocity respectively, w is the excitation noise, τ is the correlation time, from which the deformation angle expression at any point y′, z′ on the wing in the y and z directions is obtained;

[0074] Step 2: Use the wing deformation model based on FBG + second-order Markov in step (1) to derive the coupling angle model. In the geocentric inertial coordinate system, the angular velocity of the child node is:

[0075]

[0076] in, Represents the direction cosine matrix from the master node to the child node in the ideal state, μ is the sum of the installation error angle and deformation angle between the master and child nodes, Represents the angular velocity of the master node in the master node coordinate system relative to the geocentric inertial coordinate system.

[0077] like Figure 3 As shown in the actual flight environment, the wing bending deformation will also cause the angular velocity ω θ , the angular velocity of the same child node is in different directions under ideal conditions, and there is a certain angle between them, so it is necessary to decouple the motion of the carrier body and the dynamic deformation of the wing.

[0078] The actual angular velocity of the child node should be expressed as:

[0079]

[0080] Take the y-axis as an example After analysis and simplification, it can be expressed as:

[0081]

[0082] in, They are the angular velocities of the x-axis and z-axis of the child node in the ideal state, They are the angular velocities of the x-axis and z-axis of the child node in the actual state.

[0083] Similarly, we can get the x-axis and z-axis Taylor expansion and simplification are performed, and the specific expression is as follows:

[0084]

[0085] Among them, N coefficient matrix, is the first-order derivative of the deformation angle;

[0086] Step 3: Combine the FBG+second-order Markov-based wing deformation model in step (1) and the coupling angle model in step (2) to derive and establish a dynamic lever-arm model. The details are as follows:

[0087] Assuming the lever arm is a cantilever beam model, the dynamic lever arm changing along the y-axis direction is as follows: Figure 4 As can be seen from the figure

[0088]

[0089] Through θ x The change in the lever arm caused by θ y ,θ z Changing arm length. By using trigonometric principles and neglecting quadratic minimum terms, the arm length r is:

[0090]

[0091] Where r0 is the length of the initial arm of the master and child node system, and r0 = [x0 y0 z0] T ,θ x ,θ y ,θ z are the deformation angles in three directions,

[0092] Taking the coupling angle into account, the arm length is expressed as:

[0093]

[0094] The dynamic lever arms are:

[0095]

[0096] Step 4: Combine the models established in the above three steps to establish the "posture + velocity + angular velocity" master transfer alignment model. The specific process is as follows:

[0097] The deformation angle, coupling angle and dynamic lever arm in the y and z directions of the wing obtained by the second-order Markov model are expanded into state quantities for estimation and compensation. The deformation angle in the x direction of the wing obtained by FBG quadratic fitting is used to compensate the two attitude measurements.

[0098] The airborne distributed inertial measurement system has a complex working environment. The transfer alignment accuracy during wing maneuvers is affected by flexural deformation and dynamic lever arm. Among the different single matching methods, angular velocity matching and attitude matching can better estimate the installation error angle and flexural deformation. At the same time, due to the coupling relationship between the carrier flexural deformation and the carrier rigid body motion, after comprehensive analysis, the "attitude + velocity + angular velocity" matching method is selected.

[0099] The state equation is:

[0100]

[0101] Among them, A is the state transfer matrix, B is the system noise distribution matrix, w is the system noise, and X is the state variable, which can be expressed as:

[0102]

[0103] in, is the misalignment angle of the sub-INS platform, δv is the speed difference between the main and sub-nodes, ε b is the zero drift of the child node gyroscope measurement, Δ b is the zero drift of the sub-node accelerometer measurement, and ρ0 is the initial installation error angle of the main and sub-nodes.

[0104] The state transfer matrix is:

[0105]

[0106] in, is the antisymmetric matrix of the rotation of the navigation system relative to the inertial system, is the transformation matrix between the subsystem ideal coordinate system and the navigation coordinate system, is the rotation angular velocity of the Earth-centered Earth-fixed coordinate system relative to the Earth-centered inertial coordinate system in the navigation coordinate system, is the rotation angular velocity of the navigation coordinate system relative to the Earth-centered Earth-fixed coordinate system in the navigation coordinate system, [A] 3×2 That is, the last two columns of matrix A, and the remaining parameters can be expressed as:

[0107]

[0108]

[0109] The measurement equation is:

[0110] Y=HX+V

[0111] Where V is the system noise, H is the measurement matrix, Including attitude difference Y a , speed difference Y v , angular velocity difference Y ω , the corrected attitude measurement Y a =[δψ δθ δγ] T It is expressed as:

[0112]

[0113] Among them, B m (ij) The element in the i-th row and j-th column of the direction cosine matrix from the main system carrier coordinate system to the navigation coordinate system.

[0114] The measurement matrix is ​​expressed as:

[0115]

[0116] in, is the symmetric form of the angular velocity of the main system relative to the geocentric inertial coordinate system, for The last two columns in the matrix are the y and z directions, and the parameter expressions are as follows:

[0117]

[0118] The above description is only a preferred embodiment of the present invention and does not constitute any other form of limitation to the present invention. Any modification or equivalent change made based on the technical essence of the present invention still falls within the scope of protection required by the present invention.

Claims

1. A transfer alignment method based on FBG+second-order Markov, including a demonstration and verification of a wing demonstration and verification platform, a main IMU, a sub-IMU, and a FBG, characterized in that: The specific steps are as follows: (1) Modeling the wing deflection deformation by using FBG and second-order Markov, deriving the formula for measuring the wing deflection deformation angle by FBG, deriving the second-order Markov model of deflection deformation, and establishing the wing deformation model based on FBG+second-order Markov; In the step (1), the formula for measuring the wing deflection deformation angle by FBG and the second-order Markov model of deflection deformation are derived, and the wing deformation model based on FBG+second-order Markov is established, as follows: Considering the complex flight conditions and the need for temperature compensation and layout design of surface-mounted FBGs during actual flight, when operating FBGs to measure the wing deflection angle, the high aspect ratio wing is regarded as an Euler-Bernoulli model. The wavelength change ΔW at any point x′ in the x direction on the wing is F(x) The relationship between the deformation angle θ is as follows: Among them, P c is the photoelastic coefficient, W F(x) are the central wavelength at point x′, a is the thickness of the cantilever beam, and l is the length of the cantilever beam; Considering the filtering order and filtering effect, the empirical modeling method uses the second-order Markov model to simulate the flexural deformation, which is specifically expressed as follows: in, θ, ω are deformation angle and angular velocity respectively, w is the excitation noise, τ is the correlation time, from which the deformation angle expression at any point y′, z′ on the wing in the y and z directions is obtained; (2) Using the FBG+second-order Markov based wing deformation model in step (1), derive the coupling angle model; In step (2), the coupling angle model is derived by combining the wing deformation model based on FBG + second-order Markov, as follows: In the geocentric inertial coordinate system, the angular velocity of the subnode for: in, Represents the direction cosine matrix from the master node to the child node in the ideal state, μ is the sum of the installation error angle and deformation angle between the master and child nodes, Represents the angular velocity of the master node in the master node coordinate system relative to the geocentric inertial coordinate system; In actual flight conditions, wing deflection will also cause angular velocity ω θ , the angular velocity of the same child node in the ideal situation is in different directions, and there is a certain angle, so it is necessary to decouple the motion of the carrier body and the dynamic deformation of the wing, and the coupling angle The specific expressions are as follows: Among them, N coefficient matrix, is the first-order derivative of the deformation angle; (3) establishing a dynamic lever arm model, combining the FBG-based wing deformation model of step (1) and the coupling angle model of step (2) for derivation; In the step (3), the wing deformation model based on FBG+second-order Markov in step (1) and the coupling angle model in step (2) are combined to derive and establish a dynamic lever arm model, as follows: Assuming the arm is a cantilever beam model, through the principles of trigonometric geometry and ignoring the quadratic minimum term, the arm length r is: Where r0 is the length of the initial arm of the master and child node system, and r0 = [x0 y0 z0] T ,θ x ,θ y ,θ z are the deformation angles in three directions, Taking the coupling angle into account, the arm length is expressed as: The dynamic lever arm δr is: (4) In combination with the models established in the above three steps, a master-sub transfer alignment model of "posture + velocity + angular velocity" is established; In the step (4), in combination with the models established in the above three steps, a master-sub transfer alignment model of "posture + velocity + angular velocity" is established, and the specific process is as follows: The deformation angle, coupling angle and dynamic lever arm in the y and z directions of the wing obtained by the second-order Markov model are expanded into state quantities for estimation and compensation, and the deformation angle in the x direction of the wing obtained by FBG quadratic fitting is used to compensate the two attitude measurements; The state equation is: Among them, A is the state transfer matrix, B is the system noise distribution matrix, w is the system noise, and X is the state variable, which can be expressed as: in, is the misalignment angle of the sub-INS platform, δv is the speed difference between the main and sub-nodes, ε b is the zero drift of the child node gyroscope measurement, Δ b The zero drift of the sub-node accelerometer measurement, ρ0 is the initial installation error angle of the main and sub-nodes; The state transfer matrix is: in, is the antisymmetric matrix of the rotation of the navigation system relative to the inertial system, is the transformation matrix between the subsystem ideal coordinate system and the navigation coordinate system, is the rotation angular velocity of the Earth-centered Earth-fixed coordinate system relative to the Earth-centered inertial coordinate system in the navigation coordinate system, is the rotation angular velocity of the navigation coordinate system relative to the Earth-centered Earth-fixed coordinate system in the navigation coordinate system, That is, the last two columns of matrix A, and the remaining parameters are expressed as: The measurement equation is: Y=HX+V Where V is the system noise, H is the measurement matrix, is the measured value, including the attitude difference Y a , speed difference Y v , angular velocity difference Y ω , the corrected attitude measurement Y a =[δψ δθ δγ] T It is expressed as: Among them, B m (ij) The element of the i-th row and j-th column in the direction cosine matrix from the main system carrier coordinate system to the navigation coordinate system; The measurement matrix is ​​expressed as: in, is the symmetric form of the angular velocity of the main system relative to the geocentric inertial coordinate system, for The last two columns in the matrix are the y and z directions, and some parameter expressions are as follows:

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