CN110146111A - A kind of Initial Alignment Method of centering rod - Google Patents
A kind of Initial Alignment Method of centering rod Download PDFInfo
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- CN110146111A CN110146111A CN201910475763.4A CN201910475763A CN110146111A CN 110146111 A CN110146111 A CN 110146111A CN 201910475763 A CN201910475763 A CN 201910475763A CN 110146111 A CN110146111 A CN 110146111A
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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 Initial Alignment Methods of centering rod, comprising the following steps: 1) obtains GNSS and MIMU inertial navigation real time data, and carry out posture renewal, definition resolves required reference frame；2) method for utilizing geometrical constraint obtains different observation points according to GNSS, establishes measurement equation group；3) it according to equation group, solves and calculates azimuthal misalignment angle；4) MIMU inertial navigation orientation is corrected using azimuthal misalignment angle, realizes the initial alignment of centering rod.In the present invention, by the position of three measurement points, the high-precision that centering rod can be realized initially is aligned, and method is simple, easy to operate.
Description
Technical field
The invention belongs to field of measuring technique, and in particular to a kind of Initial Alignment Method of centering rod.
Background technique
In engineering measuring technologies fields such as construction lofting, topography mapping and photogrammetric laying photo control points, it is widely used
Real time dynamic differential method measures (Real Time Kinematic, RTK) method.RTK is a kind of current common satellite navigation
(Global Navigation Satellite System, GNSS) measurement method uses carrier phase dynamic real-time difference
Method can obtain the positioning accuracy of Centimeter Level in real time, greatly improve measurement operating efficiency.GNSS receiver measurement is to put
It sets in the position of the antenna phase center on centering rod top, and actually survey and draw needs is usually position sharp under centering rod, is passed
The level(l)ing bubble that system operation mode needs to adjust on centering rod is placed in the middle, and operating efficiency is low, is difficult to reality under the environment such as corner, pipeline
The inclination measurement of existing centering rod.
Using inclination measurement technology without keeping centering rod vertical, realizes " stop and adopt, adopt and walk ", can be improved work
Industry speed, while solving centering rod and cannot arrive the measurement of the particular points such as corner, precipice side.There are two main classes for inclination measurement technology: one
It is to be established by means of micro inertial measurement unit (Miniature Inertial Measurement Unit, MIMU) or magnetic compass
Transformational relation between centering rod body coordinate system and geographic coordinate system, automatic compensated tilt error；Second is that " shaking " tilts
Measurement method is measured multiple points in space by shaking centering rod, space is carried out using centering pole length as constraint condition and is crossed
Calculate the position of measurement point.Above-mentioned two classes method all haves the defects that certain.Slope compensation is carried out using MIMU, works as centering rod
When inclination angle is larger, position compensation precision is primarily limited to the alignment of orientation precision of MIMU inertial navigation；And " one is shaken using centering rod
Shake " method, measurement requires repeatedly to rock every time, and measurement efficiency is not high.
Summary of the invention
The purpose of the present invention is to provide a kind of Initial Alignment Methods of centering rod, utilize the high-precision side of MIMU inertial navigation
Position Initial Alignment Method, need to only keep under centering rod point motionless, GNSS antenna is successively tilted to three Angle Positions, can be realized pair
Standard is compared with " at a distance from hand-held one section of 10m of GNSS receiver walking or so ", only need to be in spatial rotational without movement.The present invention
In initial alignment process, without a wide range of movement, take up space small.
In order to realize that above-mentioned technical effect, the present invention are achieved by following technological means.
A kind of Initial Alignment Method of centering rod, comprising the following steps:
1) GNSS and MIMU inertial navigation real time data is obtained, and carries out posture renewal, definition resolves required reference coordinate
System；
2) method for utilizing geometrical constraint obtains different observation points according to GNSS, establishes measurement equation group；
3) it according to equation group, solves and calculates azimuthal misalignment angle；
4) azimuthal misalignment angle is utilized, MIMU inertial navigation orientation is corrected, realizes the initial alignment of centering rod.
As a further improvement of the present invention, the reference frame needed for definition resolves in the step 1) specifically:
B- carrier coordinate system indicates three axis orthogonal coordinate system of inertial navigation MIMU system, wherein X-axis, y-axis and z-axis difference
It is directed toward " on the right side-preceding-" of carrier；
N- navigational coordinate system indicates the geographic coordinate system of carrier position, thirdly axis is respectively directed to local east orientation, north orientation
With day to；
Cusp P under P- centering rod0With the three-dimensional coordinate of ground face contact；
If GNSS antenna is placed at the top of centering rod, centering rod bottom is with ground contact pointsObtain centering rod upper end
GNSS receiving antenna phase center point PiIdeal three-dimensional coordinateThen Formula of Coordinate System Transformation are as follows:
Wherein,For the ideal pose battle array of MIMU inertial navigation output；lbIt is GNSS antenna center relative to centering rod bottom
Ideal lever arm vector.
It as a further improvement of the present invention, further include the foundation of three-dimensional coordinate error model, specifically: by MIMU inertial navigation
Posture battle array error and lever arm vector error be added formula (1) in, obtain formula (2), it may be assumed that
Wherein,For the posture battle array of inertial reference calculation output, nominal lever arm vectorInertial navigation MIMU misalignment angle error φi=
[φi,E φi,N φi,U]T, lever arm error is
By increase posture battle array error and lever arm vector error establish GNSS coordinate measure with inertial navigation azimuthal error and
Relationship between lever arm error provides mathematical model for MIMU inertial alignment.
It as a further improvement of the present invention, further include the processing of above-mentioned formula (2), specially by formula (2) by neglecting
Slightly second order obtains formula (3) after handling in a small amount, it may be assumed that
Wherein,For projection of the lever arm under navigational coordinate system.
It in order to linearize and facilitate processing, in the technical program, is handled in a small amount using by ignoring second order, so that entire fortune
Calculate more convenient calculating.
As a further improvement of the present invention, the method that the step 2) utilizes geometrical constraint obtains different according to GNSS
Observation point establishes measurement equation group, specifically: it keeps centering rod bottom to fix, rotates centering rod, be at three different positions
The point set, is denoted as P respectively1 n、And P3 n, any two point is taken, is denoted as P respectivelyi nWithIt is poor that they are madeWith reference to
Formula (3) can obtain
It is abbreviated as formula (5):
Wherein,It measures, indicate GNSS output and is used to construct
Lead the deviation of MIMU output inclined twice measurement between difference；
The difference between the measurement twice of inertial navigation posture battle array；
MIMU inertial navigation is after accelerometer levels, generally horizontal misalignment φi,EAnd φi,NAll than orientation misalignment φi,U
It is small, if ignoring φi,EAnd φi,N, then formula (5) can be approximately
Or
Wherein, rememberφi U=[0 0 φi,U]T,
By centering rod rotate in three point P1 n、And P3 nIt substitutes into formula (7) respectively, constructs two measurement equations simultaneously
Equation group is formed, as follows:
It is abbreviated as
Z=HX (9).
By establishing above-mentioned equation group, so that operation becomes simply, and facilitate calculating.
As a further improvement of the present invention, the step 3) solves according to equation group and calculates azimuthal misalignment angle specifically:
Pass through three point P1 n、WithIt can be in the hope of the unknown number X in formula (9), i.e.,
X=H-1Z (10)
Azimuthal misalignment angle φ different three times is calculatedi,U。
As a further improvement of the present invention, the step 4) utilizes azimuthal misalignment angle, corrects MIMU inertial navigation orientation, realizes
The initial alignment of centering rod specifically:
Pass through azimuthal misalignment angle φ different three timesi,UThe azimuthal misalignment angle φ of middle third time3,UCorrect attitude matrix
Realize the initial alignment of centering rod.
As a further improvement of the present invention, in the step 2), the centering rod slewing area is 10 ° -45 °.
In practical operation, rotational angle is usually no more than 60 °, and mainly rotational angle degree is bigger, and GNSS antenna receives star
Measurement error is bigger, is unfavorable for calculating；The degree of rotational angle is smaller, and Geometric Constrained Structure is bad, and it is big to calculate error.
Beneficial effects of the present invention are as follows:
RTK, which is carried out, using MIMU inertial navigation assisted GNSS measures operation, it can behind the azimuth by correctly solving inertial navigation
The error generated when effective compensation centering rod inclination, obtains the point horizontal coordinate and elevation for meeting precision, but with the proviso that
MIMU inertial navigation need to correctly be initialized, the attitude accuracy of MIMU inertial navigation especially bearing accuracy determines that centering rod inclination misses
The effect of difference compensation.The present invention gives the algorithms that line-of-sight course solves initial azimuth, real after the orientation initialization algorithm
Survey the result shows that, even if the inclination angle of centering rod has reached nearly 40 ° during test, the horizontal positioning accuracy of RTK measurement is excellent
In 1.25cm.
During entire test of the invention, between 10~40 °, 20 differences are inclined for the variation of centering rod inclined angle alpha
The P calculated under rake angle0Point three-dimensional localization error, at this point, measuring again after rolling stabilizing, being in tilt angle motion process cannot
Measurement.In position error statistics, horizon location errorWithRespectively less than 1.25cm, and altitude location errorIt is small
In 0.56cm.
Detailed description of the invention
Fig. 1 is the centering rod displacement structure schematic diagram in embodiment 1 provided by the invention；
Fig. 2 is φ in embodiment 1 provided by the inventionUSchematic diagram；
Fig. 3 is centering rod tilt angle varied figure provided by the invention.
Specific embodiment
In order to be easy to understand the technical means, the creative features, the aims and the efficiencies achieved by the present invention, tie below
Specific embodiment is closed, the present invention is further explained.
A kind of Initial Alignment Method of centering rod provided by the invention, comprising the following steps:
1) GNSS and MIMU inertial navigation real time data is obtained, and carries out posture renewal, definition resolves required reference coordinate
System；
2) method for utilizing geometrical constraint obtains different observation points according to GNSS, establishes measurement equation group；
3) it according to equation group, solves and calculates azimuthal misalignment angle；
4) azimuthal misalignment angle is utilized, MIMU inertial navigation orientation is corrected, realizes the initial alignment of centering rod.
As a further improvement of the present invention, the reference frame needed for definition resolves in the step 1) specifically:
B- carrier coordinate system indicates three axis orthogonal coordinate system of inertial navigation MIMU system, wherein X-axis, y-axis and z-axis difference
It is directed toward " on the right side-preceding-" of carrier；
N- navigational coordinate system indicates the geographic coordinate system of carrier position, thirdly axis is respectively directed to local east orientation, north orientation
With day to；
Cusp P under P- centering rod0With the three-dimensional coordinate of ground face contact；
If GNSS is placed at the top of centering rod, centering rod bottom is with ground contact pointsCentering rod upper end GNSS is obtained to connect
Receive antenna phase center point PiIdeal three-dimensional coordinateThen Formula of Coordinate System Transformation are as follows:
Wherein,For the ideal pose battle array of MIMU inertial navigation output；lbIt is GNSS receiving antenna center relative to centering rod bottom
The ideal lever arm vector in portion.
Further, further include the foundation of three-dimensional coordinate error model, specifically: by the posture battle array error of MIMU inertial navigation and
Lever arm vector error is added in formula (1), obtains formula (2), it may be assumed that
Wherein,For the posture battle array of inertial reference calculation output, nominal lever arm vectorInertial navigation MIMU misalignment angle error φi=
[φi,E φi,N φi,U]T, lever arm error is
It as a further improvement of the present invention, further include the processing of above-mentioned formula (2), specially by formula (2) by neglecting
Slightly second order obtains formula (3) after handling in a small amount, it may be assumed that
Wherein,For projection of the lever arm under navigational coordinate system.
It in order to linearize and facilitate processing, in the technical program, is handled in a small amount using by second order, so that entire operation is more
Add and facilitates calculating.
As a further improvement of the present invention, the method that the step 2) utilizes geometrical constraint obtains different according to GNSS
Observation point establishes measurement equation group, specifically: it keeps centering rod bottom to fix, rotates centering rod, be at three different positions
The point set, is denoted as P respectively1 n、And P3 n, any two point is taken, is denoted as P respectivelyi nWithIt is poor that they are madeWith reference to
Formula (3) can obtain
It is abbreviated as formula (5):
Wherein,It measures, indicate GNSS output and is used to construct
Lead the deviation of MIMU output inclined twice measurement between difference；It is poor between measurement twice for inertial navigation posture battle array
Point；
MIMU inertial navigation is after accelerometer levels, generally horizontal misalignment φi,EAnd φi,NAll than orientation misalignment φi,U
It is small, if ignoring φi,EAnd φi,N, then formula (5) can be approximately
Or
Wherein, rememberφi U=[0 0 φi,U]T,
By centering rod rotate in three point P1 n、And P3 nIt substitutes into formula (7) respectively, constructs two measurement equations simultaneously
Equation group is formed, as follows:
It is abbreviated as
Z=HX (9).
By establishing above-mentioned equation group, so that operation becomes simply, and facilitate calculating.
As a further improvement of the present invention, the step 3) solves according to equation group and calculates azimuthal misalignment angle specifically:
Pass through three point P1 n、And P3 nIt can be in the hope of the unknown number X in formula (9), i.e.,
X=H-1Z (10)
Azimuthal misalignment angle φ different three times is calculatedi,U。
As a further improvement of the present invention, in the step 2), the centering rod slewing area is 10 ° -45 °.
When rotational angle is less than 10 °, Geometric Constrained Structure is bad, and it is big to calculate error；When rotational angle is greater than 45 °,
GNSS antenna receipts star measurement error is bigger, is unfavorable for calculating.
In the present invention, azimuthal misalignment angle is calculated by calculating, is then modified, just realizes the initial side of centering rod
Position alignment, specifically, the present invention are mainly using the calculation method of " inertial navigation+Satellite observation point geometry constrains ", quickly just
The azimuth of beginningization inertial navigation, using MIMU carry out slope compensation, when centering rod inclination angle is larger, position compensation precision mainly by
It is limited to the alignment of orientation precision of MIMU inertial navigation, the present invention mainly discusses the high Precision Initial Alignment Method of MIMU inertial navigation, should
Method need to only keep sharp motionless under centering rod, and GNSS antenna is successively tilted to three Angle Positions, alignment can be realized.
Embodiment 1
Referring to shown in attached drawing 1-3, the Initial Alignment Method in the present embodiment is divided into two large divisions.
First part, high Precision Alignment Algorithm
As shown in Figure 1, MIMU is connected in the top of centering rod together with GNSS receiver.MIMU body coordinate system is abbreviated as
B system.Cusp is denoted as P under centering rod0, GNSS antenna phase center is denoted as Pi(i=1,2,3 ...),It is in the projection that b is fastened
Constant value is denoted as lever arm vectorGNSS output is usually the high geographical coordinate of longitude and latitude, is not difficult to be converted into
Locality station heart rectangular co-ordinate, such as with P1Select " east-north-day " rectangular co-ordinate (unit rice) for origin, behind be abbreviated the coordinate
System is n system.
When centering rod is placed on the ground in certain obliquity PiWhen, it is assumed that cusp P under centering rod0With ground face contact
Three-dimensional coordinate isAssuming that when error free, centering rod upper end GPS receiving antenna phase center point PiIdeal three-dimensional coordinate beInertial navigation output ideal pose battle array beAccording to geometrical relationship, then there is following coordinate conversion public
Formula is set up
In practical application, the posture battle array of inertial reference calculation output has error, is directly exported, is denoted as by MIMU inertial navigationLever arm nominal value also has error, is denoted asAfter the foundation processing that formula (1) passes through three-dimensional coordinate error model, become
Wherein, φi=[φi,E φi,N φi,U]TFor inertial navigation misalignment angle error,For lever arm mistake
Difference.
Formula (2) are unfolded and omit a small amount of about the second order of error, can be obtained
Wherein,For projection of the nominal lever arm under inertial navigation navigation system.
It keeps point under centering rod motionless with ground contact points, carries out inclined twice measurement, be denoted as P respectivelyi nWithBy it
Make differenceIt can be obtained with reference to formula (3)
It is abbreviated as
Wherein,It is measured for construction, indicates GPS output and inertial navigation
Difference between the inclined twice measurement of the deviation of output；The difference between the measurement twice of inertial navigation posture battle array.
Inertial navigation is after accelerometer levels, generally horizontal misalignment φi,EAnd φi,NAll than orientation misalignment φi,USmall
It is more, if ignoring φi,EAnd φi,N, then formula (5) can be approximately
Or
Wherein, rememberφi U=[0 0 φi,U]T,
Formula (7) unknown errors parameter containing there are five, can not pass through a measurement equation solution.If being measured three times,
It is denoted as P respectively1 n、And P3 n, then two measurement equations and composition equation group can be constructed according to formula (7), it is as follows
It is abbreviated as
Z=HX (9)
When point is motionless under centering rod and tilts a certain fixed angle (such as with plumb line angle be 30 °), space fortune
Dynamic rail mark forms a conical surface, three measurement points is uniformly chosen on the conical surface, the calculation matrix H constituted with this is reversible, at this moment
Unknown parameter X can directly be acquired by formula (9), i.e.,
X=H-1Z (10)
If azimuthal misalignment angle φi,UIt is not low-angle, then also can solves correctly by the modified method of successive ignition
The azimuth initialization under Large azimuth angle is realized at azimuth.
Particularly, it is assumed that the z-axis of MIMU is parallel to centering rod installation, and at this moment only along telescopic direction, there are lever arm mistakes for centering rod
Difference, i.e.,Assume again that time of measuring is shorter, i.e. azimuthal misalignment angle φ caused by gyroscopic drifti,UVariation
Less, constant value φ can be regarded asU.Measurement equation then can be obtained by measurement twice
Wherein,Representing matrixThe 3rd column vector.The least square solution of formula (11) is
Further, if lever arm vector lbIt is accurately known, i.e. δ lb=0, then formula (11) is reduced to
The least square solution at azimuthal misalignment angle is
As enabledThe measured value of the nominal lever arm vector sum GNSS of calculating of 1 position is all set to zero, then formula
(13) it can also be written as
Wherein,φU=[0 0 φU]T.The geometry of formula (15) is anticipated
Justice is: two horizontal vectorsAnd P2 HBetween angle be φU, referring to fig. 2, this is in φUFor be also when wide-angle set up.
Second part error analysis
2.1 analysis of Positioning Error
By GPS measurement Pi nWith inertial navigation lever arm calculated valueSolve point position P under centering rod0 nPractical methods be
However, theoretically being had according to formula (3)
Comparison expression (16) and formula (17), it is known thatMeasurement error be
If only considering, azimuthal misalignment angle influences,Indicate the projection of lever arm in the horizontal planeWith φi UFork
Multiply, size isWherein α is the angle of centering rod and plumb line；Size be lever arm miss
The modulus value of differenceSo position error can be estimated as
Formula (19) shows that alignment of orientation error and centering rod nominal length error can all cause the survey calculation of lower cusp
It influences, practical application centering lever arm vector should mark effect accurately, generally can reach a millimeter class precision, and Centimeter Level is surveyed and drawn and is required
For, error, which can usually be ignored, not to be remembered.Therefore, alignment of orientation precision is extremely important in MIMU inertial navigation slope compensation scheme.
2.2 alignment of orientation error analyses
Lever arm error is not considered, the formula of two obliquity computer azimuth misalignments according to formula (14), then:
Note thatComprising GNSS positioning measurement twice, thus GNSS positions noise error
Influence directly will cause on alignment of orientation, according to Least Square Theory,Variance be
Wherein, 2 σ2To measureError, σ2For the east orientation or north orientation error (variance) of the positioning of GNSS single；Referred to as horizontal accuracy dilution gfactor (Horizontal Dilution Of Precision, HDOP), due toWhenWithWhen about plumb line, symmetrical and inclination angle is bigger, HDOP value is smaller, and alignment of orientation precision is higher.
Obviously, whenWithWhen about plumb line, symmetrical and inclination angle is α, haveAt this moment alignment of orientation side
Difference is
For example, when σ=1cm, l=2m and α=40 °, the standard deviation for being computed alignment of orientation is
Part III verification experimental verification
Pilot system mainly include carrier phase difference GNSS, MIMU inertial navigation system, centering rod, data acquisition notebook and
Battery.The base station GNSS is placed on the ground fixed, and the mobile station antenna of GNSS and MIMU inertial navigation are fixedly mounted on centering rod
Top；GNSS mobile station receiver frequency acquisition 5Hz, horizontal location static accuracy are 0.7cm (1 σ)；MIMU data acquiring frequency
100Hz, gyroscope bias instaility are about 30 °/h, and accelerometer bias repeatability is about 2mg；Centering rod top GNSS antenna
Phase center is apart from lower point 1.897m；Notebook synchronous acquisition GNSS positioning and MIMU inertial sensor data, do ex-post analysis,
Steps are as follows:
(1) it is leveled by MIMU output using Mahony algorithm, referring to Fig. 3, in three obliquity P of centering rod1、P2
And P3Acquire posture battle array in placeWithAzimuth might as well be both configured to 0；
(2) it iteratively solved and is corrected according to formula (10), obtain initial attitude battle array
It (3) is to measure the inertial navigation/GNSS integrated navigation model for establishing 15 dimensions with location error, from obliquity P3Start into
Row combination Kalman filter；
(4) it keeps sharp motionless under centering rod, centering rod is tilted into different angle in different directions, it is steady in inclination every time
Shi Jinhang GNSS positioning measurement calculates P at lower point using formula (16)0Locator value.
During entire test, as shown on the solid line in figure 3, inclined angle alpha becomes centering rod tilt angle varied between 0~40 °
Change, the discrete point from 170s to 450s is the P calculated under 20 differing tilt angles0Point three-dimensional localization error.Position error system
It counts as listed in table 1, as the result is shown: horizon location errorWithRespectively less than 1.25cm, and altitude location errorFor
0.56cm。
1 position error of table counts (cm)
It can be seen from Table 1 that horizon location errorWithRespectively less than 1.25cm, and altitude location error
Less than 0.56cm.
I.e. in the present invention, RTK is carried out using MIMU inertial navigation assisted GNSS and measures operation, centering rod can be effectively compensated and incline
The error generated when tiltedly obtains the position coordinate and elevation for meeting precision, but with the proviso that need to carry out to MIMU inertial navigation correct first
Beginningization, the attitude accuracy of MIMU inertial navigation especially bearing accuracy determine the effect of centering rod heeling error compensation.
The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention.The technology of the industry
Personnel are it should be appreciated that the present invention is not limited to the above embodiments, and the above embodiments and description only describe this
The principle of invention, without departing from the spirit and scope of the present invention, various changes and improvements may be made to the invention, these changes
Change and improvement all fall within the protetion scope of the claimed invention.The claimed scope of the invention by appended claims and its
Equivalent thereof.
Claims (8)
1. a kind of Initial Alignment Method of centering rod, which comprises the following steps:
1) GNSS and MIMU inertial navigation real time data is obtained, and carries out posture renewal, definition resolves required reference frame；
2) method for utilizing geometrical constraint obtains different observation points according to GNSS, establishes measurement equation group；
3) it according to equation group, solves and calculates azimuthal misalignment angle；
4) azimuthal misalignment angle is utilized, MIMU inertial navigation orientation is corrected, realizes the initial alignment of centering rod.
2. a kind of Initial Alignment Method of centering rod according to claim 1, which is characterized in that definition in the step 1)
Reference frame needed for resolving specifically:
B- carrier coordinate system indicates three axis orthogonal coordinate system of inertial navigation MIMU system, and wherein X-axis, y-axis and z-axis are respectively directed to
Carrier " right-preceding-on "；
N- navigational coordinate system indicates the geographic coordinate system of carrier position, thirdly axis is respectively directed to local east orientation, north orientation and day
To；
Cusp P under P- centering rod0With the three-dimensional coordinate of ground face contact；
If GNSS is placed at the top of centering rod, centering rod bottom is with ground contact pointsIt obtains centering rod upper end GNSS and receives day
Phase of line central point PiIdeal three-dimensional coordinateThen Formula of Coordinate System Transformation are as follows:
Wherein,For the ideal pose battle array of MIMU inertial navigation output；lbIdeal for GNSS antenna center relative to centering rod bottom
Lever arm vector.
3. a kind of Initial Alignment Method of centering rod according to claim 2, which is characterized in that further include that three-dimensional coordinate misses
The foundation of differential mode type, specifically: the posture battle array error of MIMU inertial navigation and lever arm vector error are added in formula (1), obtained
Formula (2), it may be assumed that
Wherein,For the posture battle array of inertial reference calculation output, nominal lever arm vectorInertial navigation MIMU misalignment angle error φi=[φi,E
φi,N φi,U]T, lever arm error is
4. a kind of Initial Alignment Method of centering rod according to claim 3, which is characterized in that further include above-mentioned formula
(2) processing obtains formula (3) after specially handling formula (2) by ignoring second order in a small amount, it may be assumed that
Wherein,For projection of the lever arm under navigational coordinate system.
5. a kind of Initial Alignment Method of centering rod according to claim 4, which is characterized in that the step 2) utilizes several
The method of what constraint obtains different observation points according to GNSS, establishes measurement equation group, specifically: keep centering rod bottom to fix,
Centering rod is rotated, the point of three different locations is at, is denoted as P respectively1 n、And P3 n, any two point is taken, is denoted as respectively
Pi nWithIt is poor that they are madeIt can be obtained with reference to formula (3)
It is abbreviated as formula (5):
Wherein,It is measured for construction, indicates GNSS output and inertial navigation
Difference between the inclined twice measurement of the deviation of MIMU output；It is poor between measurement twice for inertial navigation posture battle array
Point；
MIMU inertial navigation is after accelerometer levels, generally horizontal misalignment φi,EAnd φi,NAll than orientation misalignment φi,UIt is small,
If ignoring φi,EAnd φi,N, then formula (5) can be approximately
Or
Wherein, rememberφi U=[0 0 φi,U]T,
By centering rod rotate in three point P1 n、And P3 nIt substitutes into formula (7) respectively, constructs two measurement equations and composition
Equation group is as follows:
It is abbreviated as
Z=HX (9).
6. a kind of Initial Alignment Method of centering rod according to claim 5, which is characterized in that the step 3) is according to side
Journey group solves and calculates azimuthal misalignment angle specifically:
Pass through three point P1 n、And P3 nIt can be in the hope of the unknown number X in formula (9), i.e.,
X=H-1Z (10)
Azimuthal misalignment angle φ different three times is calculatedi,U。
7. a kind of Initial Alignment Method of centering rod according to claim 6, which is characterized in that the step 4) utilization side
Position misalignment, corrects MIMU inertial navigation orientation, realizes the initial alignment of centering rod specifically:
Pass through azimuthal misalignment angle φ different three timesi,UThe azimuthal misalignment angle φ of middle third time3,UCorrect attitude matrixIt realizes
The initial alignment of centering rod.
8. a kind of Initial Alignment Method of centering rod according to claim 5, which is characterized in that in the step 2), institute
Stating centering rod slewing area is 10 ° -45 °.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110763229A (en) * | 2019-11-12 | 2020-02-07 | 武汉大学 | Portable inertial navigation positioning rod and positioning and attitude determining method thereof |
| CN112325846A (en) * | 2020-10-21 | 2021-02-05 | 北京航空航天大学 | RTK tilt measurement precision improving method |
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| CN110763229B (en) * | 2019-11-12 | 2022-04-15 | 武汉大学 | Portable inertial navigation positioning rod and positioning and attitude determining method thereof |
| CN114199115A (en) * | 2020-09-18 | 2022-03-18 | 千寻位置网络有限公司 | Centering rod length calibration method, RTK receiver system inclination measurement method and RTK receiver system inclination measurement system |
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| CN112325846A (en) * | 2020-10-21 | 2021-02-05 | 北京航空航天大学 | RTK tilt measurement precision improving method |
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