CN113720354B - Recursive transmission alignment method based on FBG strain relief - Google Patents

Recursive transmission alignment method based on FBG strain relief Download PDF

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CN113720354B
CN113720354B CN202111062685.9A CN202111062685A CN113720354B CN 113720354 B CN113720354 B CN 113720354B CN 202111062685 A CN202111062685 A CN 202111062685A CN 113720354 B CN113720354 B CN 113720354B
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fbg strain
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CN113720354A (en
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陈熙源
朱敏
马振
方琳
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Southeast University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/16—Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge
    • G01B11/165—Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge by means of a grating deformed by the object
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

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Abstract

The invention discloses a recursive transmission alignment method based on FBG strain relief, which solves the problem that the flexible deformation of a wing is difficult to accurately model. Dividing the distributed transfer alignment method into three parts, wherein one part is for wing deformation measurement; secondly, aiming at the relationship among the child nodes; thirdly, the continuity of deformation of the wing. Compared with the existing distributed transfer alignment method, the method has the advantages that the FBG strain relief is used for carrying out three-dimensional deformation measurement to assist in establishing a main sub transfer alignment model, the motion parameter relation among sub nodes is analyzed, the sub nodes n (n > 1) carry out transfer alignment by using main node information, FBG strain relief measured deformation information and n-1 sub node information, and finally fitting and correcting are carried out on the position information of each sub node. The method solves the problem of the accuracy of the one-dimensional strain auxiliary inertial measurement of the existing FBG flexible wing, considers the motion relation among the sub-nodes of the wing and the deformation continuity of the wing, and finally improves the accuracy of distributed transmission alignment.

Description

Recursive transmission alignment method based on FBG strain relief
Technical Field
The invention belongs to the technical field of inertial navigation, relates to a process of calibrating a plurality of low-precision sub-inertial navigation systems by a high-precision main inertial navigation system, and particularly relates to a recursive transfer alignment method based on FBG (fiber bragg grating sensor) strain relief.
Background
The array load technology is gradually applied to an aviation ground observation system at the present stage, and serious errors are generated in load caused by maneuvering of an observation platform, so that a pose measurement system is required to provide high-precision motion information for the system.
The distributed pose measurement system comprises a high-precision main IMU in the engine room and a plurality of sub-IMUs fixedly connected to the task load, and the sub-IMUs are transmitted and aligned by utilizing the high-precision motion information of the main IMU, so that the high-precision motion information of each point is obtained. Before choosing the transfer alignment matching mode and designing the filtering algorithm, transfer alignment error modeling must be performed. Complex deflection of the wing can lead to inaccurate information transfer between main and sub nodes, so that transfer alignment research based on a wing deformation model is necessary.
Disclosure of Invention
In order to solve the problems, the invention discloses a recursive transmission alignment method based on FBG strain relief, which is characterized in that a main sub transmission alignment model based on an FBG strain relief wing deformation model is established, a motion relation among sub nodes is combined, the recursive transmission alignment method is established, and then sub node position information is corrected through wing deformation continuity and deflection information measured by the FBG strain relief. The design solves the problem of accuracy of one-dimensional strain auxiliary inertial measurement of the existing FBG flexible wing, considers the motion relationship among the wing sub-nodes and the deformation continuity of the wing, and finally improves the accuracy of distributed transmission alignment.
In order to achieve the above purpose, the technical scheme of the invention is as follows:
a recursive transmission alignment method based on FBG strain relief is characterized in that: the demonstration verification system comprises a wing distributed demonstration verification platform, a main IMU, a sub-IMU and FBG strain flowers, and comprises the following specific steps:
(1) Deducing a formula of measuring deflection angle and deflection of three-dimensional wing deformation by using FBG strain relief, and establishing a wing deflection model based on the FBG strain relief;
(2) Establishing a main sub-transmission alignment model of 'gesture + speed' by using the wing flexural deformation model based on the FBG strain flower in the step (1);
(3) Deducing the relation among the child nodes, and establishing a recursive-main multi-child transfer alignment method by combining the transfer alignment model deduced in the step (2), and obtaining the position and posture information of the child nodes through the transfer alignment method;
(4) Fitting and correcting the sub-node position information obtained in the step (3) by utilizing the continuity of wing deformation and the deflection curve measured by FBG strain flower.
Further, in the step (1), the flexural deformation of the FBG strain relief three-dimensional wing deformation is deducedAnd (3) an angle and deflection formula is adopted, and a wing deflection deformation model based on FBG strain relief is established. The high aspect ratio wing is regarded as an Euler-Bernoulli model, and the wavelength variation DeltaW is formed at any point x ', y ', z ' corresponding to the x axis, the y axis and the z axis on the wing F(x') 、△W F(y') 、△W F(z') Express time-varying deformation angle θ F The relation of gamma is as follows:
wherein P is c Is of photoelastic coefficient, W F(x') 、W F(y') 、W F(z') The center wavelength at points x ', y ', and z ', a is the thickness of the cantilever, and l is the length of the cantilever.
The deformation of the wing can cause the change of the angular velocity of the subnode and the change of the lever arm, the model is combined with the model to carry out the derivation of the wing flexural deformation model based on FBG strain flower, and in the real state, the subnode bends the angular velocity caused by deformationAnd angular velocity in ideal condition +.>Is not collinear and has a certain error angle +.>The specific expression is as follows:
where N is a coefficient matrix.
Combining the FBG strain relief expression, the error angle calculation model and the lever arm expression, the dynamic lever arm is expressed as:
wherein r is 0 The static lever arm is initially installed for the main node and the sub node, δr is a dynamic lever arm caused by dynamic deformation, R 0 Is a matrix.
Further, in the step (2), a 'posture + speed' transfer alignment model is established by combining the wing flexural deformation model based on FBG strain relief, and the error angle is obtainedAnd the dynamic lever arm δr is used as a state variable, the deflection deformation angle measured by FBG strain relief is used for correcting the attitude error amount measurement, and a filter model is established by adopting an attitude+speed matching method, and the method specifically comprises the following steps:
the state equation is:
wherein, A is a state transition matrix, B is a system noise distribution matrix, w is system noise, X is a state variable, expressed as:
wherein,for the misalignment angle of the sub inertial navigation platform, δv is the speed difference between the main node and the sub node, ε b Zero drift, delta for child node gyroscopes b Measuring zero drift, ρ for a child node accelerometer 0 An error angle is initially installed for the main node and the sub node;
the state transition matrix is:
wherein,for an antisymmetric matrix of the rotation of the navigation system relative to the inertial system,>for the transformation matrix between the ideal coordinate system of the subsystem and the navigation coordinate system, < >>
The measurement equation is:
Y＝HX+V
wherein,the method comprises the steps of attitude angle error and speed difference, wherein V is system noise, and H is a measurement matrix.
Further, in the step (3), a recursive-main multi-sub transfer alignment method is established by combining the relationship between the sub-nodes and the transfer alignment model derived in the step (2), which is specifically as follows:
the child node 1 performs measurement correction on the deformation angle measured by the FBG strain relief, and then performs transmission alignment to obtain more accurate attitude and position information, wherein a specific equation is shown in the following;
the closer to the tail of the wing, the more complex the deformation condition of the child node, the inaccurate the result obtained by the transmission alignment of the FBG strain gauge and the main IMU, and the patent proposes a recursive transmission alignment method for the problem, wherein the child node n (n > 1) uses the main node information, the deformation information measured by the FBG strain gauge and the information of the n-1 child node for transmission alignment, and the node 2 is taken as an example for explanation, and the specific process is as follows:
firstly, a deformation angle model between a sub-node 1 and a sub-node 2 is established, and the deformation angle model is formed according to two sub-nodesAngle of deformation between pointsWhich is indicated in terms of +.>The following description is given for the sake of example:
from the analysis, child node 1, x' 1 Angle of deformation theta F (x' 1 T) and node 2, x' 2 Angle of deformation theta F (x' 2 T) is represented by the following formula:
wherein L is wing half-broadening, and h (t) is wing endpoint deformation expression.
By deduction, it is known that:
second, the pose [ ψ ] of child node 1 is utilized s1 θ s1 γ s1 ]Correcting the posture [ ψ ] of the node 2 s2 θ s2 γ s2 ]Expressed as:
wherein A is s Representing the directional cosine matrix of the carrier coordinate system of child node 1 to its navigational coordinate system。A s ( ij) represents the value corresponding to the ith row and the jth column of the matrix.
The child node 2 establishes an attitude error amount measurement with the master node as follows:
Y a ＝[δψ δθ δγ] T ＝[ψ m -ψ s2 θ m -θ s2 γ m -γ s2 ] T
and finally, carrying out transfer alignment by using the transfer alignment model in the step (3), wherein the sub-node 2 obtains attitude measurement by using three parts of information of the main node, the sub-node 1 and the FBG strain flower, and carries out transfer alignment to obtain attitude and position information, and the transfer alignment process of the other sub-nodes is similar to that of the sub-node 2.
Further, in the step (4), the sub-node position information obtained in the step (3) is fitted and corrected by using the continuity of the wing deformation and the deflection curve measured by the FBG strain flower, and the specific process is as follows:
firstly, fitting the position information of each child node obtained after the transfer alignment in the step (3), and describing the latitude as an example: estimating the k moment through transfer alignment to obtain n discrete sub-node points l g The latitude at the point is denoted as d g Wherein g is the number of child nodes and is obtained by fitting a function f L (l; beta) to determine l g And d g The relation, beta is the parameter of the fitting function, and an objective function is established to enable f L (l; beta) dependent variable f (l g ) And d g The deviation is as small as possible, LM algorithm is selected for solving, and finally a fitting function of wing latitude information at k moment is obtained;
secondly, measuring a deflection curve in the direction according to FBG strain patterns, namely, restricting the fitted latitude function curve to obtain a latitude curve which is closer to the real situation, and carrying out re-correction on the latitude value of each subnode;
and similarly, fitting and correcting the child node positions obtained after transfer alignment based on the method to obtain more accurate position information.
The beneficial effects of the invention are as follows:
compared with the prior art, the method and the device have the advantages that the FBG strain flower is used for measuring the three-dimensional strain of the flexible wing, and the problem of accuracy of the one-dimensional strain auxiliary inertial measurement of the flexible wing measured by the existing FBG is solved. And secondly, deriving an error angle and a lever arm model caused by wing deformation based on the wing deformation angle measured by the FBG strain relief, and estimating and compensating as a state quantity of a filter to further improve the reliability of the transmission alignment model. Then, aiming at the problem that the deformation condition of the sub-node wing which is closer to the wing end of the wing is more complex in distributed transmission alignment, a method for transmitting and aligning by utilizing main node information, deformation information measured by FBG strain relief and motion information of the last sub-node is provided, and the problem that the motion information which is close to the wing end node is inaccurate is further solved. Finally, the accuracy of the subnode position information is improved by combining the wing continuity and the FBG strain relief to measure the deflection curve.
Drawings
FIG. 1 is a flow chart of a recursive transfer alignment based on FBG strain relief in accordance with the present invention;
FIG. 2 is an on-board distributed transfer alignment schematic;
fig. 3 is a schematic view of deformation angle between the child node 1 and the child node 2.
Detailed Description
The present invention is further illustrated in the following drawings and detailed description, which are to be understood as being merely illustrative of the invention and not limiting the scope of the invention.
As shown in fig. 1 and fig. 2, the recursive transmission alignment method based on the FBG strain relief provided by the embodiment of the invention uses the FBG strain relief to simulate the deflection deformation of the wing in the three-dimensional direction, and establishes an error angle and a lever arm model on the basis; using an error angle and a lever arm as state variables, using a deflection deformation angle measured by FBG strain flower for correcting the measurement of the attitude error amount, and establishing a main and sub transmission alignment model by adopting an attitude+speed matching method; deducing the motion information relation among the child nodes, and establishing a recursive one-main-multi-child transfer alignment method by combining the deduced main-child transfer alignment model, wherein the motion information of the child nodes is estimated by the method; and finally, correcting the position information of the sub-nodes by utilizing the continuity of the deformation of the wing and the deflection curve measured by the FBG strain flower. The detailed analysis is performed as follows:
step 1: and (3) deducing a formula of measuring the deflection angle and deflection of the three-dimensional wing deformation by the FBG strain relief, and establishing a wing deflection model based on the FBG strain relief.
Through analysis of the wing structure and aerodynamic characteristics, the main stress direction of the wing is along the span direction, and in order to more effectively study the deformation characteristics of the wing, the wing with the large aspect ratio is regarded as an Euler-Bernoulli model. Let us take any point x' on the x-axis as an example.
The beam tip deflection value and bending moment can be expressed as:
wherein, gamma is deflection value, F is load, EI is rigidity, l is cantilever length, M is bending moment.
The relationship between stress and bending moment can be expressed as:
wherein sigma is stress, W is bending-resistant section modulus, a is thickness of the cantilever beam, and I is moment of inertia.
Deflection can be expressed as:
wherein ε is the strain.
The strain can be expressed as:
wherein P is c Is of photoelastic coefficient, W F(x') DeltaW is the center wavelength at the x' point F(x') Is the amount of wavelength change at point x'.
According to the above formula, the wavelength variation DeltaW is calculated at any point x ', y ', z ' corresponding to the x axis, y axis and z axis on the wing F(x') 、△W F(y') 、△W F(z') Express time-varying deformation angle θ F The relation of gamma is as follows:
the deflection angle and deflection of the wing can be expressed by the formula, and the deflection of the wing can cause the change of the angular speed of the child node and the change of the lever arm, so that the new model derivation can be carried out by combining the model.
In a real state, angular velocity caused by bending deformation of the child nodeAnd angular velocity in ideal condition +.>Is not collinear and has a certain error angle +.>The true angular velocity of a child node should be expressed as:
take the y-axis as an example pairAnalysis and simplification were performed, expressed as:
wherein,respectively, the angular velocity at the x-axis and the z-axis of the ideal state of the child node, +.>The angular velocity at the x-axis and the z-axis of the true state of the child node is respectively.
Similarly, the x-axis and the z-axis can be obtainedTaylor expansion and simplification are carried out, and the specific expression is as follows:
where N is a coefficient matrix.
Combining the FBG strain relief expression, the error angle calculation model and the lever arm expression, the dynamic lever arm is expressed as:
wherein r is 0 Representing the initial installation of the main and sub systems of the static lever arm, δr representing the dynamic lever arm caused by dynamic deformation, R 0 Is a matrix.
Step 2: and (3) establishing a main sub-transmission alignment filter of 'gesture + speed' by using the wing flexural deformation model based on the FBG strain relief in the step (1). Angle of errorAnd the dynamic lever arm delta r is used as a state variable, and a system model is added during modeling; using the deflection deformation angle measured by the FBG strain gauge for correcting the posture error amount measurement; the method for establishing the filter model by adopting the gesture and speed matching method comprises the following steps:
the state equation is:
wherein, A is a state transition matrix, B is a system noise distribution matrix, w is system noise, X is a state variable, expressed as:
wherein,for the misalignment angle of the sub inertial navigation platform, δv is the speed difference between the main node and the sub node, ε b Zero drift, delta for child node gyroscopes b Measuring zero drift, ρ for a child node accelerometer 0 An error angle is initially installed for the master and slave nodes.
The state transition matrix is expressed as:
wherein,an antisymmetric matrix representing the rotation of the navigation system relative to the inertial system,>representing a transformation matrix between the ideal coordinate system of the subsystem and the navigation coordinate system, < >>
The measurement equation is:
Y＝HX+V
wherein,h is the measurement matrix, and V is the system noise.
The measurement is divided into two parts, wherein one part is to subtract the attitude angle output by the main system and the attitude angle output by the subsystem to obtain a three-axis attitude angle error, and the attitude angle error is taken as an observed quantity.
Y a ＝[δψ δθ δγ] T ＝[ψ m -ψ s θ m -θ s γ m -γ s ] T
Wherein [ psi ] m θ m γ m ] T Heading angle, pitch angle and roll angle at main IMU mounting point, [ psi ] s θ s γ s ] T Is the course angle, pitch angle and roll angle at the mounting point of the sub IMU.
Second, the speed V of the output of the main system min Velocity V calculated with subsystem sin And subtracting to obtain a triaxial speed error, wherein the speed difference is taken as an observed quantity.
Y v ＝V min -V sin
The measurement matrix can be obtained according to the matching mode and the motion relation between the main subsystem and the sub-system, and is expressed as follows:
wherein,
wherein B is m Represented is a directional cosine matrix of the carrier coordinate system of the master POS to its navigation coordinate system. B (B) m (ij) Representing the ith row of the matrixThe value corresponding to the j-th column.
Step 3: and (3) establishing a recursive-main multi-sub transfer alignment method by combining the motion information relation among the sub-nodes and the transfer alignment model deduced in the step (2).
In actual conditions, deformation conditions in the aircraft flight process are complex, the deformation conditions of the child node wings close to the root of the wings are relatively low in complexity, motion information obtained through transmission alignment by combining FBG strain patterns and a main IMU is accurate, and then the measurement correction of the child node 1 is as follows:
wherein,the deformation angle at sub-node 1 was measured for FBG strain relief.
The child node 1 uses the corrected attitude quantity to perform transfer alignment so as to obtain more accurate motion information.
The closer to the tail of the wing, the more complex the deformation condition of the child node is, the inaccurate the result is obtained by the transmission alignment of the FBG strain gauge and the main IMU, and the recursive transmission alignment method is provided for the problem. The sub node n (n > 1) calculates and corrects the motion information by using the motion information of the main node+the n-1 th sub node and the deformation information measured by the FBG strain flower. Taking node 2 as an example for illustration, the specific process is as follows:
first, a deformation angle model between the child node 1 and the child node 2 is established, as shown in fig. 3. According to the deformation angle between two sub-nodesWhich is indicated in terms of +.>The following description is given for the sake of example: :
from the analysis, child node 1, x' 1 Angle of deformation theta F (x' 1 T) and node 2, x' 2 Angle of deformation theta F (x' 2 T) is represented by the following formula:
wherein L is wing half-broadening, h (t) is wing endpoint deformation expression;
by deduction:
next, the posture of child node 1 is used as [ ψ ] s1 θ s1 γ s1 ]Correcting the posture [ ψ ] of the node 2 s2 θ s2 γ s2 ]Expressed as:
wherein A is s Represented is a directional cosine matrix of the carrier coordinate system of child node 1 to its navigation coordinate system. A is that s (ij) Representing a matrixCorresponding values of the ith row and the jth column.
The child node 2 establishes an attitude error amount measurement with the master node. The expression is as follows:
Y a ＝[δψ δθ δγ] T ＝[ψ m -ψ s2 θ m -θ s2 γ m -γ s2 ] T
finally, the transfer alignment model in the step (3) is used for carrying out transfer alignment.
The child node 2 uses three parts of information of the main node, the child node 1 and the FBG strain flower to obtain attitude measurement and transmits and aligns to obtain motion information. The transfer alignment process of the remaining child nodes is similar to child node 2.
Step 4: and (3) correcting the position information of the child node estimated in the step (3) by utilizing the continuity of the wing deformation and the deflection curve measured by the FBG strain flower.
The motion information of the sub-IMUs mounted on the wing at the same time may be considered to be interrelated. And fitting the position information of each child node after the alignment of the main and sub transfer. The latitude value in the position information at the time of each node k is described as an example. Longitude and altitude are similar to latitude.
Estimating the k moment through transfer alignment to obtain n discrete sub-node points l g The latitude at the point is denoted as d g Wherein g is the number of child nodes and is obtained by fitting a function f L (l; beta) to determine l g And d g Relation, beta is the parameter of the fitting function
The objective function is as follows:
the above makes f L (l; beta) dependent variable f (l g ) And d g The deviation is as small as possible, the fitting problem is converted into a nonlinear function optimization problem, the nonlinear function is approximately linearized, the parameter to be solved is solved through an iterative algorithm, and the optimal target is continuously approximated.
Solving an objective function minimum value, and selecting an LM algorithm, wherein the process is as follows:
f (l) performing first-order Taylor expansion:
F(l+△l)＝F(l)+F'(l)△l
solving for the appropriate Δl to give ||F (l) +Δl|| 2 The minimum is reached, i.e. the objective function is:
the derivative is calculated and is equal to 0 to calculate the extreme value:
2F(l) T J(l)+2J(l) T J(l)△l＝0
the linear equation set for Δl can be obtained and simplified by the above equation:
P△l＝-J(l) T F(l)
P＝J(l) T J(l)
to ensure that l is a locally optimal solution, P must be positive, so a new approach is used to construct an approximate P matrix on the basis of the above.
P＝J(l) T J(l)+μI
The damping coefficient mu corresponds to a weight, and the LM algorithm corresponds to a combination of Gaussian Newton's method and rapid descent method.
And obtaining the fitting function of the latitude information at the moment k of each node.
Secondly, deflection information in the direction is measured according to FBG strain patterns, and a formula is shown in the step (1). And constraining the fitted latitude function curve. And the latitude curve is closer to the actual condition, and the latitude value of each node is revised again.
And similarly, fitting and correcting the child node positions obtained after transfer alignment based on the method to obtain more accurate position information.

Claims (2)

1. A recursive transmission alignment method based on FBG strain relief is characterized in that: the demonstration verification system comprises a wing distributed demonstration verification platform, a main IMU, a sub-IMU and FBG strain flowers, and comprises the following specific steps:
(1) Deducing a formula of measuring deflection angle and deflection of three-dimensional wing deformation by using FBG strain relief, and establishing a wing deflection model based on the FBG strain relief;
the method comprises the following steps:
the high aspect ratio wing is regarded as an Euler-Bernoulli model, and the wavelength variation delta W is formed at any point x ', y ', z ' corresponding to the x axis, the y axis and the z axis on the wing F(x') 、ΔW F(y') 、ΔW F(z') Express time-varying deformation angle θ F The relation of gamma is as follows:
wherein P is c Is of photoelastic coefficient, W F(x') 、W F(y') 、W F(z') The center wavelength at points x ', y ', and z ' is respectively, a is the thickness of the cantilever beam, and l is the length of the cantilever beam;
the deformation of the wing can cause the change of the angular velocity of the subnode and the change of the lever arm, the model is combined with the model to carry out the derivation of the wing flexural deformation model based on FBG strain flower, and in the real state, the subnode bends the angular velocity caused by deformationAnd angular velocity in ideal condition +.>Is not collinear and has a certain error angle +.>The specific expression is as follows:
wherein N is a coefficient matrix;
combining the FBG strain relief expression, the error angle calculation model and the lever arm expression, the dynamic lever arm is expressed as:
wherein r is 0 The static lever arm is initially installed for the main node and the sub node, δr is a dynamic lever arm caused by dynamic deformation, R 0 Is a matrix;
(2) Establishing a main sub-transmission alignment model of 'gesture + speed' by using the wing flexural deformation model based on the FBG strain flower in the step (1);
the method comprises the following steps:
the state equation is:
wherein, A is a state transition matrix, B is a system noise distribution matrix, w is system noise, X is a state variable, expressed as:
wherein,for the misalignment angle of the sub inertial navigation platform, δv is the speed difference between the main node and the sub node, ε b Measuring zero drift, delta for a child node gyroscope b Measuring zero drift, ρ for a child node accelerometer 0 An error angle is initially installed for the main node and the sub node;
the state transition matrix is:
wherein,for an antisymmetric matrix of the rotation of the navigation system relative to the inertial system,>for the transformation matrix between the ideal coordinate system of the subsystem and the navigation coordinate system, < >>
The measurement equation is:
Y＝HX+V
wherein,comprising an attitude difference Y a Speed difference Y v V is system noise, H is measurement matrix;
(3) Deducing the relation among the child nodes, and establishing a recursive-main multi-child transfer alignment method by combining the transfer alignment model deduced in the step (2), and obtaining the position and posture information of the child nodes through the transfer alignment method;
the method comprises the following steps:
(31) The child node 1 performs measurement correction on the deformation angle measured by the FBG strain relief, and then performs transfer alignment to obtain more accurate attitude and position information;
(32) The sub-node n uses the main node information, the FBG strain relief measured deformation information and the n-1 sub-node information to conduct transfer alignment, wherein n is more than 1, and the node 2 is taken as an example for illustration, and the specific process is as follows:
first, according to the deformation angle between two sub-nodesEstablishing a deformation angle model between the child node 1 and the child node 2 in the x-axis direction +.>The following description is given for the sake of example:
from the analysis, child node 1, x' 1 Angle of deformation theta F (x' 1 T) and node 2, x' 2 Angle of deformation theta F (x' 2 T) is represented by the following formula:
wherein L is wing half-broadening, h (t) is wing endpoint deformation expression;
by deduction:
second, the pose [ ψ ] of child node 1 is utilized s1 θ s1 γ s1 ]Correcting the posture [ ψ ] of the node 2 s2 θ s2 γ s2 ]Expressed as:
wherein A is s Representing a directional cosine matrix from the carrier coordinate system of the child node 1 to its navigation coordinate system; a is that s (ij) Representing the corresponding values of the ith row and the jth column of the matrix;
the child node 2 establishes an attitude error amount measurement with the master node as follows:
Y a ＝[δψ δθ δγ] T ＝[ψ m -ψ s2 θ m -θ s2 γ m -γ s2 ] T
finally, using the transfer alignment model in the step (3) to perform transfer alignment, wherein the sub-node 2 uses three parts of information of the main node, the sub-node 1 and the FBG strain flower to obtain gesture measurement and transfer alignment to obtain gesture and position information, and the transfer alignment process of the other sub-nodes is equal to that of the sub-node 2;
(4) Fitting and correcting the sub-node position information obtained in the step (3) by utilizing the continuity of wing deformation and the deflection curve measured by FBG strain flower.
2. The recursive transfer alignment method based on the FBG strain relief according to claim 1, wherein in the step (4), the sub-node position information obtained in the step (3) is fitted and corrected by using the continuity of the wing deformation and the deflection curve measured by the FBG strain relief, and the specific process is as follows:
firstly, fitting the position information of each sub-node obtained after transfer alignment in the step (3), and describing the latitude value in the position information of each node k moment by taking the latitude value as an example, wherein the longitude and the altitude are the same as the latitude processing method; estimating the k moment through transfer alignment to obtain n discrete sub-node points l g The latitude at the point is denoted as d g Where g=1, 2, …, n by fitting a function f L (l; beta) to determine l g And d g The relation, beta is the parameter of the fitting function, and an objective function is established to enable f L (l; beta) dependent variable f (l g ) And d g The deviation is as small as possible, LM algorithm is selected for solving, and finally a fitting function of wing latitude information at k moment is obtained;
then, measuring a deflection curve in the direction according to FBG strain patterns, namely, restricting the fitted latitude function curve to obtain a latitude curve which is closer to the real situation, and carrying out re-correction on the latitude value of each subnode;
and similarly, fitting and correcting the child node positions obtained after transfer alignment based on the method to obtain more accurate position information.
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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108413887A (en) * 2018-02-22 2018-08-17 北京航空航天大学 Fiber grating assists wing deformation measurement method, device and the platform of distribution POS
CN109724626A (en) * 2019-03-08 2019-05-07 哈尔滨工程大学 A kind of model compensation method for polar region Transfer Alignment Dynamic flexural lever arm effect

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8019538B2 (en) * 2007-07-25 2011-09-13 Honeywell International Inc. System and method for high accuracy relative navigation

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108413887A (en) * 2018-02-22 2018-08-17 北京航空航天大学 Fiber grating assists wing deformation measurement method, device and the platform of distribution POS
CN109724626A (en) * 2019-03-08 2019-05-07 哈尔滨工程大学 A kind of model compensation method for polar region Transfer Alignment Dynamic flexural lever arm effect

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
Modal Estimation by FBG for Flexible Structures Attitude Control;HAO JIANG;IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS;第50卷(第4期);正文第2642-2650页 *
基于光纤光栅的分布式POS 柔性基线测量方法;顾宾;中国惯性技术学报;第27卷(第3期);正文第307-313页 *
基于最小二乘拟合法的分布式POS 全局估计方法;叶文;北京航空航天大学学报;第46卷(第5期);正文第862-868页 *

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