CN107631666A - A kind of body roll angle detecting system and method based on earth magnetism and sun optic angle - Google Patents
A kind of body roll angle detecting system and method based on earth magnetism and sun optic angle Download PDFInfo
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Abstract
The invention discloses a kind of body roll angle detecting system and method based on earth magnetism and sun optic angle, including four photosensitive tubes and the magnetic survey module being arranged in body, GPS module and controller, wherein, magnetic survey module, GPS module and controller are set gradually from top to bottom, wherein, magnetic survey module is located at the top of the bullet of body, four photosensitive tubes are circumferentially uniformly embedded in the outer wall of body, wherein, the output end of magnetic survey module, the output end of GPS module and the output end of four photosensitive tubes are connected with the input of controller, the system and method can realize the detection of body roll angle, and without using gyroscope and accelerometer, it is simultaneously simple in construction, cost is low.
Description
Technical field
The present invention relates to a kind of body roll angle detecting system and method, and in particular to one kind is based on earth magnetism and sun optic angle
Body roll angle detecting system and method.
Background technology
The fixed-wing bispin bullet that guidance task can be completed is the study hotspot of guided cartridge recent years, and such shell exists
Control system is disposed on traditional rifle cannon or mortar, makes it have homing capability, and relatively with using other lower guided munitions
Cost is lower.Such shell is unpowered device, launching acceleration is more than 10000g.
The roll angle detection of fixed-wing bispin bullet is then the basis of shell navigation and TRAJECTORY CONTROL.Roll angle detection typically makes
With gyroscope and accelerometer measurement in a closed series.But because the superelevation acceleration of body, causes mems gyroscopes and accelerometer meeting
Damaged during transmitting, and fibre optic gyroscope is because price is prohibitively expensive, the accelerometer cost of resistance to high acceleration also ten
Divide costliness, run counter to the original intention of fixed-wing bispin bullet design.Therefore one kind is designed without using gyroscope and accelerometer, and is tied
The body roll angle detection technique that structure is simple, cost is cheap is very crucial.
The content of the invention
The shortcomings that it is an object of the invention to overcome above-mentioned prior art, there is provided a kind of based on earth magnetism and sun optic angle
Body roll angle detecting system and method, the system and method can realize the detection of body roll angle, and without using gyro
Instrument and accelerometer, at the same it is simple in construction, and cost is low.
To reach above-mentioned purpose, the body roll angle detecting system of the present invention based on earth magnetism and sun optic angle includes
Four photosensitive tubes and magnetic survey module, GPS module and the controller being arranged in body, wherein, magnetic survey module,
GPS module and controller are set gradually from top to bottom, wherein, magnetic survey module is located at the top of the bullet of body, and four are photosensitive
Pipe is circumferentially uniformly embedded in the outer wall of body, wherein, the output end of magnetic survey module, the output end of GPS module and four
The output end of individual photosensitive tube is connected with the input of controller.
The amplified circuit of magnetic survey module and analog-digital converter are connected with controller, controller by push-pull circuit with
Magnetic survey module is connected.
GPS module is connected by RS422 Interface and Controler.
Photosensitive tube is connected through analog-digital converter with controller.
Body roll angle detection method of the present invention based on earth magnetism and sun optic angle comprises the following steps:
1) GPS module obtains the velocity information of body, then sends the velocity information of body into controller, controller
The angle of pitch α and yaw angle β of body, photosensitive tube collection sun light irradiation angle x are calculated according to the velocity information of body, then will collection
To sun light irradiation angle x be converted to photoelectric current y, then the photoelectric current y is sent into controller, controller is according to reception
The final roll angle φ of photosensitive tube over the ground is calculated to photoelectric current y, the angle of pitch α of body and yaw angle β;
2) the real-time locality magnetic vector v of magnetic survey module, then sends the ground magnetic vector v collected to controller
In, controller carries out denoising to described ground magnetic vector v, the ground magnetic vector X after denoising is obtained, then according to the ground magnetic vector after denoising
X calculates the roll angle θ of body;
3) controller calculates the final rolling of body according to the final roll angle φ of the roll angle θ and photosensitive tube of body over the ground
Angle
Sun light irradiation angle x and photoelectric current y corresponding relation is:
Y=Asin2ax
Wherein, α is scale value, A=1.
The concrete operations of step 1) are:
90 ° of illumination ranges of each photosensitive tube are intercepted, then the photoelectric current waveform that four photosensitive tubes are detected to obtain enters successively
Row combination, obtains combined waveform, the combined waveform then is divided into 8 sections of waveforms as interval using peak point and valley point, wherein, often
The corresponding two sections of waveforms of individual photosensitive tube, the angle base value of every section of waveformIf the peak value of either segment waveform and
Valley is respectively p and q, then has y=sin2Ax,A is solved, obtains y=sin2Fitting is bent corresponding to ax
Line;
The photoelectric current that current photosensitive tube obtains is updated in corresponding matched curve, obtains shining upon for current photosensitive tube
Angle x, then using angular deviations of the sun irradiation angle x of current photosensitive tube as current photoelectric current in corresponding section waveform
Then by the angular deviationIt is added on the angle base value angle δ of this section of waveform, obtains the relative roll angle of this section of waveformFinally by the relative roll angle of this section of waveformWith the result that reference angle γ is added over the ground as photosensitive tube over the ground
Final roll angle
Reference angle γ is over the ground:
A=cos β tan ξ-cos δ tan α
B=sin δ tan α-sin β tan ξ
Wherein, λ, ξ are respectively azimuth and the elevation angle of the sun of the current time sun.
The concrete operations of step 2) are:
The position of magnetic survey module is adjusted, makes the seat of the sensitive direction of principal axis and body of Magnetic Sensor in magnetic survey module
Mark system direction is consistent, calculates Magnetic Sensor and collects maximums and minimum value of the ground magnetic vector v in sensitive axes y, z, Ran Hougen
Average ms of the ground magnetic vector v in sensitive axes y, z direction is calculated according to maximums of the ground magnetic vector v in sensitive axes y, z and minimum value,
Ground magnetic vector v is individually subtracted in sensitive axes y, z in the numerical value of ground magnetic vector v that Magnetic Sensor collects in sensitive axes y, z again
The average m in direction, make the ellipse of at the origin centered on the magnetic vector figure conversion of Magnetic Sensor, calculate the oval long axis direction
And short-axis direction, then by the ELLIPTIC REVOLUTION υ, make the oval major axis and short axle respectively on sensitive axes y and z, then
Scaling is carried out to the oval major axis and short axle, completes the calibration for the ground magnetic vector v that Magnetic Sensor collects, wherein, scaling ginseng
NumberObtaining the ground magnetic vector X after denoising is:
If (x1,y1,z1) it is missile coordinate system, (x2,y2,z2) it is NED coordinate systems, during projectile flight, obtain body
Roll angle θ be:
B=cos β y2-sinψx2
B=cos β sin α x2+sinβsinαy2+cosαz2
Wherein, Magnetic Sensor is twin shaft magnetoresistive transducer, x1And y1The data measured for twin shaft magnetoresistive transducer, x2、y2
And z2For the study plot magnetic vector of locality.
The final roll angle of bodyFor:
Wherein, RφTo measure test variance during φ, RθTo measure test variance during θ.
The invention has the advantages that:
Body roll angle detecting system and method for the present invention based on earth magnetism and sun optic angle in concrete operations,
The data that controller obtains according to GPS module calculate the angle of pitch and yaw angle of body, further according to photoelectric current caused by photosensitive tube
And the angle of pitch and yaw angle of body calculate the final roll angle of photosensitive tube over the ground, while controller is adopted according to magnetic survey module
The roll angle of the earth magnetism Vector operation body of collection, finally calculated according to the final roll angle of the roll angle of body and photosensitive tube over the ground
The final roll angle of bodySo as to avoid using gyroscope and accelerometer, at the same it is simple in construction, and cost is low.Need what is illustrated
It is that the data that the present invention is obtained by photosensitive tube and magnetic survey module measurement carry out data fusion, to improve the precision of measurement,
Avoid floating problem when producing using gyroscope simultaneously.
Brief description of the drawings
Fig. 1 is the structural representation of the present invention;
Fig. 2 is the hardware architecture diagram of system;
Fig. 3 is the irradiation graph of a relation of photosensitive tube 2 and sunshine;
Fig. 4 a are the current waveform figure that photosensitive tube 2 gathers;
Fig. 4 b are combined waveform figure;
Fig. 5 is the workflow diagram of sunshine rolling angle measurement system;
Angle schematic diagram on the basis of Fig. 6;
Fig. 7 is magnetic vector distribution map;
Fig. 8 is the schematic diagram of missile coordinate system and NED coordinate systems.
Wherein, 1 it is controller, 2 be photosensitive tube, 3 be magnetic survey module, 4 be GPS module, 5 be analog-digital converter, 6 is
Amplifying circuit, 7 be push-pull circuit, 8 be RS422 interfaces.
Embodiment
The present invention is described in further detail below in conjunction with the accompanying drawings:
With reference to figure 1, the body roll angle detecting system of the present invention based on earth magnetism and sun optic angle includes four light
The quick pipe 2 and magnetic survey module 3 being arranged in body, GPS module 4 and controller 1, wherein, magnetic survey module 3, GPS
Module 4 and controller 1 are set gradually from top to bottom, wherein, magnetic survey module 3 is located at the top of the bullet of body, and four are photosensitive
Pipe 2 is circumferentially uniformly embedded in the outer wall of body, wherein, the output end of magnetic survey module 3, the output end of GPS module 4 and
Input of the output end of four photosensitive tubes 2 with controller 1 is connected.
The amplified circuit 6 of magnetic survey module 3 and analog-digital converter 5 are connected with controller 1, and controller 1 is by recommending
Circuit 7 is connected with magnetic survey module 3;GPS module 4 is connected by RS422 interfaces 8 with controller 1;Photosensitive tube 2 is through mould
Number converter 5 is connected with controller 1;Analog-digital converter 5 uses high sampling rate 16 ADC of multichannel, and controller 1 uses MCU
Chip.Present invention additionally comprises the battery for providing electric energy, wherein, GPS module 4 can be replaced by big dipper module.Separately
Outside, magnetic survey module 3 is fixed by four pillar pieces, magnetic survey module 3 is located at the bullet position of body, avoids in body
Iron body and influence of the magnet to magnetic survey.
Magnetic calibration mode can be entered in magnetic survey module 3 in electric 20s, under magnetic calibration mode, user needs to fix
Body, and multiple rotary bullet is calibrated to complete the autonomous magnetic of system, the pattern can also pass through the command triggers of RS422 interfaces 8.
Subsequent system enters standby mode, and user sets magnetic vector to magnetic survey module 3 and photosensitive tube 2 by RS422 interfaces 8 and believed
Breath and sunlight vector information, and lock in time.User can pass through RS422 according to the complex environment being presently in simultaneously
Interface 8 set whether and meanwhile start magnetic survey module 3 and photosensitive tube 2.After controller 1 receives its instruction of startup, then control
System carries out the collection of data by photosensitive tube 2GPS modules 4 and magnetic survey module 3.
Body roll angle detection method of the present invention based on earth magnetism and sun optic angle comprises the following steps:
1) GPS module 4 obtains the velocity information of body, then sends the velocity information of body into controller 1, controls
Device 1 calculates the angle of pitch α and yaw angle β of body according to the velocity information of body, and photosensitive tube 2 gathers sun light irradiation angle x, then will
The sun light irradiation angle x collected is converted to photoelectric current y, then sends the photoelectric current y into controller 1, controller 1
The final roll angle φ of photosensitive tube 2 over the ground is calculated according to photoelectric current y, the angle of pitch α of body and yaw angle β is received;
The concrete operations of step 1) are:
Because the angle of attack very little during projectile flight, it can be assumed that the velocity attitude of body is the posture side of body
To, therefore the angle of pitch α and yaw angle β of body can be parsed to obtain by the velocity attitude that GPS module 4 obtains.
The smooth surface of four photosensitive tubes 2 outwardly, and is uniformly distributed circumferentially, as described in Fig. 1 and Fig. 3, incident angle compared with
In the case of small, size and the substantially proportional relation of illuminating area of photoelectric current, therefore sun light irradiation angle x and photoelectric current y
Corresponding relation is:
Y=Asin2ax
Wherein, α is scale value, A=1.
90 ° of illumination ranges of each photosensitive tube 2 are intercepted, intercept top half in Fig. 4 a waveforms, then four photosensitive tubes 2 are examined
The photoelectric current waveform measured is combined successively, obtains combined waveform, as shown in Figure 4 b, then by the combined waveform with peak point
And valley point is that interval is divided into 8 sections of waveforms, wherein, the corresponding two sections of waveforms of each photosensitive tube 2, the angle base value of every section of waveformIf the peak value and valley of either segment waveform are respectively p and q, then there is y=sin2Ax,A is solved, obtains y=sin2Matched curve corresponding to ax, specific operating process are as shown in Figure 5.
The photoelectric current that current photosensitive tube 2 obtains is updated in corresponding matched curve, the sun for obtaining current photosensitive tube 2 shines
Firing angle degree x, then using angular deviations of the sun irradiation angle x of current photosensitive tube 2 as current photoelectric current in corresponding section waveformThen by the angular deviationIt is added on the angle base value angle δ of this section of waveform, obtains the relative roll angle of this section of waveformFinally by the relative roll angle of this section of waveformWith the result that reference angle γ is added over the ground as photosensitive tube 2 over the ground
Final roll angle
Wherein, reference angle γ is over the ground:
A=cos β tan ξ-cos δ tan α
B=sin δ tan α-sin β tan ξ
Wherein, λ, ξ are respectively azimuth and the elevation angle of the sun of the current time sun.
Above formula is come by the posture of body and the elevation angle of solar angle and azimuth by conversion, and concrete principle is:Such as
Shown in Fig. 6, when some photosensitive tube 2 on body and sunray are in same plane, then the photoelectric current of the photosensitive tube 2 is just
In peak state, under ENU coordinate systems or NED coordinate systems, plane and bullet that sunlight vector and body axially form are solved
The angle in body plummet face, it is the reference angle, it is only necessary to set one of photosensitive tube 2 in this peak as 0 °, i.e., it is complete
Into demarcation.
2) the real-time locality magnetic vector v of magnetic survey module 3, then sends the ground magnetic vector v collected to controller 1
In, controller 1 carries out denoising to described ground magnetic vector v, obtains the ground magnetic vector X after denoising, is then sweared according to the earth magnetism after denoising
Measure the roll angle θ that X calculates body;
The concrete operations of step 2) are:The concrete operations of step 2) are:
The position of magnetic survey module 3 is adjusted, makes the sensitive direction of principal axis and body of Magnetic Sensor in magnetic survey module 3
Coordinate system direction is consistent, calculates Magnetic Sensor and collects maximums and minimum value of the ground magnetic vector v in sensitive axes y, z, then
Maximums and minimum value of the base area magnetic vector v in sensitive axes y, z calculate averages of the ground magnetic vector v in sensitive axes y, z direction
M, then by the numerical value of ground magnetic vector v that Magnetic Sensor collects in sensitive axes y, z be individually subtracted ground magnetic vector v sensitive axes y,
The average m in z directions, make the ellipse of at the origin centered on the magnetic vector figure conversion of Magnetic Sensor, as shown in fig. 7, it is ellipse to calculate this
Round long axis direction and short-axis direction, then by the ELLIPTIC REVOLUTION υ, the oval major axis and short axle is set to be located at sensitive axes respectively
On y and z, scaling then is carried out to the oval major axis and short axle, completes the calibration for the ground magnetic vector v that Magnetic Sensor collects,
Wherein, zooming parameterObtaining the ground magnetic vector X after denoising is:
With reference to figure 8, if (x1,y1,z1) it is missile coordinate system, (x2,y2,z2) it is NED coordinate systems, in projectile flight process
In, geomagnetic data is measured by magnetic survey module 3 in real time, by the rotation relationship of two coordinate systems, obtains the roll angle θ of body
For:
B=cos β y2-sinψx2
B=cos β sin α x2+sinβsinαy2+cosαz2
Wherein, Magnetic Sensor is twin shaft magnetoresistive transducer, x1And y1The data measured for twin shaft magnetoresistive transducer, x2、y2
And z2For the study plot magnetic vector of locality.
3) controller 1 calculates the final rolling of body according to the final roll angle φ of the roll angle θ and photosensitive tube 2 of body over the ground
CornerWherein, the final roll angle of bodyFor:
Wherein, obtained through experiment test,RφTo measure test variance during φ, RθFor
Measure test variance during θ.
In practical operation, controller 1 is according to the final roll angle of bodyControlled motor, then body is adjusted by motor
The position of upper duck rudder, realizes the amendment to body trajectory.
Claims (10)
1. a kind of body roll angle detecting system based on earth magnetism and sun optic angle, it is characterised in that including four photosensitive tubes (2)
And magnetic survey module (3), GPS module (4) and controller (1) in body are arranged at, wherein, magnetic survey module (3),
GPS module (4) and controller (1) are set gradually from top to bottom, wherein, magnetic survey module (3) is located at the top of the bullet of body,
Four photosensitive tubes (2) are circumferentially uniformly embedded in the outer wall of body, wherein, the output end of magnetic survey module (3), GPS moulds
The input of the output end of block (4) and the output end of four photosensitive tubes (2) with controller (1) is connected.
2. the body roll angle detecting system according to claim 1 based on earth magnetism and sun optic angle, it is characterised in that ground
Magnetic measurement module (3) amplified circuit (6) and analog-digital converter (5) are connected with controller (1), and controller (1) is by recommending
Circuit (7) is connected with magnetic survey module (3).
3. the body roll angle detecting system according to claim 1 based on earth magnetism and sun optic angle, it is characterised in that
GPS module (4) is connected by RS422 interfaces (8) with controller (1).
4. the body roll angle detecting system according to claim 1 based on earth magnetism and sun optic angle, it is characterised in that light
Quick pipe (2) is connected through analog-digital converter (5) with controller (1).
5. a kind of body roll angle detection method based on earth magnetism and sun optic angle, it is characterised in that based on described in claim 1
The body roll angle detecting system based on earth magnetism and sun optic angle, comprise the following steps:
1) GPS module (4) obtains the velocity information of body, and the velocity information of body is sent into controller (1), controller
(1) angle of pitch α and yaw angle β of body, photosensitive tube (2) collection sun light irradiation angle x are calculated according to the velocity information of body, then
The sun light irradiation angle x collected is converted into photoelectric current y, then sent the photoelectric current y into controller (1), is controlled
Device (1) basis receives photoelectric current y, the angle of pitch α of body and yaw angle β calculates the final roll angle φ of photosensitive tube (2) over the ground;
2) the real-time locality magnetic vector v of magnetic survey module (3), then sends the ground magnetic vector v collected to controller (1)
In, controller (1) carries out denoising to described ground magnetic vector v, the ground magnetic vector X after denoising is obtained, then according to the earth magnetism after denoising
Vector X calculates the roll angle θ of body;
3) controller (1) calculates the final rolling of body according to the final roll angle φ of the roll angle θ and photosensitive tube (2) of body over the ground
Corner
6. the body roll angle detection method according to claim 5 based on earth magnetism and sun optic angle, it is characterised in that too
Sunlight irradiation angle x and photoelectric current y corresponding relation is:
Y=Asin2ax
Wherein, α is scale value, A=1.
7. the body roll angle detection method according to claim 5 based on earth magnetism and sun optic angle, it is characterised in that step
Rapid concrete operations 1) are:
90 ° of illumination ranges of each photosensitive tube (2) are intercepted, then the photoelectric current waveform that four photosensitive tube (2) detections are obtained is successively
It is combined, obtains combined waveform, the combined waveform is then divided into 8 sections of waveforms using peak point and valley point as interval, wherein,
Each corresponding two sections of waveforms of photosensitive tube (2), the angle base value of every section of waveformIf either segment waveform
Peak value and valley are respectively p and q, then have y=sin2Ax,A is solved, obtains y=sin2Corresponding to ax
Matched curve;
The photoelectric current that current photosensitive tube (2) obtains is updated in corresponding matched curve, the sun for obtaining current photosensitive tube (2) shines
Firing angle degree x, then the angle using the sun irradiation angle x of current photosensitive tube (2) as current photoelectric current in corresponding section waveform are inclined
DifferenceThen by the angular deviationIt is added on the angle base value angle δ of this section of waveform, obtains the relative roll angle of this section of waveformFinally by the relative roll angle of this section of waveformIt is right as photosensitive tube (2) with the result that reference angle γ is added over the ground
The final roll angle on ground
8. the body roll angle detection method according to claim 7 based on earth magnetism and sun optic angle, it is characterised in that right
Ground reference angle γ is:
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A=cos β tan ξ-cos δ tan α
B=sin δ tan α-sin β tan ξ
Wherein, λ, ξ are respectively azimuth and the elevation angle of the sun of the current time sun.
9. the body roll angle detection method according to claim 5 based on earth magnetism and sun optic angle, it is characterised in that step
Rapid concrete operations 2) are:
The position of magnetic survey module (3) is adjusted, makes the sensitive direction of principal axis and body of Magnetic Sensor in magnetic survey module (3)
Coordinate system direction is consistent, maximums and minimum value of the ground magnetic vector v that calculating Magnetic Sensor collects in sensitive axes y, z, so
Maximums and minimum value of the magnetic vector v in base area in sensitive axes y, z calculate ground magnetic vector v in the equal of sensitive axes y, z direction afterwards
Value m, then ground magnetic vector v is individually subtracted in sensitive axes in the numerical value of ground magnetic vector v that Magnetic Sensor collects in sensitive axes y, z
Y, the average m in z directions, make the ellipse of at the origin centered on the magnetic vector figure conversion of Magnetic Sensor, calculate the oval major axis
Direction and short-axis direction, then by the ELLIPTIC REVOLUTION υ degree, the oval major axis and short axle is set to be located at sensitive axes y and z respectively
On, scaling then is carried out to the oval major axis and short axle, completes the calibration for the ground magnetic vector v that Magnetic Sensor collects, wherein,
Zooming parameterObtaining the ground magnetic vector X after denoising is:
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If (x1,y1,z1) it is missile coordinate system, (x2,y2,z2) it is NED coordinate systems, during projectile flight, obtain the rolling of body
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B=cos β y2-sinψx2
B=cos β sin α x2+sinβsinαy2+cosαz2
Wherein, Magnetic Sensor is twin shaft magnetoresistive transducer, x1And y1The data measured for twin shaft magnetoresistive transducer, x2、y2And z2
For the study plot magnetic vector of locality.
10. the body roll angle detection method according to claim 5 based on earth magnetism and sun optic angle, it is characterised in that
The final roll angle of bodyFor:
Wherein, RφTo measure test variance during φ, RθTo measure test variance during θ.
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Cited By (2)
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CN110044321A (en) * | 2019-03-22 | 2019-07-23 | 北京理工大学 | The method for resolving attitude of flight vehicle using Geomagnetism Information and angular rate gyroscope |
KR20210034787A (en) * | 2019-09-23 | 2021-03-31 | 주식회사 센서피아 | Attitude measuring apparatus for a shell using a pair of geomagnetic sensors and a solar angle sensor |
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US4699333A (en) * | 1984-11-07 | 1987-10-13 | The Boeing Company | On-board flight control panel system |
US6779752B1 (en) * | 2003-03-25 | 2004-08-24 | Northrop Grumman Corporation | Projectile guidance with accelerometers and a GPS receiver |
CN103075930A (en) * | 2012-12-25 | 2013-05-01 | 中北大学 | Method for measuring initial attitude of high-speed rotating projectile body at muzzle |
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US4699333A (en) * | 1984-11-07 | 1987-10-13 | The Boeing Company | On-board flight control panel system |
US6779752B1 (en) * | 2003-03-25 | 2004-08-24 | Northrop Grumman Corporation | Projectile guidance with accelerometers and a GPS receiver |
CN103075930A (en) * | 2012-12-25 | 2013-05-01 | 中北大学 | Method for measuring initial attitude of high-speed rotating projectile body at muzzle |
CN103075930B (en) * | 2012-12-25 | 2014-09-24 | 中北大学 | Method for measuring initial attitude of high-speed rotating projectile body at muzzle |
Cited By (4)
Publication number | Priority date | Publication date | Assignee | Title |
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CN110044321A (en) * | 2019-03-22 | 2019-07-23 | 北京理工大学 | The method for resolving attitude of flight vehicle using Geomagnetism Information and angular rate gyroscope |
CN110044321B (en) * | 2019-03-22 | 2021-01-29 | 北京理工大学 | Method for resolving aircraft attitude by using geomagnetic information and angular rate gyroscope |
KR20210034787A (en) * | 2019-09-23 | 2021-03-31 | 주식회사 센서피아 | Attitude measuring apparatus for a shell using a pair of geomagnetic sensors and a solar angle sensor |
KR102235229B1 (en) * | 2019-09-23 | 2021-04-02 | 주식회사 센서피아 | Attitude measuring apparatus for a shell using a pair of geomagnetic sensors and a solar angle sensor |
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