CN101893440B - Celestial autonomous navigation method based on star sensors - Google Patents

Abstract

The invention provides a celestial autonomous navigation method based on star sensors, which comprises the following steps: calculating attitude information based on a geocentric inertial coordinate system, which is output by a star sensor; calculating the optical axis direction based on the geocentric inertial coordinate system; converting the optical axis direction based on the geocentric inertial coordinate system into optical axis direction based on a WGS84 coordinate system; reading the included angles alpha 0 and beta 0 between the X and Y directions of the star sensor and the horizontal direction from a laser level meter; calculating the direction in the WGS84 coordinate system when the optical axis direction is perpendicular to the horizontal level; calculating the longitude alpha and latitude beta of the underground point S of the carrier; and outputting the attitude q and the longitude alpha and latitude beta of the underground point of the carrier in the geocentric inertial coordinate system. The invention avoids measurement and control errors caused by horizontal reference platforms, enhances the measuring accuracy, and simultaneously outputs the attitude of three axes and the longitude and latitude of the carrier in the geographic coordinate system in real time, thereby completely realizing celestial autonomous navigation.

Description

Celestial autonomous navigation method based on star sensor

(1) technical field

The present invention relates to the celestial navigation technology, is exactly a kind of celestial autonomous navigation method based on star sensor specifically.

(2) background technology

Sixties Mo in last century early seventies, inertial technology begins to be applied to various mapping operations.The U.S. has developed the inertial positioning orientation system, is called for short the PADS system.The transporting cars that the inertial positioning orientation system is housed is after one section tortuous distance has been exercised on ground, and the horizontal level precision of being determined by system is 20 meters, and the height root-mean-square error is 10 meters.This technological achievement obviously is significant concerning the application of inertial technology.

After the inertial positioning orientation system was succeeded in developing, AUS had successively been developed inertial positioning system (Inertial Position System, IPS system) again.The purpose of inertial positioning system development is further to improve bearing accuracy on the basis of inertial positioning orientation system.Inertial positioning system determines that the orientation is to refer to realize that by electro-optic theodolite any light, electrical communication do not take place for this system and the external world on the northern basis at gyrocompass.Therefore good concealment is worked and is not subjected to the restriction of environmental baseline.It can provide initial alignment needed azimuth reference.Yet the azimuth reference precision of Que Dinging depends primarily on the level of gyro and accelerometer in this way, generally can only reach several angles branch, and its site error can accumulate in time and increase.This can meet the demands concerning short-range navigational system; And just can not satisfy accuracy requirement to the navigational system of long distance.Therefore merely rely on raising inertia type instrument precision to improve very difficulty of bearing accuracy.

Radio navigation system utilizes radio vectored flight device along specified course, the navigation technology that arrives at the destination at the appointed time.Typical navigational system has rowland A, rowland C, Omega, goniometer etc.These systems utilize the propagation characteristic of radiowave can measure the navigation parameter of carrier (orientation, distance and speed), calculate the deviation with specified course, thereby make carrier eliminate deviation to keep correct course line.But radio navigation system operating distance is limited, have the service blind area, the long-range navigation precision is lower, be easy to be attacked, and its application and development are limited to.

Satellite navigation has advanced science and technology development greatly as the main mode of modern times navigation.Its advantage is the influence that the radio wave propagation is not subjected to factors such as ground meteorology, landform substantially, and the foundation of the station is not subjected to the restriction of geographical conditions yet, and distance is also unrestricted, therefore can set up a Global Navigation System at an easy rate.Yet the common trait of satellite navigation is that its navigation signal is extremely faint by the navigation message of specified beacon with characteristic frequency broadcast specific format.The technical characterictic that " three fixed one is weak " determined that satellite navigation system is vulnerable and controlled.

GPS (Global Position System, GPS) be that a kind of of U.S. development can be regularly and the navigational system of the spatial intersection of range finding fixed point, can provide continuously to global user, real-time, high accuracy three-dimensional position, three-dimensional velocity and temporal information.

Yet gps signal passes earthward from the space, and it is not perfectly safe, still can be disturbed and destruction.In " allied forces' action ", gps signal may be subjected to the involuntary interference of U.S. army's electronic warfare air plane (as EA-6B) and unmanned jammer, and mil is managing to overcome this problem.As long as this explanation takes suitable measure just can disturb gps system, reduce its bearing accuracy, make to rely on the armament systems off-course that GPS carries out navigator fix or guidance.Russia put on display a kind of GPS jammer in 1997 on the airplane exhibition of Moscow, this jammer can disturb GPS and GLONASS satellite-signal, can suppress the operate as normal of several hundred kilometers with inner receiver.

Along with the degree of dependence to GPS is increasing, will inevitably worry more and more that also its gps satellite is under attack simultaneously.Gps satellite does not take anti-nuclear effect to reinforce and preventing laser weapon salvo, does not have the anticollision detector, does not have motor-driven change rail ability yet.So more under attack than being easier to, along with the increase of its effect, it also will inevitably become the target of being attacked.

GPS is controlled by US military in addition, and its army's code encryption degree height can't utilize; Though its people's sign indicating number is available, poor anti jamming capability; Newly Yan Zhi gps satellite may have some areas closing function.Thereby the utilization of GPS is subjected to U.S.'s restriction.

The vitals of celestial navigation is a star sensor.Star sensor is widely used on the various spacecrafts as the higher attitude sensor of a kind of precision.Compare with other satellite navigations such as GPS with inertial navigation, the many advantages that possess such as the precision height, do not need long ground positioning and directing; And star sensor has the not available advantage of GPS navigation aspect anti-interference.Therefore present most of scholar adopts the drift that utilizes astronomical parameter correction angle measurement gyro; Perhaps provide inertial navigation information by inertial navigation system, GPS provides position or Position And Velocity information, and celestial navigation (star sensor) provides attitude information, and these information simple combination are got up just to obtain integrated navigation information, thereby realizes navigational system.Yet these systems have only utilized star sensor output high-accuracy posture information, also can only use as the correcting device of inertial navigation, do not use as a kind of independently navigation means.

In order to make full use of the star sensor precise information.A lot of scholars adopt inertial equipment to provide horizontal reference to realize some astronomical autonomous positioning, because the restriction of inertial equipment parts and the restriction of platform control method are difficult to the dynamically complete level of control platform datum, thereby have reduced the precision of horizontal reference.The error of horizontal reference reduces the reduction that causes navigation accuracy.The objective requirement that this and high precision are navigated is incompatible.Be subjected to the bottleneck of horizontal reference restriction having become celestial navigation to the high precision development.

In recent years, occurred reflecting independent navigation based on the starlight of star sensor.This navigate mode ultimate principle is as follows: observe two fixed stars on star sensor simultaneously, the starlight height of a fixed star is much larger than atmospheric height, starlight is reflected, the starlight of another fixed star is subjected to atmospheric refraction, angular distance between such two bundle starlights will be different from nominal value, and the variable quantity of this angular distance is the starlight refraction angle.Utilize the relation and the atmospheric density of starlight refraction angle and atmospheric density with height change ready-made mathematical model to be arranged also, thereby determine the height of starlight in atmospheric envelope, this has highly reflected the geometric relationship between the carrier and the earth.This navigate mode requires atmospheric density more accurate with the mathematical model of height change.Yet, be subjected to atmosphericly to influence, the influence of factor such as changes of seasons and weather, be difficult to set up more accurate atmosphere mathematical model in the world.And adopt this air navigation aid must the visual field in part fixed star starlight pass atmospheric envelope, cause these fixed stars to have deviation as the position on plane, thereby reduced the output attitude of star sensor at star sensor.

(3) summary of the invention

The object of the present invention is to provide a kind of real-time output three-axis attitude, export the celestial autonomous navigation method based on star sensor of the longitude and latitude of carrier under geographic coordinate system in real time.

The object of the present invention is achieved like this: described celestial autonomous navigation method based on star sensor, and step is as follows:

Step 1: calculate the attitude information of star sensor output based on geocentric inertial coordinate system;

Step 2: calculating is pointed to based on the optical axis under the geocentric inertial coordinate system according to attitude information;

Step 3: point to pointing to be converted to based on the optical axis under the WGS84 coordinate system based on the optical axis under the geocentric inertial coordinate system; From laser leveler, read the angle α of star sensor X and Y direction and horizontal direction ₀And β ₀

Step 4: according to α ₀And β ₀Sensing when calculating the optical axis sensing under the WGS84 coordinate system with horizontal vertical;

Step 5: the longitude α and the latitude β that calculate underground some S of carrier;

Step 6: attitude q and underground some longitude α and the latitude β of output carrier under geocentric inertial coordinate system.

The present invention is based on the celestial autonomous navigation method of star sensor, adopt photoelectric sensor to measure the angle of carrier platform (being the celestial navigation system platform) and surface level, avoided like this because measurement and the departure that the horizontal reference platform brings, thereby improved measuring accuracy.When exporting three-axis attitude in real time, also can export longitude and the latitude of carrier under geographic coordinate system in real time, so realize celestial autonomous navigation fully.

(4) description of drawings

Fig. 1 is a systematic schematic diagram of the present invention;

Fig. 2 is the celestial autonomous navigation method workflow diagram that the present invention is based on star sensor;

Fig. 3 is an employing model satellite star sensor test result oscillogram of the present invention;

Fig. 4 is local longitude and a latitude error of exporting the calculating of three appearance angles and angle measurement device according to star sensor continuously of the present invention;

Fig. 5 is applied to the workflow block diagram of certain carrier for the present invention;

Fig. 6 is applied to the synoptic diagram of certain carrier, O for the present invention _s-X _sY _sZ _s: star sensor image space coordinate system, O _s'-X _s' Y _s, Z _s': the translation of star sensor image space coordinate system, wherein O _s' be an O _sSubpoint on ground surface, O _hX _hY _hZ _h: with O _s' be a horizontal coordinates of initial point.

(5) embodiment

The invention will be further described for example below in conjunction with accompanying drawing.

Embodiment 1: in conjunction with Fig. 1, a kind of celestial autonomous navigation method based on star sensor of Fig. 2 the present invention, step is as follows:

Step 1: calculate the attitude information of star sensor output based on geocentric inertial coordinate system;

Step 2: calculating is pointed to based on the optical axis under the geocentric inertial coordinate system according to attitude information;

Step 3: point to pointing to be converted to based on the optical axis under the WGS84 coordinate system based on the optical axis under the geocentric inertial coordinate system; From laser leveler, read the angle α of star sensor X and Y direction and horizontal direction ₀And β ₀

Step 4: according to α ₀And β ₀Sensing when calculating the optical axis sensing under the WGS84 coordinate system with horizontal vertical;

Step 5: the longitude α and the latitude β that calculate underground some S of carrier;

Step 6: attitude q and underground some longitude α and the latitude β of output carrier under geocentric inertial coordinate system.

Embodiment 2: in conjunction with Fig. 1-Fig. 4, celestial navigation system will really be realized independent navigation, and mainly the problem of Xie Jueing is: breaking away from by inertial equipment provides the constraint of horizontal reference and asks the measurement physical quantity of carrier navigation information.This shows, break away from the restriction of horizontal reference, seek the measurement physical quantity of carrier navigation information in addition, is the certainty that realizes the high precision celestial navigation.The objective of the invention is: set up celestial autonomous navigation system based on star sensor.Total system as shown in Figure 1.Each coordinate system is defined as follows:

Geocentric inertial coordinate system O ₀-x ₀y ₀z ₀: true origin O ₀In geocenter, x ₀Axle points to T ₀Mean equinox constantly, z ₀Axle points to T ₀Mean pole constantly, y ₀Axle is at T ₀In the mean equator face constantly, form right-handed coordinate system eastwards.Frequent employing Besselian year (Bessel, or be called Besselian year.Its length is the length of mean tropical year, i.e. 365.2421988 mean solar days.Bessel commonly used is meant the moment that sun mean longitude equals 280 epoch, for example 1950.0, and be not 0 o'clock on the 1st January of nineteen fifty, but 22: 09: 2 on the 31st Dec in 1949) first as T ₀, for example Shi Misong star catalogue (Smi thsonian AstrophysicalObservatory Star Catalog) adopts 2000.0 to be T ₀, be called epoch 2000.0 (being called for short J2000.0).This programme adopts the J2000.0 inertial coordinates system.

WGS-84 coordinate system O _w-x _wy _wz _wTrue origin O _wBe earth centroid, the z of its earth's core rectangular coordinate system in space _wAxle points to the agreement earth utmost point (CTP) direction of BIH (international time) 1984.0 definition, x _wAxle points to the zero meridian ellipse of BIH 1984.0 and the intersection point in CTP equator, y _wAxle and z _wAxle, x _wThe vertical formation of axle right-handed coordinate system;

Geographic coordinate system (sky, northeast coordinate system) O _e-x _ey _ez _e: true origin O _eThe moving object and the earth line of centres and earth surface intersection point (or getting the subpoint that movable body is gone up at the earth's surface), x _eAxle points to east, y in local level _eAxle energized north in local level, z _eAxle is along local ground vertical line direction and point to zenith.x _e-O _e-y _eBe ground level or surface level;

Star sensor image space coordinate system O _s-x _sy _sz _s: O _sFor star sensor as planar central, x _s, y _sBe respectively two axles that are parallel to the picture planimetric coordinates, x _s, y _s, z _sConstitute the right-hand rule.

If the longitude α of underground some S of carrier is (0≤α＜2 π; When 0≤α＜π is east longitude, is west longitude when π≤α＜2 π.Together following) and latitude β (pi/2≤β＜pi/2; When-pi/2≤β＜0 is south latitude, is north latitude when 0≤β＜pi/2.Down together).The direction vector of S under the WGS-84 coordinate system is so:

${\stackrel{\→}{S}}_{\mathrm{oi}}=\left(\begin{array}{c}\cos \mathrm{\β}\cos \mathrm{\α}\\ \cos \mathrm{\β}\sin \mathrm{\α}\\ \sin \mathrm{\β}\end{array}\right)---\left(1\right)$

Measure two picture planar axes x of star sensor respectively according to the recognition result of star sensor and laser level measurement component _sAnd y _sBe respectively α with the angle of horizontal direction ₀And β ₀Derive the mathematical model of calculating the direction vector of carrier under the WGS-84 coordinate system, again basis

(1) can obtain longitude α and the latitude β of carrier face of land millet cake S, thereby realize location carrier.When so this system exports attitude of carrier, the position that can export carrier again.

The present invention proposes the celestial autonomous navigation method based on star sensor, and main contents are as follows:

For same reference frame, because carrier (referring generally to aircraft) attitude is well-determined, attitude parameter is described and is embodied in the axial physical quantity of reference coordinate, is called attitude parameter, and various ways is arranged.The most general attitude parameter is the direction cosine A between body coordinate axis and the reference coordinate axle.

According to the definition of direction cosine, the geometric direction of carrier coordinate system in reference frame can be defined as:

$\left[\begin{array}{c}{x}_o\\ y_o\\ z_o\end{array}\right]=A\left[\begin{array}{c}{x}_0\\ y_0\\ z_0\end{array}\right]---\left(2\right)$

Subscript o wherein, 0 expression carrier coordinate system and reference frame.

$A=\left[\begin{array}{ccc}{A}_{\mathrm{xx}}& A_{\mathrm{xy}}& A_{\mathrm{xz}}\\ A_{\mathrm{yx}}& A_{\mathrm{yy}}& A_{\mathrm{yz}}\\ A_{\mathrm{zx}}& A_{\mathrm{zy}}& A_{\mathrm{zz}}\end{array}\right]---\left(3\right)$

In the problem identificatioin of carrier three-axis attitude, because matrix A has been determined the state of carrier in reference frame fully, so claim that direction cosine matrix A is an attitude matrix.

Can change mutually between the various forms of attitude parameters.Therefore direction cosine matrix A can be expressed as follows again:

$A=\left[\begin{array}{ccc}{q}_1^2-q_2^2-q_3^2+q_4^2& 2(q_1{q}_2+q_3{q}_4)& 2(q_1{q}_3-q_2{q}_4)\\ 2(q_1{q}_2-q_3{q}_4)& -q_1^2+q_2^2-q_3^2+q_4^2& 2(q_2{q}_3+q_1{q}_4)\\ 2(q_1{q}_3+q_2{q}_4)& 2(q_2{q}_3-q_1{q}_4)& -q_1^2-q_2^2+q_3^2+q_4^2\end{array}\right]---\left(4\right)$

Q=q wherein ₁I+q ₂J+q ₃K+q ₄, be the attitude information of star sensor under geocentric inertial coordinate system.

So the unit vector that the star sensor optical axis points under geocentric inertial coordinate system is:

${\stackrel{\→}{r}}_0=\left\{\begin{array}{ccc}2(q_1{q}_3+q_2{q}_4)& 2(q_2{q}_3-q_1{q}_4)& -q_1^2-q_2^2+q_3^2+q_4^2\end{array}\right\}---\left(5\right)$

Calculate the star sensor optical axis and point to vector under the WGS84 coordinate system:

${\stackrel{\→}{r}}_w={\left[\mathrm{ER}\right]}^{-1}{\stackrel{\→}{r}}_0---\left(6\right)$

Wherein [ER] is the earth rotation matrix, is expressed as:

[ER]＝R _z(θ _g) (7)

R wherein _z(θ _z) represent around z axle rotation θ _zThe transformation matrix of coordinates at angle.

$R_z\left({\mathrm{\θ}}_g\right)=\left[\begin{array}{ccc}\cos {\mathrm{\θ}}_g& \sin {\mathrm{\θ}}_g& 0\\ -\sin {\mathrm{\θ}}_g& \cos {\mathrm{\θ}}_g& 0\\ 0& 0& 1\end{array}\right]---\left(8\right)$

θ _g(unit: radian) be true sidereal time, can be expressed as:

${\mathrm{\θ}}_g={\stackrel{\‾}{\mathrm{\θ}}}_g+\mathrm{\Δ\ψ}\cos (\stackrel{\‾}{\mathrm{\ϵ}}+\mathrm{\Δ\ϵ})---\left(9\right)$

Be mean obliquity, computing formula is:

$\stackrel{\‾}{\mathrm{\ϵ}}=84381\text{'}\text{'}.448-46\text{'}\text{'}.8150\·T_u-0\text{'}\text{'}.00059\·{T_u}^2+0\text{'}\text{'}.001813\·{T_u}^3---\left(10\right)$

T _uIt is the Julian century number of starting at from 2000.0.Be expressed as follows;

$T_u=\frac{\mathrm{JD}\left(t\right)-2451545.0}{36525}---\left(11\right)$

JD (t) expression is calculated the scholar of moment t correspondence and is omited the sky.

(unit: Greenwich mean sidereal time (GMST) radian), computing formula is as follows:

${\stackrel{\‾}{\mathrm{\θ}}}_g=2\mathrm{\π}[\frac{{67310.}^{S}54841}{86400.0}+(\frac{{87600}^h}{24}+\frac{8640184.812866}{86400.0})T_U$ (12)

$+\frac{{0.}^{S}093104}{86400.0}{T}_U^2-\frac{6.2\×{10}^{-6}}{86400.0}{T}_U^3]$

Δ ε, Δ ψ are respectively nutation in obliquity and nutation of longitude.Calculation expression is as follows:

$\mathrm{\Δ\ψ}=\underset{i=1}{\overset{106}{\mathrm{\Σ}}}(A_i+A_i^{\text{'}}t)\sin \left(\underset{j=1}{\overset{5}{\mathrm{\Σ}}}{k}_{\mathrm{ij}}{\mathrm{\α}}_j\left(t\right)\right)---\left(13\right)$

$\mathrm{\Δ\ϵ}=\underset{i=1}{\overset{106}{\mathrm{\Σ}}}(B_i+B_i^{\text{'}}t)\cos \left(\underset{j=1}{\overset{5}{\mathrm{\Σ}}}{k}_{\mathrm{ij}}{\mathrm{\α}}_j\left(t\right)\right)---\left(14\right)$

A wherein _i, A ' _i, B _i, B ' _i, k _IjBe constant, can in IAU1980 nutating sequence table, find.T is the carrier time.

Angle according to carrier diaxon and surface level is respectively α again ₀And β ₀, the pointing vector in the time of can calculating optical axis perpendicular to surface level under the WGS84 coordinate system:

${\stackrel{\→}{S}}_{\mathrm{oi}}=R_x\left({\mathrm{\β}}_0\right)R_y\left({\mathrm{\α}}_0\right){\stackrel{\→}{r}}_w---\left(15\right)$

R wherein _x(β ₀) represent around x axle rotation β ₀The transformation matrix of coordinates at angle.That is:

$R_x\left({\mathrm{\β}}_0\right)=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos {\mathrm{\β}}_0& \sin {\mathrm{\β}}_0\\ 0& -\sin {\mathrm{\β}}_0& \cos {\mathrm{\β}}_0\end{array}\right]---\left(16\right)$

R _y(α ₀) represent around y axle rotation alpha ₀The transformation matrix of coordinates at angle.That is:

$R_y\left({\mathrm{\α}}_0\right)=\left[\begin{array}{ccc}\cos {\mathrm{\α}}_0& 0& -\sin {\mathrm{\α}}_0\\ 0& 1& 0\\ \sin {\mathrm{\α}}_0& 0& \cos {\mathrm{\α}}_0\end{array}\right]---\left(17\right)$

According to Just can calculate longitude α and the latitude β of carrier face of land millet cake S.

Main performance index:

We select certain model satellite star sensor for use, and (hypercomplex number is q=q in the table as the attitude output block of celestial navigation system ₀* i+q ₁* j+q ₂* k+q ₃), the laser level angle measurement parts of employing XXX model are measured the angle of star sensor X-axis and Y-axis and horizontal direction.

Because star sensor can directly be exported the three-axis attitude of carrier, star sensor system itself has determined the precision and the reliability of attitude, adopts the navigator of certain model to carry out outfield experiments in certain research station respectively.Utilize these experimental results to calculate the longitude and the latitude on the local face of land respectively, feasibility and reliability in order to verify these data are positioned over the somewhere to this navigational system, behind the long-play, preserve test data.The experiment in continuous 1046 seconds in certain research station, by analysis, this navigational system is respectively 0.9637281519 " (3 σ) and 1.3609644735 " (3 σ) at longitude and latitudinal precision.

Embodiment 3: in conjunction with Fig. 5, Fig. 6, a kind of celestial autonomous navigation method based on star sensor of the present invention comprises three subsystems: star sensor system and two laser level measuring systems.The three-axis attitude of the main carrier of star sensor; Two laser level measuring systems are mainly measured the angle of carrier diaxon and surface level.

The course of work: fixed star is imaged on star sensor as (such as CCD or APS) on the plane by the star sensor optical lens, and imaging circuit is converted into a complete star chart to the electric signal as fixed star in the plane, and is kept in the storer; Star picture extraction software reads the star chart data in the storer, and extracts star as coordinate from star chart; Importance in star map recognition software adopts whole day ball recognizer according to the star catalogue information that is kept in the star sensor, and these stars are discerned (if star sensor has prior imformation, importance in star map recognition software adopts the star track algorithm) as coordinate; Attitude Calculation software adopts corresponding Attitude Calculation algorithm and recognition result, and according to these importance in star map recognition result, and utilize the observation star of having discerned, calculate the attitude information q of star sensor under geocentric inertial coordinate system.Measure two angles of star sensor respectively according to the laser level measurement component, the pointing vector when calculating optical axis under the WGS84 coordinate system perpendicular to surface level as planar axes and horizontal direction.And export this vector and the attitude information of star sensor under geocentric inertial coordinate system.These information are exactly independent navigation information.

The celestial autonomous navigation method based on star sensor that the present invention proposes is the recognition result according to star sensor, can calculate the direction vector of star sensor Os-Zs axle under earth inertial coordinates system Through coordinate conversion get final product the direction vector under the WGS-84 coordinate system Utilize the laser level measurement component to measure two picture planar axes x of star sensor respectively _sAnd y _sBe respectively α with the angle of horizontal direction ₀And β ₀Direction vector Respectively around xs axle and ys axle rotation β ₀And α ₀Direction vector after the angle Be exactly the direction vector of S under the WGS-84 coordinate system, substitution again (1) can be obtained longitude α and the latitude β of carrier face of land millet cake S, thereby realizes the location to carrier.So this navigational system is not only exported the carrier three-axis attitude, and the position of output carrier.Thereby realization celestial autonomous navigation.

Claims (1)

1. celestial autonomous navigation method based on star sensor, it is characterized in that: step is as follows:

Step 1: calculate the attitude information of star sensor output based on geocentric inertial coordinate system;

Step 2: calculating is pointed to based on the optical axis under the geocentric inertial coordinate system according to attitude information;

Step 3: point to pointing to be converted to based on the optical axis under the WGS84 coordinate system based on the optical axis under the geocentric inertial coordinate system; From laser leveler, read two angle α of star sensor as planar axes and horizontal direction ₀And β ₀

Step 4: according to α ₀And β ₀Sensing when calculating the optical axis sensing under the WGS84 coordinate system with horizontal vertical;

Step 5: the longitude α and the latitude β that calculate underground some S of carrier;

Step 6: attitude q and underground some longitude α and the latitude β of output carrier under geocentric inertial coordinate system.