CN102679945B - Satellite pointing and attitude measuring method and device based on three-point reflecting cooperation - Google Patents

Abstract

The invention discloses a satellite pointing and attitude measuring method and a satellite pointing and attitude measuring device based on three-point reflecting cooperation, and belong to an angle measurement technology in the field of measurement. According to the device, three cube-corner prisms are arranged on a small satellite to be measured; the three cube-corner prisms form a right triangle of which the normal vector does not change along with the rotation of the small satellite to be measured; a laser of a reference small satellite is dead against the midpoint of hypotenuse of the right triangle formed by the three cube-corner prisms; and constructing a mathematic relation of the distance between the two cube-corner prisms on the small satellite to be measured, which are positioned on the right-angle sides, and the projection distance of the two cube-corner prisms on the reference small satellite. According to the method, the reference line deflection angle and spatial attitude angle of the small satellite to be measured relative to the reference small satellite are measured. By adoption of the device and the method, the pointing and spatial attitude of the small satellite to be measured relative to the reference small satellite can be indirectly acquired only by measuring the angle of the small satellite to be measured relative to the reference small satellite; the measurement device is simple, and the measurement result is accurate.

Description

Satellite sensing based on three point reflection cooperations and attitude measurement method and device

Technical field

The invention belongs to and measure measurement of angle technology in field tests, relate generally in a kind of Small Satellite Formation Flying technology, by measurement of angle, indirectly obtain moonlet to be measured with respect to measuring method and the device of benchmark moonlet position and distance.

Background technology

Along with scientific and technical fast development, Small Satellite Formation Flying technology is subject to the great attention of various countries.Small Satellite Formation Flying refers to that a Small Satellite Group take that certain is some benchmark, keeps a given shape, orbits the earth with the identical orbital period.The mutual collaborative work of each of formation flight moonlet, the tasks such as the processing of shared signal, communication and useful load.The Small Satellite Group of formation flight not only can substitute with lower cost, higher reliability and viability traditional large satellite of single identical function, can also break through the size restrictions of traditional large satellite, application and the performance of expansion large satellite, comprise earth observation, three-dimensional imaging, accurate location, atmospheric exploration, astronomical sight and geophysical observatory etc., there is huge Military value and civilian value.

Although Small Satellite Formation Flying technology has broad application prospects, be faced with the challenge of supertech difficulty.Because the superiority of the moonlet of formation flight is to be measured with the accurate control of Satellite Formation Flying formation and realized by high-precision Inter-satellite Baseline, and the measuring accuracy of baseline is required to reach a centimetre magnitude, even millimeter magnitude, pointing accuracy and attitude measurement accuracy all require to reach a rad magnitude, therefore, embody the superiority of Small Satellite Formation Flying, first will carry out high-acruracy survey to Formation Flying Small Satellites state.

Quantity of state comprises flying speed, height and the rotational angle of every moonlet, and the measurement of quantity of state is divided into again absolute status measurement and relative status is measured.With absolute status measurement, compare, relative status surveying party realizes Small Satellite Formation Flying's autonomous flight, formation keeping and control etc. and has prior meaning, in numerous relative status amounts, and the position of moonlet relative datum moonlet to be measured, comprising angle and distance, is the basis that keeps satellite communication.

In space flight intersection field, as in January, 2008, publish an article for No. 1 measuring method > > of relative position and attitude between the spacecraft of < < based on binocular vision of aerospace journal the 29th volume, in March, 2010 and for example, optical technology the 36th volume is delivered the article such as relative pose Measurement Algorithm > > between the spacecraft of < < based on monocular vision for No. 2, a kind of method all extensively adopting is respectively according to the attitude of the attitude of benchmark moonlet and moonlet to be measured, set up the three-dimensional coordinate of benchmark moonlet and the three-dimensional coordinate of moonlet to be measured, and moonlet three-dimensional coordinate to be measured is rotated with translation and can be overlapped with benchmark moonlet three-dimensional coordinate, and rotation amount and translational movement can obtain by matrix operation.This method proposes for the docking technique solving in space flight intersection field, although can accurately measure moonlet to be measured with respect to benchmark moonlet direction of living in and attitude, the shortcoming of this method is the distance that cannot measure between moonlet to be measured and benchmark moonlet.

In laser ranging field, as China Patent Publication No. CN101349757A, open day on January 21st, 2009, invention < < active collaboration type phase laser distance measuring method and device > >, a kind of laser distance measurement method is disclosed, the method is utilized twin-beam one way cooperation measurement pattern, the attenuated form that makes measuring system light echo energy is quadratic power attenuation function, therefore can increase to a great extent system light echo energy and signal to noise ratio (S/N ratio), be applicable to long-distance ranging.This method is applied to Formation Flying Small Satellites relative status and measures, can accurately obtain two distances between moonlet, yet the shortcoming of this method maximum is to measure the angle of moonlet relative datum moonlet to be measured.

Summary of the invention

The present invention is directed to above-mentioned problems of the prior art, designed a kind ofly only by measurement of angle, can obtain moonlet to be measured with respect to the sensing of benchmark moonlet and the measuring method of spatial attitude and device simultaneously.

The object of the present invention is achieved like this:

Satellite based on three point reflection cooperations points to and attitude measurement method, comprises the following steps:

A, first constantly, the laser beam of laser instrument transmitting is through Amici prism transmission, again by after the first prism of corner cube, the second prism of corner cube, pyrometric cone prismatic reflection, Yan Yuan returns on road, through Amici prism, reflect by telescope imaging for the second time, and gathered by imageing sensor, and view data is flowed to computing machine process; By mathematical operation, obtain the first prism of corner cube in the situation that not considering magnification of telescope and the second prism of corner cube with laser beam vertical direction on projector distance d ₁with the second prism of corner cube and pyrometric cone prism with laser beam vertical direction on projector distance d ₂;

B, according to the orbit radius r of benchmark moonlet ₁, moonlet to be measured orbit radius r ₂, the distance l on moonlet to be measured between the first prism of corner cube and the second prism of corner cube ₁, utilize the first prism of corner cube that a step obtains and the second prism of corner cube with laser beam vertical direction on projector distance d ₁, use calculating formula:

$d_1=l_1\frac{r_1-{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\cos \mathrm{\&alpha;}}{\sqrt{r_1^2+{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2^2-2r_1{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\cos \mathrm{\&alpha;}}}$

Try to achieve the angle α of the benchmark moonlet radius of gyration and the moonlet radius of gyration to be measured;

C, according to the orbit radius r of benchmark moonlet ₁, moonlet to be measured orbit radius r ₂, the distance l on moonlet to be measured between the second prism of corner cube and pyrometric cone prism ₂, utilize the second prism of corner cube that a step obtains and pyrometric cone prism with laser beam vertical direction on projector distance d ₂, and the benchmark moonlet radius of gyration that obtains of b step and the angle α of the moonlet radius of gyration to be measured, and the coordinate of establishing benchmark moonlet is (r ₁, 0,0), use calculating formula:

$h=\frac{\sqrt{{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">l</figure-callout>}}_2^2-{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">d</figure-callout>}}_2^2}\sqrt{r_1^2{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2^2-2r_1{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\cos \mathrm{\&alpha;}}}{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}$

The distance h of trying to achieve benchmark moonlet place rotational plane and moonlet to be measured place rotational plane, the coordinate of moonlet to be measured is (r ₂cos α, r ₂sin α, h);

D, second constantly, the laser beam of laser instrument transmitting is through Amici prism transmission, again by after the first prism of corner cube, the second prism of corner cube, pyrometric cone prismatic reflection, Yan Yuan returns on road, for the second time through Amici prism reflection by telescope imaging and gathered by imageing sensor, and view data flowed to computing machine process; By mathematical operation, obtain the first prism of corner cube and the second prism of corner cube with laser beam vertical direction on projector distance d ' ₁;

E, according to the orbit radius r of benchmark moonlet ₁, moonlet to be measured orbit radius r ₂, the distance l on moonlet to be measured between the first prism of corner cube and the second pyramid rib ₁, the distance l between the second pyramid rib and pyrometric cone rib ₂, utilize the first prism of corner cube that a step obtains and the second prism of corner cube with laser beam vertical direction on projector distance d ₁, the benchmark moonlet radius of gyration that b step obtains and the angle α of the moonlet radius of gyration to be measured, d walk the first prism of corner cube of obtaining and the second prism of corner cube with laser beam vertical direction on projector distance d ' ₁, use calculating formula:

$\mathrm{\&beta;}=\arcsin \frac{l_1{d}_1^{\&prime;}(r_1-{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\cos \mathrm{\&alpha;})}{l_2{d}_1\sqrt{r_1^2+{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2^2-2r_1{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\cos \mathrm{\&alpha;}}}-\arcsin \frac{r_1-{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\cos \mathrm{\&alpha;}}{\sqrt{r_1^2+{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2^2-2r_1{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\cos \mathrm{\&alpha;}}}$

Try to achieve relative first constantly, the angle that benchmark moonlet and moonlet to be measured turn over, and to obtain the now coordinate of benchmark moonlet be (r ₁cos β, r ₁sin β, 0), the coordinate of moonlet to be measured is (r ₂cos (alpha+beta), r ₂sin (alpha+beta), h);

F, according to the orbit radius r of benchmark moonlet ₁, the orbit radius r of moonlet to be measured ₂, the benchmark moonlet radius of gyration and the angle α of the moonlet radius of gyration to be measured that utilize b step to obtain, and the benchmark moonlet place rotational plane that obtains of c step and the distance h of moonlet to be measured place rotational plane, use calculating formula:

$d=\sqrt{r_1^2+{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2^2-2r_1{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\cos \mathrm{\&alpha;}+{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">h</figure-callout>}}^2}$

Obtain the distance d between benchmark moonlet and moonlet to be measured.

Satellite based on three point reflection cooperations points to and attitude measuring, be included in and on benchmark moonlet, configure laser instrument, Amici prism, telescope, imageing sensor and computing machine, Amici prism is positioned on the emitting light path of laser instrument, telescope and imageing sensor are positioned on the reflected light path of Amici prism, and computing machine is communicated with imageing sensor; On moonlet to be measured, configure the first prism of corner cube, the second prism of corner cube, pyrometric cone prism, the laser beam of the laser instrument transmitting of benchmark moonlet is through Amici prism transmission, again by after the first prism of corner cube, the second prism of corner cube, pyrometric cone prismatic reflection, Yan Yuan returns on road, for the second time through Amici prism reflection by telescope imaging and gathered by imageing sensor, and view data flowed to computing machine process; The first prism of corner cube, the second prism of corner cube, the pyrometric cone prism triangular arrangement that meets at right angles on moonlet to be measured, wherein the second prism of corner cube is positioned at place, summit, right angle, and the first prism of corner cube and the second prism of corner cube place straight line and the second prism of corner cube and pyrometric cone prism place straight line are orthogonal; The normal vector direction of the first prism of corner cube, the second prism of corner cube and pyrometric cone prism place plane is constant; The laser beam of the laser instrument transmitting on benchmark moonlet is through Amici prism transmission, and the direction of transmitted light beam is pointed to the mid point of moonlet the first prism of corner cube to be measured and pyrometric cone prism line.

Feature of the present invention is:

1. on moonlet to be measured, configured three prism of corner cubes, and allowed planar form right angle triangle of these three prism of corner cubes, this is that the present invention is different from one of essential characteristic of existing method and apparatus;

2. the normal vector direction that guarantees three prism of corner cube place planes is constant, and namely prism of corner cube does not rotate with moonlet to be measured, and this is that the present invention is different from one of essential characteristic of existing method and apparatus;

3. the laser instrument that remains benchmark moonlet faces the hypotenuse point midway that three prism of corner cubes form, and this is that the present invention is different from one of essential characteristic of existing method and apparatus;

Above-mentioned three features can guarantee that on moonlet to be measured, distance between two prism of corner cubes on right-angle side becomes definite mathematical relation with their projector distances on benchmark moonlet.Utilize the corresponding mathematical relation of device of the present invention, can measure the angle of moonlet relative datum moonlet to be measured.

The beneficial effect that These characteristics is brought is: only by the angle of moonlet relative datum moonlet to be measured is measured, just can indirectly obtain moonlet to be measured with respect to benchmark moonlet position and distance, measurement mechanism is simple, and measurement result is accurate.

Accompanying drawing explanation

Fig. 1 is that Formation Flying Small Satellites group is around earth rotation schematic diagram

Fig. 2 is that the satellite based on three point reflection cooperations points to and attitude measuring structural representation

Fig. 3 is the first moment Formation Flying Small Satellites relative position schematic diagram

Fig. 4 is the second moment Formation Flying Small Satellites relative position schematic diagram

Piece number explanation in figure: 1 laser instrument, 2 Amici prisms, 3 telescopes, 4 imageing sensors, 5 computing machines, 6 first prism of corner cubes, 7 second prism of corner cubes, 8 pyrometric cone prisms.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the invention is described in detail.

Satellite based on three point reflection cooperations points to and attitude measuring, be included in and on benchmark moonlet, configure laser instrument 1, Amici prism 2, telescope 3, imageing sensor 4 and computing machine 5, Amici prism 2 is positioned on the emitting light path of laser instrument 1, telescope 3 and imageing sensor 4 are positioned on the reflected light path of Amici prism 2, and computing machine 5 is communicated with imageing sensor 4; On moonlet to be measured, configure the first prism of corner cube 6, the second prism of corner cube 7, pyrometric cone prism 8, the laser beam of laser instrument 1 transmitting of benchmark moonlet is through Amici prism 2 transmissions, again by after the first prism of corner cube 6, the second prism of corner cube 7,8 reflections of pyrometric cone prism, Yan Yuan returns on road, for the second time through Amici prism 2 reflection by telescope 3 imagings and gathered by imageing sensor 4, and view data flowed to computing machine 5 process; The first prism of corner cube 6, the second prism of corner cube 7, pyrometric cone prism 8 triangular arrangement that meets at right angles on moonlet to be measured, wherein the second prism of corner cube 7 is positioned at place, summit, right angle, and the first prism of corner cube 6 and the second prism of corner cube 7 place straight lines and the second prism of corner cube 7 and pyrometric cone prism 8 place straight lines are orthogonal; The normal vector direction of the first prism of corner cube 6, the second prism of corner cube 7 and pyrometric cone prism 8 place planes is constant; The laser beam of laser instrument 1 transmitting on benchmark moonlet is through Amici prism 2 transmissions, and the direction of transmitted light beam is pointed to the mid point of moonlet the first prism of corner cube 6 to be measured and pyrometric cone prism 8 lines.

Satellite based on three point reflection cooperations points to and attitude measurement method, comprises the following steps:

A, first constantly, the laser beam of laser instrument 1 transmitting is through Amici prism 2 transmissions, again by after the first prism of corner cube 6, the second prism of corner cube 7,8 reflections of pyrometric cone prism, Yan Yuan returns on road, for the second time through Amici prism 2 reflection by telescope 3 imagings and gathered by imageing sensor 4, and view data flowed to computing machine 5 process; By mathematical operation, obtain in the situation that not considering telescope 3 magnification, the first prism of corner cube 6 and the second prism of corner cube 7 with laser beam vertical direction on projector distance d ₁=86.6mm, the second prism of corner cube 7 and pyrometric cone prism 8 with laser beam vertical direction on projector distance d ₂=65.5mm, this moment Formation Flying Small Satellites relative position is as shown in Figure 2;

B, according to the orbit radius r of benchmark moonlet ₁=10km, the orbit radius r of moonlet to be measured ₂=10km, the distance l on moonlet to be measured between the first prism of corner cube 6 and the second prism of corner cube 7 ₁=100mm, utilize the first prism of corner cube 6 that a step obtains and the second prism of corner cube 7 with laser beam vertical direction on projector distance d ₁=86.6mm, uses calculating formula:

$d_1=l_1\frac{r_1-{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\cos \mathrm{\&alpha;}}{\sqrt{r_1^2+{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2^2-2r_1{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\cos \mathrm{\&alpha;}}}$

$86.6\&times;{10}^{-3}=100\&times;{10}^{-3}\&times;\frac{10\&times;{10}^3-10\&times;{10}^3\cos \mathrm{\&alpha;}}{\sqrt{{(10\&times;{10}^3)}^2+{(10\&times;{10}^3)}^2-2\&times;(10\&times;{10}^3)(10\&times;{10}^3)\cos \mathrm{\&alpha;}}}$

Can be in the hope of angle α=120 ° of the benchmark moonlet radius of gyration and the moonlet radius of gyration to be measured;

C, according to the orbit radius r of benchmark moonlet ₁=10km, the orbit radius r of moonlet to be measured ₂=10km, the distance l on moonlet to be measured between the second prism of corner cube 7 and pyrometric cone prism 8 ₂=100mm, utilize the second prism of corner cube 7 that a step obtains and pyrometric cone prism 8 with laser beam vertical direction on projector distance d ₂=65.5mm, and b step the benchmark moonlet radius of gyration and angle α=120 ° of the moonlet radius of gyration to be measured that obtain, use calculating formula:

$h=\frac{\sqrt{{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">l</figure-callout>}}_2^2-{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">d</figure-callout>}}_2^2}\sqrt{r_1^2+{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2^2-2r_1{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\cos \mathrm{\&alpha;}}}{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}$

$h=\frac{\sqrt{{(100\&times;{10}^{-3})}^2-{(65.5\&times;{10}^{-3})}^2}\sqrt{{(10\&times;{10}^3)}^2+{(10\&times;{10}^3)}^2-2\&times;(10\&times;{10}^3)\&times;\cos \left(\frac{2\mathrm{\&pi;}}{3}\right)}}{65.5\&times;{10}^{-3}}$

Can be in the hope of the distance h=20km of benchmark moonlet place rotational plane and moonlet to be measured place rotational plane, and if the coordinate that can access benchmark moonlet be (10,0,0), the coordinate of moonlet to be measured is (5,8.66,20), the km of unit;

D, second constantly, the laser beam of laser instrument 1 transmitting is through Amici prism 2 transmissions, again by after the first prism of corner cube 6, the second prism of corner cube 7,8 reflections of pyrometric cone prism, Yan Yuan returns on road, for the second time through Amici prism 2 reflection by telescope 3 imagings and gathered by imageing sensor 4, and view data flowed to computing machine 5 process; By mathematical operation, obtain the first prism of corner cube 6 and the second prism of corner cube 7 with laser beam vertical direction on projector distance d ' ₁=100mm, this moment Formation Flying Small Satellites relative position is as shown in 3;

E, according to the orbit radius r of benchmark moonlet ₁=10km, the orbit radius r of moonlet to be measured ₂=10km, the distance l on moonlet to be measured between the first prism of corner cube 6 and the second prism of corner cube 7 ₁=100mm, the distance l between the second prism of corner cube 7 and pyrometric cone prism 8 ₂=100mm, utilize the first prism of corner cube 6 that a step obtains and the second prism of corner cube 7 with laser beam vertical direction on projector distance d ₁=86.6mm, the benchmark moonlet radius of gyration that b step obtains and angle α=120 ° of the moonlet radius of gyration to be measured, d walk the first prism of corner cube 6 of obtaining and the second prism of corner cube 7 with laser beam vertical direction on projector distance d ' ₁=100mm, uses calculating formula:

$\mathrm{\&beta;}=\arcsin \frac{l_1{d}_1^{\&prime;}(r_1-{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\cos \mathrm{\&alpha;})}{l_2{d}_1\sqrt{r_1^2+{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2^2-2r_1{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\cos \mathrm{\&alpha;}}}-\arcsin \frac{r_1-{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\cos \mathrm{\&alpha;}}{\sqrt{r_1^2+{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2^2-2r_1{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\cos \mathrm{\&alpha;}}}$

$\mathrm{\&beta;}=\arcsin \frac{100\&times;{10}^{-3}\&times;100\&times;{10}^{-3}\&times;(10\&times;{10}^3-10\&times;{10}^3\&times;\cos \left(\frac{2\mathrm{\&pi;}}{3}\right))}{100\&times;{10}^{-3}\&times;86.6\&times;{10}^{-3}\&times;\sqrt{{(10\&times;{10}^3)}^2+{(10\&times;{10}^3)}^2-2\&times;(10\&times;{10}^3)\&times;(10\&times;{10}^3)\&times;\cos \left(\frac{2\mathrm{\&pi;}}{3}\right)}}$

$-\arcsin \frac{10\&times;{10}^3-10\&times;{10}^3\&times;\cos \left(\frac{2\mathrm{\&pi;}}{3}\right)}{\sqrt{{(10\&times;{10}^3)}^2+{(10\&times;{10}^3)}^2-2\&times;(10\&times;{10}^3)\&times;(10\&times;{10}^3)\&times;\cos \left(\frac{2\mathrm{\&pi;}}{3}\right)}}$

Can be in the hope of relative first constantly, the angle that benchmark moonlet and moonlet to be measured turn over, and to access the now coordinate of benchmark moonlet be (8.66,5,0), the coordinate of moonlet to be measured is (8.66,5,20), the km of unit;

F, according to the orbit radius r of benchmark moonlet ₁, the orbit radius r of moonlet to be measured ₂, the benchmark moonlet radius of gyration and angle α=120 ° of the moonlet radius of gyration to be measured that utilize b step to obtain, and the benchmark moonlet place rotational plane that obtains of c step and the distance h=20km of moonlet to be measured place rotational plane, use calculating formula:

$d=\sqrt{r_1^2+{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2^2-2r_1{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\cos \mathrm{\&alpha;}+{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">h</figure-callout>}}^2}$

$d=\sqrt{{(10\&times;{10}^3)}^2+{(10\&times;{10}^3)}^2-2\&times;(10\&times;{10}^3)\&times;(10\&times;{10}^3)\&times;\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000728206800012.png"\; state="\{\{state\}\}">cos</figure-callout>}\frac{2\mathrm{\&pi;}}{3}+{(20\&times;{10}^3)}^2}=26.458\mathrm{km}$

The distance that can try to achieve between benchmark moonlet and moonlet to be measured is 26.458km.

Claims (2)

1. the satellite based on three point reflection cooperations points to and attitude measurement method, it is characterized in that comprising the following steps:

A, first constantly, the laser beam of laser instrument transmitting is through Amici prism transmission, again by after the first prism of corner cube, the second prism of corner cube, pyrometric cone prismatic reflection, Yan Yuan returns on road, through Amici prism, reflect by telescope imaging for the second time, and gathered by imageing sensor, and view data is flowed to computing machine process; In the situation that not considering magnification of telescope, the first prism of corner cube obtaining by mathematical operation and the second prism of corner cube with laser beam vertical direction on projector distance d ₁with the second prism of corner cube and pyrometric cone prism with laser beam vertical direction on projector distance d ₂;

B, according to the orbit radius r of benchmark moonlet ₁, the orbit radius r of moonlet to be measured ₂, the distance l on moonlet to be measured between the first prism of corner cube and the second prism of corner cube ₁, utilize the first prism of corner cube that a step obtains and the second prism of corner cube with laser beam vertical direction on projector distance d ₁, use calculating formula:

$d_1=l_1\frac{r_1-r_2\cos \mathrm{\&alpha;}}{\sqrt{{r_1}^2+{r_2}^2-2r_1{r}_2\cos \mathrm{\&alpha;}}}$

Try to achieve the angle α of the benchmark moonlet radius of gyration and the moonlet radius of gyration to be measured;

C, according to the orbit radius r of benchmark moonlet ₁, the orbit radius r of moonlet to be measured ₂, the distance l on moonlet to be measured between the second prism of corner cube and pyrometric cone prism ₂, utilize the second prism of corner cube that a step obtains and pyrometric cone prism with laser beam vertical direction on projector distance d ₂, and the benchmark moonlet radius of gyration that obtains of b step and the angle α of the moonlet radius of gyration to be measured, and the coordinate of establishing benchmark moonlet is (r ₁, 0,0), use calculating formula:

$h=\frac{\sqrt{l_2^2-d_2^2}\sqrt{{r_1}^2+r_2^2-2r_1{r}_2\cos \mathrm{\&alpha;}}}{d_2}$

The distance h of trying to achieve benchmark moonlet place rotational plane and moonlet to be measured place rotational plane, the coordinate of moonlet to be measured is (r ₂cos α, r ₂sin α, h);

D, second constantly, the laser beam of laser instrument transmitting is through Amici prism transmission, again by after the first prism of corner cube, the second prism of corner cube, pyrometric cone prismatic reflection, Yan Yuan returns on road, for the second time through Amici prism reflection by telescope imaging and gathered by imageing sensor, and view data flowed to computing machine process; By mathematical operation, obtain the first prism of corner cube and the second prism of corner cube with laser beam vertical direction on projector distance d ' ₁;

E, according to the orbit radius r of benchmark moonlet ₁, the orbit radius r of moonlet to be measured ₂, the distance l on moonlet to be measured between the first prism of corner cube and the second prism of corner cube ₁, the distance l between the second prism of corner cube and pyrometric cone prism ₂, utilize the first prism of corner cube that a step obtains and the second prism of corner cube with laser beam vertical direction on projector distance d ₁, the benchmark moonlet radius of gyration that b step obtains and the angle α of the moonlet radius of gyration to be measured, d walk the first prism of corner cube of obtaining and the second prism of corner cube with laser beam vertical direction on projector distance d ' ₁, use calculating formula:

$\mathrm{\&beta;}=\arcsin \frac{l_1{d}_1^{\&prime;}(r_1-r_2\cos \mathrm{\&alpha;})}{l_2{d}_1\sqrt{{r_1}^2+r_2^2-2r_1{r}_2\cos \mathrm{\&alpha;}}}-\arcsin \frac{r_1-r_2\cos \mathrm{\&alpha;}}{\sqrt{{r_1}^2+-r_2^2-2r_1{r}_2\cos \mathrm{\&alpha;}}}$

Try to achieve relative first constantly, the angle beta that benchmark moonlet and moonlet to be measured turn over, and to obtain the now coordinate of benchmark moonlet be (r ₁cos β, r ₁sin β, 0), the coordinate of moonlet to be measured is (r ₂cos (alpha+beta), r ₂sin (alpha+beta), h);

F, according to the orbit radius r of benchmark moonlet ₁, the orbit radius r of moonlet to be measured ₂, the benchmark moonlet radius of gyration and the angle α of the moonlet radius of gyration to be measured that utilize b step to obtain, and the benchmark moonlet place rotational plane that obtains of c step and the distance h of moonlet to be measured place rotational plane, use calculating formula:

$d=\sqrt{{r_1}^2+r_2^2+2r_1{r}_2\cos \mathrm{\&alpha;}+h^2}$

Obtain the distance d between benchmark moonlet and moonlet to be measured.

2. the satellite based on three point reflection cooperations points to and attitude measuring, be included in and on benchmark moonlet, configure laser instrument (1), Amici prism (2), telescope (3), imageing sensor (4) and computing machine (5), Amici prism (2) is positioned on the emitting light path of laser instrument (1), telescope (3) and imageing sensor (4) are positioned on the reflected light path of Amici prism (2), and computing machine (5) is communicated with imageing sensor (4); On moonlet to be measured, configure the first prism of corner cube (6), the second prism of corner cube (7), pyrometric cone prism (8), the laser beam of the laser instrument of benchmark moonlet (1) transmitting is through Amici prism (2) transmission, again by after the first prism of corner cube (6), the second prism of corner cube (7), pyrometric cone prism (8) reflection, Yan Yuan returns on road, pass through for the second time Amici prism (2) reflection and gather by telescope (3) imaging and by imageing sensor (4), and view data is flowed to computing machine (5) process; It is characterized in that: the first prism of corner cube (6), the second prism of corner cube (7), pyrometric cone prism (8) triangular arrangement that meets at right angles on moonlet to be measured, wherein the second prism of corner cube (7) is positioned at place, summit, right angle, and the first prism of corner cube (6) and the second prism of corner cube (7) place straight line and the second prism of corner cube (7) and pyrometric cone prism (8) place straight line are orthogonal; The normal vector direction of the first prism of corner cube (6), the second prism of corner cube (7) and pyrometric cone prism (8) place plane is constant; The laser beam of the laser instrument on benchmark moonlet (1) transmitting is through Amici prism (2) transmission, and the direction of transmitted light beam is pointed to the mid point of moonlet the first prism of corner cube to be measured (6) and pyrometric cone prism (8) line.

Images