CN115267256B - Model observation calibration method of accelerometer assembly - Google Patents
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Abstract
The invention discloses a model observation calibration method of an accelerometer component, which comprises the following steps: s1, establishing an accelerometer component sensitive axis system and an accelerometer component calibration orthogonal coordinate system for constructing a calibration model, and constructing the calibration model of the accelerometer component; s2, installing an inertial navigation system provided with an accelerometer component on a three-axis table, controlling the accelerometer component to sequentially move to twenty-four positions, and collecting an actual output result of the accelerometer component with the same duration at each position as calibration data; s3, processing the calibration data of the step S2 by using a particle swarm algorithm to obtain the optimal calibration parameters of the accelerometer component; the method solves the problems that the traditional discrete calibration method is influenced by errors such as turntable precision, shock absorber deformation and the like on the calibration precision, and the dynamic precision of the inertial navigation system is poor due to the fact that the second-order nonlinear coefficient cannot be calibrated, and effectively improves the navigation precision of the inertial navigation system, and the accuracy and the practicability are good.
Description
Technical Field
The invention relates to the technical field of accelerometer component calibration of an inertial navigation system, in particular to a model observation calibration method of an accelerometer component.
Background
The inertial measurement device is a core component of an inertial navigation system and consists of a gyroscope assembly and an accelerometer assembly, wherein the accelerometer assembly consists of three accelerometers which are orthogonally installed. The high-precision accelerometer component calibration is an important technology for improving the measurement precision of an inertial measurement device and inhibiting the navigation error of an inertial navigation system. The traditional calibration method of the accelerometer component is discrete calibration based on multi-position static test, the calibration principle is that high-precision rotary tables or hexahedron and other calibration equipment are utilized to provide gesture references, gravity under different gestures is used as accurate specific force input, the pulse output of the accelerometer is compared, each calibration parameter of the accelerometer component is estimated, and the calibration parameters are divided into six-position static test, twelve-position static test and twenty-four-position static test according to the gesture number provided during test, and the twenty-four-position static test is most commonly used in engineering at present. However, the discrete calibration has the problems that the calibration precision is limited by the precision of a turntable, the precision cannot be accurately calibrated due to the deformation influence of a shock absorber of an inertial measurement device, and the like, and the application of the method in the calibration of a high-precision accelerometer component is limited.
The model observation calibration method of the accelerometer component is to calibrate each parameter in a calibration model by utilizing the principle that the model of the accelerometer component measured by specific force is equal to the local gravity acceleration under the static condition. Because the observed quantity is irrelevant to the attitude precision of the turntable output, the method avoids the influence of errors such as turntable precision, shock absorber deformation and the like on the calibration precision in principle.
In recent years, in order to solve the problem of discrete calibration in high-precision accelerometer component calibration, a model observation calibration method is widely applied to accelerometer component calibration, for example Zhang Gongliang and the like have published research on an error parameter estimation method of a land-based high-precision laser gyro strapdown inertial navigation system, wherein a model observation calibration method for calibrating a accelerometer component in the land-based high-precision laser gyro strapdown inertial navigation system is disclosed; dai Shaowu et al disclose a new method for calibrating MIMU based on model observation, which adopts the model observation method to calibrate accelerometer components in MIMU; dong Chunmei et al disclose a method for calibrating the mode observation of a laser gyro strapdown inertial navigation system, wherein a method for calibrating the mode observation of an accelerometer component in the laser gyro strapdown inertial navigation system is provided; constant waves and the like disclose comparative researches of two solving methods during triaxial accelerometer module observation calibration, and the solving methods in the accelerometer module observation calibration method are analyzed. However, these model observation calibration methods only consider the linear model error of the accelerometer component, and do not consider the second-order nonlinear coefficient of the accelerometer component. However, the second-order nonlinear coefficient error of the accelerometer component is the most important dynamic error source of the inertial navigation system except the linear model error, so that the model observation calibration method without considering the second-order nonlinear coefficient of the accelerometer component cannot guarantee the navigation precision of the inertial navigation system in a dynamic environment.
Disclosure of Invention
The invention aims to provide a model observation calibration method of an accelerometer component, which solves the problems that the prior model calibration method of the accelerometer component does not consider the second-order nonlinear coefficient of the accelerometer component and cannot ensure the navigation precision of an inertial navigation system in a dynamic environment.
For this purpose, the technical scheme of the invention is as follows:
a method for calibrating the mode observation of an accelerometer component comprises the following steps:
S1, establishing an accelerometer component sensitive axis system and an accelerometer component calibration orthogonal coordinate system for constructing a calibration model, and constructing the calibration model of the accelerometer component; wherein,
Establishing an accelerometer component sensitive axis system, namely an a system: the mass center of the accelerometer component is taken as an origin O, the sensitive axis of the X-direction accelerometer is taken as an X a axis, the sensitive axis of the Y-direction accelerometer is taken as a Y a axis, and the sensitive axis of the Z-direction accelerometer is taken as a Z a axis;
Establishing an accelerometer component calibration orthogonal coordinate system, namely an o-system: the mass center of the accelerometer component is taken as an origin O, the X o axis is consistent with the X a axis of the a-system, the Y o axis is in a plane formed by the X a axis and the Y a axis of the a-system, the small angle beta yz,Zo axis is different from the Y a axis, the Z a axis of the a-system rotates by a small angle beta zx around the X o axis, and then rotates by a small angle beta zy around the Y o axis;
Furthermore, the calibration model of the accelerometer assembly is constructed as follows:
in the method, in the process of the invention, For the acceleration component on the X o axis in the o-system after calibration of the accelerometer component,/>For the acceleration component on Y o axis in o-system after calibration of the accelerometer component,/>The acceleration component on the Z o axis in the o system after the calibration of the accelerometer component; n x is the actual output of the X-direction accelerometer, N y is the actual output of the Y-direction accelerometer, and N z is the actual output of the Z-direction accelerometer; /(I)Inverse of the scale factor of the X-direction accelerometer,/>Inverse of the scale factor of the Y-direction accelerometer,/>Reciprocal of the scale factor for the Z-direction accelerometer; k x2 is the second-order nonlinear coefficient of the X-direction accelerometer, K y2 is the second-order nonlinear coefficient of the Y-direction accelerometer, and K z2 is the second-order nonlinear coefficient of the Z-direction accelerometer; beta yz is the deflection angle of the Y-direction accelerometer sensitive axis Y a around the o-system Z o axis, beta zy is the deflection angle of the Z-direction accelerometer sensitive axis Z a around the o-system Y o axis, and beta zx is the deflection angle of the Z-direction accelerometer sensitive axis Z a around the o-system X o axis; /(I)Zero bias for X-direction accelerometer,/>Zero bias for Y-direction accelerometer,/>Zero offset for the Z-direction accelerometer;
based on the calibration model of the accelerometer assembly, Beta yz,βzy,βzx,Kx2,Ky2 and K z2 are twelve calibration parameters to be solved;
S2, installing an inertial navigation system provided with an accelerometer component on a three-axis table, controlling the accelerometer component to sequentially move to twenty-four positions, and collecting an actual output result of the accelerometer component with the same duration at each position as calibration data;
Wherein, twenty-four positions include: position No.1 is: the X axis points north, the Y axis points east, and the Z axis points ground; position No.2 is: the X axis points north, the Y axis is inclined to 45 degrees in the east direction, and the Z axis is inclined to 45 degrees in the west direction; position No.3 is: the X axis points north, the Y axis points ground and the Z axis points west; position No.4 is: the X axis points north, the Y axis is oriented to 45 degrees in the west direction, and the Z axis is oriented to 45 degrees in the west direction; position No.5 is: the X axis indicates north, the Y axis indicates west, and the Z axis indicates sky; position No.6 is: the X axis points north, the Y axis is oriented to 45 degrees in the west direction, and the Z axis is oriented to 45 degrees in the east direction; position No.7 is: the X axis indicates north, the Y axis indicates heaven, and the Z axis indicates east; position No.8 is: the X axis points north, the Y axis is oriented 45 degrees to the east, and the Z axis is oriented 45 degrees to the east; position No.9 is: the Y axis points north, the Z axis points east, and the X axis points ground; position No.10 is: the Y axis points north, the Z axis is inclined to 45 degrees in the east direction, and the X axis is inclined to 45 degrees in the west direction; position No.11 is: the Y axis points north, the Z axis points ground and the X axis points west; position No.12 is: the Y axis points north, the Z axis is oriented to 45 degrees in the west direction, and the X axis is oriented to 45 degrees in the west direction; position No.13 is: the Y axis indicates north, the Z axis indicates west, and the X axis indicates sky; position No.14 is: the Y axis points north, the Z axis is oriented to 45 degrees in the west direction and oriented to 45 degrees in the east direction in the X axis; position No.15 is: the Y axis indicates north, the Z axis indicates heaven, and the X axis indicates east; position No.16 is: the Y axis points north, the Z axis is oriented 45 degrees to the east, and the X axis is oriented 45 degrees to the east; position No.17 is: the Z axis points north, the X axis points east, and the Y axis points ground; position No.18 is: the Z axis points north, the X axis is inclined to 45 degrees in the east direction, and the Y axis is inclined to 45 degrees in the west direction; position No.19 is: the Z axis points north, the X axis points ground and the Y axis points west; position No.20 is: the Z axis points north, the X axis is oriented to 45 degrees in the west direction, and the Y axis is oriented to 45 degrees in the west direction; position No.21 is: the Z axis indicates north, the X axis indicates west, and the Y axis indicates sky; position No.22 is: the Z axis points north, the X axis is oriented to 45 degrees in the west direction and the Y axis is oriented to 45 degrees in the east direction; position No.23 is: the Z axis points north, the X axis points sky, and the Y axis points east; position No.24 is: the Z axis points north, the X axis is oriented 45 degrees to the east, and the Y axis is oriented 45 degrees to the east;
s3, processing the calibration data of the step S2 by using a particle swarm algorithm to obtain the optimal calibration parameters of the accelerometer component; the method comprises the following specific steps:
S301, constructing a particle group which is suitable for calibration parameters, and prescribing an updating rule of the particle group; the particle group consists of m particles, each particle is a twelve-dimensional vector, and twelve components of the twelve-dimensional vector are respectively in one-to-one correspondence with twelve calibration parameters;
S302, constructing an adaptive function And setting the range of e j;
s303, substituting the calibration data obtained in the step S2 and the calibration parameters obtained in the step S301 into an equation set of the accelerometer component calibration model, and solving to obtain the equation set Current value of (i.e./>)
S304, calculating the step S303Substituting the value into the adaptive function of S302, calculating the value of e j, judging whether the value of e j meets the criterion of stopping updating of the particle group, if so, stopping updating, and then obtaining twelve components of the particle as optimal calibration parameters; if not, updating the particle population according to the rule formulated in the step S301, and repeating the steps S303 and S304; the criterion for stopping updating of the particle population is the range of e j set in step S302.
Further, in step S2, after the inertial navigation system with the accelerometer assembly mounted thereon is mounted on the three-axis table, the test is performed after preheating for at least four hours at power-on.
Further, in step S2, the actual output of the accelerometer assembly is acquired for at least 5 minutes at each location.
Preferably, in step S3, m.gtoreq.200.
Preferably, in step S302, e j is set to have an absolute value of 0.00001 or less.
Compared with the prior art, the mode observation calibration method of the accelerometer component has the beneficial effects that:
(1) The method overcomes the influence of errors such as turntable precision, shock absorber deformation and the like on the calibration precision in the traditional discrete calibration method; meanwhile, the problem that the dynamic accuracy of an inertial navigation system is poor due to the fact that the existing mode observation calibration method without considering the second-order nonlinear coefficient cannot calibrate the second-order nonlinear coefficient is solved, and the method has good practical value;
(2) The dynamic position accuracy of the inertial navigation system obtained by the method for calibrating the accelerometer component by using the mode observation is 27.34% higher than that of the traditional discrete calibration method which does not consider the second-order nonlinear coefficient, 29.54% higher than that of the traditional discrete calibration method which does not consider the second-order nonlinear coefficient, 8.82% higher than that of the traditional mode observation calibration method which does not consider the second-order nonlinear coefficient, and the accuracy and the precision of the method for calibrating the accelerometer component by using the method are proved, so that the navigation accuracy of the inertial navigation system can be improved well, and the accuracy and the practicability are good.
Drawings
FIG. 1 is a flow chart of a method of modular observation calibration of an accelerometer assembly of the present invention;
FIG. 2 is a schematic diagram of the structure of an accelerometer assembly according to the present invention;
FIG. 3 is a schematic diagram of an accelerometer component sensitive axis system and an accelerometer component calibration orthogonal coordinate system constructed in step S101 of the method for calibrating a mode observation of an accelerometer component according to the present invention;
fig. 4 is a schematic diagram of a twenty-four position calibration test scenario provided in step S201 of the mode observation calibration method of the accelerometer assembly of the present invention.
Detailed Description
The invention will now be further described with reference to the accompanying drawings and specific examples, which are in no way limiting.
As shown in fig. 1, the specific implementation steps of the method for calibrating the mode observation of the accelerometer assembly are as follows:
S1, constructing a calibration model of an accelerometer component, and determining calibration parameters of the accelerometer component;
specifically, the implementation steps of step S1 are as follows:
S101, establishing an accelerometer component sensitive axis system and an accelerometer component calibration orthogonal coordinate system for constructing a calibration model, and determining a conversion relation among the coordinate systems; wherein,
(1) Establishing an accelerometer component sensitive axis system (hereinafter referred to as a system):
As shown in fig. 2, the accelerometer assembly is composed of an accelerometer assembly bracket 1 and three accelerometers, wherein the three accelerometers are respectively installed in a mode of being orthogonal to each other, and the three accelerometers are divided into an X-direction accelerometer 4, a Y-direction accelerometer 3 and a Z-direction accelerometer 2 based on different installation directions; therefore, based on the installation directions of the three accelerometers, a sensitive shaft system (a system) of the accelerometer component is established;
The physical meaning of the coordinate system is that three coordinate axes represent real acceleration sensitive axes of three accelerometers, and the physical meaning is specifically defined as: the origin O point of a coordinate system of the a system is the mass center of the accelerometer component, and three coordinate axes are an X-direction accelerometer sensitive axis X a, a Y-direction accelerometer sensitive axis Y a and a Z-direction accelerometer sensitive axis Z a respectively;
(2) As shown in fig. 3, an accelerometer component calibration orthogonal coordinate system (hereinafter, simply referred to as o-system) is established:
Because of the processing errors of the accelerometer component bracket and the installation errors of the three accelerometers, the sensitive axes of the three accelerometers installed in the accelerometer component are not ideal orthogonal, namely, a system is a non-orthogonal coordinate system, and the navigation solution of the inertial navigation system requires that the sensitive acceleration information of the three accelerometers be projected to the orthogonal coordinate system; thus, based thereon, an accelerometer component calibration orthogonal coordinate system (o-system) is established;
The physical meaning of the coordinate system is that a non-orthogonal a-system is converted into an orthogonal coordinate system for navigation solution through the coordinate system, which is specifically defined as: the origin O point of the O-system coordinate system and the origin O point of the a-system coordinate system are overlapped to be the same point, the X o axis of the O-system is consistent with the X a axis of the a-system, the Y o axis is in a plane formed by the X a axis and the Y a axis of the a-system, the Z a axis which is different from the Y a axis by a small angle beta yz,Zo is rotated by a small angle beta zx around the X o axis, and then rotated by a small angle beta zy around the Y o axis;
(3) Based on the definition of the coordinate system of the a system and the o system, the conversion matrix between the sensitive axis system of the accelerometer component and the calibration orthogonal coordinate system of the accelerometer component is obtained as follows:
in the method, in the process of the invention, For a conversion matrix from a system to o system, beta yz is the deflection angle of the Y-direction accelerometer sensitive axis Y a around the o system Z o axis, beta zy is the deflection angle of the Z-direction accelerometer sensitive axis Z a around the o system Y o axis, and beta zx is the deflection angle of the Z-direction accelerometer sensitive axis Z a around the o system X o axis;
s102, constructing an input/output model of a single accelerometer;
in order to restrain the dynamic error of the inertial navigation system, the second-order nonlinear coefficient of the accelerometer is considered, and an input-output model of single acceleration is constructed as follows:
Where f a is the true acceleration to which the individual accelerometer is sensitive in the direction of the sensitive axis, N is the actual output of the individual accelerometer, K 1 is the scale factor of the individual accelerometer, K 2 is the inverse of the scale factor of the single accelerometer, K 2 is the second order nonlinear coefficient of the scale factor of the single accelerometer, and b a is the offset of the single accelerometer;
S103, constructing a calibration model of the accelerometer component based on the accelerometer component sensitive axis system and the accelerometer component calibration orthogonal coordinate system established in the step S101 and the input/output model of the single accelerometer constructed in the step S102; in particular, the method comprises the steps of,
Because the accelerometer component is formed by orthogonal installation of three accelerometers, the input/output model of a single acceleration is expanded into a calibration model of the accelerometer component by taking a conversion matrix from a system to o system into consideration;
The matrix expression of the calibration model of the accelerometer component is as follows:
Wherein f o is the acceleration vector projected under the o-system after the calibration of the accelerometer component, and the expression is:
Wherein, For the acceleration component on the X o axis in the o-system after calibration of the accelerometer component,/>For the acceleration component on Y o axis in o-system after calibration of the accelerometer component,/>The acceleration component on the Z o axis in the o system after the calibration of the accelerometer component;
the expression of the transformation matrix from a system to o system is as follows:
Wherein, beta yz is the deflection angle of the Y-direction accelerometer sensitive axis Y a around the o-system Z o axis, beta zy is the deflection angle of the Z-direction accelerometer sensitive axis Z a around the o-system Y o axis, and beta zx is the deflection angle of the Z-direction accelerometer sensitive axis Z a around the o-system X o axis;
K 1 is a scale factor matrix of the accelerometer component, expressed as:
Wherein K x1 is the scale factor of the X-direction accelerometer, K y1 is the scale factor of the Y-direction accelerometer, and K z1 is the scale factor of the Z-direction accelerometer;
an inverse matrix of the scale factor for an accelerometer component, expressed as:
Wherein, Inverse of the scale factor of the X-direction accelerometer,/>Inverse of the scale factor of the Y-direction accelerometer,/>Reciprocal of the scale factor for the Z-direction accelerometer;
n is the actual output vector of the accelerometer component, expressed as:
N＝[Nx Ny Nz]T，
Wherein N x is the actual output of the X-direction accelerometer, N y is the actual output of the Y-direction accelerometer, and N z is the actual output of the Z-direction accelerometer;
K 2 is a second order nonlinear coefficient matrix of the accelerometer component, and its expression is:
wherein, K x2 is the second order nonlinear coefficient of the X-direction accelerometer, K y2 is the second order nonlinear coefficient of the Y-direction accelerometer, and K z2 is the second order nonlinear coefficient of the Z-direction accelerometer;
f a is the true sensitivity acceleration vector of the accelerometer component, and its expression is:
fa＝[fx fy fz]T，
Wherein f x is the real acceleration sensitive to the X-direction accelerometer, f y is the real acceleration sensitive to the Y-direction accelerometer, and f z is the real acceleration sensitive to the Z-direction accelerometer;
f a(2) is a vector of square values of true sensitive acceleration of the accelerometer component, expressed as:
Wherein, The square value of the true acceleration f x, which is sensitive to the X-direction accelerometer,/>Is the square value of the true acceleration f y sensitive to the Y-direction accelerometer,/>The square value of the real acceleration f z sensitive to the Z-direction accelerometer;
b a is the zero offset vector of the accelerometer component, and its expression is:
Wherein, Zero bias for X-direction accelerometer,/>Zero bias for Y-direction accelerometer,/>Zero offset for the Z-direction accelerometer;
Ignoring the measurement noise of the second and higher order micro-and accelerometer components, f o(2) is approximately equal to f a(2),bo is approximately equal to b a, and therefore, Can be further arranged into:
Where f o(2) is a vector of square values of the acceleration projected by the accelerometer component under the o-system after calibration, and the expression is:
b o is the projection vector of the zero offset of the accelerometer component under the o system after calibration, and the expression is:
Wherein, For zero bias component of accelerometer component on X o axis in o system after calibration,/>For zero bias component of accelerometer component on Y o axis in o system after calibration,/>Zero offset component of the accelerometer component on Z o axis in o system after calibration;
further, the matrix expression of the calibration model of the accelerometer assembly is transformed into a system of equations in scalar form, i.e. the calibration model of the accelerometer assembly:
S104, determining calibration parameters of the accelerometer component;
The calibration model of the accelerometer assembly obtained in step S103 is as follows: the input of the calibration model of the accelerometer component is the actual output N x of the X-direction accelerometer, the actual output N y of the Y-direction accelerometer and the actual output N z of the Z-direction accelerometer in the accelerometer component; the output of the accelerometer component calibration model is the acceleration component of sensitive acceleration on the X o axis in the o system after calibration Acceleration component/>, on Y o axis in o-system after calibrationAnd the acceleration component/>, after calibration, on the Z o axis in the o-system
Meanwhile, in order to obtain the acceleration component of the accelerometer component on the o-system based on the actual output result of the accelerometer component, the calibration parameters of twelve accelerometer components participating in calculation are also determined according to the calibration model of the accelerometer component, and the method specifically comprises the following steps: three zero bias parameters, i.e. zero bias of the X-direction accelerometerZero bias/>, of Y-direction accelerometerZero offset with Z-direction accelerometerInverse of the three scaling factors, i.e. inverse of the scaling factor of the X-direction accelerometer/>Inverse/>, of the scale factor of a Y-direction accelerometerAnd inverse/>, of the scale factor of the Z-direction accelerometerThree mounting error angles, namely a deflection angle beta yz of a Y-direction accelerometer sensitive axis Y a around an o-system Z o axis, a deflection angle beta zy of a Z-direction accelerometer sensitive axis Z a around an o-system Y o axis and a deflection angle beta zx of a Z-direction accelerometer sensitive axis Z a around an o-system X o axis; three second order nonlinear coefficients, namely the second order nonlinear coefficient K x2 of the X-direction accelerometer, the second order nonlinear coefficient K y2 of the Y-direction accelerometer and the second order nonlinear coefficient K z2 of the Z-direction accelerometer.
S2, designing twenty-four-position static tests to obtain calibration data through the tests;
specifically, the implementation steps of step S2 are as follows:
s201, designing a twenty-four-position test scheme;
Considering that the calibration of the second-order nonlinear model of the accelerometer usually adopts twenty-four-position static test as a calibration test scheme, in order to better identify the second-order nonlinear coefficient of the accelerometer, other positions except the space and the ground need to be introduced in the traditional twenty-four-position static test; based on this, the first and second light sources,
As shown in fig. 4, the twenty-fourth test protocol of the present application is:
Numbering twenty-four test positions as No. 1-No. 24 respectively, and dividing the twenty-four test positions into three groups, wherein positions No.1 to No.8 are a first group, positions No.9 to No.16 are a second group, and positions No.17 to No.24 are a third group; in particular, the method comprises the steps of,
In the first group, the X axis of the accelerometer component is fixed to point to north, and the other two axes (the Y axis and the Z axis) rotate 45 degrees around the north direction axis to serve as a position; based on this, the first and second light sources,
Position No.1 is: the X axis points north, the Y axis points east, and the Z axis points ground;
position No.2 is: the X axis points north, the Y axis is inclined to 45 degrees in the east direction, and the Z axis is inclined to 45 degrees in the west direction;
position No.3 is: the X axis points north, the Y axis points ground and the Z axis points west;
position No.4 is: the X axis points north, the Y axis is oriented to 45 degrees in the west direction, and the Z axis is oriented to 45 degrees in the west direction;
position No.5 is: the X axis indicates north, the Y axis indicates west, and the Z axis indicates sky;
position No.6 is: the X axis points north, the Y axis is oriented to 45 degrees in the west direction, and the Z axis is oriented to 45 degrees in the east direction;
position No.7 is: the X axis indicates north, the Y axis indicates heaven, and the Z axis indicates east;
Position No.8 is: the X axis points north, the Y axis is oriented 45 degrees to the east, and the Z axis is oriented 45 degrees to the east;
in the second group, the Y-axis of the accelerometer component is fixed to point north, and each of the other two axes (X-axis and Z-axis) rotates 45 degrees around the north-oriented axis to serve as a position; based on this, the first and second light sources,
Position No.9 is: the Y axis points north, the Z axis points east, and the X axis points ground;
position No.10 is: the Y axis points north, the Z axis is inclined to 45 degrees in the east direction, and the X axis is inclined to 45 degrees in the west direction;
Position No.11 is: the Y axis points north, the Z axis points ground and the X axis points west;
Position No.12 is: the Y axis points north, the Z axis is oriented to 45 degrees in the west direction, and the X axis is oriented to 45 degrees in the west direction;
position No.13 is: the Y axis indicates north, the Z axis indicates west, and the X axis indicates sky;
position No.14 is: the Y axis points north, the Z axis is oriented to 45 degrees in the west direction and oriented to 45 degrees in the east direction in the X axis;
position No.15 is: the Y axis indicates north, the Z axis indicates heaven, and the X axis indicates east;
Position No.16 is: the Y axis points north, the Z axis is oriented 45 degrees to the east, and the X axis is oriented 45 degrees to the east;
In the third group, the Z axis of the accelerometer component is fixed to point north, and each of the other two axes (X axis and Y axis) rotates 45 degrees around the north axis to serve as a position; based on this, the first and second light sources,
Position No.17 is: the Z axis points north, the X axis points east, and the Y axis points ground;
position No.18 is: the Z axis points north, the X axis is inclined to 45 degrees in the east direction, and the Y axis is inclined to 45 degrees in the west direction;
position No.19 is: the Z axis points north, the X axis points ground and the Y axis points west;
Position No.20 is: the Z axis points north, the X axis is oriented to 45 degrees in the west direction, and the Y axis is oriented to 45 degrees in the west direction;
Position No.21 is: the Z axis indicates north, the X axis indicates west, and the Y axis indicates sky;
position No.22 is: the Z axis points north, the X axis is oriented to 45 degrees in the west direction and the Y axis is oriented to 45 degrees in the east direction;
position No.23 is: the Z axis points north, the X axis points sky, and the Y axis points east;
position No.24 is: the Z axis points north, the X axis is oriented 45 degrees to the east, and the Y axis is oriented 45 degrees to the east;
s202, installing an inertial navigation system provided with an accelerometer component on a three-axis turntable, and starting up and preheating for 4 hours to eliminate the influence of temperature change on a calibration result;
And S203, after preheating, performing a calibration test according to the twenty-four-position test scheme designed in the step S201, wherein after the accelerometer component moves to each position, the actual output results of the accelerometer component with the same duration are collected, wherein the actual output results comprise an X-direction accelerometer actual output N x, a Y-direction accelerometer actual output N y and a Z-direction accelerometer actual output N z, and the actual output results are used as calibration data.
In this embodiment, the inertial navigation system consists of three laser gyroscopes with zero bias stability of 0.01 °/h and three accelerometers with zero bias stability of 10 μg; the turntable is a three-axis turntable with the attitude control precision of 5' (1 sigma); in step S203, the accelerometer assembly, when moving to each position, collects the actual output for a period of 5 minutes.
S3, processing the calibration data of the step S2 by using a particle swarm algorithm to obtain the optimal calibration parameters of the accelerometer component;
specifically, the implementation step of step S3 is as follows:
s301, constructing a particle group which is suitable for calibration parameters, and prescribing an updating rule of the particle group;
Based on twelve calibration parameters calculated by a calibration model of the accelerometer component, constructing a corresponding particle population, wherein the particle population is composed of m particles, each particle is a twelve-dimensional vector, twelve components of the twelve-dimensional vector are respectively in one-to-one correspondence with the twelve calibration parameters, and therefore, each particle is also a group of potential calibration results;
The particle update rules in the particle population are: updating the individual optimum, the global optimum and the speed and the position of each particle by using a particle swarm algorithm, and randomly initializing and updating twelve components of each particle in a corresponding setting range respectively;
In this embodiment, the particle population is constructed from 200 particles; each particle is a twelve-dimensional vector, and twelve calibration parameters corresponding to twelve components of the particle are randomly initialized in a corresponding setting range; specifically, the setting ranges of the twelve calibration parameters are respectively: -3000～3000μg；/>-3000～3000μg；/>-3000～3000μg；-800～800μm/s/pulse；/>-800～800μm/s/pulse；/>-800～800μm/s/pulse;βyz：-50～50″;βzy：-50～50″;βzx：-50～50″;Kx2：-300～300μg/g2;Ky2：-300～300μg/g2;Kz2：-300～300μg/g2;
the particle update rules in the particle population are: for m (m=200) particles constructed in the twelve-dimensional target search space, for the ith particle,
The ith particle is represented as a ten-dimensional vector, namely: x i＝{xi1,xi2,…,xi12, i=1, 2, …, m;
The speed of movement of the ith particle is also expressed as a ten-dimensional vector, namely: v i＝{vi1,vi2,…,vi12, i=1, 2, …, m;
the optimal position searched so far for by the ith particle is the individual extremum, namely: p best＝{pi1,pi2,…,pi12, i=1, 2, …, m;
The optimal position searched so far for by the whole particle swarm is a global extremum, namely: g best＝{pg1,pg2,…,pg12 };
when the two optimal values are found, the ith particle updates the position and the speed of the ith particle according to a speed updating formula and a position updating formula; wherein,
The speed update formula is as follows ：vidn＝ω*vid+c1r1(pid-xid)+c2r2(pgd-xid),
The location update formula is: the number x idn＝xid+vid of the total number of the components,
In the above two equations, v idn is the updated particle velocity component, and x idn is the updated particle position component; v id is the particle velocity component before update; x id is the particle position component before updating; p id is the individual extremum component of the optimal position before updating; p gd is the global extremum component of the optimal position before updating; c 1 and c 2 are learning factors empirically set to: c 1＝c2＝2;r1 and r 2 are uniform random numbers in the range of [0,1 ]; ω is inertial weight, empirically taken as ω=0.5;
S302, constructing an adaptive function The expression is as follows:
Wherein, the expression of e j is:
according to the principle of model observation calibration, the model of the acceleration of the accelerometer component under the o-system is equal to the gravitational acceleration, namely:
Wherein g is the local gravitational acceleration; in this embodiment, the local gravitational acceleration g=9.81 m/s 2;
Square the two sides of the above formula to obtain: thus, there is no error in the calibration parameters: however, since the components in each particle are subject to errors from the calibration parameters, therefore, Physical meaning of not equal to 0, e j is: the deviation of the acceleration measured by the accelerometer component after calibration and the local gravity acceleration is higher as the value of e j is smaller; therefore, in order to obtain a high-precision calibration result, the adaptive function/>The smaller the better;
Based on this, the value of the deviation e j of the acceleration measured by the calibrated accelerometer assembly from the local gravitational acceleration, i.e. Manually setting, and taking the result as a stopping criterion for updating the calibration parameters so as to obtain an optimal solution result for defining the adaptive function, wherein the optimal solution result corresponds to the set calibration precision;
s303, substituting the calibration data obtained in the step S2 and the calibration parameters obtained in the step S301 into an equation set of the accelerometer component calibration model:
In (3) calculating to obtain the corresponding particle
The calibration parameters are updated in real time, and the numerical value updated each time accords with the range defined by each calibration parameter in step S301, and the calibration parameters updated once are substituted into the equation set of the calibration model of the accelerometer assembly: In the method, the corresponding calibrated acceleration after each updated calibration parameter is obtained as/>, in the equation set Is respectively marked as: /(I)
S304, calculating the step S303Substituting the value into the adaptive function of S302, calculating the value of e j, judging whether the value of e j meets the criterion of stopping updating of the particle group, if so, stopping updating, and then obtaining twelve components of the particle as optimal calibration parameters; if not, updating the particle population according to the rule formulated in the step S301, and repeating the steps S303 and S304; the criterion for stopping updating of the particle population is the range of e j set in step S302.
In this embodiment, the criteria for stopping updating the particle population are: the absolute value of e j is less than or equal to 0.00001.
Through the step S3, the optimal calibration parameters of the accelerometer assembly are shown in the following table 1:
Table 1:
In order to verify the correctness and accuracy of the model observation calibration method of the accelerometer component, the inertial navigation system which is the same as the embodiment is adopted, and the calibration parameters are obtained by adopting other three methods. The method I is a traditional discrete calibration method which does not consider the second-order nonlinear coefficient, the method II is a traditional discrete calibration method which considers the second-order nonlinear coefficient, and the method III is a traditional mode observation calibration method which does not consider the second-order nonlinear coefficient. The calibration parameter results for the accelerometer assembly obtained using the four calibration parameter methods are shown in table 2 below.
Table 2:
further, in order to comprehensively and objectively evaluate the merits of the calibration parameters obtained by the various methods, the inertial navigation system is installed in a test vehicle to carry out a vehicle-mounted test.
The vehicle-mounted test comprises the following specific test steps: the inertial navigation system and the power supply battery are arranged on a trunk of the test car, and the GPS antenna is arranged on the roof of the test car. In the test, the test vehicle is static for 10 minutes after the system is electrified, so that the inertial navigation system is subjected to static initial alignment, then the test vehicle runs for 1 hour, and then pure inertial navigation calculation is performed by utilizing the data of the inertial navigation system; in the whole test process, the computer is used for synchronously collecting the original data of the inertial navigation system of the system and the GPS output position information. The original data are respectively compensated by four groups of calibration parameters and are resolved by the same inertial navigation program, and gyroscopes in the four groups of parameters adopt the same calibration parameters so as to avoid the influence of the gyroscopes on the verification result. And finally, comparing the position result obtained by compensating by adopting four groups of calibration parameters and resolving by utilizing the same inertial navigation program with the GPS output position to obtain the position precision obtained by the inertial navigation system under four methods. To avoid trial errors, a total of three trials were performed.
The inertial navigation system position error results under calibration parameters obtained using the four calibration methods are shown in table 3 below.
Table 3:
| test number | Method one | Method II | Method III | The application is that |
| First group of | 1.23n mile | 1.29n mile | 0.96n mile | 0.83n mile |
| Second group of | 1.27n mile | 1.32n mile | 1.07n mile | 1.02n mile |
| Third group of | 1.33n mile | 1.36n mile | 1.03n mile | 0.95n mile |
The three sets of test results in table 3 are averaged to obtain the average position error of the inertial navigation system as shown in table 4 below.
Table 4:
| Name of the name | Method one | Method II | Method III | The application is that |
| Average position error | 1.28n mile | 1.32n mile | 1.02n mile | 0.93n mile |
As can be seen from the results obtained by calculation in Table 4, when the inertial navigation system is subjected to navigation calculation by using different calibration parameters, the position accuracy obtained by the method provided by the invention is 27.34% higher than that obtained by the traditional discrete calibration method (namely the method I) which does not consider the second-order nonlinear coefficient, is 29.54% higher than that obtained by the traditional discrete calibration method (namely the method II) which does not consider the second-order nonlinear coefficient, is 8.82% higher than that obtained by the traditional module observation calibration method (namely the method III) which does not consider the second-order nonlinear coefficient, and the accuracy of the module observation calibration method of the accelerometer component provided by the invention are proved, so that the navigation accuracy of the inertial navigation system can be well improved, and the practicability is good.
The invention, in part, is not disclosed in detail and is well known in the art. While the foregoing describes illustrative embodiments of the present invention to facilitate an understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, but is to be construed as protected by all the inventions by the appended claims insofar as such variations are within the spirit and scope of the present invention as defined and defined by the appended claims.
Claims (5)
1. The method for calibrating the model observation of the accelerometer component is characterized by comprising the following steps:
S1, establishing an accelerometer component sensitive axis system and an accelerometer component calibration orthogonal coordinate system for constructing a calibration model, and constructing the calibration model of the accelerometer component; wherein,
Establishing an accelerometer component sensitive axis system, namely an a system: the mass center of the accelerometer component is taken as an origin O, the sensitive axis of the X-direction accelerometer is taken as an X a axis, the sensitive axis of the Y-direction accelerometer is taken as a Y a axis, and the sensitive axis of the Z-direction accelerometer is taken as a Z a axis;
Establishing an accelerometer component calibration orthogonal coordinate system, namely an o-system: the mass center of the accelerometer component is taken as an origin O, the X o axis is consistent with the X a axis of the a-system, the Y o axis is in a plane formed by the X a axis and the Y a axis of the a-system, the small angle beta yz,Zo axis is different from the Y a axis, the Z a axis of the a-system rotates by a small angle beta zx around the X o axis, and then rotates by a small angle beta zy around the Y o axis;
Furthermore, the calibration model of the accelerometer assembly is constructed as follows:
in the method, in the process of the invention, For the acceleration component on the X o axis in the o-system after calibration of the accelerometer component,/>For the acceleration component on Y o axis in o-system after calibration of the accelerometer component,/>The acceleration component on the Z o axis in the o system after the calibration of the accelerometer component; n x is the actual output of the X-direction accelerometer, N y is the actual output of the Y-direction accelerometer, and N z is the actual output of the Z-direction accelerometer; /(I)Inverse of the scale factor of the X-direction accelerometer,/>Inverse of the scale factor of the Y-direction accelerometer,/>Reciprocal of the scale factor for the Z-direction accelerometer; k x2 is the second-order nonlinear coefficient of the X-direction accelerometer, K y2 is the second-order nonlinear coefficient of the Y-direction accelerometer, and K z2 is the second-order nonlinear coefficient of the Z-direction accelerometer; beta yz is the deflection angle of the Y-direction accelerometer sensitive axis Y a around the o-system Z o axis, beta zy is the deflection angle of the Z-direction accelerometer sensitive axis Z a around the o-system Y o axis, and beta zx is the deflection angle of the Z-direction accelerometer sensitive axis Z a around the o-system X o axis; /(I)Zero bias for X-direction accelerometer,/>Zero bias for Y-direction accelerometer,/>Zero offset for the Z-direction accelerometer;
Based on the calibration model of the accelerometer assembly, Beta yz,βzy,βzx,Kx2,Ky2 and K z2 are twelve calibration parameters to be solved;
S2, installing an inertial navigation system provided with an accelerometer component on a three-axis table, controlling the accelerometer component to sequentially move to twenty-four positions, and collecting an actual output result of the accelerometer component with the same duration at each position as calibration data;
Wherein, twenty-four positions include: position No.1 is: the X axis points north, the Y axis points east, and the Z axis points ground; position No.2 is: the X axis points north, the Y axis is inclined to 45 degrees in the east direction, and the Z axis is inclined to 45 degrees in the west direction; position No.3 is: the X axis points north, the Y axis points ground and the Z axis points west; position No.4 is: the X axis points north, the Y axis is oriented to 45 degrees in the west direction, and the Z axis is oriented to 45 degrees in the west direction; position No.5 is: the X axis indicates north, the Y axis indicates west, and the Z axis indicates sky; position No.6 is: the X axis points north, the Y axis is oriented to 45 degrees in the west direction, and the Z axis is oriented to 45 degrees in the east direction; position No.7 is: the X axis indicates north, the Y axis indicates heaven, and the Z axis indicates east; position No.8 is: the X axis points north, the Y axis is oriented 45 degrees to the east, and the Z axis is oriented 45 degrees to the east; position No.9 is: the Y axis points north, the Z axis points east, and the X axis points ground; position No.10 is: the Y axis points north, the Z axis is inclined to 45 degrees in the east direction, and the X axis is inclined to 45 degrees in the west direction; position No.11 is: the Y axis points north, the Z axis points ground and the X axis points west; position No.12 is: the Y axis points north, the Z axis is oriented to 45 degrees in the west direction, and the X axis is oriented to 45 degrees in the west direction; position No.13 is: the Y axis indicates north, the Z axis indicates west, and the X axis indicates sky; position No.14 is: the Y axis points north, the Z axis is oriented to 45 degrees in the west direction and oriented to 45 degrees in the east direction in the X axis; position No.15 is: the Y axis indicates north, the Z axis indicates heaven, and the X axis indicates east; position No.16 is: the Y axis points north, the Z axis is oriented 45 degrees to the east, and the X axis is oriented 45 degrees to the east; position No.17 is: the Z axis points north, the X axis points east, and the Y axis points ground; position No.18 is: the Z axis points north, the X axis is inclined to 45 degrees in the east direction, and the Y axis is inclined to 45 degrees in the west direction; position No.19 is: the Z axis points north, the X axis points ground and the Y axis points west; position No.20 is: the Z axis points north, the X axis is oriented to 45 degrees in the west direction, and the Y axis is oriented to 45 degrees in the west direction; position No.21 is: the Z axis indicates north, the X axis indicates west, and the Y axis indicates sky; position No.22 is: the Z axis points north, the X axis is oriented to 45 degrees in the west direction and the Y axis is oriented to 45 degrees in the east direction; position No.23 is: the Z axis points north, the X axis points sky, and the Y axis points east; position No.24 is: the Z axis points north, the X axis is oriented 45 degrees to the east, and the Y axis is oriented 45 degrees to the east;
s3, processing the calibration data of the step S2 by using a particle swarm algorithm to obtain the optimal calibration parameters of the accelerometer component; the method comprises the following specific steps:
S301, constructing a particle group which is suitable for calibration parameters, and prescribing an updating rule of the particle group; the particle group consists of m particles, each particle is a twelve-dimensional vector, and twelve components of the twelve-dimensional vector are respectively in one-to-one correspondence with twelve calibration parameters;
S302, constructing an adaptive function And setting the range of e j;
s303, substituting the calibration data obtained in the step S2 and the calibration parameters obtained in the step S301 into an equation set of the accelerometer component calibration model, and solving to obtain the equation set Current value of (i.e./>)
S304, calculating the step S303Substituting the value into the adaptive function of S302, calculating the value of e j, judging whether the value of e j meets the criterion of stopping updating of the particle group, if so, stopping updating, and then obtaining twelve components of the particle as optimal calibration parameters; if not, updating the particle population according to the rule formulated in the step S301, and repeating the steps S303 and S304; the criterion for stopping updating of the particle population is the range of e j set in step S302.
2. The method according to claim 1, wherein in step S2, after the inertial navigation system with the accelerometer assembly mounted thereon is mounted on the three-axis table, the test is performed after preheating for at least four hours at power-on.
3. The method of calibrating a modular observation of an accelerometer assembly according to claim 1, wherein in step S2, the actual output of the accelerometer assembly is acquired at each location for at least 5 minutes.
4. The method of calibrating a mode observation of an accelerometer assembly according to claim 1, wherein m is equal to or greater than 200 in step S3.
5. The method of calibrating a modulo viewing of an accelerometer assembly according to claim 1, wherein in step S302, e j is set to an absolute value equal to or less than 0.00001.
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