CN104462776A - Method for absolutely radiometric calibration of low orbit earth observation satellite with moon as reference - Google Patents

Abstract

The invention provides a method for absolutely radiometric calibration of a low orbit earth observation satellite with moon as reference. The method comprises the following steps that the time during which the low orbit earth observation satellite can observe the moon is primarily determined through a satellite tool kit; the starting time of moon imaging, the ending time of moon imaging, the camera exposure time, the satellite attitude angle during imaging, the pitching angular velocity and the like are determined; according to the parameters, moon imaging is conducted, so that an image of moon is obtained; the image of the moon is analyzed through a ROLO absolutely radiometric calibration model, and absolutely radiometric calibration coefficients are obtained. By the adoption of the method, an onboard calibration device and an operating mechanism are not needed, a special ground reference source is not needed, the long-term stability of moon and the attitude maneuver capacity of the satellite are fully utilized, and the image of moon is obtained and used as a reference source.

Description

A kind of low orbit Earth observation satellite is to moon absolute radiation calibration method

Technical field

The present invention relates to a kind of Calibration Method, particularly a kind of low orbit Earth observation satellite is to moon absolute radiation calibration method, belongs to remote sensing satellite calibration technology field.

Background technology

Can be there is larger degeneration in Optical remote satellite radiance in-orbit, the precision and stability of quantification remote sensing application to absolute radiometric calibration proposes strict demand.At present, the calibration based on onboard process device and ground calibration field is conventional absolute radiation calibration method in-orbit.1) calibration of onboard process device mainly comprises the modes such as the calibration of calibration lamp, the calibration of sun diffusing panel, but be subject to the impact of the own optical of outer space radiation environment, scaling system, electronics and physical construction, performance can decay in time, affects calibration precision.2) ground calibration radiometric calibration site mainly utilizes ground to lay target, be absolute radiation calibration method the most frequently used at present, but the method needs synchro measure atmospheric parameter, and serious by weather effect, efficiency is low, cost is high, complicated operation.

The moon is as the celestial body nearest apart from the earth, and menology has the exclusive advantage such as fabulous reflectivity long-time stability, the consistance of spectral response, the unicity of the empty background of surrounding deep cooling; Simultaneously, moon In-flight calibration effectively can avoid atmospheric interference, special on-board equipment need not be developed, there is repeatedly similar geometry observation condition every month, become one of Main Means of the calibration of earth observation Optical remote satellite in the world, for the stability of long term monitoring radiation quality in-orbit.The advantage utilizing the moon to carry out Optical remote satellite In-flight calibration is: 1. as the reflecting body that solar radiation is natural, and the stability of its reflectivity is better than 10 ^-8/ year; 2. moon brightness sharpness of border is around deep cooling empty background and fixed star point target etc., very little in visible ray short-wave infrared spectral coverage stray radiation; 3. the moon self reflectance spectrum is smooth, and do not have obvious reflection peak or absorb paddy, the reflectivity of visible spectrum is similar with the reflection characteristic of ocean to land under fair weather condition; 4. the moon is without air, calibration process relative simplicity, has the observation airplane meeting of many days every month, and has similar observation geometrical property.

Owing to having above many advantages, for meeting the demand of high stability quantification application, the moon has become one of main standard reference source of earth observation remote sensing satellite calibration in the world, and moon In-flight calibration is the important means solving the application of current remote sensing image data quantitativeization.From 1997, United States Geological Survey (USGS) just carried out moon automatic Observation project (ROLO), established the ROLO absolute radiometric calibration model of moon brightness.Since ROLO model, existing a considerable amount of satellite utilizes the moon to carry out radiation calibration and radiance monitoring, as MISR, MERIS, ASTER, MODIS, SeaWIFS, VIIRS, ALI, HYPERION and Pleiades etc. of low orbit satellite and the MSG/SEVIRI etc. of geostationary satellite, they mainly utilize the exhausted degree radiation information of radiance difference between moon radiation calibration model monitoring different loads, the long-term decay of instrument radiance, the radiation difference between spectral coverage and spectral coverage and instrument, the effective guarantee application of satellite in orbit businessization calibration.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, provide a kind of low orbit Earth observation satellite to moon absolute radiation calibration method, do not adopt onboard process equipment, substantially do not affect imaging task, or ground calibration field need not be used less as far as possible prerequisite under, take full advantage of the attitude maneuver imaging capability of satellite self, for the radiation calibration lunar data that whole period in orbit provides High-precision high-frequency secondary, meet the great-leap-forward development of low orbit Earth observation satellite quantification application.

Technical solution of the present invention is: a kind of low orbit Earth observation satellite is to moon absolute radiation calibration method, and step is as follows:

(1) Satellite Tool Kit determination low orbit Earth observation satellite is utilized can to observe the time of the moon, Satellite Tool Kit is utilized to obtain the attitude of satellite angle corresponding to the time that can observe the moon, calculating can observe the moon phasing degree corresponding to the time of the moon, again according to the attitude maneuver ability of satellite, select from the time that can observe the moon moon imaging time, perform step (2);

Described attitude maneuver ability refers to satellite pitching angle theta, roll angle Φ and crab angle maximum maneuvering range, must within the attitude maneuver limit of power of satellite to the pose adjustment size of satellite during moon imaging; Described moon phasing degree meets ROLO moon absolute radiometric calibration model, and the moon phasing degree scope selected in this model is: [1.55 °, 97 °];

(2) selected by step (1) to moon imaging time, determining to proceed to start time to moon imaging pattern from imaging pattern over the ground, from moon imaging pattern being proceeded to end time of imaging pattern over the ground and satellite linear array CCD camera to the imaging frequency n of moon push-scanning image, and determining the Satellite Camera time shutter t of each imaging _m, imaging initial time, the imaging end time, attitude of satellite angle, satellite rate of pitch d θ _m; The attitude of satellite angle of described each imaging comprise each imaging initial time attitude angle, intermediate time attitude angle and finish time attitude angle; Described attitude angle comprises the angle of pitch, roll angle and crab angle, described satellite linear array CCD camera to the imaging initial time of moon push-scanning image number of times, each imaging and the imaging end time all given in advance;

(3) when Earth observation satellite in orbit the time arrive determine in step (2) from imaging pattern over the ground proceed to the moon imaging pattern start time time, satellite enters attitude maneuver pattern, satellite adjusts according to the attitude of satellite angle determined in step (2), proceeds to moon imaging pattern by imaging pattern over the ground;

(4) when the time arrives the first time imaging initial time determined in step (2) to Earth observation satellite in orbit, the linear array CCD camera of Earth observation satellite is according to the Satellite Camera time shutter t of each imaging determined in step (2) _mstart moon imaging, obtain lunar map picture, if be greater than 1 to the imaging frequency n of moon push-scanning image, then perform step (5), otherwise perform step (6);

(5) according to the Satellite Camera time shutter t of each imaging determined in step (2) _m, imaging initial time, imaging end time and attitude of satellite angle, complete according to the method in step (4) all to moon push-scanning image, obtain all lunar map pictures, enter step (6);

(6) complete moon push-scanning image, Earth observation satellite enters attitude maneuver pattern, proceeds to imaging pattern over the ground to moon imaging pattern;

(7) utilize ROLO absolute radiometric calibration model to process all lunar map pictures obtained in step (6), obtain Absolute Radiometric Calibration Coefficients.

The Satellite Camera time shutter t of each imaging is determined in described step (2) _m, specifically realized by following steps:

(2a) the projection line speed v of satellite at moonscape is calculated _m, specifically by formula:

$v_m=\sqrt{\frac{\mathrm{\μ}}{R_e+H}}\×\frac{(R_{\mathrm{em}}-R_m)}{R_e+H}$

Provide, wherein, μ is Gravitational coefficient of the Earth, R _efor earth radius, H is the orbit altitude of satellite transit; R _emfor earth center is to the distance of moon ball center, R _mfor the moon radius of a ball;

(2b) the projected size GIFOV of each pixel on the moon in satellite linear array CCD camera is calculated _m, specifically by formula:

${\mathrm{GIFOV}}_m=\frac{p\×(R_{\mathrm{em}}-R_m-H-R_e)}{f}$

Provide, wherein, p is the size of each pixel in satellite linear array CCD camera, and f is the focal length of Satellite Camera;

(2c) each pixel projected size on the moon in the satellite linear array CCD camera in the projection line speed and step (2b) of moonscape of the satellite in step (2a) is utilized, calculate the Satellite Camera time shutter of each imaging, specifically by formula:

$t_m=\frac{{\mathrm{FIFOV}}_m}{v_m}=\frac{p}{f\×\sqrt{\frac{\mathrm{\μ}}{{(R_e+H)}^3}}}\×\frac{R_{\mathrm{em}}-R_m-H-R_e}{R_{\mathrm{em}}-R_m}$

Provide.

Intermediate time attitude angle in described step (2), is realized by following steps:

(3a) according to imaging initial time and the imaging end time of each imaging of satellite given in advance in step (2), calculate the imaging intermediate time of each imaging of satellite, determine the position vector between the imaging intermediate time satellite of each imaging and the moon according to satellite orbit and moon ephemeris further ;

(3b) according to the position vector between the imaging intermediate time satellite in step (3a) and the moon , be calculated to be the pitching angle theta of picture intermediate time _mid, roll angle Φ _midand crab angle the pitching angle theta of imaging intermediate time _midspecifically by formula:

The roll angle Φ of imaging intermediate time _midspecifically by formula:

${\mathrm{\Φ}}_{\mathrm{mid}}=\arcsin \left[\frac{\left|r_2\right|}{\sqrt{{r_1}^2+{r_2}^2+{r_3}^2}}\right]$

Provide, wherein, r ₁for the position vector between imaging intermediate time satellite and the moon at satellite orbit coordinate system B _xprojected size on direction of principal axis, r ₃for the position vector between imaging intermediate time satellite and the moon at satellite orbit coordinate system B _zprojected size on direction of principal axis; r ₂for the position vector between imaging intermediate time satellite and the moon at satellite orbit coordinate system B _yprojected size on direction of principal axis; Wherein, satellite orbit coordinate system B _o-B _xb _yb _zinitial point B _oin orbit, B _xaxle points to satellite working direction, B _zaxle points to the earth's core by centroid of satellite, B _yaxle is perpendicular to by B _xwith B _zthe orbit plane that axle is formed;

Described crab angle constant in imaging process, and be 0.

Described step (2) Satellite attitude rate of pitch d θ _m, detailed process is as follows:

If satellite linear array CCD camera realizes square sample imaging, then attitude of satellite rate of pitch d θ by adjustment attitude rate of pitch _mby formula:

$d{\mathrm{\θ}}_m=\sqrt{\frac{\mathrm{\μ}}{{(R_e+H)}^3}}[\frac{R_e}{H}-\frac{(R_{\mathrm{em}}-R_m)}{(R_{\mathrm{em}}-R_m-H-R_e)}]$

Provide, wherein, μ is Gravitational coefficient of the Earth, R _efor earth radius, H is the orbit altitude of satellite transit; R _emfor earth center is to the distance of moon ball center, R _mfor the moon radius of a ball;

Otherwise, attitude of satellite rate of pitch d θ _mbe zero.

In described step (2) initial time attitude angle and finish time attitude angle, concrete computation process is as follows:

Initial time pitching angle theta _startby formula:

${\mathrm{\θ}}_{\mathrm{start}}={\mathrm{\θ}}_{\mathrm{mid}}-d{\mathrm{\θ}}_m\·\frac{t}{2}$

Provide, wherein, t is the difference in each imaging process between imaging end time and imaging initial time;

Initial time roll angle Φ _startby formula:

Φ _start＝Φ _mid

Provide,

Finish time pitching angle theta _endby formula:

${\mathrm{\θ}}_{\mathrm{end}}={\mathrm{\θ}}_{\mathrm{mid}}-d{\mathrm{\θ}}_m\·\frac{t}{2}$

Provide,

Finish time roll angle Φ _endby formula:

Φ _end＝Φ _mid

Provide.

Determine in described step (2) to proceed to start time to moon imaging pattern from imaging pattern over the ground, from end time moon imaging pattern being proceeded to imaging pattern over the ground, be specially:

From imaging pattern over the ground proceed to the moon imaging pattern start time by formula:

t _start＝t _start1-t′

Provide, wherein, t _startfor imaging pattern proceeds to the start time to moon imaging pattern over the ground, t _start1for the initial time of first time to moon imaging, t ' is that imaging pattern proceeds to the attitude maneuver time to moon imaging pattern over the ground, specifically by formula:

$t^{\′}=\max \{\frac{{\mathrm{\θ}}_{\mathrm{start}1}-{\mathrm{\θ}}_0}{\mathrm{d\θ}},\frac{{\mathrm{\Φ}}_{\mathrm{start}1}-{\mathrm{\Φ}}_0}{\mathrm{d\Φ}}\}+t_w$

Provide, wherein t _wfor the attitude stabilization time, θ _start1for the angle of pitch of first time to moon imaging initial time, θ ₀for the angle of pitch of imaging over the ground, d θ is satellite rate of pitch, Φ _start1for the roll angle of first time to moon imaging initial time, Φ ₀for the roll angle of imaging over the ground, d Φ satellite rate of roll;

The end time of imaging pattern is over the ground proceeded to by formula to moon imaging pattern:

t _end＝t _endn+t″

Provide, wherein, t _endfor proceeding to the end time of imaging pattern over the ground to moon imaging pattern, t _endnbe n-th end time to moon imaging, t " for proceeding to the attitude maneuver time of imaging pattern over the ground to moon imaging pattern, specifically by formula:

$t^{\′\′}=\max \{\frac{{\mathrm{\θ}}_{\mathrm{endn}}-{\mathrm{\θ}}_1}{\mathrm{d\θ}},\frac{{\mathrm{\Φ}}_{\mathrm{endn}}-{\mathrm{\Φ}}_1}{\mathrm{d\Φ}}\}+t_w^{\′}$

Provide, wherein t ' _wfor the attitude stabilization time, θ _endnbe n-th angle of pitch to the imaging finish time moon, θ ₁for the angle of pitch of imaging over the ground, d θ is satellite rate of pitch, Φ _endnbe n-th roll angle to the imaging finish time moon, Φ ₁for the roll angle of imaging over the ground, d Φ satellite rate of roll.

The present invention compared with prior art beneficial effect is:

(1) the present invention adopts the moon as the absolute radiometric calibration source of remote sensing satellite, the moon possesses the long-time stability of reference source, star not needing robot scaling equipment and travelling mechanism, without the need to laying special ground target as reference source, saving calibration cost yet;

(2) the present invention is directed to low orbit Optical remote satellite, under the prerequisite ensureing reliability and security, the attitude maneuver ability taking full advantage of satellite realizes satellite and is scaled to picture to moon high-quality, and to the moon imaging process when star sensor is unavailable, give the accuracy requirement of other alternative sensor;

(3) the present invention's proposition can repeatedly to moon push-scanning image in a satellite imagery task, can realize multi-disc CCD obtains lunar map picture respectively on the one hand, and the repeatedly push-scanning image that can realize same a slice CCD on the other hand sets up the non-linear absolute radiometric calibration model of camera as input.

Accompanying drawing explanation

Fig. 1 is that a kind of low orbit Earth observation satellite of the present invention is to the process flow diagram of moon absolute radiation calibration method;

Fig. 2 is the moon phase angle schematic diagram between the sun of the present invention, the moon, satellite;

Fig. 3 (a) is the schematic diagram of square sample grid, and Fig. 3 (b) is the schematic diagram transforming to square sample from the rectangularly-sampled result of common line array CCD to the moon;

Fig. 4 is that Low Earth Orbiting Satellite of the present invention is to the position of moon imaging and attitude relation schematic diagram;

Fig. 5 is the repeatedly push-scanning image schematic diagram of Low Earth Orbiting Satellite of the present invention to moon imaging task;

Fig. 6 be the present invention when 0.0035196 second integral time, MTF decline be no more than 10% constraint condition, under different integration progression, to the requirement of the attitude accuracy of other alternative sensor;

Fig. 7 be the present invention when 0.00036259 second integral time, MTF decline be no more than 10% constraint condition, under different integration progression, to the requirement of the attitude accuracy of other alternative sensor;

Embodiment

A kind of low orbit Earth observation satellite is to moon absolute radiation calibration method, and as shown in Figure 1, the method is realized by following steps concrete steps:

1, low orbit Earth observation satellite can observe the time of the moon to utilize Satellite Tool Kit STK to determine, Satellite Tool Kit is utilized to obtain the attitude of satellite angle corresponding to the time that can observe the moon, calculating can observe the moon phasing degree corresponding to the time of the moon, again according to the attitude maneuver ability of satellite, select from the time that can observe the moon moon imaging time, perform step 2;

Described attitude maneuver ability refers to satellite pitching angle theta, roll angle Φ and crab angle maximum maneuvering range, must within the attitude maneuver limit of power of satellite to the pose adjustment size of satellite during moon imaging.

Space Remote Sensors observes the moon, the spoke brightness of the moon constantly changes, the track of the earth, the sun, moon three constantly changes, cause life distance, the moon distance change, the radiant illumination that the moon is subject to changes, the spoke brightness value observed from satellite is also changing, the principal element of whole lunar surface radiance when the phase angle variations of the moon and the optical libration of the moon are the impact observation moon.

The moon phasing degree corresponding to date and time of selected moon imaging plan should meet the demand of ROLO moon absolute radiometric calibration model, and the moon phase angle range selected in ROLO database is [1.55 °, 97 °].As shown in Figure 2, moon phasing degree is defined as the angle between the sun-moon-satellite.

2, selected by step 1 to moon imaging time, determining to proceed to start time to moon imaging pattern from imaging pattern over the ground, from moon imaging pattern being proceeded to end time of imaging pattern over the ground and satellite linear array CCD camera to the imaging frequency n of moon push-scanning image, and determining the Satellite Camera time shutter t of each imaging _m, imaging initial time, the imaging end time, attitude of satellite angle, satellite rate of pitch d θ _m; The attitude of satellite angle of described each imaging comprise each imaging initial time attitude angle, intermediate time attitude angle and finish time attitude angle; Described attitude angle comprises the angle of pitch, roll angle and crab angle, described satellite linear array CCD camera to the imaging initial time of moon push-scanning image number of times, each imaging and the imaging end time all given in advance.

For linear TDI CCD, for meeting its imaging synchronism, the square sample imaging to the moon be realized, can by realizing the integral time of adjustment TDI camera or adjustment measuring satellite angular velocities the square sample imaging to the moon.And for common line array CCD, time non-adjustable upon exposure, satellite conveniently can push away the speed of sweeping to moon imaging, then adopts the square sample of resampling process acquisition to the moon, also can by the square sample imaging of adjustment measuring satellite angular velocities realization to the moon; The square sample imaging of time shutter realization to the moon adjusting linear array CCD camera can also be passed through by timing upon exposure.

2.1, the Satellite Camera time shutter t of each imaging is determined _m, specifically realized by following steps:

(1) the projection line speed v of satellite at moonscape is calculated _m

According to two-particle systems rule, with the earth be barycenter satellite rings around angular velocity be:

$\mathrm{\ω}=\sqrt{\frac{\mathrm{\μ}}{{(R_e+H)}^3}}$

Wherein μ is Gravitational coefficient of the Earth, R _efor earth radius, H is the orbit altitude of satellite transit

Projection line speed is at the earth's surface:

$v_e=\mathrm{\ω}\×R_e=\sqrt{\frac{\mathrm{\μ}}{{(R_e+H)}^3}}\×R_e=\sqrt{\frac{\mathrm{\μ}}{(R_e+H)}}\×\frac{R_e}{R_e+H}$

In the projection line speed of moonscape be:

$v_m=\mathrm{\ω}\×{(R_{\mathrm{em}}-R_m)}_{}=\sqrt{\frac{\mathrm{\μ}}{{(R_e+H)}^3}}\×(R_{\mathrm{em}}-R_m)=\sqrt{\frac{\mathrm{\μ}}{(R_e+H)}}\×\frac{(R_{\mathrm{em}}-R_m)}{R_e+H}---\left(1\right)$

Wherein, R _emfor earth center is to the distance of moon ball center, R _mfor the moon radius of a ball.

(2) the projected size GIFOV of each pixel on the moon in satellite linear array CCD camera is calculated _m

Each pixel projected size is on earth:

${\mathrm{GIFOV}}_e=\frac{p\×H}{f}$

Wherein, p is the size of each pixel in satellite linear array CCD camera, and f is the focal length of Satellite Camera.

The projected size of each pixel on the moon is:

${\mathrm{GIFOV}}_m=\frac{p\×(R_{\mathrm{em}}-R_m-H-R_e)}{f}$

(3) utilize each pixel projected size on the moon in the satellite linear array CCD camera in the projection line speed and step (2) of moonscape of the satellite in step (1), calculate the Satellite Camera time shutter of each imaging.

Imaging over the ground, designs according to this principle of projected size that pixel resolution equals on earth over the ground, i.e. GSD usually _e=GIFOV _e, to ensure the square grid size of sampling.As Fig. 3 (a) is depicted as the schematic diagram of square sample grid, namely consistent with the imaging resolution on velocity reversal in the horizontal direction.

Thus, time shutter size is:

$t_e=\frac{{\mathrm{GSD}}_e}{v_e}=\frac{\frac{p\×H}{f}}{\sqrt{\frac{\mathrm{\μ}}{{(R_e+H)}^3}}\×R_e}=\frac{p}{f\×\sqrt{\frac{\mathrm{\μ}}{{(R_e+H)}^3}}}\×\frac{H}{R_e}---\left(2\right)$

If to moon imaging, still need this principle of projected size ensureing to equal on the moon the pixel resolution of moon imaging, i.e. GSD _m=GIFOV _m, to ensure the square grid size of sampling, thus, time shutter size is:

$\left.\begin{array}{c}{t}_m=\frac{{\mathrm{GSD}}_m}{v_m}=\frac{\frac{p\×(R_{\mathrm{em}}-R_m-H-R_e)}{f}}{\sqrt{\frac{\mathrm{\μ}}{{(R_e+H)}^3}}\×(R_{\mathrm{em}}-R_m)}=\frac{p}{f\×\sqrt{\frac{\mathrm{\μ}}{{(R_e+H)}^3}}}\×\frac{R_{\mathrm{em}}-R_m-H-R_e}{R_{\mathrm{em}}-R_m}\\ =t_e\×\frac{R_e}{H}\×\frac{R_{\mathrm{em}}-R_m-H-R_e}{R_{\mathrm{em}}-R_m}\end{array}\right\{---\left(3\right)$

Drawn by formula (2) and formula (3): if the square sample to the moon will be retained, then the t of moon imaging _mwith the t of imaging over the ground _ebetween multiple proportion be

Therefore, for TDICCD, due to need multistage between synchronous, need according to pixel resolution equal with projected size (GSD=GIFOV) this principle to adjust the time shutter.

For common line array CCD, can timing upon exposure, its time shutter can be calculated according to above-mentioned steps; Time non-adjustable upon exposure, can rectangularly-sampled be caused to moon imaging, the resolution on velocity reversal now and the resolution in horizontal direction inconsistent, the later stage needs resampling to be processed into square sample.As Fig. 3 (b) is depicted as the schematic diagram that the rectangularly-sampled result of common line array CCD to the moon transforms to square sample.

2.2, intermediate time attitude angle size is calculated according to the position relationship of intermediate time satellite and the moon

Satellite crab angle constant in moon imaging process, and be 0.Therefore, satellite needs to be realized by the adjustment angle of pitch and roll angle to moon imaging, as Fig. 4 (a) is depicted as Low Earth Orbiting Satellite to the position of moon imaging and attitude relation schematic diagram, and B _o-B _xb _yb _zfor satellite orbit coordinate system, initial point B _oin orbit, B _xaxle points to satellite working direction, B _zaxle points to the earth's core by centroid of satellite, B _yaxle is perpendicular to by B _xwith B _zthe orbit plane that axle is formed; S _xs _ys _zfor satellite body coordinate system.According to the initial of each push-scanning image and end time, calculate the position vector relation of intermediate time satellite and the moon, calculate satellite accordingly to the angle of pitch of moon push-scanning image intermediate time and roll angle size:

(1) according to imaging initial time and the imaging end time of each imaging of satellite given in advance, calculate the imaging intermediate time of each imaging of satellite, determine the position vector between the imaging intermediate time satellite of each imaging and the moon according to satellite orbit and moon ephemeris further , this vector is at B _x, B _y, B _zprojection on direction is respectively r ₁, r ₂, r ₃, be expressed as the S of satellite body coordinate system during imaging _zdirection is vector direction, r ₁for the position vector between imaging intermediate time satellite and the moon at satellite orbit coordinate system B _xprojected size on direction of principal axis, r ₃for the position vector between imaging intermediate time satellite and the moon at satellite orbit coordinate system B _zprojected size on direction of principal axis; r ₂for the position vector between imaging intermediate time satellite and the moon at satellite orbit coordinate system B _yprojected size on direction of principal axis.

Moon ephemeris adopts JPL ephemeris, and JPL ephemeris is the numerical value of the relative position of each major planet, the sun, the earth and the moon calculated according to the up-to-date astronomical constants determined and celestial motion theory by U.S. jet propulsion laboratory, speed, nutation of longitude and physical libration of the moon and variability thereof.

(2) as shown in Fig. 4 (b), around B _yaxle rotates to an angle and makes to rotate rear new B _z' axle and vector at B _xb _zprojection in plane overlaps, and this angle is the pitching angle theta of imaging intermediate time _mid, B _xaxle rotates to B _x', obtain according to projection relation:

(3) around B _x' axle rotates to an angle and make B _z' axle rotates to and vector the direction overlapped, i.e. S _zdirection, this angle is the roll angle Φ of imaging intermediate time _mid:

${\mathrm{\Φ}}_{\mathrm{mid}}=\arcsin \left[\frac{\left|r_2\right|}{\sqrt{{r_1}^2+{r_2}^2+{r_3}^2}}\right]$

2.3, the attitude of satellite rate of pitch d θ of push-scanning image is calculated _msize

Line array CCD is realized to the situation of square sample imaging by adjustment attitude angular velocity, then need the attitude of satellite rate of pitch d θ calculating push-scanning image _msize.

(1) the projection line velocity magnitude on the moon is calculated

The rate of pitch d θ of setting to moon imaging process Satellite _m, then what cause in the projection line velocity magnitude of moonscape is:

v _m'＝dθ _m×(R _em-R _m-H-R _e)

The projection line speed on moonscape caused around earth rotation by satellite rings is again the v in formula (1) _m, therefore, there is rate of pitch d θ _mthe projection line velocity magnitude V of satellite on moonscape _mavailable v _mwith v _m' sum carrys out approximate representation:

$V_m=v_m+{v_m}^{\′}=\sqrt{\frac{\mathrm{\μ}}{(R_e+H)}}\×\frac{(R_{\mathrm{em}}-R_m)}{R_e+H}+d{\mathrm{\θ}}_m\×(R_{\mathrm{em}}-R_m-H-R_e)---\left(4\right)$

(2) the rate of pitch d θ of satellite is calculated _msize

When the time shutter is constant, namely equal with to the time shutter of moon imaging to the time shutter of earth imaging, for ensureing this principle of projected size equaled on the moon the pixel resolution of moon imaging, i.e. GSD _m=GIFOV _m, to ensure the square grid size of sampling, can be obtained by formula (3) and (4):

$t_m=\frac{{\mathrm{GSD}}_m}{V_m}=\frac{\frac{p\×(R_{\mathrm{em}}-R_m-H-R_e)}{f}}{\sqrt{\frac{\mathrm{\μ}}{(R_e+H)}}\×\frac{(R_{\mathrm{em}}-R_e)}{R_e+H}+d{\mathrm{\θ}}_m\×(R_{\mathrm{em}}-R_m-H-R_e)}---\left(5\right)$

Combine the time shutter to earth imaging, i.e. formula (2), according to t _m=t _e, then rate of pitch d θ _mfor:

$d{\mathrm{\θ}}_m=\sqrt{\frac{\mathrm{\μ}}{{(R_e+H)}^3}}[\frac{R_e}{H}-\frac{(R_{\mathrm{em}}-R_m)}{(R_{\mathrm{em}}-R_m-H-R_e)}]---\left(6\right)$

In the present embodiment, according to the above-mentioned R provided _e, R _em, R _m, H numerical value, and Kepler's constant μ, obtains rate of pitch d θ according to formula (6) _m:

Otherwise, attitude of satellite rate of pitch d θ _mbe zero.

2.4, calculate push-scanning image initial time attitude angle and finish time attitude angle size

Line array CCD is realized to the situation of square sample imaging by adjustment attitude angular velocity, according to the rate of pitch size d θ calculated _m, and the pitching angle theta calculated and roll angle Φ, then show that to the time continued of moon imaging be t according to the initial of push-scanning image and end time, then t=end time-initial time, initial time pitching angle theta _startby formula:

${\mathrm{\θ}}_{\mathrm{start}}={\mathrm{\θ}}_{\mathrm{mid}}-d{\mathrm{\θ}}_m\·\frac{t}{2}$

Provide, wherein, t is the difference in each imaging process between imaging end time and imaging initial time;

Initial time roll angle Φ _startby formula:

Φ _start＝Φ _mid

Provide,

Finish time pitching angle theta _endby formula:

${\mathrm{\θ}}_{\mathrm{end}}={\mathrm{\θ}}_{\mathrm{mid}}-d{\mathrm{\θ}}_m\·\frac{t}{2}$

Provide,

Finish time roll angle Φ _endby formula:

Φ _end＝Φ _mid

Provide.

For not being realize the situation of square sample imaging by adjustment attitude angular velocity, then equal with roll angle with the pitching of intermediate time to the initial time of moon push-scanning image, finish time, be namely expressed as θ _start=θ _end=θ, Φ _start=Φ _end=Φ;

2.5, determine to proceed to start time to moon imaging pattern, from end time moon imaging pattern being proceeded to imaging pattern over the ground from imaging pattern over the ground.

From imaging pattern over the ground proceed to the moon imaging pattern start time by formula:

t _start＝t _start1-t′

Provide, wherein, t _startfor imaging pattern proceeds to the start time to moon imaging pattern over the ground, t _start1for the initial time of first time to moon imaging, t ' is that imaging pattern proceeds to the attitude maneuver time to moon imaging pattern over the ground, specifically by formula:

$t^{\′}=\max \{\frac{{\mathrm{\θ}}_{\mathrm{start}1}-{\mathrm{\θ}}_0}{\mathrm{d\θ}},\frac{{\mathrm{\Φ}}_{\mathrm{start}1}-{\mathrm{\Φ}}_0}{\mathrm{d\Φ}}\}+t_w$

Provide, wherein t _wfor the attitude stabilization time, θ _start1for the angle of pitch of first time to moon imaging initial time, θ ₀for the angle of pitch of imaging over the ground, d θ is satellite rate of pitch, Φ _start1for the roll angle of first time to moon imaging initial time, Φ ₀for the roll angle of imaging over the ground, d Φ satellite rate of roll;

The end time of imaging pattern is over the ground proceeded to by formula to moon imaging pattern:

t _end＝t _endn+t″

Provide, wherein, t _endfor proceeding to the end time of imaging pattern over the ground to moon imaging pattern, t _endnbe n-th end time to moon imaging, t " for proceeding to the attitude maneuver time of imaging pattern over the ground to moon imaging pattern, specifically by formula:

$t^{\′\′}=\max \{\frac{{\mathrm{\θ}}_{\mathrm{endn}}-{\mathrm{\θ}}_1}{\mathrm{d\θ}},\frac{{\mathrm{\Φ}}_{\mathrm{endn}}-{\mathrm{\Φ}}_1}{\mathrm{d\Φ}}\}+t_w^{\′}$

Provide, wherein t ' _wfor the attitude stabilization time, θ _endnbe n-th angle of pitch to the imaging finish time moon, θ ₁for the angle of pitch of imaging over the ground, d θ is satellite rate of pitch, Φ _endnbe n-th roll angle to the imaging finish time moon, Φ ₁for the roll angle of imaging over the ground, d Φ satellite rate of roll.

3, when Earth observation satellite in orbit the time arrive in step 2 determine from imaging pattern over the ground proceed to the moon imaging pattern start time time, satellite carries out attitude maneuver pattern, satellite adjusts according to the attitude of satellite angle determined in step 2, is proceeded to moon imaging pattern by imaging pattern over the ground.

Satellite is in the whole process of moon imaging, and when not having effective star chart to use, attitude measurement needs to be measured as master from star sensor and proceeds to the metering system reaching accuracy requirement based on inertial sensor or other.

Described inertial sensor or other reach the metering system of accuracy requirement, mainly without effective star chart under causing the disabled situation of star sensor, the inertial sensor that the certain attitude accuracy of demand fulfillment requires or other sensor carry out alternative star sensor, require it is that caused MTF decline number percent can not more than 5 ~ 10% to the pointing accuracy of inertia or other sensor and attitude stability;

The improper picture that attitude of satellite precision causes moves computing method (see " attitude of satellite precision is on the impact of TDI CCD camera ", Harbin Institute of Technology's journal, 34 (3), 2002): according to the focal distance f of CCD camera, pixel dimension τ, attitude pointing accuracy δ degree and attitude stability δ ' degree/second, then to the time shutter t of moon imaging _mthe improper picture along TDI, vertical TDI direction of interior generation moves dx, dy and is respectively:

$\left\{\begin{array}{c}\mathrm{dx}=f\tan \left({\mathrm{\δ}}^{\′}{t}_m\right)\\ \mathrm{dy}=\mathrm{\τ}\tan \mathrm{\δ}+\mathrm{\τ}\tan \left({\mathrm{\δ}}^{\′}{t}_m\right)+f\tan \left({\mathrm{\δ}}^{\′}{t}_m\right)\end{array}\right.---\left(7\right)$

Moving by improper picture the MTF caused is:

$\left\{\begin{array}{c}{\mathrm{MTF}}_x=\frac{\sin [N_{\mathrm{TDI}}\mathrm{\πdx}/\left(2\mathrm{\τ}\right)]}{N_{\mathrm{TDI}}\sin [\mathrm{\πdx}/\left(2\mathrm{\τ}\right)]}\\ {\mathrm{MTF}}_y=\frac{\sin [N_{\mathrm{TDI}}\mathrm{\πdy}/\left(2\mathrm{\τ}\right)]}{N_{\mathrm{TDI}}\sin [\mathrm{\πdy}/\left(2\mathrm{\τ}\right)]}\end{array}\right.---\left(8\right)$

4, when the time arrives the first time imaging initial time determined in step 2 to Earth observation satellite in orbit, the linear array CCD camera of Earth observation satellite is according to the Satellite Camera time shutter t of each imaging determined in step 2 _mstart moon imaging, obtain lunar map picture, if be greater than 1 to the imaging frequency n of moon push-scanning image, then perform step 5, otherwise perform step 6.

5, according to the Satellite Camera time shutter t of each imaging determined in step 2 _m, imaging initial time, imaging end time and attitude of satellite angle, complete according to the method in step 4 all to moon push-scanning image, obtain all lunar map pictures, enter step 6.

6, complete moon push-scanning image, Earth observation satellite enters attitude maneuver pattern, proceeds to imaging pattern over the ground to moon imaging pattern.

7, utilize ROLO absolute radiometric calibration model to process all lunar map pictures obtained in step 6, obtain Absolute Radiometric Calibration Coefficients.

The experimental formula of the moon disk equivalent reflectivity A utilizing ROLO to provide is as follows:

$\begin{array}{c}\ln A=\underset{i=0}{\overset{3}{\mathrm{\Σ}}}{a}_i*g^i+\underset{j=0}{\overset{3}{\mathrm{\Σ}}}{b}_i*{\mathrm{\Φ}}^{2j-1}+c_1*\mathrm{\θ}+c_2*\mathrm{\φ}+c_3*\mathrm{\Φ}*\mathrm{\θ}+c_4*\mathrm{\Φ}*\mathrm{\φ}\\ +d_1*e^{-g/p_1}+d_2*e^{-g/p_2}+d_3*\cos ((g-p_3)/p_4)\end{array}$

In formula, g is moon phase angle, and φ is the longitude of observation camera in moon spherical coordinates, the latitude that θ is observation camera in moon spherical coordinates, and the longitude that Φ is the sun in moon spherical coordinates, a, b, c, d, p are coefficient entry.

Section 1 in above formula is the elementary item of moon brightness, closely related with moon phase angle, and the moon phase angle range selected in ROLO database is 1.55 ° of <g<97 °; The expression that Section 2 is similar to, by the asymmetry according to moonscape, is mainly subject to the impact on moonscape dark area and highland; Section 3 to Section 6 and containing four of c with libration with shine upon relevant; Last three is nonlinear empirical term, represents that full moon liquidates the impact of effect and residual error respectively.

Embodiment

In the present embodiment, given satellite orbital altitude H=645km, earth radius R _e=6378km, moon radius R _m=1737km, the moon centre distance get R _em=384400km, camera focus f=2.6m, Kepler's constant μ=3.986 × 10 ⁵km ³/ s ², the size p=10 μm of each pixel in satellite linear array CCD camera.

1, the Satellite Camera time shutter t of each imaging is determined _m

The time shutter t to earth imaging is obtained according to formula (2) _efor:

$t_e=\frac{p}{f\&times;\sqrt{\frac{\mathrm{\&mu;}}{{(R_e+H)}^3}}}\&times;\frac{H}{R_e}=\frac{10\&times;{10}^{-9}}{2.6\&times;{10}^{-3}\&times;\sqrt{\frac{3.986\&times;{10}^5}{{(6378+645)}^3}}}\&times;\frac{645}{6378}=0.36259\&times;{10}^{-3}s$

The time shutter t to moon imaging is obtained according to formula (3) _mfor:

$\begin{array}{c}{t}_m=\frac{p}{f\&times;\sqrt{\frac{\mathrm{\&mu;}}{{(R_e+H)}^3}}}\&times;\frac{R_{\mathrm{em}}-R_m-H-R_e}{R_{\mathrm{em}}-R_m}=\\ \frac{10\&times;{10}^{-9}}{2.6\&times;{10}^{-3}\&times;\sqrt{\frac{3.986\&times;{10}^5}{{\left(6378+645\right)}^3}}}\&times;\frac{384400-1737-645-6378}{384400-1737}=3.5196\&times;{10}^{-3}s\end{array}$

Therefore, if adopt square sample imaging, then satellite is to the time shutter t of moon imaging _mbe about earth time shutter t _e9.7 times.

2, the attitude of satellite rate of pitch d θ of push-scanning image is calculated _msize

Can be obtained by formula (6), rate of pitch:

3, satellite is in the whole process of moon imaging, and when not having effective star chart to use, attitude measurement needs to be measured as master from star sensor and proceeds to the metering system reaching accuracy requirement based on inertial sensor or other.

The integration progression N of camera is set in the present invention _tDI=6,12,24,48,72,96 adjustable, under integration progression at different levels, for the decline meeting mtf value is no more than 10%.

(1) situation of time shutter realization to moon square sample is adjusted, then to the time shutter t of moon imaging for needing _m=3.5196 × 10 ^-3s, calculates attitude pointing accuracy δ degree and attitude stability δ ' degree/second according to formula (7) and formula (8):

1) obtain corresponding dx, dy by formula (7) and be all no more than 0.846,0.4187,0.2088,0.1043,0.0695,0.0521 (unit: μm).

2) scope that can not exceed according to dx, dy is again as constraint condition, and formula (7) structure critical equation:

$\left\{\begin{array}{c}\mathrm{dx}\&GreaterEqual;f\tan \left({\mathrm{\&delta;}}^{\&prime;}{t}_m\right)\\ \mathrm{dy}\&GreaterEqual;\mathrm{\&tau;}\tan \mathrm{\&delta;}+\mathrm{\&tau;}\tan \left({\mathrm{\&delta;}}^{\&prime;}{t}_m\right)+f\tan \left({\mathrm{\&delta;}}^{\&prime;}{t}_m\right)\end{array}\right.$

Qualified attitude pointing accuracy δ and attitude stability δ ' is obtained as shown in Figure 5 by trial method, the bottom-left quadrant of figure bend is the region satisfied condition, the oblique line that Fig. 6 (a) is corresponding under giving 6,12,24 grades of integration progression, the oblique line that Fig. 6 (b) is corresponding under having gone out 48,72,96 grades of integration progression, can find out, along with the increase of integration progression, more and more stricter to the requirement of attitude accuracy, suitable δ and δ ' can be selected according to the precision of sensor in actual applications.

(2) time shutter is adjusted, then to the time shutter t of moon imaging for not needing _mwith the time shutter t to moon imaging _eequal, t _m=t _e=0.36259 × 10 ^-3s, calculates attitude pointing accuracy δ degree and attitude stability δ ' degree/second according to formula (7) and formula (8):

1) obtain corresponding dx, dy by formula (7) and be all no more than 0.846,0.4187,0.2088,0.1043,0.0695,0.0521 (unit: μm).

2) scope that can not exceed according to dx, dy is again as constraint condition, and formula (7) structure critical equation:

$\left\{\begin{array}{c}\mathrm{dx}\&GreaterEqual;f\tan \left({\mathrm{\&delta;}}^{\&prime;}{t}_m\right)\\ \mathrm{dy}\&GreaterEqual;\mathrm{\&tau;}\tan \mathrm{\&delta;}+\mathrm{\&tau;}\tan \left({\mathrm{\&delta;}}^{\&prime;}{t}_m\right)+f\tan \left({\mathrm{\&delta;}}^{\&prime;}{t}_m\right)\end{array}\right.$

Qualified attitude pointing accuracy δ and attitude stability δ ' is obtained as shown in Figure 5 by trial method, the bottom-left quadrant of figure bend is the region satisfied condition, the oblique line that Fig. 7 (a) is corresponding under giving 6,12,24 grades of integration progression, the oblique line that Fig. 7 (b) is corresponding under having gone out 48,72,96 grades of integration progression, can find out, along with the increase of integration progression, more and more stricter to the requirement of attitude accuracy, suitable δ and δ ' can be selected according to the precision of sensor in actual applications.

The unspecified part of the present invention belongs to general knowledge as well known to those skilled in the art.

Claims (6)

1. low orbit Earth observation satellite is to a moon absolute radiation calibration method, it is characterized in that step is as follows:

(1) Satellite Tool Kit determination low orbit Earth observation satellite is utilized can to observe the time of the moon, Satellite Tool Kit is utilized to obtain the attitude of satellite angle corresponding to the time that can observe the moon, calculating can observe the moon phasing degree corresponding to the time of the moon, again according to the attitude maneuver ability of satellite, select from the time that can observe the moon moon imaging time, perform step (2);

Described attitude maneuver ability refers to satellite pitching angle theta, roll angle Φ and crab angle maximum maneuvering range, must within the attitude maneuver limit of power of satellite to the pose adjustment size of satellite during moon imaging; Described moon phasing degree meets ROLO moon absolute radiometric calibration model, and the moon phasing degree scope selected in this model is: [1.55 °, 97 °];

(2) selected by step (1) to moon imaging time, determining to proceed to start time to moon imaging pattern from imaging pattern over the ground, from moon imaging pattern being proceeded to end time of imaging pattern over the ground and satellite linear array CCD camera to the imaging frequency n of moon push-scanning image, and determining the Satellite Camera time shutter t of each imaging _m, imaging initial time, the imaging end time, attitude of satellite angle, satellite rate of pitch d θ _m; The attitude of satellite angle of described each imaging comprise each imaging initial time attitude angle, intermediate time attitude angle and finish time attitude angle; Described attitude angle comprises the angle of pitch, roll angle and crab angle, described satellite linear array CCD camera to the imaging initial time of moon push-scanning image number of times, each imaging and the imaging end time all given in advance;

(3) when Earth observation satellite in orbit the time arrive determine in step (2) from imaging pattern over the ground proceed to the moon imaging pattern start time time, satellite enters attitude maneuver pattern, satellite adjusts according to the attitude of satellite angle determined in step (2), proceeds to moon imaging pattern by imaging pattern over the ground;

(4) when the time arrives the first time imaging initial time determined in step (2) to Earth observation satellite in orbit, the linear array CCD camera of Earth observation satellite is according to the Satellite Camera time shutter t of each imaging determined in step (2) _mstart moon imaging, obtain lunar map picture, if be greater than 1 to the imaging frequency n of moon push-scanning image, then perform step (5), otherwise perform step (6);

(5) according to the Satellite Camera time shutter t of each imaging determined in step (2) _m, imaging initial time, imaging end time and attitude of satellite angle, complete according to the method in step (4) all to moon push-scanning image, obtain all lunar map pictures, enter step (6);

(6) complete moon push-scanning image, Earth observation satellite enters attitude maneuver pattern, proceeds to imaging pattern over the ground to moon imaging pattern;

(7) utilize ROLO absolute radiometric calibration model to process all lunar map pictures obtained in step (6), obtain Absolute Radiometric Calibration Coefficients.

2. a kind of low orbit Earth observation satellite according to claim 1 is to moon absolute radiation calibration method, it is characterized in that: the Satellite Camera time shutter t determining each imaging in described step (2) _m, specifically realized by following steps:

(2a) the projection line speed v of satellite at moonscape is calculated _m, specifically by formula:

$v_m=\sqrt{\frac{\mathrm{\&mu;}}{(R_e+H)}}\&times;\frac{(R_{\mathrm{em}}-R_m)}{R_e+H}$

Provide, wherein, μ is Gravitational coefficient of the Earth, R _efor earth radius, H is the orbit altitude of satellite transit; R _emfor earth center is to the distance of moon ball center, R _mfor the moon radius of a ball;

(2b) the projected size GIFOV of each pixel on the moon in satellite linear array CCD camera is calculated _m, specifically by formula:

${\mathrm{GIFOV}}_m=\frac{p\&times;(R_{\mathrm{em}}-R_m-H-R_e)}{f}$

Provide, wherein, p is the size of each pixel in satellite linear array CCD camera, and f is the focal length of Satellite Camera;

(2c) each pixel projected size on the moon in the satellite linear array CCD camera in the projection line speed and step (2b) of moonscape of the satellite in step (2a) is utilized, calculate the Satellite Camera time shutter of each imaging, specifically by formula:

$t_m=\frac{{\mathrm{GIFOV}}_m}{v_m}=\frac{p}{f\&times;\sqrt{\frac{\mathrm{\&mu;}}{{(R_e+H)}^3}}}\&times;\frac{R_{\mathrm{em}}-R_m-H-R_e}{R_{\mathrm{em}}-R_m}$

Provide.

3. a kind of low orbit Earth observation satellite according to claim 1 is to moon absolute radiation calibration method, it is characterized in that: intermediate time attitude angle in described step (2), is realized by following steps:

(3a) according to imaging initial time and the imaging end time of each imaging of satellite given in advance in step (2), calculate the imaging intermediate time of each imaging of satellite, determine the position vector between the imaging intermediate time satellite of each imaging and the moon according to satellite orbit and moon ephemeris further

(3b) according to the position vector between the imaging intermediate time satellite in step (3a) and the moon be calculated to be the pitching angle theta of picture intermediate time _mid, roll angle Φ _midand crab angle the pitching angle theta of imaging intermediate time _midspecifically by formula:

The roll angle Φ of imaging intermediate time _midspecifically by formula:

${\mathrm{\&Phi;}}_{\mathrm{mid}}=\arcsin \left[\frac{\left|r_2\right|}{\sqrt{{r_1}^2+{r_2}^2+{r_3}^2}}\right]$

Provide, wherein, r ₁for the position vector between imaging intermediate time satellite and the moon at satellite orbit coordinate system B _xprojected size on direction of principal axis, r ₃for the position vector between imaging intermediate time satellite and the moon at satellite orbit coordinate system B _zprojected size on direction of principal axis; r ₂for the position vector between imaging intermediate time satellite and the moon at satellite orbit coordinate system B _yprojected size on direction of principal axis; Wherein, satellite orbit coordinate system B _o-B _xb _yb _zinitial point B _oin orbit, B _xaxle points to satellite working direction, B _zaxle points to the earth's core by centroid of satellite, B _yaxle is perpendicular to by B _xwith B _zthe orbit plane that axle is formed;

Described crab angle constant in imaging process, and be 0.

4. a kind of low orbit Earth observation satellite according to claim 1 is to moon absolute radiation calibration method, it is characterized in that: described step (2) Satellite attitude rate of pitch d θ _m, detailed process is as follows:

If satellite linear array CCD camera realizes square sample imaging, then attitude of satellite rate of pitch d θ by adjustment attitude rate of pitch _mby formula:

${\mathrm{d\&theta;}}_m=\sqrt{\frac{\mathrm{\&mu;}}{{(R_e+H)}^3}}[\frac{R_e}{H}-\frac{(R_{\mathrm{em}}-R_m)}{(R_{\mathrm{em}}-R_m-H-R_e)}]$

Provide, wherein, μ is Gravitational coefficient of the Earth, R _efor earth radius, H is the orbit altitude of satellite transit; R _emfor earth center is to the distance of moon ball center, R _mfor the moon radius of a ball;

Otherwise, attitude of satellite rate of pitch d θ _mbe zero.

5. a kind of low orbit Earth observation satellite according to claim 1 is to moon absolute radiation calibration method, it is characterized in that: in described step (2) initial time attitude angle and finish time attitude angle, concrete computation process is as follows:

Initial time pitching angle theta _startby formula:

${\mathrm{\&theta;}}_{\mathrm{start}}={\mathrm{\&theta;}}_{\mathrm{mid}}-{\mathrm{d\&theta;}}_m\&CenterDot;\frac{t}{2}$

Provide, wherein, t is the difference in each imaging process between imaging end time and imaging initial time;

Initial time roll angle Φ _startby formula:

Φ _start＝Φ _mid

Provide,

Finish time pitching angle theta _endby formula:

${\mathrm{\&theta;}}_{\mathrm{end}}={\mathrm{\&theta;}}_{\mathrm{mid}}+{\mathrm{d\&theta;}}_m\&CenterDot;\frac{t}{2}$

Provide,

Finish time roll angle Φ _endby formula:

Φ _end＝Φ _mid

Provide.

6. a kind of low orbit Earth observation satellite according to claim 1 is to moon absolute radiation calibration method, it is characterized in that: determine in described step (2) to proceed to start time to moon imaging pattern from imaging pattern over the ground, from end time moon imaging pattern being proceeded to imaging pattern over the ground, be specially:

From imaging pattern over the ground proceed to the moon imaging pattern start time by formula:

t _start＝t _start1-t′

Provide, wherein, t _startfor imaging pattern proceeds to the start time to moon imaging pattern over the ground, t _start1for the initial time of first time to moon imaging, t ' is that imaging pattern proceeds to the attitude maneuver time to moon imaging pattern over the ground, specifically by formula:

$t^{\&prime;}=\max \{\frac{{\mathrm{\&theta;}}_{\mathrm{start}1}-{\mathrm{\&theta;}}_0}{\mathrm{d\&theta;}},\frac{{\mathrm{\&Phi;}}_{\mathrm{start}1}-{\mathrm{\&Phi;}}_0}{\mathrm{d\&Phi;}}\}+t_w$

Provide, wherein t _wfor the attitude stabilization time, θ _start1for the angle of pitch of first time to moon imaging initial time, θ ₀for the angle of pitch of imaging over the ground, d θ is satellite rate of pitch, Φ _start1for the roll angle of first time to moon imaging initial time, Φ ₀for the roll angle of imaging over the ground, d Φ satellite rate of roll;

The end time of imaging pattern is over the ground proceeded to by formula to moon imaging pattern:

t _end＝t _endn+t″

Provide, wherein, t _endfor proceeding to the end time of imaging pattern over the ground to moon imaging pattern, t _endnbe n-th end time to moon imaging, t " for proceeding to the attitude maneuver time of imaging pattern over the ground to moon imaging pattern, specifically by formula:

$t^{\&prime;\&prime;}=\max \{\frac{{\mathrm{\&theta;}}_{\mathrm{endn}}-{\mathrm{\&theta;}}_1}{\mathrm{d\&theta;}},\frac{{\mathrm{\&Phi;}}_{\mathrm{endn}}-{\mathrm{\&Phi;}}_1}{\mathrm{d\&Phi;}}\}+t_w^{\&prime;}$

Provide, wherein t ' _wfor the attitude stabilization time, θ _endnbe n-th angle of pitch to the imaging finish time moon, θ ₁for the angle of pitch of imaging over the ground, d θ is satellite rate of pitch, Φ _endnbe n-th roll angle to the imaging finish time moon, Φ ₁for the roll angle of imaging over the ground, d Φ satellite rate of roll.