CN104124528B - Exceedingly high line stabilization tracking in a kind of inertia/GNSS/ satellite beacon combined moving - Google Patents
Exceedingly high line stabilization tracking in a kind of inertia/GNSS/ satellite beacon combined moving Download PDFInfo
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Abstract
A kind of based on inertia/GNSS/ satellite beacon modular antenna tenacious tracking system, adopt low cost MEMS inertia/GNSS integrated navigation system as motion sensor, this system is arranged on the base part of antenna stabilization tracking control system, the angular speed that integrated navigation system exports by control system resolves the angular velocity of satellite motion obtaining antenna surface after coordinate transform, carries out first order stable inertia tracing control to antenna; In addition, inertia/GNSS integrated navigation system can calculate the angle of pitch of the pedestal of degree of precision, roll angle, azimuth by Kalman filter Integrated Navigation Algorithm, can carry out two-stage stabilising tracing control to antenna surface; On this basis, moved and signal peak recognition technology by antenna surface active scan, satellite signal receiver can calculate azimuth and the angle of pitch that satellite is departed from current antenna face, the tenacious tracking completing the third level controls, thus control antenna obtains better tracking effect, form closed loop stability contorting.
Description
Technical field
The present invention relates to exceedingly high line stabilization tracking in a kind of antenna for satellite communication in motion tenacious tracking method, particularly a kind of inertia/GNSS/ satellite beacon combined moving.
Background technology
Communication in moving utilizes geostationary satellite as relaying, can realize between mobile vehicle (car in motion, ship etc.) in real time, the multimedia messages such as high bandwidth, incessantly transitive graph picture, video, speech, be the developing direction of satellite communication industry most prospect.
The key technology of communication in moving is the stable of antenna platform and tracking technique, this is a complicated multi-disciplinary technology-intensive synthesis, and it contains the multinomial technology such as inertial navigation technology, data acquisition and signal processing technology, Precision Machinery Design technology, precision optical machinery kinematics, servo control technique, communication technology of satellite and system engineering.This kind of tenacious tracking system is electromechanical integration, automatic control technology is main body, is the product of multidisciplinary combination.
Abroad from the seventies just be devoted to the research of mobile satellite communication, wherein the U.S., Japan and Canada maintain the leading position.It is reported, united states, japan and other countries develops mobile-satellite TV receiving system already, the tenacious tracking technology of antenna platform is applied to commercial field, and the aircraft as the Shinkansen bullet train of the many commercial yacht of the U.S., Japan, the automobile of Ford, Boeing is first-class is all equipped with mobile-satellite TV receiving system.
External communication in moving equipment development is more rapid, the vehicle-mounted station of marine satellite, Ship Station, airborne station etc. as Grumman Co., Ltd of the U.S., KVH company, overocean communications (SeaTel) company, Japanese NHK company have been the products of the quite stable of introducing to the market, are widely used in commercialization and military domain.Although external communication in moving equipment has reliable in quality, steady performance, but there is several inevitable problem: (1), technical scheme generally adopt traditional steady prosecutor case, system selects the inertia device of higher cost, the control precision of system places one's entire reliance upon the precision of inertia device, generally need to select optical fiber or laser-inertial navigation system, the cost of system is difficult to be controlled; Meanwhile, due to import tariff and agential middle profit, the price that user is purchased is often higher, and general user is difficult to bear its selling price, therefore cannot use by spread; (2), external product relates to import, and supply time and the supply of material quantity of product cannot be protected, simultaneously, the technical support of product and after-sale service cannot be ensured in time, relate in particular to the technological transformation of user's handling characteristics, generally cannot complete, thus limit popularization; (3) principal antenna of Countries is forbidden or is limited to Chinese import, and especially some high-performance relate to the antenna of Military Application, and as KU, KA dual-band antenna, KA antenna etc. all restricts export; (4) antenna for satellite communication in motion is generally all used in the emergency communication fields such as government, public security, People's Armed Police, army, has very harsh requirement to the confidentiality of communication system, and external imported product cannot ensure and control completely in confidentiality; (5) import antenna for satellite communication in motion generally all uses GPS navigation system not to be equipped with BDStar navigation system, and this makes system in case of emergency fall cannot to use.
Compared to abroad, the mobile satellite communication industry start-up time of China is not long, although lack part experience, but achieve preliminary success, some producers have been had to develop communication in moving product, 54 institutes of such as electronics technology group, 38 institutes, 39 institutes, 714 institutes, Aerospace Science and Technology Corporation 503 etc.As 54 the vehicle-mounted antenna for satellite communication in motion of KU wave band developed obtain application among a small circle in military system, 38 antenna for satellite communication in motion developed in No. 7, Divine Land, No. 8, No. 9 return capsules search and rescue in safeguards systems and obtain successful Application.But from current domestic existing antenna for satellite communication in motion development situation, the following Railway Project of main existence: (1) these research institutes exploitation antenna for satellite communication in motion system mainly Government and army etc. to the department of price relative insensitivity, the cost of system is not effectively controlled, simultaneously because technical scheme is relatively conservative, what adopt is all traditional High Accuracy Inertial stability contorting schemes, system cost cannot fundamentally be controlled, therefore, the application of product is very restricted equally; (2) domestic at present communication in moving exploitation producer is all mainly traditional microwave communication institute, the design of the professional speciality of these institutes mainly antenna system, communication link, relatively less to the study general of movement measurement system, servo tracking control system, and the technological core of antenna for satellite communication in motion and key are the measurement of high accuracy real time kinematics and servo tracking control system, therefore, it is not very good for having researched and developed the performance index such as the stablizing effect of successful antenna for satellite communication in motion, real-time tracking precision, moving condition adaptability at present.
Motion-sensing and FEEDBACK CONTROL are that satellite antenna system points to basis that is stable and real-time high-precision tracking, traditional antenna stabilization tracking system often has three kinds of solutions: the first control program adopts gyro angular speed feedback and satellite-signal to scan the scheme combined, program implementation is fairly simple, there is higher bandwidth and real-time, but often there are following 3 problems: 1, system is just followed the tracks of based on angular speed and signal feedback controls, do not introduce attitude angle, azimuthal concept, antenna is not once follow the tracks of upper satellite, again seek star and can become very difficult, simultaneously, due to the existence of gyroscopic drift, seek star under dynamic condition and lose star and catch again and seem more difficult, 2, the drift of low cost MEMS gyro makes the pointing accuracy of system be difficult to be guaranteed, if select high accuracy gyroscope, cost is more difficult control also, 3, the frequency being better than satellite-signal scanning is relatively low, generally be no more than 1Hz, when there is error in angular speed tracking, the simple satellite-signal scan tracing that leans on often can not guarantee good tracking effect, the overall tracking accuracy of system is not high, especially jolting, the section such as continuous turning, the tracking performance of system can decline greatly, is generally difficult to meet consumers' demand.The second control program is the scheme adopting gyro angular speed feedback and single-pulse track to combine, the program is same with the first scheme to be existed and has higher bandwidth and real-time, but the problem 1 described in scheme one and problem 2 exist equally, in addition, monopulse receiver is the microwave signal process device based on satellite-signal intensity and phase compare principle design, can broadly export the tracking error angle of antenna by high-band in real time, system can guarantee to have good tracking effect, but the microwave network of monopulse receiver and Circuits System are all very complicated, cost is very expensive, general user is difficult to bear, the third control program is the gesture feedback scheme based on high accuracy inertial navigation system, the program directly adopts attitude angle, azimuth FEEDBACK CONTROL, antenna directional angle is comparatively accurate, but because attitude angle, azimuth export the slow frame of comparatively angular speed, system promptness declines to some extent, meanwhile, in order to obtain the attitude measurement information of degree of precision, generally also need to select high-precision optical fiber or laser-inertial navigation system, the cost of system is extremely expensive.
Summary of the invention
Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, provides exceedingly high line stabilization tracking in a kind of inertia/GNSS/ satellite beacon combined moving.
The technology of the present invention solution is:
The present invention proposes a kind of based on inertia/GNSS/ satellite beacon modular antenna tenacious tracking system, system adopts low cost MEMS inertia/GNSS integrated navigation system as motion sensor, this integrated navigation system is arranged on the base part of antenna stabilization tracking control system, can export the information such as the angular speed of pedestal, acceleration, position, speed, attitude.The angular speed that integrated navigation system exports by control system resolves the angular velocity of satellite motion obtaining antenna surface after coordinate transform, and stablizes instruction with this angular speed as inner ring, carries out first order stable inertia to antenna, in addition, inertia/GNSS integrated navigation system can calculate the angle of pitch of the pedestal of degree of precision, roll angle, azimuth by Kalman filter Integrated Navigation Algorithm, control system by these three angles by obtaining the three axle drift angles of antenna surface relative to satellite after coordinate transform, and in this, as input instruction, two-stage stabilising and Attitude Tracking are carried out to antenna surface, on this basis, moved and signal peak recognition technology by antenna surface active scan, satellite signal receiver can calculate azimuth and the angle of pitch that satellite is departed from current antenna face, on the one hand, these two drift angles can directly as control command, to the azimuth of antenna surface, the angle of pitch carries out Correction and Control, complete the tenacious tracking of the third level, obtain more accurate tracking effect, meanwhile, this drift angle can be obtained after coordinate inverse transformation attitude angle and the gyro angular speed output error of inertia/GNSS integrated navigation system, and attitude angle is carried out to integrated navigation system, angular speed correction, with make inertia/GNSS integrated navigation system satellite beacon auxiliary under obtain more accurate attitude, course output information, thus control antenna obtains better tracking effect, form closed loop stability contorting.
Exceedingly high line stabilization tracking in a kind of inertia/GNSS/ satellite beacon combined moving, comprises the following steps:
1. by the base corner rate information of inertia system measurement
the angular rate information under antenna coordinate system is obtained by Coordinate Conversion
wherein:
θ
a, γ
a,
be respectively base coordinate system relative to the angle of pitch of antenna coordinate system, roll angle, azimuth;
2. will
as instruction angle, the control of first order tenacious tracking is carried out to antenna, wherein
be respectively the angular velocity of satellite motion of antenna coordinate system pitch axis, polaxis, azimuth axis;
3. by the pitching angle theta of inertia/GNSS integrated navigation system output
b, roll angle γ
b, azimuth
calculating antenna surface is the pitch demand angle θ needed satelloid
p, polarization instruction angle γ
p, orientation instruction angle
4. 3. step is calculated pitch demand angle θ
p, polarization instruction angle γ
p, orientation instruction angle
as control command, control motor driven antenna face, carry out second level tenacious tracking control, make antenna surface can to satelloid.
5., on the basis of aforementioned stable, moved and signal peak recognition technology by antenna surface active scan, satellite signal receiver can calculate the azimuth that satellite is departed from current antenna face
with angle of pitch Δ θ
p, using two drift angles as control command, carry out Correction and Control to the azimuth of antenna surface, the angle of pitch, the tenacious tracking completing the third level controls.
6. pass through
and Δ θ
pcorrect orientation instruction angle is obtained after correction
with pitch demand angle θ
p', by coordinate inverse transformation, the pitching of inertial navigation system, roll, azimuth revision directive Δ θ can be back-calculated to obtain
b, Δ γ
b,
and calculate correct inertial navigation pitching, roll, azimuth be:
θ
b′＝θ
b+Δθ
b
γ
b′＝γ
b+Δγ
b
By above formula (3) substitute into formula (1), formula (2), repeated execution of steps 1.-6., can realize controlling the tenacious tracking of antenna.
The described step 5. motion of antenna surface active scan and the implementation method of signal peak recognition technology is:
1) when antenna surface is completely to satelloid, the intensity of the signal that antenna receives is maximum, when the azimuth of antenna surface, the angle of pitch depart from satellite certain angle, the intensity of the signal that antenna receives will weaken to some extent, the azimuth axis in control antenna face, pitch axis certain among a small circle in do scanning motion, the intensity of the satellite-signal that antenna receives in writing scan process, antenna surface pitching drift angle, functional relation between drift angle, orientation and signal strength signal intensity can be set up:
In formula, V
maxrepresent that antenna surface is to satellite-signal intensity level maximum during satelloid, V represents satellite-signal intensity level under current state,
represent drift angle, orientation
the drop-out value of the satellite-signal intensity caused; f
2(Δ θ) represents the drop-out value of the satellite-signal intensity that pitching drift angle Δ θ causes;
2) move in space according to certain rules around its azimuth axis and pitch axis in control antenna face, and its characteristics of motion is:
In formula,
be respectively the scanning motion angular speed of antenna surface pitch axis, azimuth axis, ω
0for the maximum angular rate of pitch orientation, azimuth direction scanning motion, f is the frequency of antenna surface scanning motion;
3) the satellite-signal intensity V in record antenna surface scanning motion process and the pitching drift angle Δ θ of correspondence and drift angle, orientation
and it is as follows to set up corresponding relation:
4) known according to formula (5), Δ θ and
phase 90 °, when | Δ θ | time maximum,
be 0; When
time maximum, Δ θ is 0; According to formula (4) and formula (5), be defined in
when being 0, signal strength signal intensity when Δ θ forward is maximum is
signal strength signal intensity when Δ θ negative sense is maximum is
when Δ θ is 0,
signal strength signal intensity when forward is maximum is
signal strength signal intensity when negative sense is maximum is
5) will
pitching drift angle described in substitution formula (4), the functional relation between drift angle, orientation and signal strength signal intensity, can calculate pitching drift angle Δ θ and the drift angle, orientation of antenna surface and satellite
value.
Operation principle of the present invention is: mobile satellite communication antenna (being called for short " communication in moving "), satellite antenna can be made on the carrier (car, ship, aircraft) of movement to aim at geostationary satellite all the time, realize realtime graphic and the transfer of data of high bandwidth, to be widely used prospect in departments such as national defence, frontier defense, anti-terrorism, emergency disaster relief, transport by sea, governments, be the most important means of emergency communication and remote communication, can really realize " interconnected ubiquitous ".
Servo tracking control system technology is the core technology of " communication in moving " antenna, in order to make satellite antenna can real-time high-precision ground tracking satellite, following 2 subject matters must be solved:
(1) in carrier movement process, athletic posture and the location variation that carrier measured in real time, accurately by high performance transducer is needed;
(2) according to the attitudes vibration of carrier, real-time resolving antenna directional angle is at the variable quantity in space, and the motion of carrier is isolated fast by the servo tracking control system that high performance motor forms, antenna directional angle is consistent at inertial space, guarantees the maximum of locking satellite signal.
The base of antenna for satellite communication in motion is provided with a set of inertial navigation system, this system can measure the positional information (longitude of carrier exactly, latitude), attitude information (pitching, roll, orientation) and three axis angular rate information, control system goes out the satellite angle of pitch under geographic coordinate system according to the positional information calculation of used satellite longitude and carrier, polarizing angle, azimuth, pass through ordinate transform in conjunction with inertial navigation attitude information again, by the satellite angle of pitch of geographic coordinate system, polarizing angle, azimuth is converted to the antenna corner under carrier (as car body) coordinate system.The real-time position according to carrier, course and attitude information are calculated the azimuth of antenna relative satellite, the angle of pitch and polarizing angle by servo system, control motor adjust to corresponding corner to satelloid according to position closed loop (adopting encoder feedback to realize).
The present invention's advantage is compared with prior art: the present invention proposes the tenacious tracking technology of a kind of gyro, integrated navigation system, satellite-signal three grades feedback, and first system utilizes gyro angular speed feedback signal to carry out feedfoward control, guarantees the promptness of system; Then low cost MEMS inertia device and satellite navigation system (the GPS/ Big Dipper) are carried out information fusion, realize stability and the accuracy of attitude measurement, utilize attitude signal to carry out secondary feedback simultaneously, guarantee the accuracy of antenna directional angle, because system adopts GPS/ Big Dipper signal supplementary inertial to measure, revise the error of MEMS inertia device, thus make low cost inertia device can meet the requirement of high accuracy control, on the basis of guaranteeing control system performance, greatly reduce the cost of system; Finally satellite-signal is introduced closed-loop control system, satellite-signal recognition technology is utilized to estimate the tracking drift angle of antenna, guarantee that antenna directional angle is in signal maximum position all the time by three grades of feedbacks, again guarantee pointing accuracy, improve the tracking reliability of system, system can decline at combined navigation system performance or ensure stability and the reliability of system works in idle situation, and can relax control system further and rely on the precision of inertia device, reduces costs further.In addition, satellite beacon signals can revise the attitude error of inertia/GNSS integrated navigation system, and estimate the angular speed error obtaining gyro further, thus the tenacious tracking precision of the first order (speed ring) and the second level (attitude ring) can be improved.
Accompanying drawing explanation
Fig. 1 is antenna stabilization tracking flow chart of the present invention.
Embodiment
1, an exceedingly high line stabilization tracking in inertia/GNSS/ satellite beacon combined moving, its implementation process as shown in Figure 1, specifically comprises the following steps:
1. by the base corner rate information of inertia system measurement
the angular rate information under antenna coordinate system is obtained by Coordinate Conversion
wherein:
θ
a, γ
a,
be respectively base coordinate system relative to the angle of pitch of antenna coordinate system, roll angle, azimuth;
2. will
as instruction angle, the control of first order tenacious tracking is carried out to antenna, wherein
be respectively the angular velocity of satellite motion of antenna coordinate system pitch axis, polaxis, azimuth axis.
3. by the pitching angle theta of inertia/GNSS integrated navigation system output
b, roll angle γ
b, azimuth
calculating antenna surface is the pitch demand angle θ needed satelloid
p, polarization instruction angle γ
p, orientation instruction angle
4. 3. step is calculated pitch demand angle θ
p, polarization instruction angle γ
p, orientation instruction angle
as control command, control motor driven antenna face, the tenacious tracking realizing the second level controls, thus guarantees that antenna surface can accurately to satelloid.
5., on the basis of aforementioned stable, moved and signal peak recognition technology by antenna surface active scan, satellite signal receiver can calculate the azimuth that satellite is departed from current antenna face
with angle of pitch Δ θ
p, using two drift angles as control command, carry out Correction and Control to the azimuth of antenna surface, the angle of pitch, the tenacious tracking completing the third level controls.
6. pass through
and Δ θ
pcorrect orientation instruction angle is obtained after correction
with pitch demand angle θ
p', by coordinate inverse transformation, the pitching of inertial navigation system, roll, azimuth revision directive Δ θ can be back-calculated to obtain
b, Δ γ
b,
and calculate correct inertial navigation pitching, roll, azimuth be:
θ
b′＝θ
b+Δθ
b
γ
b′＝γ
b+Δγ
b
By above formula (3) substitute into formula (1), formula (2), repeated execution of steps 1.-6., can realize controlling the tenacious tracking of antenna.
The described step 5. motion of antenna surface active scan and the implementation method of signal peak recognition technology is:
1) when antenna surface is completely to satelloid, the intensity of the signal that antenna receives is maximum, when the azimuth of antenna surface, the angle of pitch depart from satellite certain angle, the intensity of the signal that antenna receives will weaken to some extent, the azimuth axis in control antenna face, pitch axis certain among a small circle in do scanning motion, the intensity of the satellite-signal that antenna receives in writing scan process, antenna surface pitching drift angle, functional relation between drift angle, orientation and signal strength signal intensity can be set up:
In formula, V
maxrepresent that antenna surface is to satellite-signal intensity level maximum during satelloid, V represents satellite-signal intensity level under current state,
represent drift angle, orientation
the drop-out value of the satellite-signal intensity caused; f
2(Δ θ) represents the drop-out value of the satellite-signal intensity that pitching drift angle Δ θ causes;
2) move in space according to certain rules around its azimuth axis and pitch axis in control antenna face, and its characteristics of motion is:
In formula,
be respectively the scanning motion angular speed of antenna surface pitch axis, azimuth axis, ω
0for the maximum angular rate of pitch orientation, azimuth direction scanning motion, f is the frequency of antenna surface scanning motion;
3) the satellite-signal intensity V in record antenna surface scanning motion process and the pitching drift angle Δ θ of correspondence and drift angle, orientation
and it is as follows to set up corresponding relation:
4) known according to formula (5), Δ θ and
phase 90 °, when | Δ θ | time maximum,
be 0; When
time maximum, Δ θ is 0; According to formula (4) and formula (5), be defined in
when being 0, signal strength signal intensity when Δ θ forward is maximum is
signal strength signal intensity when Δ θ negative sense is maximum is
when Δ θ is 0,
signal strength signal intensity when forward is maximum is
signal strength signal intensity when negative sense is maximum is
5) will
substitution formula (4), can calculate pitching drift angle Δ θ and the drift angle, orientation of antenna surface and satellite
value.
Non-elaborated part of the present invention belongs to techniques well known.
Obviously, for the person of ordinary skill of the art, other execution mode also may be made with reference to embodiment mentioned above.Embodiment in the present invention is all exemplary instead of circumscribed.All amendments within the essence of claim technical scheme of the present invention all belong to its scope required for protection.
Claims (2)
1. an exceedingly high line stabilization tracking in inertia/GNSS/ satellite beacon combined moving, is characterized in that: comprise the following steps:
1. by the base corner rate information of inertia system measurement
the angular rate information under antenna coordinate system is obtained by Coordinate Conversion
wherein:
θ
a, γ
a,
be respectively base coordinate system relative to the angle of pitch of antenna coordinate system, roll angle, azimuth;
2. will
as instruction angle, the control of first order tenacious tracking is carried out to antenna, wherein
be respectively the angular velocity of satellite motion of antenna coordinate system pitch axis, polaxis, azimuth axis;
3. by the pitching angle theta of inertia/GNSS integrated navigation system output
b, roll angle γ
b, azimuth
calculating antenna surface is the pitch demand angle θ needed satelloid
p, polarization instruction angle γ
p, orientation instruction angle
4. 3. step is calculated pitch demand angle θ
p, polarization instruction angle γ
p, orientation instruction angle
as control command, control motor driven antenna face, second level tenacious tracking control is carried out to antenna, make antenna surface can to satelloid;
5., on the basis of aforementioned stable, moved and signal peak recognition technology by antenna surface active scan, satellite signal receiver can calculate the azimuth that satellite is departed from current antenna face
with angle of pitch Δ θ
p, using two drift angles as control command, carry out Correction and Control to the azimuth of antenna surface, the angle of pitch, the tenacious tracking completing the third level controls;
6. pass through
and Δ θ
pcorrect orientation instruction angle is obtained after correction
with pitch demand angle θ '
p, by coordinate inverse transformation, the pitching of inertial navigation system, roll, azimuth revision directive Δ θ can be back-calculated to obtain
b, Δ γ
b,
and calculate correct inertial navigation pitching, roll, azimuth be:
θ′
b＝θ
b+Δθ
b
γ′
b＝γ
b+Δγ
b
Repeated execution of steps 1.-6., can realize controlling the tenacious tracking of antenna.
2. an exceedingly high line stabilization tracking in inertia/GNSS/ satellite beacon combined moving, is characterized in that: the described step 5. motion of antenna surface active scan and the implementation method of signal peak recognition technology is:
1) when antenna surface is completely to satelloid, the intensity of the signal that antenna receives is maximum, when the azimuth of antenna surface, the angle of pitch depart from satellite certain angle, the intensity of the signal that antenna receives will weaken to some extent, azimuth axis, the pitch axis in control antenna face do scanning motion within the specific limits, the intensity of the satellite-signal that antenna receives in writing scan process, antenna surface pitching drift angle, functional relation between drift angle, orientation and signal strength signal intensity can be set up:
In formula, V
maxrepresent that antenna surface is to satellite-signal intensity level maximum during satelloid, V represents satellite-signal intensity level under current state,
represent drift angle, orientation
the drop-out value of the satellite-signal intensity caused; f
2(Δ θ) represents the drop-out value of the satellite-signal intensity that pitching drift angle Δ θ causes;
2) move in space according to certain rules around its azimuth axis and pitch axis in control antenna face, and its characteristics of motion is:
In formula,
be respectively the scanning motion angular speed of antenna surface pitch axis, azimuth axis, ω
0for the maximum angular rate of pitch orientation, azimuth direction scanning motion, f is the frequency of antenna surface scanning motion;
3) the satellite-signal intensity V in record antenna surface scanning motion process and the pitching drift angle Δ θ of correspondence and drift angle, orientation
and it is as follows to set up corresponding relation:
4) according to step 2) known, Δ θ and
phase 90 °, when | Δ θ | time maximum,
be 0; When
time maximum, Δ θ is 0; According to step 1), be defined in
when being 0, signal strength signal intensity when Δ θ forward is maximum is
signal strength signal intensity when Δ θ negative sense is maximum is
when Δ θ is 0,
signal strength signal intensity when forward is maximum is
signal strength signal intensity when negative sense is maximum is
5) will
substitute into step 1) described in antenna surface pitching drift angle, functional relation between drift angle, orientation and signal strength signal intensity, pitching drift angle Δ θ and the drift angle, orientation of antenna surface and satellite can be calculated
value.
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