CN113916219A - Inertial measurement system error separation method based on centrifuge excitation - Google Patents

Inertial measurement system error separation method based on centrifuge excitation Download PDF

Info

Publication number
CN113916219A
CN113916219A CN202110819229.8A CN202110819229A CN113916219A CN 113916219 A CN113916219 A CN 113916219A CN 202110819229 A CN202110819229 A CN 202110819229A CN 113916219 A CN113916219 A CN 113916219A
Authority
CN
China
Prior art keywords
measurement system
inertial measurement
error
centrifuge
coordinate system
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202110819229.8A
Other languages
Chinese (zh)
Other versions
CN113916219B (en
Inventor
魏宗康
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijign Institute of Aerospace Control Devices
Original Assignee
Beijign Institute of Aerospace Control Devices
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beijign Institute of Aerospace Control Devices filed Critical Beijign Institute of Aerospace Control Devices
Priority to CN202110819229.8A priority Critical patent/CN113916219B/en
Publication of CN113916219A publication Critical patent/CN113916219A/en
Application granted granted Critical
Publication of CN113916219B publication Critical patent/CN113916219B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/183—Compensation of inertial measurements, e.g. for temperature effects
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Automation & Control Theory (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Navigation (AREA)

Abstract

The invention discloses an inertial measurement system error separation method based on centrifugal machine large overload excitation, which utilizes the characteristic that the length of a lever arm of a centrifugal machine is not changed and combines a rotation angle in the rotation process of the lever arm of the centrifugal machine to obtain a motion track of an inertial measurement system arranged on the lever arm; in addition, a motion track with errors can be obtained by performing navigation calculation on the apparent acceleration of the inertial measurement system, wherein the errors are mainly caused by the measurement errors of a gyroscope and an accelerometer; by comparing the difference value of the two tracks, each error coefficient of the inertial measurement system can be processed by adopting a least square method, and the precision of inertial navigation is improved by error compensation.

Description

Inertial measurement system error separation method based on centrifuge excitation
Technical Field
The invention relates to an error separation method of an inertial measurement system based on centrifuge excitation, in particular to an error calibration and compensation method of a dynamic installation deviation matrix, which is mainly used in the fields of aviation and aerospace of high-precision inertial navigation.
Background
The inertial navigation is widely applied to the fields of missiles, airplanes, ships, weapons and the like, and mainly used for determining the position, the speed and the attitude information of a carrier relative to a navigation system in real time. In the process of realizing the navigation function, the precision of the inertial device (comprising a gyroscope and an accelerometer) directly determines the precision of the attitude, the position and the speed. In order to realize high-precision navigation, the precision of the accelerometer must be improved from hardware, but due to the basic subjects such as materials and processes, the precision of the inertial device is difficult to be improved greatly in a short period. And the use accuracy of the inertial device can be remarkably improved in a short time by adopting an error compensation method.
The precondition of error compensation is to calibrate the error coefficient. At present, based on a gravity field multi-position rolling test, only low-order error terms such as zero offset and scale factors can be separated, and confidence coefficients of the separated high-order error terms such as quadratic terms, odd quadratic terms, cross-coupling terms and the like are low. Therefore, the development of a high-order error term separation method based on the large overload excitation of the centrifugal machine is a key technology.
When the error coefficient of the inertia device is separated by using the centrifugal machine, the centrifugal machine with high precision is required. In the present disclosure, the acceleration of the centrifuge is used as the reference for error separation of the inertial device. The basic principle of a centrifuge is a single-shaft rate turntable, which generates centripetal acceleration during the rotation of a centrifuge arm. When a constant centripetal acceleration is required, the rotational speed of the centrifuge is required to be very smooth. For example, a gyro accelerometer is used as the measured object, and the linearity can reach 1 × 10-5This requires that the rotational speed of the centrifuge be more stable than 3X 10-6. In the practical application process, the rotational speed stability of the developed centrifugal machine can only reach 1 multiplied by 10-4The requirement of error separation of the inertial device cannot be met. Therefore, how to effectively separate the error of the high-precision inertia device on a centrifuge with relatively low precision is a key technology.
Therefore, an inertial measurement system error separation method based on the large overload excitation of the centrifuge needs to be researched to improve the use precision of an inertial device through error compensation, and further improve the precision of inertial navigation.
Disclosure of Invention
The technical problem of the invention is solved: the method overcomes the defects of the prior art, provides the error separation method of the inertial measurement system based on the excitation of the centrifugal machine, separates various error coefficients of the inertial measurement system, and improves the precision of inertial navigation through error compensation.
The technical scheme of the invention is as follows: an inertial measurement system error separation method based on centrifuge excitation comprises the following steps:
s1, establishing an inertial measurement system error separation test system: one end of one side of a lever arm of the centrifuge is provided with a reverse platform, an inertia measurement system is arranged on the reverse platform, and the other end is provided with a reverse platformThe side-mounted counterweight is used for balancing the mass of the reverse rotation platform and the inertia measurement system, and the rotating speed of the reverse rotation platform relative to the arm of the centrifugal machine lever when rotating
Figure BDA0003171409130000021
With rotational speed of the arms of the centrifuge relative to the ground
Figure BDA0003171409130000022
Are opposite numbers, i.e.
Figure BDA0003171409130000023
Figure BDA0003171409130000024
Wherein, omega is the rotating speed of the base of the centrifuge;
s2, performing an inertial measurement system error separation test: driving a centrifugal machine lever arm to rotate at a high speed around a base to form centripetal acceleration, wherein the centripetal acceleration is the excitation of an inertial measurement system arranged on the centrifugal machine lever arm, and the movement track of the inertial measurement system arranged on the centrifugal machine lever arm is obtained by utilizing the characteristic that the length of the centrifugal machine lever arm is not changed and combining the rotation angle of the centrifugal machine lever arm in the rotation process and is recorded as a reference movement track; performing navigation calculation on the apparent acceleration of the inertial measurement system to obtain a motion track with an error, and recording the motion track as a measured motion track; comparing the difference value of the measured motion track and the reference motion track to obtain a position error sequence value of the inertial measurement system;
s3, substituting the position error sequence value of the inertial measurement system into the inertial navigation position error model, and separating each error coefficient of the inertial measurement system by adopting a least square method;
and S4, correcting the errors of the inertial measurement system participating in navigation calculation by using the determined error coefficient of the inertial measurement system, and further realizing the compensation of the navigation calculation of the inertial measurement system.
Centrifuge base coordinate system and northeast geographic coordinate system (Ox)eyeze) Coincide with, wherein, OxeEast of finger and OyeNorth arrow OzeFinger Tian, IIISatisfying the right-hand coordinate system;
coordinate system of arm of centrifugal machinepypzpWherein, OxpCoincident with the lever arm and pointing outwards, OypIn a horizontal plane perpendicular to the lever arm, OzpPointing to the sky, wherein the three meet the right-hand coordinate system;
inverse platform coordinate system QxqyqzqWherein, OxqAnd OyqIn the horizontal plane, OzqPointing to the sky, wherein the three meet the right-hand coordinate system;
coordinate system of inertial measurement system QxbybzbThe coordinate system and the inverse platform coordinate system QxqyqzqThe coordinate axes are in the same direction.
The step S2 is specifically implemented as follows:
s2.1, at initial t0At the moment, the initial alignment of the inertial measurement system is completed, so that the inertial navigation coordinate system and the northeast world coordinate system OxeyezePhysical coincidence;
s2.2, obtaining initial t according to measurement0The rotation angle phi of the arm of the centrifugal machine relative to the base at any moment0Calculating initial t in the reference motion trajectory0Time inertial measurement system relative northeast world coordinate system OxeyezeInitial value of (x) of positionew,0,yew,0,yew,0) And setting an initial t in the reference motion track0Relative northeast world coordinate system Ox of time inertia measurement systemeyezeThe initial value of the speed is 0, when the next calculation period comes, k is initialized to 1, and then the step S3.2 to the step S3.5 are sequentially executed;
s3.2, according to the measured angle value phi of the arm of the centrifuge in rotation relative to the basekCalculating the current tkTime inertia measurement system relative to the northeast world coordinate system (Ox)eyeze) The position of (a);
s3.3, obtaining the angular velocity according to the measurement of a gyroscope in the inertial measurement system
Figure BDA0003171409130000031
Obtaining apparent acceleration by combined measurement of accelerometers
Figure BDA0003171409130000032
Navigation resolving is carried out to obtain the current tkPosition of time of day
Figure BDA0003171409130000033
S3.4, calculating the position errors of corresponding track points in the reference motion track and the measurement motion track:
Figure BDA0003171409130000041
s3.5, when the next calculation cycle comes, the process returns to step S3.2 to re-execute step S3.2 to step 3.5 until the end time t is reachedNStep S3.6 is entered;
s3.6, summarizing corresponding track point position errors in the reference motion track and the measured motion track to obtain a position error sequence value Y:
Figure BDA0003171409130000042
in the step (3.1) and the step (3.2):
initial t in reference motion trajectorykInitial position value (x) of time inertial measurement system relative to northeast world coordinate systemew,k,yew,k,yew,k) The calculation formula of (2) is as follows:
Figure BDA0003171409130000043
wherein R is half of the length of the centrifuge lever arm (2).
The navigation resolving formula in S4.3 is as follows:
Figure BDA0003171409130000044
in the formula,
Figure BDA0003171409130000045
is composed of
Figure BDA0003171409130000046
The anti-symmetric matrix of (a) is,
Figure BDA0003171409130000047
as the rotational speed of the earth
Figure BDA0003171409130000048
The anti-symmetric matrix of (a) is,
Figure BDA0003171409130000049
in order to be the acceleration of the gravity,
Figure BDA00031714091300000410
is a coordinate transformation matrix of the coordinate system of the inertial measurement system (3) relative to the northeast geographic coordinate system.
The inertial navigation position error model of the step S3 is
Y is CX, position error sequence value
Figure BDA0003171409130000051
C is an environment function matrix and C is an environment function matrix,
Figure BDA0003171409130000052
wherein,
Figure BDA0003171409130000053
k is 0 to N; the inertial measurement system has an error coefficient of
Figure BDA0003171409130000054
In the formula, Δ T is a calculation period,
Figure BDA0003171409130000055
in order to measure the system accelerometer error inertially,
Figure BDA0003171409130000056
Figure BDA0003171409130000057
the inertial measurement system measures the error of the gyroscope,
Figure BDA0003171409130000058
Figure BDA0003171409130000059
Aφ＝[Aφ1 Aφ2 Aφ3]；
Figure BDA00031714091300000510
Figure BDA00031714091300000511
Figure BDA00031714091300000512
wherein phi isx、φy、φzRespectively yaw angle, pitch angle and roll angle of the inertial measurement system relative to the northeast geographic coordinate system.
The error coefficient X of the inertial measurement system is properly increased or decreased according to the following combined model of the accelerometer and the gyroscope:
(a) coefficient xa1、xa2、…、xapSelecting error coefficients from an accelerometer combination error model:
Figure BDA0003171409130000061
in the formula, k0x、k0y、k0zIs the zero offset of the x, y, z accelerometers, in g; delta kx、δky、 δkzIs the linearity of the x, y, z accelerometers; delta Kax、δKay、δKazThe asymmetry error coefficients of the x, y and z accelerometers are obtained; k is a radical ofyx、kzx、kxy、kzy、kxz、kyzThe mounting error angle of the x, y and z accelerometers is given in rad; k2x、K2y、K2zIs the quadratic term error coefficient of the x, y and z accelerometers, and the unit is g/g2；δK2x、δK2y、δK2zIs the odd quadratic error coefficient of the x, y and z accelerometers, and the unit is g/g2；Kxxy、Kxxz、Kxyz、Kyxy、kyxz、kyyz、Kzxy、kzxz、kzyzIs the error coefficient of cross coupling terms of x, y and z accelerometers, and has the unit of g/g2；K3x、K3y、K3zThe error coefficients of cubic terms of the acceleration meters of x, y and z are respectively, and the unit is g/g3；
(b) Coefficient xg1、xg2、…、xgqSelecting error coefficients from a combined error model of the gyroscope:
Figure BDA0003171409130000062
in the formula, DFx、DFy、DFzConstant drift of the x, y and z gyroscopes is shown in degree/h; d1x、 D1y、D1z、D2x、D2y、D2z、D3x、D3y、D3zIs the first term drift of the x, y and z gyroscopes, and the unit is degree/h/g; d4x、D4y、D4z、D5x、D5y、D5z、D6x、D6y、D6zIs the quadratic term drift of the x, y and z gyroscopes, and has the unit of degree/h/g2；D7x、D7y、D7z、D8x、D8y、D8z、D9x、D9y、 D9zIs the cross-coupling quadratic term drift of the x, y and z gyroscopes, and has the unit of degree/h/g2。
The least squares method of step S3 solves the following equation:
X＝(CTC)-1CTY
and in the solving process, a significance test is adopted, and the non-significant state variables are directly set to be zero.
In the compensation in step S4, the position error is directly corrected, and the corrected position error Δ Y is Y — CX.
Compared with the prior art, the invention has the following advantages:
(1) the high-order error item of the inertial device is identified by the inertial measurement system error difference separation method based on the large overload excitation of the centrifugal machine, and the method has higher confidence coefficient compared with a gravity field multi-position calibration method;
(2) the error difference separation method of the inertial measurement system based on the large overload excitation of the centrifugal machine overcomes the difficulty that the reference is inaccurate when the acceleration of the centrifugal machine is taken as the reference separation error coefficient, and when the angle output by the centrifugal machine is taken as the reference, on one hand, the speed error and the position error are converged, on the other hand, the noise is eliminated by adopting integral, so that the identification accuracy and the robust stability are improved;
(3) the invention provides an inertial measurement system error difference separation method based on large overload excitation of a centrifuge, which is not only suitable for a high-precision centrifuge with stable rotating speed, but also suitable for a low-precision centrifuge with variable rotating speed, and reduces index requirements of equipment development.
Drawings
FIG. 1 is a schematic view of an inertial measurement system placed on a centrifuge inversion platform;
FIG. 2 is a schematic diagram of a centrifuge base, lever arm, and inverted platform coordinate system;
FIG. 3 illustrates the angle of rotation of a centrifuge lever arm in an example of the invention;
FIG. 4 is an illustration of the angular velocity of rotation of a centrifuge lever arm in an example of the invention;
FIG. 5(a) is a graph of the true trajectory of the movement of a centrifuge lever arm in relation to the x-axis of a base coordinate system over time in an example of the present invention;
FIG. 5(b) is a true trace of the movement of a centrifuge lever arm in relation to the y-axis of a base coordinate system over time in an example of the present invention;
FIG. 6 shows the movement of a centrifuge lever arm relative to a base to form a movement of Ox according to an exemplary embodiment of the present inventioneyeA trajectory of a plane;
FIG. 7(a) is a graph of the movement of a centrifuge lever arm in a navigation solution over time with respect to the x-axis of a base coordinate system in an example of the present invention;
FIG. 7(b) is a graph of the motion of a centrifuge lever arm in a navigation solution over time with respect to the y-axis of a base coordinate system in an example of the present invention;
FIG. 8 illustrates the movement of a navigation solution centrifuge lever arm relative to a base to synthesize a movement to Ox in an example of the inventioneyeA trajectory of a plane;
FIG. 9(a) is a graph of x-axis position error over time in an example of the present invention;
FIG. 9(b) is a graph of the time course of the y-axis position error in an example of the present invention;
FIG. 10(a) is a graph of the movement of a centrifuge lever arm with respect to the x-axis of a base coordinate system over time for a compensated navigation solution in an example of the present invention;
FIG. 10(b) is a graph of the movement of a centrifuge lever arm with respect to the y-axis of a base coordinate system over time for a compensated navigation solution in an example of the present invention;
FIG. 11 illustrates the movement of the compensated centrifuge lever arm relative to the base resulting in Ox in accordance with an exemplary embodiment of the present inventioneyeA trajectory of a plane;
FIG. 12 is a flow chart of the present invention.
Detailed Description
The invention is described in further detail below with reference to the following figures and specific examples:
the invention provides an inertial measurement system error separation method based on centrifugal machine large overload excitation, which comprises the following steps:
s1, establishing an inertial measurement system error separation test system: a reverse rotation platform 4 is arranged at the tail end of the arm 2 of the centrifugal machine, a balance weight 5 is arranged at the other side of the arm and is used for balancing the mass sum of the reverse rotation platform and an inertia measurement system, the inertia measurement system 3 is arranged on the reverse rotation platform 4, and the rotating speed of the reverse rotation platform 4 relative to the arm 2 of the centrifugal machine when rotating
Figure BDA0003171409130000081
In relation to the rotational speed of the centrifuge boom arm 2 relative to the ground
Figure BDA0003171409130000082
Are opposite numbers, i.e.
Figure BDA0003171409130000091
Wherein, ω is the rotation speed of the centrifuge base 1;
centrifuge base 1 coordinate system and northeast geographic coordinate system OxeyezeCoincide with, wherein, OxeEast of finger and OyeNorth arrow OzePointing to the sky, wherein the three meet the right-hand coordinate system;
2 coordinate system of centrifugal machine lever armpypzpWherein, OxpCoincident with the lever arm and pointing outwards, OypIn a horizontal plane perpendicular to the lever arm, OzpPointing to the sky, wherein the three meet the right-hand coordinate system;
4-coordinate system of the reverse platform is QxqyqzqWherein, OxqAnd OyqIn the horizontal plane, OzqPointing to the sky, wherein the three meet the right-hand coordinate system;
inertial measurement system 3 coordinate system QxbybzbThe coordinate system and the 4-coordinate system Qx of the inversion platformqyqzqThe directions of the coordinate axes are the same.
The latitude of the position of the centrifuge is L, the gravity acceleration is g, the height is h, and the earth rotation speed is omegaieFromThe length of the heart arm 2 is 2R.
S2, performing an inertial measurement system error separation test: driving a centrifugal machine lever arm 2 to rotate around a base 1 at a high speed to form centripetal acceleration, wherein the centripetal acceleration is the excitation of an inertial measurement system 3 installed on the centrifugal machine lever arm 2, and the excitation is not lower than 5g as a preferred scheme; the characteristic that the length of the arm of the centrifugal machine is unchanged is utilized, and the rotation angle of the arm 2 of the centrifugal machine in the rotation process is combined to obtain the motion track of an inertia measurement system 3 arranged on the arm 2 of the centrifugal machine, and the motion track is recorded as a reference motion track; performing navigation calculation on the apparent acceleration of the inertial measurement system 3 to obtain a motion track with an error, and recording the motion track as a measurement motion track; comparing the difference value of the measured motion track and the reference motion track to obtain a position error sequence value of the inertial measurement system;
the method specifically comprises the following steps:
s2.1, at initial t0At the moment, the initial alignment of the inertial measurement system is completed, so that the inertial navigation coordinate system and the northeast world coordinate system OxeyezePhysical coincidence (make
Figure BDA0003171409130000093
) Or calculated by mathematical alignment
Figure BDA0003171409130000092
An initial value of (d);
Figure BDA0003171409130000094
is a coordinate transformation matrix of the coordinate system of the inertial measurement system 3 relative to the geographical coordinate system of the northeast.
S2.2, obtaining initial t according to measurement0The angle of rotation phi of the centrifuge arm 2 relative to the base 1 at the moment0Calculating initial t in the reference motion trajectory0Time inertial measurement system relative northeast world coordinate system OxeyezeInitial value of (x) of positionew,0,yew,0,yew,0) And setting an initial t in the reference motion track0Relative northeast world coordinate system Ox of time inertia measurement systemeyezeHas an initial velocity value of 0, i.e.
Figure BDA0003171409130000101
When the next calculation period comes, initializing k to 1, and then sequentially executing the step S2.3 to the step S2.6;
initial t in reference motion trajectory0Initial position value (x) of time inertial measurement system relative to northeast world coordinate systemew,0,yew,0,yew,0) The calculation formula of (2) is as follows:
Figure BDA0003171409130000102
where R is half the length of the centrifuge boom arm 2.
The initial position value of the inertial measurement system during navigation calculation is set as:
Figure BDA0003171409130000103
namely: measuring a first point (x) in the movement pathen,0,yen,0,yen,0) Is compared with the first track point (x) in the reference motion trackew,0,yew,0,yew,0) The positions are the same.
S2.3, according to the measured angle value phi of the centrifuge lever arm 2 rotating relative to the base 1kCalculating the current tkTime inertia measurement system relative to the northeast world coordinate system (Ox)eyeze) The position of (a);
initial t in reference motion trajectorykInitial position value (x) of time inertial measurement system relative to northeast world coordinate systemew,k,yew,k,yew,k) The calculation formula of (2) is as follows:
Figure BDA0003171409130000104
where R is half the length of the centrifuge boom arm 2.
S2.4, obtaining the angular velocity according to the measurement of a gyroscope in the inertial measurement system
Figure BDA0003171409130000105
Obtaining apparent acceleration by combined measurement of accelerometers
Figure BDA0003171409130000111
Navigation resolving is carried out to obtain the current tkPosition of time of day
Figure BDA0003171409130000112
Navigation solution is performed using the following navigation equations:
Figure BDA0003171409130000113
in the formula,
Figure BDA0003171409130000114
is composed of
Figure BDA0003171409130000115
The anti-symmetric matrix of (a) is,
Figure BDA0003171409130000116
as the rotational speed of the earth
Figure BDA0003171409130000117
The anti-symmetric matrix of (a) is,
Figure BDA0003171409130000118
is the acceleration of gravity. Solving for t according to the formulakPosition of time of day
Figure BDA0003171409130000119
S2.5, calculating the position errors of corresponding track points in the reference motion track and the measurement motion track:
Figure BDA00031714091300001110
s2.6, when the next calculation cycle comes, the process returns to step S3.2 to re-execute step S2.3 to step 2.6 until the end time t is reachedNStep S3.6 is entered;
s2.7, summarizing corresponding track point position errors in the reference motion track and the measured motion track to obtain a position error sequence value Y:
Figure BDA00031714091300001111
s3, substituting the position error sequence value of the inertial measurement system into the inertial navigation position error model, and separating each error coefficient of the inertial measurement system by adopting a least square method;
the inertial navigation position error model is as follows:
Y＝CX
in the formula, the position error sequence value
Figure BDA0003171409130000121
C is an environment function matrix and C is an environment function matrix,
Figure BDA0003171409130000122
wherein,
Figure BDA0003171409130000123
k is 0 to N; the inertial measurement system has an error coefficient of
Figure BDA0003171409130000124
In the formula, Δ T is a calculation period,
Figure BDA0003171409130000125
in order to measure the system accelerometer error inertially,
Figure BDA0003171409130000126
Figure BDA0003171409130000127
the inertial measurement system measures the error of the gyroscope,
Figure BDA0003171409130000128
Figure BDA0003171409130000129
Aφ＝[Aφ1 Aφ2 Aφ3]；
Figure BDA00031714091300001210
Figure BDA00031714091300001211
Figure BDA00031714091300001212
wherein phi isx、φy、φzRespectively yaw angle, pitch angle and roll angle of the inertial measurement system relative to the northeast geographic coordinate system.
The error coefficient X of the inertial measurement system is properly increased or decreased according to the following combined model of the accelerometer and the gyroscope:
(a) coefficient xa1、xa2、…、xapSelecting error coefficients from an accelerometer combination error model:
Figure BDA0003171409130000131
in the formula, k0x、k0y、k0zIs the acceleration of x, y and zZero offset in g; delta kx、δky、 δkzIs the linearity of the x, y, z accelerometers; delta Kax、δKay、δKazThe asymmetry error coefficients of the x, y and z accelerometers are obtained; k is a radical ofyx、kzx、kxy、kzy、kxz、kyzThe mounting error angle of the x, y and z accelerometers is given in rad; k2x、K2y、K2zIs the quadratic term error coefficient of the x, y and z accelerometers, and the unit is g/g2；δK2x、δK2y、δK2zIs the odd quadratic error coefficient of the x, y and z accelerometers, and the unit is g/g2；Kxxy、Kxxz、Kxyz、Kyxy、kyxz、kyyz、Kzxy、kzxz、kzyzIs the error coefficient of cross coupling terms of x, y and z accelerometers, and has the unit of g/g2；K3x、K3y、K3zThe error coefficients of cubic terms of the acceleration meters of x, y and z are respectively, and the unit is g/g3；
(b) Coefficient xg1、xg2、…、xgqSelecting error coefficients from a combined error model of the gyroscope:
Figure BDA0003171409130000132
in the formula, DFx、DFy、DFzConstant drift of the x, y and z gyroscopes is shown in degree/h; d1x、 D1y、D1z、D2x、D2y、D2z、D3x、D3y、D3zIs the first term drift of the x, y and z gyroscopes, and the unit is degree/h/g; d4x、D4y、D4z、D5x、D5y、D5z、D6x、D6y、D6zIs the quadratic term drift of the x, y and z gyroscopes, and has the unit of degree/h/g2；D7x、D7y、D7z、D8x、D8y、D8z、D9x、D9y、 D9zIs the cross-coupling quadratic term drift of the x, y and z gyroscopes, and has the unit of degree/h/g2。
The least squares method solves for:
X＝(CTC)-1CTY
and in the solving process, a significance test is adopted, and the non-significant state variables are directly set to be zero.
And S4, correcting the errors of the inertial measurement system participating in navigation calculation by using the determined error coefficient of the inertial measurement system, further realizing the compensation of the navigation calculation of the inertial measurement system and improving the inertial navigation precision.
The compensation is performed by directly correcting the position error, and the corrected position error Δ Y is Y — CX.
In the step, the compensation is to correct the bound values of the errors of the gyroscope and the accelerometer participating in the navigation calculation by using the determined error coefficient of the inertial measurement system, so as to realize the compensation of the inertial navigation calculation.
Example (b):
for the purpose of image illustration, the invention provides an error separation method of an inertial measurement system based on the excitation of the large overload of a centrifuge, and the preferred embodiment is as follows:
let the arm length 2R of the centrifuge be 6m and the inertial measurement system be placed on the inverted platform of the centrifuge as shown in fig. 1. The relationship between the centrifuge base, lever arm and inverted platform coordinate system is shown in fig. 2.
In a certain test, the sampling time of the rotation angle of the centrifuge is 0.02s, the running time is 255s, and the total number of data N is 12750. The rotation angle phi and the angular velocity omega are shown in fig. 3 and 4, respectively. Using formulas
Figure BDA0003171409130000141
The calculated time-dependent movement locus of the centrifuge lever arm relative to the base coordinate system is shown in fig. 5(a) and 5(b), and synthesized into OxeyeTrajectory of a planeAs shown in fig. 6. And the movement locus x of the arm of the centrifuge calculated by navigation relative to the base coordinate system along with timeen,k、yen,kAs shown in FIGS. 7(a) and 7(b), synthesized to OxeyeThe planar trajectory is shown in fig. 8. Position error xen,k-xew,k、yen,k-yew,kAs shown in fig. 9(a) and 9(b), it can be seen that the x-axis maximum error is greater than 30m and the y-axis maximum error is greater than 100 m.
By using the error separation method of the invention, a group of significant error terms is delta Kay＝5.17×10-4、 Kzxy＝0.068g/g2、D4y＝-0.04°/h/g2、D5y＝0.43°/h/g2And the remaining error coefficients are zero. Compensating the four error coefficients, and then re-performing navigation calculation to obtain a movement locus x of the arm of the centrifuge relative to a base coordinate system along with timeen,k、yen,kAs shown in FIGS. 10(a) and 10(b), synthesized to OxeyeThe planar locus is shown in fig. 11, and it can be seen that the maximum error of the x-axis and the y-axis is less than 0.5 m.
Comparing fig. 11 with fig. 9(a) and fig. 9(b), it can be seen that according to the method of the present invention, not only the significant error term is identified, but also the navigation error is significantly eliminated, which indicates that the method of the present invention can well meet the error separation requirement under the condition of the centrifuge being heavily overloaded.
The above embodiment can verify that the error separation method of the inertial measurement system based on the centrifuge large overload excitation is correct, and fig. 12 is a flowchart for implementing the present invention.
The above description is only one embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.

Claims (9)

1. An inertial measurement system error separation method based on centrifuge excitation is characterized by comprising the following steps:
s1, establishing an inertial measurement system error separation test system: the end of one side of the centrifuge lever arm (2) is provided with a reverse rotation platform (4), the inertia measurement system (3) is arranged on the reverse rotation platform (4), the other side is provided with a balance weight (5) for balancing the mass of the reverse rotation platform and the inertia measurement system, and the rotating speed of the reverse rotation platform (4) relative to the centrifuge lever arm (2) when rotating
Figure FDA0003171409120000011
The rotation speed of the arm (2) of the centrifuge relative to the ground
Figure FDA0003171409120000012
Are opposite numbers, i.e.
Figure FDA0003171409120000013
Wherein omega is the rotating speed of the centrifuge base (1);
s2, performing an inertial measurement system error separation test: the centrifugal machine lever arm (2) is driven to rotate at a high speed around the base (1) to form centripetal acceleration, the centripetal acceleration is the excitation of an inertia measurement system (3) installed on the centrifugal machine lever arm (2), the movement track of the inertia measurement system (3) installed on the centrifugal machine lever arm (2) is obtained by utilizing the characteristic that the length of the centrifugal machine lever arm is unchanged and combining the rotation angle of the centrifugal machine lever arm (2) in the rotation process, and the movement track is recorded as a reference movement track; performing navigation calculation on the apparent acceleration of the inertial measurement system (3) to obtain a motion track with error, and recording the motion track as a measured motion track; comparing the difference value of the measured motion track and the reference motion track to obtain a position error sequence value of the inertial measurement system;
s3, substituting the position error sequence value of the inertial measurement system into the inertial navigation position error model, and separating each error coefficient of the inertial measurement system by adopting a least square method;
and S4, correcting the errors of the inertial measurement system participating in navigation calculation by using the determined error coefficient of the inertial measurement system, and further realizing the compensation of the navigation calculation of the inertial measurement system.
2. The method for separating the errors of the inertial measurement system based on the excitation of the centrifuge as recited in claim 1, wherein:
centrifuge base (1) coordinate system and northeast geographic coordinate system OxeyezeCoincide with, wherein, OxeEast of finger and OyeNorth arrow OzePointing to the sky, wherein the three meet the right-hand coordinate system;
coordinate system of a centrifugal machine lever arm (2) is OxpypzpWherein, OxpCoincident with the lever arm and pointing outwards, OypIn a horizontal plane perpendicular to the lever arm, OzpPointing to the sky, wherein the three meet the right-hand coordinate system;
the coordinate system of the reverse platform (4) is QxqyqzqWherein, OxqAnd OyqIn the horizontal plane, OzqPointing to the sky, wherein the three meet the right-hand coordinate system;
the coordinate system of the inertial measurement system (3) is QxbybzbThe coordinate system and the coordinate system Qx of the reversal platform (4)qyqzqThe directions of the coordinate axes are the same.
3. The method for separating errors of an inertial measurement system based on excitation of a centrifuge as claimed in claim 1, wherein the step S2 is implemented as follows:
s2.1, at initial t0At the moment, the initial alignment of the inertial measurement system is completed, so that the inertial navigation coordinate system and the northeast world coordinate system OxeyezePhysical coincidence;
s2.2, obtaining initial t according to measurement0The rotation angle phi of the arm (2) of the centrifuge relative to the base (1) at any moment0Calculating initial t in the reference motion trajectory0Time inertial measurement system relative northeast world coordinate system OxeyezeInitial value of (x) of positionew,0,yew,0,yew,0) And setting the middle of the reference motion trackBeginning t0Relative northeast world coordinate system Ox of time inertial measurement systemeyezeThe initial value of the speed is 0, when the next calculation period comes, k is initialized to 1, and then the step S3.2 to the step S3.5 are sequentially executed;
s3.2, according to the measured angle value phi of the centrifuge lever arm (2) rotating relative to the base (1)kCalculating the current tkTime inertia measurement system relative to the northeast world coordinate system (Ox)eyeze) The position of (a);
s3.3, obtaining the angular velocity according to the measurement of a gyroscope in the inertial measurement system
Figure FDA0003171409120000021
The accelerometer is combined to measure and obtain apparent acceleration
Figure FDA0003171409120000022
Navigation resolving is carried out to obtain the current tkPosition of time of day
Figure FDA0003171409120000023
S3.4, calculating the position errors of corresponding track points in the reference motion track and the measurement motion track:
Figure FDA0003171409120000031
s3.5, when the next calculation cycle comes, the process returns to step S3.2 to re-execute step S3.2 to step 3.5 until the end time t is reachedNStep S3.6 is entered;
s3.6, summarizing corresponding track point position errors in the reference motion track and the measured motion track to obtain a position error sequence value Y:
Figure FDA0003171409120000032
4. an inertial measurement system error separation method based on centrifuge excitation according to claim 2, characterized in that in the step (3.1) and step (3.2):
initial t in reference motion trajectorykInitial position value (x) of time inertial measurement system relative to northeast world coordinate systemew,k,yew,k,yew,k) The calculation formula of (2) is as follows:
Figure FDA0003171409120000033
wherein R is half of the length of the centrifuge lever arm (2).
5. The method for separating the errors of the inertial measurement system based on the excitation of the centrifuge as recited in claim 1, wherein the navigation solution formula in S4.3 is as follows:
Figure FDA0003171409120000034
in the formula,
Figure FDA0003171409120000035
is composed of
Figure FDA0003171409120000036
The anti-symmetric matrix of (a) is,
Figure FDA0003171409120000037
as the rotational speed of the earth
Figure FDA0003171409120000038
The anti-symmetric matrix of (a) is,
Figure FDA0003171409120000039
in order to be the acceleration of the gravity,
Figure FDA00031714091200000310
is a coordinate transformation matrix of the coordinate system of the inertial measurement system (3) relative to the northeast geographic coordinate system.
6. The method for separating the errors of the inertial measurement system based on the excitation of the centrifuge as recited in claim 1, wherein: the inertial navigation position error model of the step S3 is
Y＝CX
In the formula, the position error sequence value
Figure FDA0003171409120000041
C is an environment function matrix and C is an environment function matrix,
Figure FDA0003171409120000042
wherein,
Figure FDA0003171409120000043
k is 0 to N; the inertial measurement system has an error coefficient of
Figure FDA0003171409120000044
In the formula, Δ T is a calculation period,
Figure FDA0003171409120000045
in order to measure the system accelerometer error inertially,
Figure FDA0003171409120000046
Figure FDA0003171409120000047
the inertial measurement system measures the error of the gyroscope,
Figure FDA0003171409120000048
Figure FDA0003171409120000049
Aφ＝[Aφ1 Aφ2 Aφ3]；
Figure FDA00031714091200000410
Figure FDA00031714091200000411
Figure FDA00031714091200000412
wherein phi isx、φy、φzRespectively yaw angle, pitch angle and roll angle of the inertial measurement system relative to the northeast geographic coordinate system.
7. The method for separating the errors of the inertial measurement system based on the excitation of the centrifuge as recited in claim 6, wherein: the error coefficient X of the inertial measurement system is properly increased or decreased according to the following combined model of the accelerometer and the gyroscope:
(a) coefficient xa1、xa2、…、xapSelecting error coefficients from an accelerometer combination error model:
Figure FDA0003171409120000051
in the formula, k0x、k0y、k0zIs the zero offset of the x, y, z accelerometers, in g; delta kx、δky、δkzIs the linearity of the x, y, z accelerometers; delta Kax、δKay、δKazAs the asymmetry error coefficient of the x, y, z accelerometers；kyx、kzx、kxy、kzy、kxz、kyzIs the installation error angle of the x, y and z accelerometers, and the unit is rad; k2x、K2y、K2zIs the quadratic term error coefficient of the x, y and z accelerometers, and the unit is g/g2；δK2x、δK2y、δK2zIs the odd quadratic term error coefficient of the x, y and z accelerometers, and the unit is g/g2；Kxxy、Kxxz、Kxyz、Kyxy、kyxz、kyyz、Kzxy、kzxz、kzyzIs the error coefficient of cross coupling terms of the x, y and z accelerometers, and has the unit of g/g2；K3x、K3y、K3zThe error coefficients of the cubic terms of the x accelerometer, the y accelerometer and the z accelerometer are respectively, and the unit is g/g3；
(b) Coefficient xg1、xg2、…、xgqSelecting error coefficients from a combined error model of the gyroscope:
Figure FDA0003171409120000052
in the formula, DFx、DFy、DFzConstant drift of the x, y and z gyroscopes is shown in degree/h; d1x、D1y、D1z、D2x、D2y、D2z、D3x、D3y、D3zIs the first term drift of the x, y and z gyroscopes, and the unit is degree/h/g; d4x、D4y、D4z、D5x、D5y、D5z、D6x、D6y、D6zIs the quadratic term drift of the x, y and z gyroscopes, and has the unit of degree/h/g2；D7x、D7y、D7z、D8x、D8y、D8z、D9x、D9y、D9zIs the cross-coupling quadratic term drift of the x, y and z gyroscopes, and has the unit of degree/h/g2。
8. The method for separating the errors of the inertial measurement system based on the excitation of the centrifuge as recited in claim 1, wherein: the least squares method of step S3 solves the following equation:
X＝(CTC)-1CTY
and in the solving process, a significance test is adopted, and the non-significant state variables are directly set to be zero.
9. The method for separating the errors of the inertial measurement system based on the excitation of the centrifuge as recited in claim 1, wherein: in the compensation in step S4, the position error is directly corrected, and the corrected position error Δ Y is Y — CX.
CN202110819229.8A 2021-07-20 2021-07-20 Inertial measurement system error separation method based on centrifugal machine excitation Active CN113916219B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110819229.8A CN113916219B (en) 2021-07-20 2021-07-20 Inertial measurement system error separation method based on centrifugal machine excitation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110819229.8A CN113916219B (en) 2021-07-20 2021-07-20 Inertial measurement system error separation method based on centrifugal machine excitation

Publications (2)

Publication Number Publication Date
CN113916219A true CN113916219A (en) 2022-01-11
CN113916219B CN113916219B (en) 2024-07-09

Family

ID=79232931

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110819229.8A Active CN113916219B (en) 2021-07-20 2021-07-20 Inertial measurement system error separation method based on centrifugal machine excitation

Country Status (1)

Country Link
CN (1) CN113916219B (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115931009A (en) * 2023-03-13 2023-04-07 北京航空航天大学 Inertial device centrifugal measurement method based on gyroscope and laser ranging
CN115979311A (en) * 2023-03-20 2023-04-18 伸瑞科技（北京）有限公司 PIGA (particle image guided Algorithm) cross quadratic term coefficient calibration method, system, equipment and medium

Citations (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102221372A (en) * 2011-03-25 2011-10-19 北京航空航天大学 Method for calibrating error of inertia measurement unit by using centrifugal machine and turntable
CN106643792A (en) * 2016-10-26 2017-05-10 中国科学院长春光学精密机械与物理研究所 Inertial measurement unit and geomagnetic sensor integrated calibration apparatus and calibration method
CN109813343A (en) * 2019-03-21 2019-05-28 哈尔滨工业大学 A kind of measurement method of centrifuge Initial Alignment Error
CN110345838A (en) * 2018-12-21 2019-10-18 哈尔滨工业大学 A kind of measurement method of four axis centrifuge working radius
CN110398258A (en) * 2019-08-13 2019-11-01 广州广电计量检测股份有限公司 A kind of performance testing device and method of inertial navigation system
CN110553642A (en) * 2019-07-26 2019-12-10 北京航天控制仪器研究所 Method for improving inertial guidance precision
CN111623770A (en) * 2020-04-28 2020-09-04 北京航天控制仪器研究所 Method for improving inertial guidance precision based on speed error open-loop correction
CN111637883A (en) * 2020-04-28 2020-09-08 北京航天控制仪器研究所 Method for improving inertial guidance precision based on speed and position error closed-loop feedback
CN111780752A (en) * 2020-06-10 2020-10-16 北京航天控制仪器研究所 Method for improving inertial guidance precision with observable attitude error
CN111780753A (en) * 2020-06-10 2020-10-16 北京航天控制仪器研究所 Method for improving inertial guidance precision through attitude error feedback correction
CN112665610A (en) * 2019-10-15 2021-04-16 哈尔滨工程大学 External measurement information compensation method for SINS/DVL integrated navigation system

Patent Citations (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102221372A (en) * 2011-03-25 2011-10-19 北京航空航天大学 Method for calibrating error of inertia measurement unit by using centrifugal machine and turntable
CN106643792A (en) * 2016-10-26 2017-05-10 中国科学院长春光学精密机械与物理研究所 Inertial measurement unit and geomagnetic sensor integrated calibration apparatus and calibration method
CN110345838A (en) * 2018-12-21 2019-10-18 哈尔滨工业大学 A kind of measurement method of four axis centrifuge working radius
CN109813343A (en) * 2019-03-21 2019-05-28 哈尔滨工业大学 A kind of measurement method of centrifuge Initial Alignment Error
CN110553642A (en) * 2019-07-26 2019-12-10 北京航天控制仪器研究所 Method for improving inertial guidance precision
CN110398258A (en) * 2019-08-13 2019-11-01 广州广电计量检测股份有限公司 A kind of performance testing device and method of inertial navigation system
CN112665610A (en) * 2019-10-15 2021-04-16 哈尔滨工程大学 External measurement information compensation method for SINS/DVL integrated navigation system
CN111623770A (en) * 2020-04-28 2020-09-04 北京航天控制仪器研究所 Method for improving inertial guidance precision based on speed error open-loop correction
CN111637883A (en) * 2020-04-28 2020-09-08 北京航天控制仪器研究所 Method for improving inertial guidance precision based on speed and position error closed-loop feedback
CN111780752A (en) * 2020-06-10 2020-10-16 北京航天控制仪器研究所 Method for improving inertial guidance precision with observable attitude error
CN111780753A (en) * 2020-06-10 2020-10-16 北京航天控制仪器研究所 Method for improving inertial guidance precision through attitude error feedback correction

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115931009A (en) * 2023-03-13 2023-04-07 北京航空航天大学 Inertial device centrifugal measurement method based on gyroscope and laser ranging
CN115931009B (en) * 2023-03-13 2023-04-28 北京航空航天大学 Inertial device centrifugal measurement method based on gyroscope and laser ranging
CN115979311A (en) * 2023-03-20 2023-04-18 伸瑞科技（北京）有限公司 PIGA (particle image guided Algorithm) cross quadratic term coefficient calibration method, system, equipment and medium
CN115979311B (en) * 2023-03-20 2023-07-04 伸瑞科技（北京）有限公司 PIGA cross quadratic term coefficient calibration method, system, equipment and medium

Also Published As

Publication number Publication date
CN113916219B (en) 2024-07-09

Similar Documents

Publication Publication Date Title
CN103808331B (en) A kind of MEMS three-axis gyroscope error calibrating method
CN107655493B (en) SINS six-position system-level calibration method for fiber-optic gyroscope
CN106017507B (en) A kind of used group quick calibrating method of the optical fiber of precision low used in
CN103900565B (en) A kind of inertial navigation system attitude acquisition method based on differential GPS
CN107063254B (en) Gesture resolving method for gyros and geomagnetic combination
CN104764463B (en) A kind of self-sensing method of inertial platform leveling collimating fault
CN103090866B (en) Method for restraining speed errors of single-shaft rotation optical fiber gyro strapdown inertial navigation system
CN113916219B (en) Inertial measurement system error separation method based on centrifugal machine excitation
CN104596543B (en) Gyroscope combined error coefficient scaling method under a kind of benchmark uncertain condition
CN105628025B (en) A kind of constant speed offset frequency/machine laser gyroscope shaking inertial navigation system air navigation aid
CN105509768B (en) A kind of error calibrating method of single shaft north finder
CN102645223B (en) Serial inertial navigation vacuum filtering correction method based on specific force observation
CN111780752B (en) Method for improving inertial guidance precision with observable attitude error
CN110887507A (en) Method for quickly estimating all zero offsets of inertial measurement units
CN113701747B (en) Inertial measurement system attitude angle error separation method based on centrifugal machine excitation
CN113865583B (en) Accelerometer combination dynamic installation deviation matrix determining and compensating method
CN111780751B (en) Information redundancy method for improving inertial guidance precision
RU2683144C1 (en) Method of defining errors of orientation axles of laser gyroscopes and pendulum accelerometers in a strap down inertial navigation system
CN109084755B (en) Accelerometer zero offset estimation method based on gravity apparent velocity and parameter identification
CN111637883B (en) Method for improving inertial guidance precision based on speed and position error closed-loop feedback
CN110940357B (en) Inner rod arm calibration method for self-alignment of rotary inertial navigation single shaft
CN113865585B (en) Method and system for separating and compensating combined high-order error coefficient of gyroscope
CN109029499A (en) A kind of accelerometer bias iteration optimizing estimation method based on gravity apparent motion model
CN111141285B (en) Aviation gravity measuring device
CN112985368B (en) Rapid compass alignment method of underwater vehicle before launching of mobile carrying platform

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant