CN110160554B - Single-axis rotation strapdown inertial navigation system calibration method based on optimization method - Google Patents
Single-axis rotation strapdown inertial navigation system calibration method based on optimization method Download PDFInfo
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- CN110160554B CN110160554B CN201910360691.9A CN201910360691A CN110160554B CN 110160554 B CN110160554 B CN 110160554B CN 201910360691 A CN201910360691 A CN 201910360691A CN 110160554 B CN110160554 B CN 110160554B
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Abstract
The invention discloses a single-axis rotation strapdown inertial navigation system calibration method based on an optimization method, which comprises the following steps of: firstly, a single-axis rotating strapdown inertial navigation system is installed on a double-axis rotary table by a tool, the system is powered on, a transposition mechanism is turned to zero and closed, after the temperature of the system is stable, the system is sequentially turned to 18 positions by the rotary table, then 9 sets of speed experiments are carried out by the double-axis rotary table by matching with the transposition mechanism, data are optimized and estimated by a nonlinear optimization method to obtain 18 error parameters, finally, the system is installed on a three-axis rotary table, 3 positions experiments and 3 sets of speed experiments are carried out, and an orthogonal coordinate system of an accelerometer and a gyroscope is calibrated to be under a coordinate system of the three-axis rotary table. The invention has the advantages of automatic calibration and independence on the precision of the rotary table, and can realize the calibration before the system leaves the factory and the long-time re-calibration after the system leaves the factory.
Description
Technical Field
The invention relates to the technical field of inertial navigation, in particular to a single-axis rotation strapdown inertial navigation system calibration method based on an optimization method.
Background
The rotation modulation technology utilizes the periodic rotation of the indexing mechanism to eliminate or reduce the navigation error caused by an inertial device so as to improve the precision of the inertial navigation system. Because the requirement on the precision of the inertial device is reduced to a certain extent, the advantage of meeting the navigation precision of the system can be widely applied to a high-precision inertial navigation system. Although the single-axis rotation modulation technology can eliminate or reduce navigation errors caused by x-axis and y-axis inertial devices through rotation modulation, the error of the z-axis inertial device cannot be eliminated through modulation. Therefore, inertial device errors remain a major factor affecting the navigation accuracy of the system.
Calibration, as a first step after assembly of the single axis rotational modulation system, is one of the most efficient ways to ensure the accuracy of the inertial device. The inertial navigation system calibration is divided into the following steps according to whether the inertial components are calibrated according to navigation errors: 1) A discrete calibration method, 2) a system level calibration method; the calibration method before and after the system leaves factory is divided into the following steps: 1) calibrating an element level before delivery, 2) calibrating a system before delivery, and 3) re-calibrating the system for a long time after delivery; the equipment adopted by calibration is divided into: 1) calibrating a three-axis turntable, 2) calibrating a high-precision hexahedron, and 3) calibrating a double-axis turntable. The calibration before the system leaves a factory generally adopts a discrete calibration method based on a high-precision three-axis turntable or a high-precision hexahedron, the method has high requirements on equipment precision, and the calibration precision completely depends on the precision of the turntable. Although the system-level calibration can ensure that the calibration precision does not depend on the precision of the turntable, the error of the inertial device is estimated by the navigation error through a navigation calculation process by adopting a least square method or a filtering algorithm, the algorithm is complicated, the method can only ensure that the inertial device is calibrated to the same orthogonal coordinate system, although the navigation result is not influenced, the alignment result has larger deviation with the true value because the orthogonal coordinate system calibrated by the inertial device is not the navigation coordinate system.
Based on the method, the calibration method of the high-precision single-axis rotation strapdown inertial navigation system is researched, the requirement on the precision of calibration equipment is low, automatic calibration can be realized, the algorithm is simple, and meanwhile, the calibration of an inertial device to a navigation coordinate system is guaranteed so as not to influence the alignment result, and the method becomes the direction of industry development.
Disclosure of Invention
The invention aims to solve the technical problem of providing a single-axis rotation strapdown inertial navigation system calibration method based on an optimization method, which can reduce the precision requirement on calibration equipment, realize automatic calibration, calibrate an inertial device to a navigation coordinate system and has a simple algorithm.
In order to solve the technical problem, the invention provides a single-axis rotation strapdown inertial navigation system calibration method based on an optimization method, which comprises the following steps:
(1) Installing the single-shaft rotating strapdown inertial navigation system on the double-shaft turntable by using the tool, powering on the system, resetting the indexing mechanism to zero and closing the indexing mechanism until the temperature of the system is stable;
(2) The system is sequentially rotated to 18 positions by using the rotary table, and each position acquires the output data of the accelerometer for 1 minute;
(3) Matching with a transposition mechanism in the single-shaft rotating strapdown inertial navigation system, performing 9 sets of forward and reverse rotation rate experiments by using a double-shaft turntable, and collecting gyroscope output whole-cycle data;
(4) Carrying out optimization estimation on the data in the step (2) and the step (3) by using a nonlinear optimization method to obtain error parameters of 18 inertial devices, carrying out off-line compensation, and calibrating the accelerometer and the gyroscope to an orthogonal coordinate system p system and an orthogonal coordinate system o system respectively from a sensitive coordinate system a system and a sensitive coordinate system g system respectively;
(5) Installing the system on a three-axis turntable, powering on the system, resetting the indexing mechanism to zero and closing the indexing mechanism until the temperature of the system is stable;
(6) Sequentially pointing three axes of an accelerometer to the sky, sequentially acquiring accelerometer output for 2 minutes at 3 positions, respectively performing 3 sets of positive and negative rotation rate experiments on a gyroscope around the three axes, acquiring the whole-cycle data output by the gyroscope, calibrating an orthogonal coordinate system p system and an orthogonal coordinate system o system of the accelerometer and the gyroscope calibrated in the step (3) to a three-axis turntable coordinate system r system, and converting a matrix into a three-axis turntable coordinate system r system
And with
And performing orthogonalization.
Preferably, in the step (3), the gyroscope calibration is realized by matching with a transposition mechanism in the single-shaft rotation strapdown inertial navigation system, the system is fixed at the position where the z-shaft points to the east through a tooling, and the system and the upward rotating shaft of the inner frame of the double-shaft turntable and the north rotating shaft of the outer frame jointly form a 3-degree-of-freedom mechanism, so that a 3-shaft gyroscope rate experiment can be carried out under the matching of the transposition mechanism, and the gyroscope is calibrated.
Preferably, in step (4), the data in step (2) and step (3) are optimized and estimated by a nonlinear optimization method, error parameters of 18 inertial devices are obtained and compensated off-line, and the accelerometer and the gyroscope are calibrated to an orthogonal coordinate system p system and an orthogonal coordinate system o system from a system a and a system g of respective sensitive coordinate systems:
respectively calibrating the accelerometer and the gyroscope to an orthogonal coordinate system p system and an orthogonal coordinate system o system by adopting a calibration method based on nonlinear optimization to obtain the corresponding zero offset of the triaxial accelerometer
Scale factor K for a triaxial accelerometer ax 、K ay 、K az Accelerometer mounting error E ayx 、E azx 、E azy Three-axis optical fiber gyro zero-bias epsilon x 、ε y 、ε z Scale factor K of triaxial fiber-optic gyroscope gx 、K gy 、K gz And mounting error of fiber optic gyroscope E gyx 、E gzx 、E gzy The method comprises 18 error parameters, and specifically comprises the following steps:
(41) Establishing an inertial device error model:
in order to ensure that the calibration precision does not depend on the precision of the double-shaft turntable, the output of the accelerometer and the output of the gyroscope are calibrated to an orthogonal coordinate system p system and an orthogonal coordinate system o system respectively from an a system and a g system without calibrating the inertial device to a coordinate system of the double-shaft turntable;
the accelerometer error model is established as follows:
wherein the content of the first and second substances,
for a projection of the triaxial accelerometer output in the accelerometer sensitive coordinate system a,
for a projection of the triaxial accelerometer output in an orthogonal coordinate system p,
for a three-axis accelerometer with zero offset, v a ＝[v ax v ay v az ] T Measuring error of a triaxial accelerometer, wherein M is an accelerometer scale factor and an installation error matrix, and the expression is
Wherein, K ai (i = x, y, z) is the i-axis accelerometer scale factor, E ayx 、E azx 、E azy Mounting errors for the accelerometer;
the gyro error model is established as follows:
wherein the content of the first and second substances,
for the projection of the output of the three-axis gyroscope in the gyroscope sensitive coordinate system g,
for the projection of the triaxial gyro output in the orthogonal coordinate system o, ε = [ ε = x ε y ε z ] T Zero-offset, v, for a three-axis gyroscope g ＝[v gx v gy v gz ] T The measurement error of the three-axis gyroscope is measured, N is a gyroscope scale factor and a mounting error matrix, and the expression is
Wherein, K gi (i = x, y, z) is the i-axis gyro scale factor, E gyx 、E gzx 、E gzy The installation error of the gyroscope;
(42) Establishing an IMU error parameter optimizing cost function:
the two norms projected under the orthogonal coordinate system p system according to the output of the triaxial accelerometer are theoretically equal to the two norms of the gravity acceleration, namely
||f p || 2 ＝||G n || 2 (5)
Wherein, the first and the second end of the pipe are connected with each other,
projection of the triaxial accelerometer output in p-system, G n ＝[0 0 -g] T Is the projection of the gravity acceleration vector under the navigation coordinate system n system, | ·| calculation 2 Is a two-norm symbol;
from the equations (1) and (5), an accelerometer error parameter optimization cost function is established as
Wherein the content of the first and second substances,
is the output of the accelerometer in the i-th position,
squared symbols of a two-norm;
because the earth rotation angular rate is small and cannot be directly used for calibrating the gyroscope, the gyro error parameter is calibrated by using the rotation angular rate of the rotary table in an auxiliary way, and the vector sum equal to the earth rotation angular rate and the rotation angular rate of the rotary table is output according to the gyro angular rate, namely
Wherein the content of the first and second substances,
for the projection of the gyro angular rate output in the o-system,
is the projection of the angular velocity of the earth rotation in the o system,
the projection of the rotation angular rate of the turntable in the o system is obtained;
substituting the formula (3) into the formula (1), integrating the time, rotating the turntable forward for a full circle,
wherein
The gyroscope angular rate output for the whole revolution of the turntable is projected in an o-system,
the angular rate of the gyroscope is output in g system projection, t for the positive rotation of the turntable 1 The time for rotating the turntable forward for a whole circle is taken;
the turntable is turned over for the whole circle, and the turntable can be obtained,
wherein
The gyro angular rate output is projected in the o-system for the entire revolution of the turntable,
projecting in g-system, t, for the whole-cycle gyro angular rate output of the turntable reversal 2 Time for the turntable to rotate in reverse for a full revolution;
equation (8) to equation (9), and the number of whole revolution of the turntable in the normal rotation and reverse rotation is made the same so that t = t 1 ＝t 2 And then, obtaining the composite material,
wherein theta is the rotating angle of the rotary table in positive and negative rotation for the whole circle;
the optimization cost function of the gyro scale factor and the installation error matrix N is established by the formula (10)
Wherein the content of the first and second substances,
for the gyro angular rate output in the j-th group of forward rotation rate experiments,
outputting the gyro angular rate in the j-th group of inversion rate experiments;
finally, according to the position experiment, a gyro zero-bias optimizing cost function is established as
Wherein the content of the first and second substances,
outputting the gyro angular rate in the ith group of position experiments;
(43) Optimizing and estimating by using a nonlinear optimization method:
using equations (6), (11) and (12) as objective functions to construct a nonlinear least square optimization problem and give initial values to the optimization problem
Wherein M is 0 For the accelerometer scale factors and initial values of the mounting error matrix,
for the initial zero-offset, N, of the accelerometer 0 Is the initial value of the gyro scale factor and the installation error matrix, epsilon 0 The initial value of zero offset of the gyroscope is;
and (3) substituting accelerometer and gyroscope data acquired by the position and rate experiments in the step (2) and the step (3) into the equations (6), (11) and (12), performing optimization iteration, estimating 18 error parameters, and calibrating the accelerometer and the gyroscope to a p system and an o system respectively.
Preferably, in the step (6), three axes of the accelerometer point to the sky in sequence, the accelerometer output is collected at 3 positions in sequence for 2 minutes, the gyroscope is subjected to 3 sets of positive and negative rotation rate experiments around the three axes respectively, the gyroscope output whole-cycle data is collected, the accelerometer and the gyroscope are calibrated to a three-axis turntable coordinate system r system through an orthogonal coordinate system p system and an orthogonal coordinate system o system calibrated in the step (3), and the transformation matrix is converted
And
the orthogonalization specifically comprises the following steps:
(61) Position and rate experimental data acquisition
Installing a strapdown inertial navigation system to a three-axis rotary table, finding zero by the rotary table, electrifying the system, after the system works stably, setting the rotary table to enable the three axes x, y and z of the system to point to the sky in sequence, outputting each acquisition accelerometer for 2 minutes, calculating an output average value of an adding table, setting the rotary table to enable the system to point to the sky around the three axes x, y and z and performing positive and negative rotation rate experiments at the speed of 10 degrees/s respectively, and outputting whole-cycle data by each acquisition gyro;
(62) Computing transformation matrices
According to the conversion relation of the accelerometer in a rotating table coordinate system r system and an orthogonal coordinate system p system:
wherein
Outputs projections for the accelerometer under the coordinate system r of the turntable,
for accelerometer inputThe projection in the p-system is obtained,
is a transformation matrix from p to r;
substituting (61) position experiment data into formula (13):
wherein g is the acceleration of gravity of the earth,
outputting an average value of 2-minute data for the j-axis pointing to the i-axis time, and calibrating the accelerometer to a three-axis turntable coordinate system r from the orthogonal coordinate system p calibrated in the step (3) by using a formula (14);
(63) Computing transformation matrices
According to the conversion relation of the gyroscope in a turntable coordinate system r system and an orthogonal coordinate system o system:
during forward rate experiments with the gyroscope x-axis pointing to the sky, the expansion (13):
wherein the content of the first and second substances,
is the projection of the i-axis gyro output in the o-system of the orthogonal system in the x-axis forward velocity experiment, C ij (i =1,2,3,j =1,2,3) is a conversion matrix
Row i and column j element of (2), omega r For the rotation angular rate, omega, of the rotary shaft of the turntable ie The rotation angle rate of the earth, L is the latitude of a calibration place, and phi (t) is the rotation angle of a rotating shaft of the rotary table;
summing the data for a complete revolution of the turret, equation (14)
Wherein A is the number of recorded data in the whole rotation circle of the turntable, the x-axis of the gyroscope points to the sky to perform a reverse rate experiment, and the sum of the data of the whole rotation circle of the turntable is as follows:
wherein, the first and the second end of the pipe are connected with each other,
for the projection of the i-axis gyro output in the o-system of the orthogonal system in the experiment of reverse rate around the x-axis, equations (15) - (16) are provided
Similarly, the gyroscope's y-axis and z-axis are pointing to the sky to perform positive and negative rate experiments, including
Wherein the content of the first and second substances,
the input of the i-axis gyroscope output in an orthogonal system o system in the y-axis positive direction, the y-axis negative direction, the z-axis positive direction and the z-axis negative direction rate experiments respectivelyShadow;
calculating a transformation matrix according to equations (17), (18) and (19)
Its transposed matrix
And (4) calibrating the gyroscope to a three-axis turntable coordinate system r from the orthogonal coordinate system o calibrated in the step (3).
The invention has the beneficial effects that: the automatic calibration before delivery can be quickly completed by using the double-shaft rotary table and the three-shaft rotary table, the calibration time is short, the algorithm is simple, the inertia device can be calibrated to the same orthogonal coordinate system firstly, and then calibrated to the rotary table coordinate system, and the alignment precision is improved; the invention can finish long-time recalibration after leaving factory only by using the double-shaft turntable, has low requirement on the precision of calibration equipment, can realize automatic calibration and improve the alignment and navigation precision.
Drawings
FIG. 1 is a schematic flow chart of the calibration method of the present invention.
FIG. 2 is a schematic diagram of a position experiment of the single-axis rotational strapdown inertial navigation system 18 according to the present invention.
FIG. 3 is a schematic diagram of a velocity experiment of the single-axis rotational strapdown inertial navigation system 9 according to the present invention.
FIG. 4 is a schematic diagram of the simulated acceleration meter cost function convergence according to the present invention.
FIG. 5 is a schematic diagram of the convergence of the gyro scale factor and the mounting error matrix cost function in the simulation of the present invention.
FIG. 6 is a schematic diagram of gyro zero-bias cost function convergence in simulation of the present invention.
Detailed Description
As shown in fig. 1, a calibration method of a single-axis rotation strapdown inertial navigation system based on an optimization method includes the following steps:
(1) Installing the single-shaft rotary strapdown inertial navigation system on the double-shaft rotary table by using a tool, powering on the system, resetting the indexing mechanism to zero and closing the indexing mechanism until the temperature of the system is stable;
(2) According to the position diagram shown in fig. 2, the system is sequentially rotated to 18 positions by using the turntable, and each position acquires the output data of the accelerometer for 1 minute;
(3) According to the schematic diagram of the rotation mode shown in fig. 3, a transposition mechanism in the single-shaft rotation strapdown inertial navigation system is matched, 9 sets of forward and reverse rotation rate experiments are performed by using a double-shaft turntable, and gyroscope output whole-cycle data is collected;
(4) Carrying out optimization estimation on the data in the step (2) and the step (3) by using a Ceres nonlinear optimization library to obtain error parameters of 18 inertial devices, carrying out off-line compensation, and respectively calibrating the accelerometer and the gyroscope to an orthogonal coordinate system p system and an orthogonal coordinate system o system from respective sensitive coordinate systems a system and g system;
(5) Installing the system on a three-axis turntable, powering on the system, resetting the indexing mechanism to zero and closing the indexing mechanism until the temperature of the system is stable;
(6) Sequentially pointing three axes of the accelerometer to the sky, sequentially collecting the output of the accelerometer at 3 positions for 2 minutes, respectively performing 3 sets of positive and negative rotation rate experiments on the gyroscope around the three axes, collecting the output whole-cycle data of the gyroscope, calibrating the accelerometer and the gyroscope to be under a coordinate system r of the three-axis turntable from an orthogonal coordinate system p system and an orthogonal coordinate system o system calibrated in the step (3), and converting the matrix
And
and carrying out orthogonalization.
Further, in the step (4), a calibration method based on Ceres nonlinear optimization is adopted, and the accelerometer and the gyroscope are respectively calibrated to an orthogonal coordinate system p system and an orthogonal coordinate system o system by using the position and rate experiments in the steps (2) and (3), so that the corresponding triaxial accelerometer zero-offset is obtained
Scale factor K for triaxial accelerometer ax 、K ay 、K az Accelerometer mounting error E ayx 、E azx 、E azy Three-axis optical fiber gyro zero bias epsilon x 、ε y 、ε z Triaxial fiber optic gyroscope scale factor K gx 、K gy 、K gz And mounting error of fiber optic gyroscope E gyx 、E gzx 、E gzy There are 18 error parameters.
In the step (6), through position and speed experiments, the conversion matrix is determined by using the conversion relation between the theoretical output of the inertial device on the three-axis turntable and the outputs of the accelerometer and the gyroscope in a p system and an o system respectively
And with
The specific steps of the step (4) are as follows:
(41) Establishing an inertial device error model:
in order to ensure that the calibration accuracy does not depend on the accuracy of the double-shaft turntable, the outputs of the accelerometer and the gyroscope are calibrated to an orthogonal coordinate system p system and an orthogonal coordinate system o system respectively from an a system and a g system without calibrating the inertial device to a double-shaft turntable coordinate system.
The accelerometer error model is established as follows:
wherein the content of the first and second substances,
for a projection of the triaxial accelerometer output in the accelerometer sensitive coordinate system a,
for a projection of the triaxial accelerometer output in an orthogonal coordinate system p,
for a three-axis accelerometer with zero offset, v a ＝[v ax v ay v az ] T Error is measured for a three-axis accelerometer. M is accelerometer scale factor and installation errorMatrix of the expression
Wherein, K ai (i = x, y, z) is the i-axis accelerometer scale factor, E ayx 、E azx 、E azy An accelerometer installation error.
The gyro error model is established as follows:
wherein the content of the first and second substances,
for the projection of the output of the three-axis gyroscope in the gyroscope sensitive coordinate system g,
for the projection of the triaxial gyro output in the orthogonal coordinate system o, ε = [ ε = x ε y ε z ] T Is a three-axis gyro zero-bias, v g ＝[v gx v gy v gz ] T The three-axis gyroscope measurement error is obtained. N is a gyro scale factor and an installation error matrix, and the expression is
Wherein, K gi (i = x, y, z) is the i-axis gyro scale factor, E gyx 、E gzx 、E gzy Is a gyro mounting error.
(42) Establishing an IMU error parameter optimizing cost function:
the two norms projected under the orthogonal coordinate system p system according to the output of the triaxial accelerometer are theoretically equal to the two norms of the gravity acceleration, namely
||f p || 2 ＝||G n || 2 (5)
Wherein the content of the first and second substances,
projection of the triaxial accelerometer output in p-system, G n ＝[0 0 -g] T Is the projection of the gravity acceleration vector under the navigation coordinate system n system, | ·| calculation 2 Are two norm symbols.
Establishing an accelerometer error parameter optimizing cost function according to the formula (1) and the formula (5)
Wherein the content of the first and second substances,
is the output of the accelerometer in the i-th position,
is the squared sign of the two norms.
Because the earth rotation angular rate is small and cannot be directly used for calibrating the gyroscope, the gyro error parameter is calibrated by using the rotation angular rate of the rotary table in an auxiliary way, and the vector sum equal to the earth rotation angular rate and the rotation angular rate of the rotary table is output according to the gyro angular rate, namely
Wherein the content of the first and second substances,
for the projection of the gyro angular rate output in the o-system,
is the projection of the angular velocity of the earth rotation in the o system,
for projection of angular rate of rotation of the turntable on the o system。
Substituting the formula (3) into the formula (1), integrating the time, rotating the turntable forward for a full circle,
wherein
The gyroscope angular rate output for the whole revolution of the turntable is projected in an o-system,
the angular rate of the gyroscope is output in g system projection, t, for the positive rotation of the turntable 1 The time for rotating the turntable in the whole circle is used.
The turntable is turned over for the whole circle, and the turntable can be obtained,
wherein
The gyro angular rate output for the entire revolution of the turntable is inverted and projected on the o-system,
projecting in g-system, t, for the whole-cycle gyro angular rate output of the turntable reversal 2 The time taken for the turret to reverse for a full revolution.
Equation (8) to equation (9), and the number of whole revolution of the turntable in the normal rotation and reverse rotation is made the same so that t = t 1 ＝t 2 And then, obtaining the composite material,
wherein theta is the rotating angle of the rotary table in positive and negative rotation for a whole circle.
The optimization cost function of the gyro scale factor and the installation error matrix N is established by the formula (10)
Wherein the content of the first and second substances,
for the gyro angular rate output in the j-th group of forward rotation rate experiments,
and outputting the gyro angular rate in the j-th group of inversion rate experiments.
Finally, according to the position experiment, a gyro zero-bias optimizing cost function is established as
Wherein the content of the first and second substances,
and outputting the gyro angular rate in the ith group of position experiments.
(43) Optimization estimation by using Ceres optimization library
Using equations (6), (11) and (12) as objective functions to construct a nonlinear least square optimization problem and give initial values to the optimization problem
Wherein M is 0 The initial values of the accelerometer scale factors and the installation error matrix,
for the accelerometer zero-offset initial value, N 0 Is the initial value of the gyro scale factor and the installation error matrix, epsilon 0 Is the initial value of zero bias of the gyroscope.
And (3) substituting accelerometer and gyroscope data acquired by the position and rate experiments in the step (2) and the step (3) into the equations (6), (11) and (12), performing optimization iteration, estimating 18 error parameters, and calibrating the accelerometer and the gyroscope to a p system and an o system respectively.
Step (6) of determining a conversion matrix by utilizing a position and speed experiment of a three-axis turntable
And
the method comprises the following specific steps:
(61) Position and rate experimental data acquisition
And (3) installing the strapdown inertial navigation system to a three-axis turntable, finding zero by the turntable, electrifying the system, setting the turntable to enable the x, y and z three axes of the system to sequentially point to the sky after the system works stably, outputting for 2 minutes by each acquisition accelerometer, and calculating an adding table output average value. And setting a turntable to enable the system to point to the sky around the three axes x, y and z, respectively carrying out forward and reverse rotation rate experiments at the rate of 10 DEG/s, and respectively acquiring gyroscope output whole-cycle data.
(62) Computing transformation matrices
According to the conversion relation of the accelerometer in a rotating table coordinate system r system and an orthogonal coordinate system p system:
wherein
Outputs projections for the accelerometer under the coordinate system r of the turntable,
for the projection of the accelerometer output in the p-system,
is a transformation matrix from p system to r system。
Substituting (61) position experimental data into formula (13):
wherein g is the acceleration of gravity of the earth,
the average of the 2 minute data is output for the j-axis pointing to the time of day i-axis accelerometer. And (5) calibrating the accelerometer from the orthogonal coordinate system p calibrated in the step (3) to the three-axis turntable coordinate system r by using the formula (14).
(63) Computing transformation matrices
According to the conversion relation of the gyroscope in a turntable coordinate system r system and an orthogonal coordinate system o system:
when the gyroscope x axis points to the sky and the forward velocity experiment is carried out, the expansion formula (13):
wherein, the first and the second end of the pipe are connected with each other,
for the projection of the i-axis gyro output in the orthogonal system o system in the x-axis forward velocity experiment, C ij (i =1,2,3,j =1,2,3) is a conversion matrix
Row i and column j element of (2), omega r For the rotation angular rate, omega, of the rotary shaft of the turntable ie The rotation angular rate of the earth, L is the latitude of the calibration place, and phi (t) is the rotation angle of the rotating shaft of the rotary table.
Summing the data for a complete revolution of the turret, equation (14)
Wherein A is the number of recorded data in the whole rotation circle of the turntable, the x-axis of the gyroscope points to the sky to perform a reverse rate experiment, and the sum of the data of the whole rotation circle of the turntable is as follows:
wherein the content of the first and second substances,
is the projection of the i-axis gyro output in the orthogonal system o system in the experiment of reverse velocity around the x axis. Formulae (15) to (16) have
Similarly, the gyroscope's y-axis and z-axis are pointing to the sky to perform positive and negative rate experiments, including
Wherein the content of the first and second substances,
the projections of the i-axis gyroscope output in an orthogonal system o system in the y-axis positive direction, the y-axis negative direction, the z-axis positive direction and the z-axis negative direction speed experiments are respectively.
Calculating a transformation matrix according to equations (17), (18) and (19)
Its transposed matrix
And (4) calibrating the gyroscope to a three-axis turntable coordinate system r from the orthogonal coordinate system o calibrated in the step (3).
The feasibility of the invention was verified by the following simulations:
(1) The system-level calibration simulation platform consists of an inertial device data generator and an optimization calibration scheme based on a Ceres optimization library;
(2) The longitude of the calibrated test site is 106.6906 degrees, the latitude is 26.5019 degrees, and the height is 1070.0m. In order to verify that the calibration method is not influenced by the precision of the rotary table, the attitude errors of the double-shaft rotary table are respectively set to be 2 degrees, 0.5 degree and 0.5 degree in the course direction, the pitch direction and the roll direction, the amplitude of the vibration angle is 2 degrees when the rotary table is controlled, and the vibration frequency is 10Hz. The random bias of the accelerometer is 0.1mg, and the random drift of the gyroscope is 0.01 degree/h.
(3) The simulation time of the biaxial turntable position experiment in the step (2) is 18min, 1min accelerometer data are collected at each position, the period is 5ms, the 1min data are averaged, optimization iteration is performed by taking the formula (6) as a cost function, 9 error parameters of the accelerometer are estimated, the convergence condition of the cost function of the accelerometer in the optimization process is shown in figure 4, and the final estimation result is shown in table 1.
(4) The simulation time of the dual-axis turntable speed experiment in the step (2) is 21.6min, each group of positive and negative rotation speed experiments set that the turntable acquires 72s of gyroscope data at a speed of 10 DEG/s, the period is 5ms, optimization iteration is carried out by taking a formula (11) as a cost function, 6 error parameters are estimated in total for a scale factor of the gyroscope and an installation error matrix N, meanwhile, optimization iteration is carried out by using the gyroscope data in the position experiment in the step (2) and taking a formula (12) as a cost function, 3 error parameters of the gyroscope zero offset are estimated, the cost function of the estimated gyroscope scale factor and the installation error matrix N and the convergence condition of the estimated gyroscope zero offset cost function are respectively shown in a graph 5 and a graph 6 in the optimization process, and the final estimation result is shown in a graph 2.
TABLE 1 accelerometer error parameter set value and calibration value table
TABLE 2 Gyro error parameter setting and calibration value table
(5) Respectively setting conversion relations between an orthogonal coordinate system p system and a rotary table coordinate system r system, and between an orthogonal coordinate system o system and the rotary table coordinate system r system, which are calibrated by the accelerometer and the gyroscope in the step (4) in the simulation by adopting Euler angles, respectively solving conversion matrix experiments according to the equations (14), (17), (18) and (19) by utilizing position and speed experiments in the inertial device data generator simulation step (6)
And
transformation matrix in simulation
Euler angle set value, calibration value and conversion matrix
The euler angle set value and the calibration value are shown in table 3 and table 4, respectively.
TABLE 3 transformation matrix
Euler angle set value and calibration value
TABLE 4 transformation matrix
Euler angle set value and calibration value
| Serial number | Euler angle | Set value | Calibration value | |
| 1 | Heading Ψ (') | 200 | 200.0002 | -0.0002 |
| 2 | Pitching eta (') | -50 | -50.0006 | 0.0006 |
| 3 | Sway gamma (') | 100 | 99.9995 | 0.0005 |
The ratio of error parameter values set in simulation to the calibrated error parameter values is shown in tables 1,2,3 and 4, wherein the maximum calibration error of the accelerometer zero offset is 0.015mg, the maximum calibration error of the scale factor error is 7.17ppm, and the maximum calibration error of the installation error is 0.26'; the maximum calibration error of the gyroscope zero offset is 1E-5 DEG/h, the maximum error of the scale factor error is 3E-4ppm, the maximum error of the installation error is 0E-4', and the maximum calibration error of the conversion matrix is 0.0006'. According to the simulation result, the method can accurately calibrate the accelerometer and the gyroscope to the p system and the o system respectively through 18 parameters, and then calibrate the inertial device to the r system of the turntable coordinate system simultaneously, so that the calibration process is simple, the calibration time is short, and the precision is high.
Claims (3)
1. A single-axis rotation strapdown inertial navigation system calibration method based on an optimization method is characterized by comprising the following steps:
(1) Installing the single-shaft rotary strapdown inertial navigation system on the double-shaft rotary table by using a tool, powering on the system, resetting the indexing mechanism to zero and closing the indexing mechanism until the temperature of the system is stable;
(2) The system is sequentially rotated to 18 positions by using a rotary table, and each position acquires the output data of the accelerometer for 1 minute;
(3) Matching with a transposition mechanism in the single-shaft rotating strapdown inertial navigation system, performing 9 sets of forward and reverse rotation rate experiments by using a double-shaft turntable, and collecting gyroscope output whole-cycle data;
(4) Carrying out optimization estimation on the data in the step (2) and the step (3) by using a nonlinear optimization method to obtain error parameters of 18 inertial devices, carrying out off-line compensation, and calibrating the accelerometer and the gyroscope to an orthogonal coordinate system p system and an orthogonal coordinate system o system respectively from respective sensitive coordinate systems a system and g system; the method specifically comprises the following steps:
calibrating the accelerometer and the gyroscope to an orthogonal coordinate system p system and an o system respectively by adopting a calibration method based on nonlinear optimization to obtain the zero bias v of the corresponding triaxial accelerometer x 、▽ y 、▽ z Scale factor K of triaxial accelerometer ax 、K ay 、K az And accelerated by the sameError of meter installation E ayx 、E azx 、E azy Three-axis optical fiber gyro zero-bias epsilon x 、ε y 、ε z Scale factor K of triaxial fiber-optic gyroscope gx 、K gy 、K gz And mounting error of fiber optic gyroscope E gyx 、E gzx 、E gzy The method comprises 18 error parameters, and specifically comprises the following steps:
(41) Establishing an inertial device error model:
in order to ensure that the calibration precision does not depend on the precision of the double-shaft turntable, the output of the accelerometer and the output of the gyroscope are calibrated to an orthogonal coordinate system p system and an orthogonal coordinate system o system respectively from an a system and a g system without calibrating the inertial device to a coordinate system of the double-shaft turntable;
the accelerometer error model is established as follows:
wherein the content of the first and second substances,
for the projection of the three-axis accelerometer output in the accelerometer sensitive coordinate system a,
for a projection of the triaxial accelerometer output in an orthogonal coordinate system p,
for a three-axis accelerometer with zero offset, v a ＝[v ax v ay v az ] T The measurement error of the triaxial accelerometer is measured, M is an accelerometer scale factor and an installation error matrix, and the expression is
Wherein, K ai (i = x, y, z) isScale factor of i-axis accelerometer, E ayx 、E azx 、E azy Mounting errors for the accelerometer;
the gyro error model is established as follows:
wherein the content of the first and second substances,
for the projection of the output of the three-axis gyroscope in the gyroscope sensitive coordinate system g,
for the projection of the triaxial gyro output in the orthogonal coordinate system o, ε = [ ε ] x ε y ε z ] T Is a three-axis gyro zero-bias, v g ＝[v gx v gy v gz ] T The measurement error of the three-axis gyroscope is shown, N is a gyroscope scale factor and an installation error matrix, and the expression is
Wherein, K gi (i = x, y, z) is the i-axis gyro scale factor, E gyx 、E gzx 、E gzy The gyro installation error is obtained;
(42) Establishing an IMU error parameter optimizing cost function:
the two norms projected under the orthogonal coordinate system p system according to the output of the triaxial accelerometer are theoretically equal to the two norms of the gravity acceleration, namely
||f p || 2 ＝||G n || 2 (5)
Wherein the content of the first and second substances,
projection of the triaxial accelerometer output in p-system, G n ＝[0 0 -g] T Is the projection of the gravity acceleration vector under the navigation coordinate system n system, | ·| calculation 2 Is a two-norm symbol;
establishing an accelerometer error parameter optimizing cost function according to the formula (1) and the formula (5)
Wherein the content of the first and second substances,
is the output of the accelerometer in the i-th position,
squared symbols of a two-norm;
because the earth rotation angular rate is small and cannot be directly used for calibrating the gyroscope, the gyro error parameter is calibrated by using the rotation angular rate of the rotary table in an auxiliary way, and the vector sum equal to the earth rotation angular rate and the rotation angular rate of the rotary table is output according to the gyro angular rate, namely
Wherein the content of the first and second substances,
for the projection of the gyro angular rate output in the o-system,
is the projection of the angular rate of rotation of the earth in the o system,
the projection of the rotation angular rate of the turntable in the o system is obtained;
substituting the formula (3) into the formula (1), integrating the time, and rotating the turntable for a full circle,
wherein
The gyroscope angular rate output for the whole revolution of the turntable is projected in an o-system,
the angular rate of the gyroscope is output in g system projection, t, for the positive rotation of the turntable 1 The time for rotating the turntable forward for a whole circle is taken;
the turntable is turned over for the whole circle, and the turntable can be obtained,
wherein
The gyro angular rate output is projected in the o-system for the entire revolution of the turntable,
projecting in g-system, t for the gyro angular rate output of the entire revolution of the turntable 2 The time taken for the turntable to rotate reversely for a whole circle;
equation (8) to equation (9), and the number of whole revolution of the turntable in the normal rotation and reverse rotation is made the same so that t = t 1 ＝t 2 And then, obtaining the composite material,
wherein theta is the rotating angle of the rotary table in positive and negative rotation for the whole circle;
the optimization cost function of the gyro scale factor and the installation error matrix N is established by the formula (10)
Wherein the content of the first and second substances,
for the gyro angular rate output in the j-th group of forward rotation rate experiments,
outputting the gyro angular rate in the j-th group of inversion rate experiments;
finally, according to the position experiment, a gyro zero-bias optimizing cost function is established as
Wherein the content of the first and second substances,
outputting the gyro angular rate in the ith group of position experiments;
(43) Optimizing and estimating by using a nonlinear optimization method:
using equations (6), (11) and (12) as objective functions to construct a nonlinear least square optimization problem and give initial values to the optimization problem
Wherein M is 0 Is the accelerometer scale factor and the initial value of the installation error matrix + 0 For the accelerometer zero-offset initial value, N 0 Is the initial value of the gyro scale factor and the installation error matrix, epsilon 0 The initial value of zero offset of the gyroscope is;
substituting accelerometer and gyroscope data acquired by the position and rate experiments in the step (2) and the step (3) into the equations (6), (11) and (12), performing optimization iteration, estimating 18 error parameters, and calibrating the accelerometer and the gyroscope to a p system and an o system respectively;
(5) Installing the system on a three-axis turntable, powering on the system, resetting the indexing mechanism to zero and closing the indexing mechanism until the temperature of the system is stable;
(6) Sequentially pointing three axes of an accelerometer to the sky, sequentially acquiring accelerometer output for 2 minutes at 3 positions, respectively performing 3 sets of positive and negative rotation rate experiments on a gyroscope around the three axes, acquiring the whole-cycle data output by the gyroscope, calibrating an orthogonal coordinate system p system and an orthogonal coordinate system o system of the accelerometer and the gyroscope calibrated in the step (4) to a three-axis turntable coordinate system r system, and converting a matrix into a three-axis turntable coordinate system r system
And
and carrying out orthogonalization.
2. The method for calibrating a single-axis rotational strapdown inertial navigation system based on an optimization method according to claim 1, wherein in the step (3), the gyroscope is calibrated by matching with an indexing mechanism inside the single-axis rotational strapdown inertial navigation system, the system is fixed at a position where a z-axis points east through a tool, and the system and a skyward rotating shaft of an inner frame of the double-axis turntable and a northward rotating shaft of an outer frame jointly form a 3-degree-of-freedom mechanism, so that a 3-axis gyroscope rate experiment can be performed under the matching of the indexing mechanism, and the gyroscope is calibrated.
3. The method for calibrating a single-axis rotation strapdown inertial navigation system based on an optimization method as claimed in claim 1, wherein in step (6), three axes of an accelerometer are sequentially pointed to the sky, outputs of the accelerometer are sequentially collected for 2 minutes at 3 positions, a gyroscope is respectively subjected to 3 sets of positive and negative rotation rate experiments around the three axes, data of the gyroscope output for the whole circle is collected, the accelerometer and the gyroscope are calibrated under a coordinate system p and a coordinate system o of a three-axis turntable by the orthogonal coordinate system p and the orthogonal coordinate system o calibrated in step (3), and a transformation matrix is converted into a coordinate system r of a three-axis turntable
And
the orthogonalization specifically comprises the following steps:
(61) Position and rate experimental data acquisition
Installing a strapdown inertial navigation system to a three-axis rotary table, finding zero by the rotary table, electrifying the system, after the system works stably, setting the rotary table to enable the three axes x, y and z of the system to point to the sky in sequence, outputting each acquisition accelerometer for 2 minutes, calculating an output average value of an adding table, setting the rotary table to enable the system to point to the sky around the three axes x, y and z and performing positive and negative rotation rate experiments at the speed of 10 degrees/s respectively, and outputting whole-cycle data by each acquisition gyro;
(62) Computing transformation matrices
According to the conversion relation of the accelerometer in a rotating table coordinate system r system and an orthogonal coordinate system p system:
wherein
Outputs projections for the accelerometer under the coordinate system r of the turntable,
for the projection of the accelerometer output in the p-system,
is a transformation matrix from p to r;
substituting (61) position experiment data into formula (13):
wherein g is the acceleration of gravity of the earth,
outputting an average value of 2-minute data for the j-axis pointing to the i-axis time, and calibrating the accelerometer to a three-axis turntable coordinate system r from the orthogonal coordinate system p calibrated in the step (3) by using a formula (14);
(63) Computing transformation matrices
According to the conversion relation of the gyroscope in a turntable coordinate system r system and an orthogonal coordinate system o system:
during forward rate experiments with the gyroscope x-axis pointing to the sky, the expansion (13):
wherein the content of the first and second substances,
for the projection of the i-axis gyro output in the orthogonal system o system in the x-axis forward velocity experiment, C ij (i =1,2,3,j =1,2,3) is a conversion matrix
I row and j column element of (c), ω r For the rotation angular rate, omega, of the rotary shaft of the turntable ie The rotation angle rate of the earth, L is the latitude of a calibration place, and phi (t) is the rotation angle of a rotating shaft of the rotary table;
summing the data for a complete revolution of the turret, equation (14)
Wherein A is the number of recorded data in the whole rotation circle of the turntable, the x-axis of the gyroscope points to the sky to perform a reverse rate experiment, and the sum of the data of the whole rotation circle of the turntable is as follows:
wherein, the first and the second end of the pipe are connected with each other,
for the projection of the i-axis gyro output in the o-system of the orthogonal system in the experiment of reverse rate around the x-axis, equations (15) - (16) are shown in
Similarly, the gyroscope's y-axis and z-axis are pointing to the sky to perform positive and negative rate experiments, including
Wherein the content of the first and second substances,
(i = x, y, z) are projections of i-axis gyroscope outputs in an orthogonal system o system in a positive speed experiment around a y-axis, a negative speed experiment around the y-axis, a positive speed experiment around the z-axis and a negative speed experiment around the z-axis respectively;
calculating a transformation matrix according to equations (17), (18) and (19)
Transposed matrix thereof
And (4) calibrating the gyroscope to a three-axis turntable coordinate system r from the orthogonal coordinate system o calibrated in the step (3).
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