CN108458714A - The Eulerian angles method for solving of acceleration of gravity is free of in a kind of attitude detection system - Google Patents
The Eulerian angles method for solving of acceleration of gravity is free of in a kind of attitude detection system Download PDFInfo
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- CN108458714A CN108458714A CN201810027570.8A CN201810027570A CN108458714A CN 108458714 A CN108458714 A CN 108458714A CN 201810027570 A CN201810027570 A CN 201810027570A CN 108458714 A CN108458714 A CN 108458714A
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- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
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Abstract
The invention discloses the Eulerian angles method for solving that acceleration of gravity is free of in a kind of attitude detection system, it is realized based on MARG sensors, MARG sensors include three-axis gyroscope, three axis accelerometer and three axle magnetometer, it is first determined the navigational coordinate system and carrier coordinate system of attitude detection system；Calculating rotates navigational coordinate system to the required transformation matrix of coordinates of carrier coordinate systemThe element of the matrix is indicated by roll angle, pitch angle and the yaw angle in Eulerian angles；Acquire the measured value of three axis accelerometer and three axle magnetometerba,bm；According to the measured value of three axis accelerometer and three axle magnetometerba,bM and transformation matrix of coordinatesObtain the Eulerian angles calculation formula not comprising acceleration of gravity.The present invention solves the Eulerian angles of testee using three axis accelerometer and the measured value of three axle magnetometer, acceleration of gravity is not contained in obtained calculation formula, influence of the acceleration of gravity when solving attitude angle is completely eliminated, to improve the precision of attitude detection.
Description
Technical field
The attitude detection technical field that MARG sensors carry out attitude detection is the present invention relates to the use of, more particularly to one kind
The Eulerian angles method for solving of acceleration of gravity is free of in attitude detection system.
Background technology
With growing, the MARG of MEMS (MEMS, Micro-Electro-Mechanical-System)
(Magnetic, Angular Rate, and Gravity) sensor is more and more applied in attitude detection field.To object
Posture is accurately detected, and is the basis for carrying out other further investigations.
The principle that gestures of object detection is carried out using MARG sensors is as follows：First, the navigation of attitude detection system is determined
Coordinate system and carrier coordinate system, calculating rotate navigational coordinate system to the required transformation matrix of coordinates of carrier coordinate system, the seat
The element marked in transformation matrix is indicated by roll angle, yaw angle and the pitch angle in Eulerian angles.Then, it is measured by 3-axis acceleration
The 3-axis acceleration of amount is calculated the roll angle and pitch angle of object to be detected by transformation matrix of coordinates, is surveyed by three axle magnetometer
The three-axle magnetic field information of amount calculates the yaw angle of object to be detected by transformation matrix of coordinates.Finally obtain object to be detected
Real-time Eulerian angles, to realize the function of attitude detection.
But it is introduced in the calculation formula in Eulerian angles based in the attitude measurement system of MARG sensors current more
Acceleration of gravity, i.e., bring into acceleration of gravity as known conditions in calculation formula.But since acceleration of gravity is not
Constant value, value can change with height and the difference of earth longitude and latitude.Also, due to the numerical value of acceleration of gravity
It is not a finite decimal, is carried out with the fashionable effective digital for needing to retain certain digit as steady state value.
The above 2 points accuracy declines that can cause attitude detection, therefore find the Eulerian angles meter without containing acceleration of gravity
Formula is calculated to be of great significance to the precision for improving attitude detection.
Invention content
In order to solve the deficiencies in the prior art, the present invention provides acceleration of gravity is free of in a kind of attitude detection system
Eulerian angles method for solving, the present invention are calculated according to the measured value of three axis accelerometer and three axle magnetometer in MARG sensors
The Eulerian angles of testee, computational methods are not influenced by acceleration of gravity, can be completely eliminated acceleration of gravity and solved
Influence when Eulerian angles improves the precision of attitude detection.
The present invention adopts the following technical scheme that：
The Eulerian angles method for solving that acceleration of gravity is free of in a kind of attitude detection system, is realized based on MARG sensors,
MARG sensors include three-axis gyroscope, three axis accelerometer and three axle magnetometer, are included the following steps：
Determine the navigational coordinate system OX of attitude detection systemnYnZnWith carrier coordinate system OXbYbZb；
Calculating rotates navigational coordinate system to the required transformation matrix of coordinates of carrier coordinate systemThe element of the matrix
It is indicated by roll angle, pitch angle and the yaw angle in Eulerian angles；
Acquire the measured value of three axis accelerometer and three axle magnetometerba,bm；
According to the measured value of three axis accelerometer and three axle magnetometerba,bM and transformation matrix of coordinatesDo not included
The Eulerian angles calculation formula of acceleration of gravity, the Eulerian angles include roll anglePitching angle theta and yaw angle ψ.
Further, the determination about navigational coordinate system and carrier coordinate system, coordinate system is as navigation seat with selecting east northeast
Mark system, carrier coordinate system follow right-hand rule, and carrier coordinate system origin is overlapped with carrier barycenter, and X-axis is parallel to carrier axis simultaneously
It is directed toward in front of carrier, Y-axis is perpendicular to X-axis and is directed toward carrier right, and Z axis is perpendicular to X/Y plane and is directed toward below carrier.
Further, the navigational coordinate system to the spin matrix of carrier coordinate system because of selected navigational coordinate system and load
The difference of body coordinate system and it is different, when navigational coordinate system for east northeast coordinate system, by navigational coordinate system OXnYnZnAccording to Z → Y
→ X sequences are rotated, and the direction cosine matrix rotated three times is respectively Cz, Cz, Cz, can be rotated to carrier coordinate
It is OXbYbZbIt overlaps；
Wherein
Then the transformation matrix of coordinates indicated with Eulerian angles is obtained：
Wherein,For the spin matrix of navigational coordinate system to carrier coordinate system,θ, ψ are respectively the roll in Eulerian angles
Angle, pitch angle and yaw angle.
Further, the measured value of three axis accelerometer and three axle magnetometer is acquiredba,bM, whereinbA=[bax,bay,baz],bM=[bmx,bmy,bmz],bA is the measured value of three axis accelerometer under carrier coordinate system,bax,bay,bazRespectively three axis
Component of the acceleration measuring magnitude in three reference axis of carrier coordinate system；bM is the measurement of three axle magnetometer under carrier coordinate system
Value,bmx,bmy,bmzRespectively component of the three axle magnetometer measured value in three reference axis of carrier coordinate system.
Further, according to the measured value of three axis accelerometer and three axle magnetometerba,bM and transformation matrix of coordinates
Derive the roll angle not comprising acceleration of gravityThe calculation formula of pitching angle theta and yaw angle ψ, calculates roll angle firstIt bows
Elevation angle theta：
Gravitational field under navigational coordinate system isnA=[0,0, g], wherein g are acceleration of gravity, three axis under carrier coordinate system
The measured value of accelerometer isbA=[bax,bay,baz], according to principle of coordinate transformationHave
Second in above-mentioned equation group is done into ratio with third formula, gravity acceleration g can be eliminated, be free of
The roll angle of gravity acceleration gWith the calculation formula of pitching angle theta
When calculating yaw angle ψ, to simplify the calculation, it is assumed that magnetic dip angle is only existed in earth's magnetic field and magnetic declination is zero, navigation
Field of magnetic forece under coordinate system isnM=(nmx,0,nmz), field of magnetic forece is under carrier coordinate systembM=(bmx,bmy,bmz), according to coordinate
Shift theoryHave
It is hereby achieved that the calculation formula of yaw angle：
Compared with prior art, the beneficial effects of the invention are as follows：
The present invention solves the Eulerian angles of testee using three axis accelerometer and the measured value of three axle magnetometer, acquired
Eulerian angles calculation formula in do not contain acceleration of gravity, completely eliminate influence of the acceleration of gravity when solving Eulerian angles,
Improve the precision of attitude detection.
Description of the drawings
The accompanying drawings which form a part of this application are used for providing further understanding of the present application, and the application's shows
Meaning property embodiment and its explanation do not constitute the improper restriction to the application for explaining the application.
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 (a)-Fig. 2 (b) is that a kind of coordinate system provided by the invention chooses mode.
Specific implementation mode
It is noted that following detailed description is all illustrative, it is intended to provide further instruction to the application.Unless another
It indicates, all technical and scientific terms used herein has usual with the application person of an ordinary skill in the technical field
The identical meanings of understanding.
It should be noted that term used herein above is merely to describe specific implementation mode, and be not intended to restricted root
According to the illustrative embodiments of the application.As used herein, unless the context clearly indicates otherwise, otherwise singulative
It is also intended to include plural form, additionally, it should be understood that, when in the present specification using term "comprising" and/or " packet
Include " when, indicate existing characteristics, step, operation, device, component and/or combination thereof.
As background technology is introduced, deficiency exists in the prior art, in order to solve technical problem as above, the application
Propose Eulerian angles method for solving in the MEMS based on accelerometer and magnetometer.
In a kind of typical embodiment of the application, as shown in Figure 1, providing micro- based on accelerometer and magnetometer
Eulerian angles method for solving in Mechatronic Systems, by the study found that carrying out gestures of object inspection using MARG posture detecting units
In the attitude detection algorithm of survey, due to being brought into acceleration of gravity as known quantity when calculating Eulerian angles, it will reduce posture
The precision of detection.
In consideration of it, the present invention is deduced one kind according to the accelerometer of Attitude Measuring Unit and the measured value of magnetometer
The Eulerian angles calculation formula for completely eliminating gravity effect, improves the precision of attitude detection system.Below in conjunction with the accompanying drawings with
The present invention will be further described for embodiment.
The present invention implementation be：
The first step：Determine the navigational coordinate system OX of attitude detection systemnYnZnWith carrier coordinate system OXbYbZb；Fig. 2 (a)-schemes
2 (b) is a kind of navigational coordinate system that this method provides and carrier coordinate system chooses mode, and navigational coordinate system is with selecting east northeast
(NED) coordinate system, carrier coordinate system follow right-hand rule, and carrier coordinate system origin is overlapped with carrier barycenter, and X-axis is parallel to carrier
Axis is simultaneously directed toward in front of carrier, and Y-axis is perpendicular to X-axis and is directed toward carrier right, and Z axis is perpendicular to X/Y plane and is directed toward below carrier.
Second step：Calculating rotates navigational coordinate system to the required transformation matrix of coordinates of carrier coordinate systemThe matrix
Element indicated by the roll angle in Eulerian angles, pitch angle and yaw angle.By navigational coordinate system OXnYnZnAccording to Z → Y → X sequences
It is rotated, the direction cosine matrix rotated three times is respectively Cz, Cz, Cz, can be rotated to carrier coordinate system
OXbYbZbIt overlaps, wherein
Then the transformation matrix of coordinates indicated with Eulerian angles can be obtained
Wherein,For the transformation matrix of coordinates of navigational coordinate system to carrier coordinate system,θ, ψ are respectively in Eulerian angles
Roll angle, pitch angle and yaw angle.
Third walks：Acquire the measured value of three axis accelerometer and three axle magnetometerba,bm.WhereinbA=[bax,bay,baz],bM=[bmx,bmy,bmz],bA is the measured value of three axis accelerometer under carrier coordinate system,bax,bay,bazRespectively 3-axis acceleration
Measure component of the magnitude in three reference axis of carrier coordinate system；bM is the measured value of three axle magnetometer under carrier coordinate system,bmx
,bmy,bmzRespectively component of the three axle magnetometer measured value in three reference axis of carrier coordinate system.
4th step：According to the measured value of three axis accelerometer and three axle magnetometerba,bM and transformation matrix of coordinatesMeter
Calculate the roll angle not comprising acceleration of gravityPitching angle theta and yaw angle ψ.Roll angle is calculated firstPitching angle theta：Navigation is sat
Mark system under gravitational field benA=[0,0, g], wherein g are acceleration of gravity, the measurement of three axis accelerometer under carrier coordinate system
Value isbA=[bax,bay,baz], according to principle of coordinate transformationHave
Second in above-mentioned equation group is done into ratio with third formula, gravity acceleration g can be eliminated, be free of
The roll angle of gravity acceleration gWith the calculation formula of pitching angle theta
When calculating yaw angle ψ, to simplify the calculation, it is assumed that magnetic dip angle is only existed in earth's magnetic field and magnetic declination is zero, navigation
Field of magnetic forece under coordinate system isnM=(nmx,0,nmz), field of magnetic forece is under carrier coordinate systembM=(bmx,bmy,bmz), according to coordinate
Shift theoryHave
It is hereby achieved that the calculation formula of yaw angle：
The technical scheme of the present invention coordinate system provided that is not limited to illustrate chooses mode, in actual attitude detection mistake
Cheng Zhong since the selection mode of coordinate system is various, but is calculated according to MARG accelerometers and magnetometer and is added without containing gravity
The Eulerian angles calculation formula that speed g influences, this formulation process is identical, therefore those skilled in the art are in the present invention
Thinking under still fall within technical scheme of the present invention for correcting made by specific coordinate system.
The foregoing is merely the preferred embodiments of the application, are not intended to limit this application, for the skill of this field
For art personnel, the application can have various modifications and variations.Within the spirit and principles of this application, any made by repair
Change, equivalent replacement, improvement etc., should be included within the protection domain of the application.
Claims (5)
1. being free of the Eulerian angles method for solving of acceleration of gravity in a kind of attitude detection system, realized based on MARG sensors,
MARG sensors include three-axis gyroscope, three axis accelerometer and three axle magnetometer；
It is characterized by comprising the following steps：
Determine the navigational coordinate system OX of attitude detection systemnYnZnWith carrier coordinate system OXbYbZb；
Calculating rotates navigational coordinate system to the required transformation matrix of coordinates of carrier coordinate systemn bC, the element of the matrix is by Euler
Roll angle, pitch angle and yaw angle in angle indicate；
Acquire the measured value of three axis accelerometer and three axle magnetometerba,bm；
According to the measured value of three axis accelerometer and three axle magnetometerba,bM and transformation matrix of coordinatesIt obtains not including gravity
The Eulerian angles calculation formula of acceleration, the Eulerian angles include roll anglePitching angle theta and yaw angle ψ.
2. the Eulerian angles method for solving of acceleration of gravity is free of in a kind of attitude detection system as described in claim 1, it is special
Sign is that, about the determination of navigational coordinate system and carrier coordinate system, coordinate system is as navigational coordinate system, carrier coordinate with selecting east northeast
System follows right-hand rule, and carrier coordinate system origin is overlapped with carrier barycenter, and X-axis is parallel to carrier axis and is directed toward in front of body, Y
Axis is perpendicular to X-axis and is directed toward carrier right, and Z axis is perpendicular to X/Y plane and is directed toward below carrier.
3. the Eulerian angles method for solving of acceleration of gravity is free of in a kind of attitude detection system as described in claim 1, it is special
Sign is, the spin matrix of the navigational coordinate system to carrier coordinate system because of selected navigational coordinate system and carrier coordinate system not
It is same and different, when navigational coordinate system for east northeast coordinate system, by navigational coordinate system OXnYnZnIt is revolved according to Z → Y → X sequences
Turn, the direction cosine matrix rotated three times is respectively Cz, Cz, Cz, can be rotated to carrier coordinate system OXbYbZbIt overlaps,
Wherein
Then the transformation matrix of coordinates indicated with Eulerian angles is obtained：
Wherein,For the spin matrix of navigational coordinate system to carrier coordinate system,θ, ψ are respectively the roll angle in Eulerian angles, are bowed
The elevation angle and yaw angle.
4. the Eulerian angles method for solving of acceleration of gravity is free of in a kind of attitude detection system as described in claim 1, it is special
Sign is to acquire the measured value of three axis accelerometer and three axle magnetometerbA=[bax,bay,baz],bM=[bmx,bmy,bmz], wherein
,bA is the measured value of three axis accelerometer under carrier coordinate system,bax,bay,bazRespectively three axis accelerometer measured value is in carrier
Component in three reference axis of coordinate system；bM is the measured value of three axle magnetometer under carrier coordinate system,bmx,bmy,bmzRespectively three
Component of the axis magnetometer measures value in three reference axis of carrier coordinate system.
5. the Eulerian angles method for solving of acceleration of gravity is free of in a kind of attitude detection system as claimed in claim 3, it is special
Sign is, according to the measured value of three axis accelerometer and three axle magnetometerba,bM and transformation matrix of coordinatesIt calculates and does not include weight
The roll angle of power accelerationPitching angle theta and yaw angle ψ；
Roll angle is calculated firstPitching angle theta：Gravitational field under navigational coordinate system isnA=[0,0, g], wherein g accelerate for gravity
It spends, the measured value of three axis accelerometer is under carrier coordinate systembA=[bax,bay,baz], according to principle of coordinate transformationHave
Second in above-mentioned equation group is done into ratio with third formula, gravity acceleration g can be eliminated, obtains being free of gravity
The roll angle of acceleration gWith the calculation formula of pitching angle theta
When calculating yaw angle ψ, to simplify the calculation, it is assumed that magnetic dip angle is only existed in earth's magnetic field and magnetic declination is zero, navigation coordinate
System under field of magnetic forece benM=(nmx,0,nmz), field of magnetic forece is under carrier coordinate systembM=(bmx,bmy,bmz), according to coordinate transform
PrincipleHave
To the calculation formula of yaw angle：
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Cited By (9)
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| CN109945889A (en) * | 2019-04-17 | 2019-06-28 | 合肥工业大学 | A kind of joint angles measurement method based on double attitude transducers |
| CN110702105A (en) * | 2019-10-12 | 2020-01-17 | 展讯通信（上海）有限公司 | Axial recognition method and device for navigation device and storage medium |
| CN111654634A (en) * | 2020-06-24 | 2020-09-11 | 杭州海康威视数字技术股份有限公司 | Method for determining inclination of engine core assembly and pan-tilt assembly in camera and camera |
| CN111795695A (en) * | 2020-05-15 | 2020-10-20 | 北京百度网讯科技有限公司 | Position information determining method, device and equipment |
| CN112188037A (en) * | 2020-09-24 | 2021-01-05 | 影石创新科技股份有限公司 | Method for generating gyroscope rotation direction and computer equipment |
| CN111998822B (en) * | 2020-10-29 | 2021-01-15 | 江西明天高科技股份有限公司 | Spatial angle attitude calculation method |
| CN112902828A (en) * | 2021-01-19 | 2021-06-04 | 陕西福音假肢有限责任公司 | Angle calculation method |
| CN113672862A (en) * | 2021-10-22 | 2021-11-19 | 中国石油大学胜利学院 | Euler angle optimization method under condition of measurement vector component missing |
| CN115164823A (en) * | 2022-05-16 | 2022-10-11 | 上海芯翌智能科技有限公司 | Method and device for acquiring gyroscope information of camera |
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| CN109945889B (en) * | 2019-04-17 | 2023-07-25 | 合肥工业大学 | Joint angle measuring method based on double-posture sensor |
| CN109945889A (en) * | 2019-04-17 | 2019-06-28 | 合肥工业大学 | A kind of joint angles measurement method based on double attitude transducers |
| CN110702105B (en) * | 2019-10-12 | 2021-09-28 | 展讯通信（上海）有限公司 | Axial recognition method and device for navigation device and storage medium |
| CN110702105A (en) * | 2019-10-12 | 2020-01-17 | 展讯通信（上海）有限公司 | Axial recognition method and device for navigation device and storage medium |
| CN111795695B (en) * | 2020-05-15 | 2022-06-03 | 阿波罗智联(北京)科技有限公司 | Position information determining method, device and equipment |
| CN111795695A (en) * | 2020-05-15 | 2020-10-20 | 北京百度网讯科技有限公司 | Position information determining method, device and equipment |
| CN111654634B (en) * | 2020-06-24 | 2022-02-08 | 杭州海康威视数字技术股份有限公司 | Method for determining inclination of engine core assembly and pan-tilt assembly in camera and camera |
| CN111654634A (en) * | 2020-06-24 | 2020-09-11 | 杭州海康威视数字技术股份有限公司 | Method for determining inclination of engine core assembly and pan-tilt assembly in camera and camera |
| CN112188037A (en) * | 2020-09-24 | 2021-01-05 | 影石创新科技股份有限公司 | Method for generating gyroscope rotation direction and computer equipment |
| WO2022063221A1 (en) * | 2020-09-24 | 2022-03-31 | 影石创新科技股份有限公司 | Method for generating rotation direction of gyroscope and computer device |
| CN112188037B (en) * | 2020-09-24 | 2023-03-24 | 影石创新科技股份有限公司 | Method for generating gyroscope rotation direction and computer equipment |
| CN111998822B (en) * | 2020-10-29 | 2021-01-15 | 江西明天高科技股份有限公司 | Spatial angle attitude calculation method |
| CN112902828A (en) * | 2021-01-19 | 2021-06-04 | 陕西福音假肢有限责任公司 | Angle calculation method |
| CN112902828B (en) * | 2021-01-19 | 2023-09-08 | 陕西福音假肢有限责任公司 | Angle calculation method |
| CN113672862A (en) * | 2021-10-22 | 2021-11-19 | 中国石油大学胜利学院 | Euler angle optimization method under condition of measurement vector component missing |
| CN115164823A (en) * | 2022-05-16 | 2022-10-11 | 上海芯翌智能科技有限公司 | Method and device for acquiring gyroscope information of camera |
| CN115164823B (en) * | 2022-05-16 | 2024-04-02 | 上海芯翌智能科技有限公司 | Method and device for acquiring gyroscope information of camera |
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