CN110160554A - A kind of single-shaft-rotation Strapdown Inertial Navigation System scaling method based on optimizing method - Google Patents
A kind of single-shaft-rotation Strapdown Inertial Navigation System scaling method based on optimizing method Download PDFInfo
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- CN110160554A CN110160554A CN201910360691.9A CN201910360691A CN110160554A CN 110160554 A CN110160554 A CN 110160554A CN 201910360691 A CN201910360691 A CN 201910360691A CN 110160554 A CN110160554 A CN 110160554A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
- G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
Abstract
The invention discloses a kind of single-shaft-rotation Strapdown Inertial Navigation System scaling method based on optimizing method, the following steps are included: single-shaft-rotation Strapdown Inertial Navigation System is mounted on double axle table first with tooling, for system electrification, indexing mechanism is returned to zero and closed, after system temperature is stablized, system is set successively to go to 18 positions using turntable, indexing mechanism is cooperated to carry out 9 groups of rate experiments using double axle table again, data are subjected to optimizing estimation using nonlinear optimization method, obtain 18 error parameters, finally mount the system on three-axle table, carry out 3 position experiments and 3 groups of rate experiments, the orthogonal coordinate system of accelerometer and gyro is demarcated to three-axle table coordinate system.The present invention has the advantages that calibration automation, does not depend on turntable precision, and calibration is demarcated again for a long time with after factory before can be realized system factory.
Description
Technical field
The present invention relates to technical field of inertial, especially a kind of single-shaft-rotation Strapdown Inertial Navigation System based on optimizing method
Scaling method.
Background technique
Rotation modulation technology utilizes indexing mechanism Periodic Rotating, eliminates or reduce navigation error caused by inertia device,
To improve inertial navigation system precision.Since it reduces inertia device required precision to a certain extent, while it can satisfy system
The advantage of navigation accuracy is widely used in High Accuracy Inertial Navigation System.Though single-shaft-rotation modulation technology can pass through rotation modulation
Navigation error caused by x-axis and y-axis inertia device is eliminated or reduces, it but can not modulation eliminating to z-axis inertial device error.Cause
This, inertial device error is still the principal element of influence system navigation accuracy.
The first step as single-shaft-rotation modulation system after the assembly is completed is demarcated, is to ensure that inertia device precision is most effective
One of mode.Inertial navigation system calibration is divided into according to whether according to navigation error calibration inertia device: 1) discrete calibration side
Method, 2) systematic calibration method；The scaling method carried out before and after dispatching from the factory according to system is divided into: 1) component-level calibration before dispatching from the factory, and 2)
Dispatch from the factory before system calibrating, 3) factory after long-time system demarcate again；It is divided into according to calibration institute using equipment: 1) three-axle table mark
It is fixed, 2) calibration of high-precision hexahedron, 3) double axle table calibration.Calibration, which generally uses, before system factory is based on high-precision three-axle table
Or the hexahedral discrete scaling method of high-precision, this method is to equipment precision requirement height, and stated accuracy places one's entire reliance upon and turns
Platform precision.Though systematic calibration can guarantee stated accuracy independent of turntable precision, must by navigation calculation process, by
Navigation error estimates inertial device error using least square method or filtering algorithm, and algorithm is relatively complicated, and this method only can
Guarantee demarcates inertia device to the same orthogonal coordinate system, although navigation results are unaffected, by inertia device institute
The orthogonal coordinate system of calibration extremely is not navigational coordinate system, causes alignment result and true value deviation larger.
Based on this, study that a kind of pair of calibration facility required precision is low, can be realized automation calibration, algorithm is simple, simultaneously
Guarantee that inertia device is demarcated to navigational coordinate system not influence the rotation Strapdown Inertial Navigation System calibration of the high-precise uniaxial of alignment result
Method becomes the direction of industry development.
Summary of the invention
Technical problem to be solved by the present invention lies in provide a kind of single-shaft-rotation Strapdown Inertial Navigation System based on optimizing method
Scaling method can reduce to calibration facility required precision, realizes automation calibration, inertia device is demarcated to navigation coordinate
System, algorithm are simple.
In order to solve the above technical problems, the present invention provides a kind of single-shaft-rotation Strapdown Inertial Navigation System calibration based on optimizing method
Method includes the following steps:
(1) single-shaft-rotation Strapdown Inertial Navigation System is mounted on double axle table using tooling, is system electrification, by indexing machine
Structure is returned to zero and is closed, and is stablized to system temperature；
(2) system is made successively to go to 18 positions using turntable, each station acquisition accelerometer output data 1 minute；
(3) cooperate the indexing mechanism inside single-shaft-rotation Strapdown Inertial Navigation System, carry out 9 groups of positive and negative revolving speeds using double axle table
Rate experiment, acquisition gyro export complete cycle data；
(4) data of step (2) and step (3) are subjected to optimizing estimation using nonlinear optimization method, obtain 18 and is used to
The error parameter of property device simultaneously compensates offline, by accelerometer and gyro by respective sensitivity coordinate system a system, g system, demarcate respectively to
Orthogonal coordinate system p system and o system；
(5) it mounts the system on three-axle table, is system electrification, indexing mechanism is returned to zero and closed, to system temperature
Stablize；
(6) three axis of accelerometer are successively directed toward day, accelerometer is successively acquired under 3 positions and is exported 2 minutes, by top
Spiral shell carries out 3 groups of positive and negative rotation rate experiments rotating around three axis, and acquisition gyro exports complete cycle data, by accelerometer and gyro by step
Suddenly (3) are demarcated orthogonal coordinate system p system and o system demarcate to three-axle table coordinate system r system, and by transition matrixWith
It is orthogonalized.
Preferably, in step (3), the indexing mechanism inside single-shaft-rotation Strapdown Inertial Navigation System is cooperated to realize Gyro Calibration,
It is that system is fixed on by the position that z-axis refers to east by tooling, with the day of double axle table inside casing to the north orientation shaft of shaft and outline border
3DOF mechanism is collectively formed, guarantees to be able to carry out 3 axis gyro rate experiments in the case where indexing mechanism cooperates, to demarcate gyro.
Preferably, in step (4), the data of step (2) and step (3) is subjected to optimizing using nonlinear optimization method and are estimated
Meter, obtains the error parameter of 18 inertia devices and compensates offline, by accelerometer and gyro by respective sensitivity coordinate system a system, g
System, demarcates respectively to orthogonal coordinate system p system and o system specifically:
Using the scaling method based on non-linear optimizing, accelerometer and gyro are demarcated respectively to orthogonal coordinate system p system
With o system, corresponding three axis accelerometer zero bias are obtainedThree axis accelerometer constant multiplier Kax、Kay、KazPlus
Speedometer installation error Eayx、Eazx、Eazy, three axis optical fibre gyro zero bias εx、εy、εz, three axis optical fibre gyro constant multiplier Kgx、Kgy、
KgzWith optical fibre gyro installation error Egyx、Egzx、EgzyTotally 18 error parameters, specifically comprise the following steps:
(41) inertial device error model is established:
To guarantee that stated accuracy independent of double axle table precision, inertia device is not demarcated to double axle table coordinate system,
And by the output of accelerometer and gyro respectively by a system and g system, calibration to orthogonal coordinate system p system and orthogonal coordinate system o system；
It is as follows to establish accelerometer error model:
Wherein,The projection in accelerometer sensitive coordinate system a system is exported for three axis accelerometer,The projection in orthogonal coordinate system p system is exported for three axis accelerometer,For three axis
Accelerometer bias, va=[vax vay vaz]TFor three axis accelerometer error in measurement, M is accelerometer constant multiplier and installation
Error matrix, expression formula are
Wherein, Kai(i=x, y, z) is i axis accelerometer constant multiplier, Eayx、Eazx、EazyFor accelerometer installation error；
It is as follows to establish gyroscope error model:
Wherein,The projection in gyro sensitivity coordinate system g system is exported for three axis accelerometer,Projection for three axis accelerometer output in orthogonal coordinate system o system, ε=[εx εy εz]TFor three axis accelerometer
Zero bias, vg=[vgx vgy vgz]TFor three axis accelerometer error in measurement, N is gyro constant multiplier and installation error matrix, and expression formula is
Wherein, Kgi(i=x, y, z) is i axis gyro constant multiplier, Egyx、Egzx、EgzyFor gyro misalignment；
(42) imu error parameter optimization cost function is established:
According to two norms of two norms and acceleration of gravity that three axis accelerometer output projects under orthogonal coordinate system p system
It is theoretically equal, i.e.,
||fp||2=| | Gn||2 (5)
Wherein,Projection for three axis accelerometer output in p system, Gn=[0 0-g]TFor gravity
Projection of the vector acceleration under navigational coordinate system n system, | | | |2For two norm signs；
By formula (1) and formula (5), establishing accelerometer error parameter optimization cost function is
Wherein,For the output of accelerometer under i-th of position,For square symbol of two norms
Number；
Since earth rotation angular speed is smaller, Gyro Calibration cannot be used directly for, therefore turntable rotation angular speed is utilized to assist
Gyro error parameter is demarcated, the vector of earth rotation angular speed and turntable rotation angular speed is equal to according to the output of gyro angular speed
With that is,
Wherein,The projection in o system is exported for gyro angular speed,For earth rotation angular speed o system projection,
Angular speed is rotated in the projection of o system for turntable；
(3) formula is substituted into (1) formula and the time is integrated, turntable rotates forward complete cycle, it can obtain,
WhereinThe output of complete cycle gyro angular speed is rotated forward for turntable to project in o system,Complete cycle gyro angle is rotated forward for turntable
Rate output is projected in g system, t1The time used in complete cycle is rotated forward for turntable；
Turntable inverts complete cycle, can obtain,
WhereinThe output of complete cycle gyro angular speed is inverted for turntable to project in o system,Complete cycle gyro angle is inverted for turntable
Rate output is projected in g system, t2The time used in complete cycle is inverted for turntable；
Formula (8)-formula (9), and keep the complete cycle week number of turntable forward and reverse identical, so that t=t1=t2, it obtains,
The wherein angle that θ is rotated by turntable positive and negative rotation complete cycle；
Gyro constant multiplier is established by formula (10) and the optimizing cost function of installation error matrix N is
Wherein,Gyro angular speed output in rate experiments is rotated forward for jth group,
Gyro angular speed output in rate experiments is inverted for jth group；
It is finally tested according to position, establishing gyro zero bias optimizing cost function is
Wherein,For gyro angular speed output in i-th group of position experiment；
(43) optimizing estimation is carried out using nonlinear optimization method:
Non-linear least square optimization problem is constructed for objective function, and assigns initial value with formula (6), (11), (12), is enabled
Wherein M0For accelerometer constant multiplier and installation error matrix initial value,For accelerometer bias initial value, N0For
Gyro constant multiplier and installation error matrix initial value, ε0For gyro zero bias initial value；
The position of step (2) and step (3) and rate experiments accelerometer collected and gyro data are substituted into formula
(6), (11), (12) carry out optimizing iteration, estimate 18 error parameters, and accelerometer and gyro are demarcated respectively to p system and o
System.
Preferably, in step (6), three axis of accelerometer is successively directed toward day, successively acquire accelerometer under 3 positions
Gyro is carried out 3 groups of positive and negative rotation rate experiments rotating around three axis by output 2 minutes, and acquisition gyro exports complete cycle data, will accelerate
The orthogonal coordinate system p system and o system that degree meter and gyro are demarcated by step (3), under calibration to three-axle table coordinate system r system, and will
Transition matrixWithIt is orthogonalized and specifically comprises the following steps:
(61) position and rate experiments data acquire
Strapdown Inertial Navigation System is installed to three-axle table, turntable seeks zero, and system electrification is set after system the operation is stable
Turntable enables three axis of x, y, z of system successively be directed toward day, and each accelerometer that acquires exports 2 minutes, and calculates and table is added to export mean value, if
Determine turntable to enable system be directed toward day around three axis of x, y, z and carry out positive and negative rotation rate experiments respectively with the rate of 10 °/s, respectively acquires gyro
Export complete cycle data；
(62) transition matrix is calculated
According to accelerometer turntable coordinate system r system and orthogonal coordinate system p system transformational relation:
WhereinThe projection under turntable coordinate system r system is exported for accelerometer,The projection in p system is exported for accelerometer,For p system to the transition matrix of r system；
(61) position experimental data is substituted into formula (13):
Wherein g is terrestrial gravitation acceleration,I axis accelerometer output 2 when being directed toward day for j axis
The average value of minute data is demarcated accelerometer to three axis by the orthogonal coordinate system p system that step (3) is demarcated using formula (14)
Turntable coordinate system r system；
(63) transition matrix is calculated
According to gyro turntable coordinate system r system and orthogonal coordinate system o system transformational relation:
When gyro x-axis is directed toward day progress forward direction rate experiments, expansion (13):
Wherein,For projection of the i axis gyro output in rhombic system o system, C in x-axis forward direction rate experimentsij
(i=1,2,3, j=1,2,3) is transition matrixThe i-th row jth column element, ωrFor turntable shaft turning rate, ωie
For earth rotation angular speed, L is latitude where calibration ground, and φ (t) is that turntable shaft rotates angle；
By the data summation of turntable rotation complete cycle, formula (14) is
Wherein A is that turntable rotates record data amount check in complete cycle, and gyro x-axis is directed toward day and carries out reverse rate experiment and will turn
The data summation of platform rotation complete cycle has:
Wherein,For projection of the i axis gyro output in rhombic system o system, formula in the experiment of x-axis reverse rate
(15)-(16), have
Similarly, gyro y-axis, z-axis are directed toward day and carry out positive and negative rate experiments, have
Wherein,Respectively around y-axis forward direction, y-axis negative sense, z-axis forward direction, z
Projection of the i axis gyro output in rhombic system o system in axis negative sense rate experiments；
Transition matrix is calculated according to formula (17), (18), (19)Its transposed matrixGyro is demarcated by step (3)
The calibration of orthogonal coordinate system o system to three-axle table coordinate system r system.
The invention has the benefit that automatic Calibration before factory can be rapidly completed using double axle table and three-axle table,
Nominal time is short, and algorithm is simple, can first demarcate inertia device to same orthogonal coordinate system, then demarcates to turntable coordinate system,
Improve alignment precision；The present invention demarcates again for a long time after capable of completing factory merely with double axle table, wants to calibration facility precision
It asks low, can be realized automation calibration, improve alignment and navigation accuracy.
Detailed description of the invention
Fig. 1 is scaling method flow diagram of the invention.
Fig. 2 is that schematic diagram is tested in 18 position of single-shaft-rotation Strapdown Inertial Navigation System of the invention.
Fig. 3 is 9 groups of rate experiments schematic diagrames of single-shaft-rotation Strapdown Inertial Navigation System of the invention.
Fig. 4 is that accelerometer cost function restrains schematic diagram in emulation of the invention.
Fig. 5 is that gyro constant multiplier and installation error matrix cost function restrain schematic diagram in emulation of the invention.
Fig. 6 is that gyro zero bias cost function restrains schematic diagram in emulation of the invention.
Specific embodiment
As shown in Figure 1, a kind of single-shaft-rotation Strapdown Inertial Navigation System scaling method based on optimizing method, includes the following steps:
(1) single-shaft-rotation Strapdown Inertial Navigation System is mounted on double axle table using tooling, is system electrification, by indexing machine
Structure is returned to zero and is closed, and is stablized to system temperature；
(2) according to position view shown in Fig. 2, system is made successively to go to 18 positions, each station acquisition using turntable
Accelerometer output data 1 minute；
(3) according to rotating manner schematic diagram shown in Fig. 3, cooperate the indexing mechanism inside single-shaft-rotation Strapdown Inertial Navigation System,
9 groups of positive and negative rotation rate experiments are carried out using double axle table, acquisition gyro exports complete cycle data；
(4) data of step (2) and step (3) are subjected to optimizing estimation using Ceres nonlinear optimization library, obtain 18
The error parameter of inertia device simultaneously compensates offline, by accelerometer and gyro by respective sensitivity coordinate system a system, g system, demarcates respectively
To orthogonal coordinate system p system and o system；
(5) it mounts the system on three-axle table, is system electrification, indexing mechanism is returned to zero and closed, to system temperature
Stablize；
(6) three axis of accelerometer are successively directed toward day, accelerometer is successively acquired under 3 positions and is exported 2 minutes, by top
Spiral shell carries out 3 groups of positive and negative rotation rate experiments rotating around three axis, and acquisition gyro exports complete cycle data, by accelerometer and gyro by step
Suddenly (3) are demarcated orthogonal coordinate system p system and o system demarcate to three-axle table coordinate system r system, and by transition matrixWith
It is orthogonalized.
Further, it in the step (4), using the scaling method based on the non-linear optimizing of Ceres, utilizes step (2)
Accelerometer and gyro are demarcated respectively to orthogonal coordinate system p system and o system, obtain phase by position and rate experiments with step (3)
The three axis accelerometer zero bias answeredThree axis accelerometer constant multiplier Kax、Kay、Kaz, accelerometer installation miss
Poor Eayx、Eazx、Eazy, three axis optical fibre gyro zero bias εx、εy、εz, three axis optical fibre gyro constant multiplier Kgx、Kgy、KgzAnd optical fibre gyro
Installation error Egyx、Egzx、EgzyTotally 18 error parameters.
By position and rate experiments in step (6), theoretical output and acceleration of the inertia device on three-axle table are utilized
Meter and the gyro transformational relation between p system and the output of o system respectively are spent, determines transition matrixWithThe tool of step (4)
Body step are as follows:
(41) inertial device error model is established:
To guarantee that stated accuracy independent of double axle table precision, inertia device is not demarcated to double axle table coordinate system,
And by the output of accelerometer and gyro respectively by a system and g system, calibration to orthogonal coordinate system p system and orthogonal coordinate system o system.
It is as follows to establish accelerometer error model:
Wherein,The projection in accelerometer sensitive coordinate system a system is exported for three axis accelerometer,The projection in orthogonal coordinate system p system is exported for three axis accelerometer,For three axis
Accelerometer bias, va=[vax vay vaz]TFor three axis accelerometer error in measurement.M is accelerometer constant multiplier and installation
Error matrix, expression formula are
Wherein, Kai(i=x, y, z) is i axis accelerometer constant multiplier, Eayx、Eazx、EazyFor accelerometer installation error.
It is as follows to establish gyroscope error model:
Wherein,The projection in gyro sensitivity coordinate system g system is exported for three axis accelerometer,Projection for three axis accelerometer output in orthogonal coordinate system o system, ε=[εx εy εz]TFor three axis accelerometer
Zero bias, vg=[vgx vgy vgz]TFor three axis accelerometer error in measurement.N is gyro constant multiplier and installation error matrix, and expression formula is
Wherein, Kgi(i=x, y, z) is i axis gyro constant multiplier, Egyx、Egzx、EgzyFor gyro misalignment.
(42) imu error parameter optimization cost function is established:
According to two norms of two norms and acceleration of gravity that three axis accelerometer output projects under orthogonal coordinate system p system
It is theoretically equal, i.e.,
||fp||2=| | Gn||2 (5)
Wherein,Projection for three axis accelerometer output in p system, Gn=[0 0-g]TAttach most importance to
Projection of the power vector acceleration under navigational coordinate system n system, | | | |2For two norm signs.
By formula (1) and formula (5), establishing accelerometer error parameter optimization cost function is
Wherein,For the output of accelerometer under i-th of position,For square symbol of two norms
Number.
Since earth rotation angular speed is smaller, Gyro Calibration cannot be used directly for, therefore turntable rotation angular speed is utilized to assist
Gyro error parameter is demarcated, the vector of earth rotation angular speed and turntable rotation angular speed is equal to according to the output of gyro angular speed
With that is,
Wherein,The projection in o system is exported for gyro angular speed,For earth rotation angular speed o system projection,
Angular speed is rotated in the projection of o system for turntable.
Formula (3) are substituted into formula (1) and the time is integrated, turntable rotates forward complete cycle, it can obtain,
WhereinThe output of complete cycle gyro angular speed is rotated forward for turntable to project in o system,Complete cycle gyro angle is rotated forward for turntable
Rate output is projected in g system, t1The time used in complete cycle is rotated forward for turntable.
Turntable inverts complete cycle, can obtain,
WhereinThe output of complete cycle gyro angular speed is inverted for turntable to project in o system,Complete cycle gyro angle is inverted for turntable
Rate output is projected in g system, t2The time used in complete cycle is inverted for turntable.
Formula (8)-formula (9), and keep the complete cycle week number of turntable forward and reverse identical, so that t=t1=t2, it obtains,
The wherein angle that θ is rotated by turntable positive and negative rotation complete cycle.
Gyro constant multiplier is established by formula (10) and the optimizing cost function of installation error matrix N is
Wherein,Gyro angular speed output in rate experiments is rotated forward for jth group,
Gyro angular speed output in rate experiments is inverted for jth group.
It is finally tested according to position, establishing gyro zero bias optimizing cost function is
Wherein,For gyro angular speed output in i-th group of position experiment.
(43) optimizing estimation is carried out using Ceres optimization library
Non-linear least square optimization problem is constructed for objective function, and assigns initial value with formula (6), (11), (12), is enabled
Wherein M0For accelerometer constant multiplier and installation error matrix initial value,For accelerometer bias initial value, N0For
Gyro constant multiplier and installation error matrix initial value, ε0For gyro zero bias initial value.
The position of step (2) and step (3) and rate experiments accelerometer collected and gyro data are substituted into formula
(6), (11), (12) carry out optimizing iteration, estimate 18 error parameters, and accelerometer and gyro are demarcated respectively to p system and o
System.
Step (6) determines transition matrix using three-axle table position and rate experimentsWithSpecific step is as follows:
(61) position and rate experiments data acquire
Strapdown Inertial Navigation System is installed to three-axle table, turntable seeks zero, and system electrification is set after system the operation is stable
Turntable enables three axis of x, y, z of system successively be directed toward day, and each accelerometer that acquires exports 2 minutes, and calculates and table is added to export mean value.If
Determine turntable to enable system be directed toward day around three axis of x, y, z and carry out positive and negative rotation rate experiments respectively with the rate of 10 °/s, respectively acquires gyro
Export complete cycle data.
(62) transition matrix is calculated
According to accelerometer turntable coordinate system r system and orthogonal coordinate system p system transformational relation:
WhereinThe projection under turntable coordinate system r system is exported for accelerometer,The projection in p system is exported for accelerometer,For p system to the transition matrix of r system.
(61) position experimental data is substituted into formula (13):
Wherein g is terrestrial gravitation acceleration,I axis accelerometer output 2 when being directed toward day for j axis
The average value of minute data.Accelerometer is demarcated by the orthogonal coordinate system p system that step (3) is demarcated to three axis using formula (14)
Turntable coordinate system r system.
(63) transition matrix is calculated
According to gyro turntable coordinate system r system and orthogonal coordinate system o system transformational relation:
When gyro x-axis is directed toward day progress forward direction rate experiments, expansion (13):
Wherein,For projection of the i axis gyro output in rhombic system o system, C in x-axis forward direction rate experimentsij
(i=1,2,3, j=1,2,3) is transition matrixThe i-th row jth column element, ωrFor turntable shaft turning rate, ωieFor
Earth rotation angular speed, L are latitude where calibration ground, and φ (t) is that turntable shaft rotates angle.
By the data summation of turntable rotation complete cycle, formula (14) is
Wherein A is that turntable rotates record data amount check in complete cycle, and gyro x-axis is directed toward day and carries out reverse rate experiment and will turn
The data summation of platform rotation complete cycle has:
Wherein,For around x-axis reverse rate experiment in i axis gyro output rhombic system o system projection.Formula
(15)-(16), have
Similarly, gyro y-axis, z-axis are directed toward day and carry out positive and negative rate experiments, have
Wherein,Respectively around y-axis forward direction, y-axis negative sense, z-axis forward direction, z
Projection of the i axis gyro output in rhombic system o system in axis negative sense rate experiments.
Transition matrix is calculated according to formula (17), (18), (19)Its transposed matrixGyro is demarcated by step (3)
The calibration of orthogonal coordinate system o system to three-axle table coordinate system r system.
Feasibility of the invention is verified by emulation as follows:
(1) systematic calibration emulation platform is demarcated by inertia device number generator with the optimizing based on Ceres optimization library
Forecast scheme configuration；
(2) longitude in rating test place is set as 106.6906 °, and it is highly 1070.0m that latitude, which is 26.5019 °,.For
Verifying scaling method is not influenced by turntable precision, is set double axle table attitude error in course, pitching and rolling direction and is respectively
2 °, 0.5 °, 0.5 °, vibration angle amplitude is 2 when turntable is controlled ", vibration frequency 10Hz.Accelerometer random bias is
0.1mg, Modelling of Random Drift of Gyroscopes are 0.01 °/h.
(3) the double axle table position experiment simulation time total 18min of step (2), each station acquisition 1min accelerometer
1min data averaged is that cost function carries out optimizing iteration, estimated acceleration with formula (6) by data, period 5ms
9 error parameters are counted, accelerometer cost function convergent in searching process is as shown in figure 4, final estimated result such as 1 institute of table
Show.
(4) the total 21.6min of double axle table rate experiments simulation time of step (2), every group of positive and negative rotation rate experiments setting
Turntable acquires 72s gyro data with 10 °/s rate, and period 5ms is that cost function carries out optimizing iteration, estimation with formula (11)
The constant multiplier and installation error matrix N of gyro totally 6 error parameters, while the gyro in utilization step (2) in the experiment of position
Data are that cost function carries out optimizing iteration with formula (12), estimate 3 error parameters of gyro zero bias, estimate in searching process
The cost function convergent of the cost function and estimation gyro zero bias of gyro constant multiplier and installation error matrix N is respectively as schemed
5, shown in Fig. 6, final estimated result is as shown in table 2.
1 accelerometer error pre-set parameter of table and calibration value table
2 gyro error pre-set parameter of table and calibration value table
(5) accelerometer and gyro in emulation is set separately using Eulerian angles and demarcates orthogonal seat extremely in step (4)
The transformational relation of p system, mark system and turntable coordinate system r system, orthogonal coordinate system o system and turntable coordinate system r system, utilizes inertia device number
According in generator simulation process (6) position and rate experiments, according to formula (14), (17), (18), (19) respectively solve conversion square
Battle arrayWithTransition matrix in emulationEulerian angles setting value and calibration value, transition matrixEulerian angles setting value and calibration
Value is respectively as shown in table 3, table 4.
3 transition matrix of tableEulerian angles setting value and calibration value
4 transition matrix of tableEulerian angles setting value and calibration value
| Serial number | Eulerian angles | Setting value | Calibration value | Residual error |
| 1 | Course Ψ (') | 200 | 200.0002 | -0.0002 |
| 2 | Pitching η (') | -50 | -50.0006 | 0.0006 |
| 3 | Rolling γ (') | 100 | 99.9995 | 0.0005 |
The error parameter value set in emulation is compared with the error parameter value calibrated such as table 1, table 2, table 3,4 institute of table
Show, wherein the maximum calibrated error of accelerometer bias is 0.015mg, and scale factor error maximum calibrated error is 7.17ppm,
Installation error maximum calibrated error is 0.26 '；Gyro zero bias maximum calibrated error is 1E-5 °/h, and scale factor error is maximum partially
Difference is 3E-4ppm, and installation error maximum deviation is 0E-4 ', and transition matrix calibrated error is up to 0.0006 '.By simulation result
As can be seen that the mentioned method of the present invention accurately can be demarcated respectively accelerometer and gyro to p system by 18 parameters
With o system, then by inertia device simultaneously demarcate to turntable coordinate system r system, demarcation flow is simple, and the nominal time is short, and precision is higher.
Claims (4)
1. a kind of single-shaft-rotation Strapdown Inertial Navigation System scaling method based on optimizing method, which comprises the steps of:
(1) single-shaft-rotation Strapdown Inertial Navigation System is mounted on double axle table using tooling, is system electrification, indexing mechanism is returned
It zero and closes, stablizes to system temperature；
(2) system is made successively to go to 18 positions using turntable, each station acquisition accelerometer output data 1 minute；
(3) cooperate the indexing mechanism inside single-shaft-rotation Strapdown Inertial Navigation System, it is real to carry out 9 groups of positive and negative rotational speed rates using double axle table
It tests, acquisition gyro exports complete cycle data；
(4) data of step (2) and step (3) are subjected to optimizing estimation using nonlinear optimization method, obtain 18 inertia devices
The error parameter of part simultaneously compensates offline, by accelerometer and gyro by respective sensitivity coordinate system a system, g system, is demarcated respectively to orthogonal
Coordinate system p system and o system；
(5) it mounts the system on three-axle table, is system electrification, indexing mechanism is returned to zero and closed, stablize to system temperature；
(6) three axis of accelerometer are successively directed toward day, accelerometer is successively acquired under 3 positions and is exported 2 minutes, by gyro point
3 groups of positive and negative rotation rate experiments are not carried out around three axis, acquisition gyro exports complete cycle data, by accelerometer and gyro by step
(3) the orthogonal coordinate system p system demarcated and o system demarcate to three-axle table coordinate system r system, and by transition matrixWithInto
Row orthogonalization.
2. the single-shaft-rotation Strapdown Inertial Navigation System scaling method based on optimizing method as described in claim 1, which is characterized in that step
Suddenly in (3), cooperate the indexing mechanism inside single-shaft-rotation Strapdown Inertial Navigation System to realize Gyro Calibration, be to be consolidated system by tooling
It is scheduled on the position that z-axis refers to east, collectively forms 3DOF machine to the north orientation shaft of shaft and outline border with the day of double axle table inside casing
Structure guarantees to be able to carry out 3 axis gyro rate experiments in the case where indexing mechanism cooperates, to demarcate gyro.
3. the single-shaft-rotation Strapdown Inertial Navigation System scaling method based on optimizing method as described in claim 1, which is characterized in that step
Suddenly in (4), the data of step (2) and step (3) is subjected to optimizing estimation using nonlinear optimization method, obtain 18 inertia devices
The error parameter of part simultaneously compensates offline, by accelerometer and gyro by respective sensitivity coordinate system a system, g system, is demarcated respectively to orthogonal
Coordinate system p system and o system, specifically:
Using the scaling method based on non-linear optimizing, accelerometer and gyro are demarcated respectively to orthogonal coordinate system p system and o
System, obtains corresponding three axis accelerometer zero bias ▽x、▽y、▽z, three axis accelerometer constant multiplier Kax、Kay、Kaz, acceleration
Count installation error Eayx、Eazx、Eazy, three axis optical fibre gyro zero bias εx、εy、εz, three axis optical fibre gyro constant multiplier Kgx、Kgy、KgzWith
Optical fibre gyro installation error Egyx、Egzx、EgzyTotally 18 error parameters, specifically comprise the following steps:
(41) inertial device error model is established:
To guarantee that stated accuracy independent of double axle table precision, inertia device is not demarcated to double axle table coordinate system, and incite somebody to action
The output of accelerometer and gyro is respectively by a system and g system, calibration to orthogonal coordinate system p system and orthogonal coordinate system o system；
It is as follows to establish accelerometer error model:
Wherein,The projection in accelerometer sensitive coordinate system a system is exported for three axis accelerometer,The projection in orthogonal coordinate system p system is exported for three axis accelerometer,For three axis
Accelerometer bias, va=[vax vay vaz]TFor three axis accelerometer error in measurement, M is accelerometer constant multiplier and installation
Error matrix, expression formula are
Wherein, Kai(i=x, y, z) is i axis accelerometer constant multiplier, Eayx、Eazx、EazyFor accelerometer installation error；
It is as follows to establish gyroscope error model:
Wherein,The projection in gyro sensitivity coordinate system g system is exported for three axis accelerometer,Projection for three axis accelerometer output in orthogonal coordinate system o system, ε=[εx εy εz]TFor three axis accelerometer
Zero bias, vg=[vgx vgy vgz]TFor three axis accelerometer error in measurement, N is gyro constant multiplier and installation error matrix, and expression formula is
Wherein, Kgi(i=x, y, z) is i axis gyro constant multiplier, Egyx、Egzx、EgzyFor gyro misalignment；
(42) imu error parameter optimization cost function is established:
Two norms for exporting two norms and acceleration of gravity that project under orthogonal coordinate system p system according to three axis accelerometer are resonable
By upper equal, i.e.,
||fp||2=| | Gn||2 (5)
Wherein,Projection for three axis accelerometer output in p system, Gn=[0 0-g]TFor gravity acceleration
Projection of the vector under navigational coordinate system n system is spent, | | | |2For two norm signs；
By formula (1) and formula (5), establishing accelerometer error parameter optimization cost function is
Wherein,For the output of accelerometer under i-th of position,For the squared symbol of two norms；
Since earth rotation angular speed is smaller, it cannot be used directly for Gyro Calibration, therefore turntable utilized to rotate angular speed auxiliary calibration
Gyro error parameter is equal to the vector sum of earth rotation angular speed and turntable rotation angular speed according to the output of gyro angular speed, i.e.,
Wherein,The projection in o system is exported for gyro angular speed,For earth rotation angular speed o system projection,To turn
Platform rotates angular speed in the projection of o system；
(3) formula is substituted into (1) formula and the time is integrated, turntable rotates forward complete cycle, it can obtain,
WhereinThe output of complete cycle gyro angular speed is rotated forward for turntable to project in o system,Complete cycle gyro angular speed is rotated forward for turntable
Output is projected in g system, t1The time used in complete cycle is rotated forward for turntable；
Turntable inverts complete cycle, can obtain,
WhereinThe output of complete cycle gyro angular speed is inverted for turntable to project in o system,Complete cycle gyro angular speed is inverted for turntable
Output is projected in g system, t2The time used in complete cycle is inverted for turntable；
Formula (8)-formula (9), and keep the complete cycle week number of turntable forward and reverse identical, so that t=t1=t2, it obtains,
The wherein angle that θ is rotated by turntable positive and negative rotation complete cycle；
Gyro constant multiplier is established by formula (10) and the optimizing cost function of installation error matrix N is
Wherein,Gyro angular speed output in rate experiments is rotated forward for jth group,It is
J group inverts gyro angular speed output in rate experiments；
It is finally tested according to position, establishing gyro zero bias optimizing cost function is
Wherein,For gyro angular speed output in i-th group of position experiment；
(43) optimizing estimation is carried out using nonlinear optimization method:
Non-linear least square optimization problem is constructed for objective function, and assigns initial value with formula (6), (11), (12), is enabled
Wherein M0For accelerometer constant multiplier and installation error matrix initial value,For accelerometer bias initial value, N0For gyro
Constant multiplier and installation error matrix initial value, ε0For gyro zero bias initial value；
By the position of step (2) and step (3) and rate experiments accelerometer collected and gyro data substitute into formula (6),
(11), (12) carry out optimizing iteration, estimate 18 error parameters, accelerometer and gyro are demarcated respectively to p system and o system.
4. the single-shaft-rotation Strapdown Inertial Navigation System scaling method based on optimizing method as described in claim 1, which is characterized in that step
Suddenly in (6), three axis of accelerometer are successively directed toward day, accelerometer is successively acquired under 3 positions and is exported 2 minutes, by gyro
3 groups of positive and negative rotation rate experiments are carried out rotating around three axis, acquisition gyro exports complete cycle data, by accelerometer and gyro by step
(3) the orthogonal coordinate system p system demarcated and o system demarcate to three-axle table coordinate system r system, and by transition matrixWithInto
Row orthogonalization specifically comprises the following steps:
(61) position and rate experiments data acquire
Strapdown Inertial Navigation System is installed to three-axle table, turntable seeks zero, and system electrification sets turntable after system the operation is stable
Three axis of x, y, z of system is enabled successively to be directed toward day, each accelerometer that acquires exports 2 minutes, and calculates and table is added to export mean value, and setting turns
Platform enables system be directed toward day around three axis of x, y, z and carries out positive and negative rotation rate experiments respectively with the rate of 10 °/s, each to acquire gyro output
Complete cycle data；
(62) transition matrix is calculated
According to accelerometer turntable coordinate system r system and orthogonal coordinate system p system transformational relation:
WhereinThe projection under turntable coordinate system r system is exported for accelerometer,
The projection in p system is exported for accelerometer,For p system to the transition matrix of r system；
(61) position experimental data is substituted into formula (13):
Wherein g is terrestrial gravitation acceleration,I axis accelerometer exports 2 minutes when being directed toward day for j axis
The average value of data is demarcated accelerometer to three-axle table by the orthogonal coordinate system p system that step (3) is demarcated using formula (14)
Coordinate system r system；
(63) transition matrix is calculated
According to gyro turntable coordinate system r system and orthogonal coordinate system o system transformational relation:
When gyro x-axis is directed toward day progress forward direction rate experiments, expansion (13):
Wherein,For projection of the i axis gyro output in rhombic system o system, C in x-axis forward direction rate experimentsij(i=
It 1,2,3, j=1,2,3) is transition matrixThe i-th row jth column element, ωrFor turntable shaft turning rate, ωieFor ground
Revolutions angular speed, L are latitude where calibration ground, and φ (t) is that turntable shaft rotates angle；
By the data summation of turntable rotation complete cycle, formula (14) is
Wherein A is that turntable rotates record data amount check in complete cycle, and gyro x-axis is directed toward day and carries out reverse rate experiment and revolve turntable
The data summation for turning complete cycle has:
Wherein,For projection of the i axis gyro output in rhombic system o system, formula in the experiment of x-axis reverse rate
(15)-(16), have
Similarly, gyro y-axis, z-axis are directed toward day and carry out positive and negative rate experiments, have
Wherein,It is respectively negative around y-axis forward direction, y-axis negative sense, z-axis forward direction, z-axis
Projection of the i axis gyro output in rhombic system o system into rate experiments；
Transition matrix is calculated according to formula (17), (18), (19)Its transposed matrixGyro is demarcated just by step (3)
Hand over the calibration of coordinate system o system to three-axle table coordinate system r system.
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