CN107270938A - Single-shaft-rotation inertial navigation system posture demodulation method based on Taylor series fitting - Google Patents
Single-shaft-rotation inertial navigation system posture demodulation method based on Taylor series fitting Download PDFInfo
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- CN107270938A CN107270938A CN201710441867.4A CN201710441867A CN107270938A CN 107270938 A CN107270938 A CN 107270938A CN 201710441867 A CN201710441867 A CN 201710441867A CN 107270938 A CN107270938 A CN 107270938A
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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 present invention relates to a kind of single-shaft-rotation inertial navigation system posture demodulation method based on Taylor series fitting, optimal two-position alignment is realized using indexing mechanism, accurate attitude of carrier and course information is obtained, while estimation and compensation gyroscopic drift；Indexing mechanism is positive and negative turns around for control in calibration process, calculates and stores measurement corner, equivalent indexable angular speed, equivalent Index angle rate of acceleration and misalignment angle information；Misalignment angle error is modeled using higher order Taylor series expansion polynomial fitting method；After demarcation terminates, misalignment angle error is compensated using fitting coefficient, posture demodulation is completed.The inventive method need not introduce extra equipment, and misalignment angle error is compensated by Mathematical Fitting method, and posture demodulation accuracy is high, and engineering practicability is strong.
Description
Technical field
The invention belongs to technical field of inertial, it is related to a kind of single-shaft-rotation inertial navigation system based on Taylor series fitting
Posture demodulation method.
Background technology
Single-shaft-rotation modulation is a kind of error auto compensatng technology of inertial navigation system, passes through the rotating process around azimuth axis
Modulation gyro and accelerometer become error slowly, to ensure the long-time navigation accuracy of inertial navigation system.But the introducing of indexing mechanism
Inertial Measurement Unit (IMU) is set to be rotated relative to carrier, it is impossible to directly obtain the posture and course information of carrier, it is necessary to be adjusted
System demodulation, and rotating shaft error and angle error are to influence the principal element of posture demodulation accuracy.
Document " study, Chinese journal of scientific instrument, 2014, Vol35 by single-shaft-rotation inertial navigation rotor shaft direction high-precision calibrating method
(12), p111-115 " discloses a kind of scaling method of single-shaft-rotation inertial navigation system rotor shaft direction error.Method analyzes orientation
Misalignment error model between rotary shaft and IMU measurement axles, on the premise of attitude of carrier is static, by exporting number to gyro
Handled according to rotating shaft angular encoder measured value, the demarcation and compensation of rotating shaft error angle can be realized.But this method is omitted
Initial alignment process, the stated accuracy of rotor shaft direction is by earth rotation component and gyro zero is inclined is influenceed；And method is by misalignment
Angle is considered as constant value, do not account for that rotating shaft between angle measurement encoder and rotary shaft is eccentric, install tilt and bearing clearance etc. because
The influence of element, posture demodulation accuracy is not high in systems in practice.
The content of the invention
The technical problem to be solved
In order to avoid the shortcomings of the prior art, the present invention proposes that a kind of single-shaft-rotation based on Taylor series fitting is used to
Guiding systems posture demodulation method, overcomes the shortcomings of that existing posture demodulation method precision is low.
Technical scheme
A kind of single-shaft-rotation inertial navigation system posture demodulation method based on Taylor series fitting, it is characterised in that step is such as
Under：
Step 1：Inertial navigation system is obtained after initial position, optimal two-position alignment is carried out using indexing mechanism, wherein first
Position angle position is 180 °, and second place angle position is 0 °；Carrier is obtained using classical kalman filter method accurate
Initial attitude and course information are simultaneously estimated gyroscopic drift and compensated；
Step 2：After two-position alignment terminates, keep inertial navigation system it is static, control indexing mechanism with 6 °/s around azimuth axis just
Invert in each circle, rotation process using traditional quaternion calculation method progress posture renewal, calculate and store：Measurement corner α,
Equivalent Rotational angular speedEquivalent Rotational angle rate of accelerationWith misalignment angle error φb；
Step 3：Umklapp process is aligned respectively using higher order Taylor series expansion fitting misalignment φbWith α,Between function close
System, obtains coefficient of polynomial fitting and preserves；
The functional relation is：
φ in formulaiRepresent the x in the case of rotating, y, z-axis misalignment component, m and n represent respectively α andFitting rank
Number, pi,kAnd ci,jFor corresponding fitting coefficient；
Step 4：By fitting coefficient pi,kAnd ci,jStore to navigational computer, in navigation stage according to fitting coefficient, indexing
Angle [alpha] and Index angle rate of accelerationBy functional relation：
Compensation misalignment is calculated, posture demodulation is completed in real time and is calculated.
Beneficial effect
A kind of single-shaft-rotation inertial navigation system posture demodulation method based on Taylor series fitting proposed by the present invention, using turn
Position mechanism realizes optimal two-position alignment, obtains accurate attitude of carrier and course information, while estimation and compensation gyroscopic drift；
Indexing mechanism is positive and negative turns around for control in calibration process, calculates and stores measurement corner, equivalent indexable angular speed, equivalent Index angle
Rate of acceleration and misalignment angle information；Misalignment angle error is modeled using higher order Taylor series expansion polynomial fitting method；Demarcation
After end, misalignment angle error is compensated using fitting coefficient, posture demodulation is completed.The inventive method need not be introduced additionally
Equipment, misalignment angle error is compensated by Mathematical Fitting method, posture demodulation accuracy is high, engineering practicability is strong.
The present invention has considered the rotating shaft bias of influence posture demodulation result, has installed the factors such as inclination and bearing clearance,
Accurate Model is carried out to misalignment angle error using higher order Taylor series expansion, it is not necessary to which auxiliary equipment can complete error calibration, engineering
It is practical.Method can effectively improve the posture demodulation accuracy of single-shaft-rotation modulation inertial navigation system, the angle of pitch, roll angle and boat
[0.5 can be reached to angle demodulation result；0.9；1.8] " (1 σ), 230 times, 140 times and 22 times have been respectively increased before relatively compensating.
Brief description of the drawings
Fig. 1 is the flow chart that inertial navigation system posture demodulation method is modulated in single shaft rotating of the present invention.
Fig. 2 is the misalignment change curve in calibration process of the embodiment of the present invention.
Fig. 3 is uncompensated attitude error curve in verification process of the embodiment of the present invention.
Fig. 4 is the posture demodulating error curve after compensating in verification process of the embodiment of the present invention.
Embodiment
In conjunction with embodiment, accompanying drawing, the invention will be further described：
1st, optimal two-position is carried out using indexing mechanism to be initially aligned：
Reference picture 1, in t0After moment, inertial navigation system bookbinding initial position, at the beginning of control indexing mechanism carries out optimal two-position
Begin to be aligned.Wherein t0Moment is first position, and indexing mechanism is in 180 °；t1Moment turns to the second place, and indexing mechanism is in
0°.Alignment procedures use Kalman filtering algorithm, while accurate initial attitude battle array is obtained, gyroscopic drift is carried out estimation and
Compensation.
The coordinate system being related in solution process is defined as follows：
B-IMU coordinate systems, reference axis points to the right side-preceding-upper direction of Inertial Measurement Unit；
M- carrier coordinate systems, reference axis points to the right side-preceding-upper direction of carrier；
N-navigational coordinate system, reference axis points to east-north-day direction of carrier geographic location.
Alignment terminates t2Moment angle position is 0 °, it is believed that IMU coordinate systems b is overlapped with carrier coordinate system m, and alignment is terminated
Posture battle arrayIt is used as the attitude matrix of carrier coordinate system
2nd, data calculation and storage.
The reference picture 1, [t after alignment terminates2,t3] ensure that carrier coordinate system m is static, controls indexing machine in time interval
Structure is with 6 °/s around each circle of azimuth axis rotating.Posture renewal is carried out in rotation process, while calculate and store indexable angle [alpha],
Equivalent indexable angular speedEquivalent angle rate of accelerationWith misalignment φb。
Remember tk-1、tk、tk+1Moment indexing angle is followed successively by αk-1、αk、αk+1, calculate tkAnd tk+1The equivalent Index angle speed at moment
Rate
Calculate tk+1Moment equivalent Index angle rate of acceleration
Rotating shaft and angle error cause to calculate the IMU coordinate system b ' obtained and true IMU coordinate systems b is misaligned, calculates two
Error matrix between coordinate system
In formulaFor navigation calculation attitude matrix,For attitude of carrier matrix,To be exported according to rotating shaft angular encoder
The transition matrix that indexable angle [alpha] is resolved
Note b ' is that the misalignment between b systems is φb, there is relational expression
Wherein I represents 3 rank unit matrix, φb× represent vector φbAntisymmetric matrix.
Misalignment is solved according to formula (4) and formula (6), obtained
Wherein φx、φy、φzFor φbThree-dimensional component,RepresentThe i-th row jth column element.
3rd, higher order Taylor series expansion fitting of a polynomial.
Due to there is bearing clearance, the misalignment in rotating stage is not exclusively overlapped, and is added during rotating switching by angle
Speed influence can produce mutation Error.After data acquisition terminates, according to equivalent indexable angular speedDistinguish [t2,t3] time interval
Rotating process.Misalignment is described using higher order Taylor series expansion multinomial, Umklapp process is aligned respectively and is fitted misalignment by formula (8)
Angle φbWith angle position α, Index angle rate of accelerationBetween functional relation, obtain coefficient of polynomial fitting simultaneously preserve.
φ in formulaiRepresent the x in the case of rotating, y, z-axis misalignment component, m and n represent α andFitting exponent number, m takes
15, n take 8, pi,kAnd ci,jFor corresponding fitting coefficient.
4th, posture demodulation compensation.
Reference picture 1, in [t3,t4] the interior control continuous rotating of indexing mechanism of time interval, by fitting coefficient pi,k、ci,jShould
For navigation procedure.According to fitting coefficient, indexable angle [alpha] and Index angle rate of accelerationCompensation misalignment is calculated by formula (8)
According to compensation misalignmentCalculate posture battle array
Then demodulation attitude matrix is calculated
Demodulation attitude angle after being compensated according to demodulation posture battle array
Wherein θ, γ and ψ are followed successively by the angle of pitch, roll angle and course angle of carrier,Representing matrixThe i-th row
Jth column element.
Apply the inventive method to below in specific embodiment.
Experiment is used to group using Laser strapdown, and wherein laser gyro precision is 0.005 °/h, and accelerometer precision is 40 μ g,
IMU data sampling frequencies are 400Hz.Successively carry out two-position alignment and misalignment demarcation after, control indexing mechanism with 6 °/s around
The positive and negative continuous rotation 8min of azimuth axis, is verified to posture demodulation effect.
Fig. 2 is the misalignment angular curve in calibration process of the embodiment of the present invention.Partial enlarged drawing on the right side of Fig. 2 shows, misalignment
Angle is not exclusively overlapped in the rotating stage, wherein φzAlso there is substantially mutation in rotating handoff procedure.Therefore method is divided
Not Ni He rotating process, and set up misalignment φbWith Index angle rate of accelerationBetween relation.
Fig. 3 is verification process of the embodiment of the present invention [t3,t4] interval interior uncompensated posture demodulating error curve.Before compensation,
Misalignment is in obvious mechanical periodicity trend, and 8min attitude errors statistical value is [122.6；130.6；40.4]″(1σ).
Fig. 4 is verification process of the embodiment of the present invention [t3,t4] it is interval in compensate after posture demodulating error curve.Using this
After inventive method compensation, the posture demodulating error statistical value of 8min rotating processes is [0.5；0.9；1.8] " (1 σ), demodulation essence
Degree has been respectively increased 230 times, 140 times, 22 times.Remaining commutation mutation Error is not regular strong, it is difficult to modeling compensation, but continues
Time is short, can be by setting angle rate of acceleration decision condition to avoid.
Claims (1)
1. a kind of single-shaft-rotation inertial navigation system posture demodulation method based on Taylor series fitting, it is characterised in that step is as follows：
Step 1：Inertial navigation system is obtained after initial position, and optimal two-position alignment, wherein first position are carried out using indexing mechanism
Angle position is 180 °, and second place angle position is 0 °；Carrier is obtained using classical kalman filter method accurately initial
Posture and course information are simultaneously estimated gyroscopic drift and compensated；
Step 2：After two-position alignment terminates, keep inertial navigation system static, control indexing mechanism is with 6 °/s around azimuth axis rotating
Posture renewal is carried out using traditional quaternion calculation method in each circle, rotation process, calculates and stores：Measure corner α, it is equivalent
Rotate angular speedEquivalent Rotational angle rate of accelerationWith misalignment angle error φb；
Step 3：Umklapp process is aligned respectively using higher order Taylor series expansion fitting misalignment φbWith α,Between functional relation, obtain
Obtain coefficient of polynomial fitting and preserve；
The functional relation is：
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And ci,jFor corresponding fitting coefficient；
Step 4：By fitting coefficient pi,kAnd ci,jStore to navigational computer, in navigation stage according to fitting coefficient, indexable angle [alpha]
With Index angle rate of accelerationBy functional relation：
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Compensation misalignment is calculated, posture demodulation is completed in real time and is calculated.
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| CN109211269A (en) * | 2018-08-16 | 2019-01-15 | 昆山天地睿航智能科技有限公司 | A kind of dual-axis rotation inertial navigation system attitude error scaling method |
| CN109751999A (en) * | 2019-01-21 | 2019-05-14 | 深圳大学 | A kind of scaling method, the apparatus and system of duct survey robot |
| CN109959390A (en) * | 2018-12-26 | 2019-07-02 | 中国电子科技集团公司第二十研究所 | A kind of installation deviation compensation method of rotation modulation system two-position |
| CN111707290A (en) * | 2020-06-12 | 2020-09-25 | 浙江大学 | Automatic calibration turntable of three-degree-of-freedom sensor |
| CN114166215A (en) * | 2021-11-19 | 2022-03-11 | 西安航天精密机电研究所 | Indexing mechanism of rotary strapdown inertial measurement unit and IMU synchronous calibration and compensation method |
| CN115077520A (en) * | 2022-08-22 | 2022-09-20 | 中国船舶重工集团公司第七0七研究所 | Attitude compensation method based on resonant inertial navigation system |
| CN115265591A (en) * | 2022-07-15 | 2022-11-01 | 北京航空航天大学 | Method for calibrating installation errors of double-shaft rotary inertial navigation unit (IMU) and indexing mechanism |
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| CN109211269A (en) * | 2018-08-16 | 2019-01-15 | 昆山天地睿航智能科技有限公司 | A kind of dual-axis rotation inertial navigation system attitude error scaling method |
| CN109211269B (en) * | 2018-08-16 | 2022-06-24 | 昆山天地睿航智能科技有限公司 | Attitude angle error calibration method for double-shaft rotary inertial navigation system |
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| CN109959390A (en) * | 2018-12-26 | 2019-07-02 | 中国电子科技集团公司第二十研究所 | A kind of installation deviation compensation method of rotation modulation system two-position |
| CN109751999A (en) * | 2019-01-21 | 2019-05-14 | 深圳大学 | A kind of scaling method, the apparatus and system of duct survey robot |
| CN109751999B (en) * | 2019-01-21 | 2020-07-24 | 深圳大学 | Calibration method, device and system of pipeline measuring robot |
| CN111707290A (en) * | 2020-06-12 | 2020-09-25 | 浙江大学 | Automatic calibration turntable of three-degree-of-freedom sensor |
| CN114166215A (en) * | 2021-11-19 | 2022-03-11 | 西安航天精密机电研究所 | Indexing mechanism of rotary strapdown inertial measurement unit and IMU synchronous calibration and compensation method |
| CN114166215B (en) * | 2021-11-19 | 2023-08-04 | 西安航天精密机电研究所 | Indexing mechanism of rotary strapdown inertial measurement unit (SIU) and IMU synchronous calibration and compensation method |
| CN115265591A (en) * | 2022-07-15 | 2022-11-01 | 北京航空航天大学 | Method for calibrating installation errors of double-shaft rotary inertial navigation unit (IMU) and indexing mechanism |
| CN115265591B (en) * | 2022-07-15 | 2024-04-09 | 北京航空航天大学 | Calibration method for mounting errors of biaxial rotation inertial navigation IMU and indexing mechanism |
| CN115077520B (en) * | 2022-08-22 | 2022-11-01 | 中国船舶重工集团公司第七0七研究所 | Attitude compensation method based on resonant inertial navigation system |
| CN115077520A (en) * | 2022-08-22 | 2022-09-20 | 中国船舶重工集团公司第七0七研究所 | Attitude compensation method based on resonant inertial navigation system |
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