RU2319172C1 - Method of determination of spacecraft coordinates - Google Patents

Abstract

FIELD: trajectory measurements of moving space object orbit parameters against starry sky background.

SUBSTANCE: proposed method consists in determination of angular coordinates of moving space object and recalculation of them into second equatorial coordinate system by reference to catalog stars whose coordinates are known at high accuracy in second equatorial coordinate system.

EFFECT: enhanced accuracy of determination of moving space object coordinates against starry sky background.

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Description

The proposed method relates to the field of trajectory measurements of the orbits of moving space objects (KOs) against the background of the starry sky using optoelectronic equipment installed on an orbital meter (spacecraft-meter - KAI).

Known methods and devices for determining the coordinates of moving objects (ed. Certificate of the USSR No. 1019673; RF patents No. 2081383, 2168753, 2172010, 2191407, 2197070, 2251712; US patents No. 3567163, 3700799, 6122572, 6163372; patent WO No. 0125722; Gryazin G.N. Optoelectronic systems for space viewing: Television systems.- L .: Engineering, Leningrad Branch, 1988, pp. 8-9, Fig. 4 and others).

Of the known methods and devices closest to the proposed are the "Method for determining the coordinates of the object and the optoelectronic device for its implementation" (RF patent No. 2.251.712, G01S 13/66, 2003), which are selected as prototypes.

The known method consists in determining the angular coordinate of the image of the object together with the image-changing elements in the field of view and then recalculating the obtained value into a stabilized coordinate system, determining the magnitude and direction of the linear velocity of the object in a stabilized coordinate system, generating the angular displacement in the stabilized picture plane based on of the obtained value and coordinates characterizing the linear displacement of the image-changing elements relative to their own system we coordinates of the object, adjusting the angular coordinates of the object image together with the image distorting elements in a stabilized coordinate system by an amount of angular displacement.

The optoelectronic device contains a serially connected optoelectronic direction finder and a transducer from a measuring to a stabilized coordinate system, a unit for determining the linear velocity of an object, a unit for generating an angular displacement value, and an adder, the second input of which is connected to the output of the transducer from the measuring to a stabilized coordinate system.

However, the known method and device do not provide accurate determination of the coordinates of a moving space object against the background of the starry sky using optoelectronic equipment mounted on an orbital meter.

An object of the invention is to increase the accuracy of determining the coordinates of a moving space object against the background of the starry sky using optical-electronic equipment mounted on an orbital meter, by linking the space object to catalog stars, the coordinates of which are known with high accuracy in the second equatorial coordinate system.

на космический объект от направления оптической оси телескопа, дальнейшие расчеты проводят на сфере единичного радиуса, используя формулы сферической тригонометрии для расчета элементов сферических треугольников, образуемых пересечением дуг больших кругов на поверхности сферы единичного радиуса, и определяют прямое восхождение α_ρ и склонение δ_ρ вектора

во второй экваториальной системе координат.The problem is solved in that the method for determining the coordinates of a space object, in accordance with the closest analogue, which consists in determining the angular coordinate of the image of the space object together with image-changing elements in the field of view and subsequent conversion of the obtained value into a stabilized coordinate system, differs from the closest analogue in that that as a stabilized coordinate system using the second equatorial coordinate system, additionally determine the linear coordinates x _ρ , y _ρ images of a space object in the instrumental coordinate system, rigidly connected with the CCD matrix of the telescope, the plane of which is set at a distance f _p from the telescope focus perpendicular to its optical axis, right ascension α _о and declination δ _{about the} optical axis of the telescope in the second equatorial coordinate system and the rotation angle φ _p between the plane of the circle declination optical axis and the vertical plane of the instrument coordinate system, and then transferred to the CCD plane along the optical axis at a distance f _n of Fok a telescope linear coordinates _ρ x, y _ρ converted into deviation angles γ _ρ, β _ρ projection image space object on the axis x _ave, y _ave instrument coordinate system on the optical axis of the telescope is determined deflection direction vector

on a space object from the direction of the optical axis of the telescope, further calculations are carried out on the sphere of unit radius using the formulas of spherical trigonometry to calculate the elements of spherical triangles formed by the intersection of the arcs of large circles on the surface of the sphere of unit radius, and determine the right ascension α _ρ and declination δ _{ρ of the} vector

in the second equatorial coordinate system.

The problem is solved in that the optoelectronic device, in accordance with the closest analogue, containing a serially connected optoelectronic direction finder and a transducer from measuring to a stabilized coordinate system, differs in that a telescope mounted on board is selected as the optoelectronic direction finder orbital meter, the instrument coordinate system is selected as the measuring coordinate system, rigidly connected with the CCD matrix, the plane of which is set at a distance If f _{p is} from the focus of the telescope perpendicular to its optical axis, the second equatorial coordinate system is selected as the stabilized coordinate system, and the converter from the instrument to the second equatorial coordinate system is made in the form of a first quadrator, adder connected to the first output of the telescope CCD matrix, the second input which through the second quadrator is connected to the second output of the CCD matrix, the square root extraction unit, the first division unit, the first arctangent calculation unit and the block in calculating the elements of a spherical triangle, the two outputs of which are the outputs of the converter from the instrument to the second equatorial coordinate system, connected in series to the first output of the CCD matrix of the telescope of the second division unit and the second arctangent calculation unit, the output of which is connected to the second input of the spherical triangle element calculation unit connected to the second output of the CCD matrix of the telescope of the third division unit and the third arctangent calculation unit, the output of which is Inonii to a third input of the computation of the spherical triangle members, wherein the second inputs of dividing blocks connected to the output of the determining the distance f _n of the CCD of the telescope focus, fourth, fifth and sixth inputs calculation unit elements spherical triangle connected to the output determination unit angle of rotation φ _ρ between the plane of the circle declination optical axis and the vertical plane of the instrument coordinate system and detection unit _of the right ascension and declination α δ _of the optical axis of the telescope second equatorial coordinate system.

The relationship between the instrument and the equatorial coordinate systems are shown in FIGS. 1 and 2. A block diagram of an optical-electronic device that implements the proposed method for determining the coordinates of a space object is shown in FIG. 3.

The optoelectronic device contains a serially connected optoelectronic direction finder 1 and a measuring transducer 2 from a measuring to a stabilized coordinate system, made in the form of a first quadrator 3, an adder 5, the second input of which through the second quadrator, are connected to the first output of the direction finder 1 (CCD) in series. 4 is connected to the second output of the telescope 1 (CCD matrix), square root extraction unit 6, first division unit 7, first spherical triangle element calculation unit 10, two cat outputs Horn are the outputs of the transducer 2 from the instrument to the second equatorial coordinate system, connected in series to the first output of the CCD matrix of the telescope of the second division unit 8 and the second arctangent calculation unit 11, the output of which is connected to the second input of the spherical triangle element calculation unit 13, connected in series to the second the output of the CCD matrix of the third division block 9 and the third arc tangent calculation block 12, the output of which is connected to the third input of the spherical element calculation block 13 triangle. Moreover, the second inputs of the division blocks 7, 8 and 9 are connected to the output of the block 14 for determining the distance f _{p of the} CCD matrix from the focus of the telescope 1, the fourth, fifth and sixth inputs of the block 13 for calculating the elements of the spherical triangle are connected to the outputs of the block 15 for determining the right ascension α _о and the declination δ _{about the} optical axis of the telescope 1 in the second equatorial coordinate system and the unit 16 for determining the rotation angle φ _ρ between the plane of the declination circle of the optical axis of the telescope 1 and the vertical plane of the instrumental coordinate system.

The proposed method is implemented as follows.

At the moments of measurements, the space object ρ is fixed on the photodetector (CCD matrix) in the form of a point, the linear coordinates of which (x _ρ , y _ρ ) are determined in the instrument coordinate system O _p X _xp , Y _pr d _pr (Fig. 1), rigidly associated with a CCD matrix, the plane of which is installed at a distance f _p from the focus of the telescope perpendicular to its optical axis. Together with the space object, at the moment of measurements, images of stars (S ₁ , S ₂ , S ₃ ) are recorded on the CCD matrix, including catalogs, the coordinates of which are recorded in the star catalog (for example, “FK-5”, “Hipparcos” ) in the form of a right ascension α _s and declination δ _{s of a} star with an accuracy of fractions of angular seconds in the second equatorial coordinate system x, y, z (Fig. 1,2). The latter is used as a stabilized coordinate system.

, направленного на измеряемый объект ρ (фиг.1).In order to attach a moving space object ρ to catalog stars, it is necessary to obtain its coordinates also in the second equatorial coordinate system, i.e. get right ascension α _ρ and declination δ _{ρ of the} vector

aimed at the measured object ρ (figure 1).

Since the direction of the telescope's optical axis (axis d _ave instrument coordinate system) is defined by two mounting angles α _mouth, η _mouth relative to the axis of the orbital motion system τ coordinates, ε, n, and the position of the axes x _ave, y _ave is determined turn angle φ _r with respect to the declination circle optical axis of the telescope, then the linear coordinates of the moving space object (x _ρ , y _ρ ) and stars (x _sj , y _sj ) are recalculated into the second equatorial coordinate system by sequentially multiplying the transition matrices between the instrument and moving orbital coordinate systems, then between the axes of the moving orbital (τ, b, n) and absolute geocentric (x, y, z) coordinate systems in accordance with the rules for transforming coordinates in space (Section 2.6.5.2.3, “Mathematics Reference for engineers and students of technical schools, authors I.N. Bronstein. K.A.Semendyaev, M .: Nauka, 1980. - S.312-314).

The relative position of the coordinate axes of the instrument (x _pr , y _pr , d _pr ), mobile orbital (τ, b, n) and absolute geocentric (x, y, z) coordinate systems is shown in figure 2, and the transition matrix between the axes of these systems coordinates are given in the work "Fundamentals of the theory of spacecraft flight". Ed. G.S. Narimanova. - M.: Mechanical Engineering, 1972. - 608 p.

во второй экваториальной системе координат по формулам:By recalculating the coordinates of the object ρ from the instrument to the absolute geocentric coordinate system (AGESC) x _ρ , y _ρ , z _ρ , we can obtain the angular coordinates of the vector

in the second equatorial coordinate system according to the formulas:

which make it possible to obtain values of the angle α _ρ in the range [0, 2π], and the angle δ _ρ in the range [-π / 2, π / 2].

However, the recalculation of angles proposed above is associated with a large number of calculations and a high risk of obtaining erroneous values of the angles α _ρ , δ _ρ , which is primarily associated with the assumption of a random error in the direction cosines between the axes of the coordinate systems or in the results of multiplying the transition matrices.

The proposed method of converting linear coordinates (x _ρ , y _ρ ) into angular coordinates (α _ρ , δ _ρ ) is devoid of the above disadvantages and can be used in the on-board computer of the orbital meter, provided that the direction of the optical axis of the telescope (angles α _o , δ _o ) in the second equatorial coordinate system and the rotation angle φ _{p of the} vertical plane of the instrument coordinate system, in which the axes d _pr , y _pr , lie relative to the plane of the declination circle of the optical axis of the telescope (arc L ₁ ρ in figure 1).

The determination of the angles α _о , δ _о and φ _{р is} carried out according to the developed forecasting algorithms and is refined at the time of measurement by linking them to catalog stars.

Thus, at the moment the position of the moving space object ρ is determined, the right ascension α _о and the declination δ _about the telescope optical axis in the second optical coordinate system, the pivot angle φ _p between the plane of the declination circle of the optical axis of the telescope and the vertical plane of the instrumental coordinate system are measured or known to be known ( y-axis _straight) linear coordinates x _{ρ, ρ} y image (projection) of the object on the plane ρ CCD (point ρ 'in Figure 1) and a distance f _n along the optical axis between telescope focal point (point O _of n 1) and the plane of the CCD (f _n is the length _of the segment O O _n).

во второй экваториальной системе координат перенесем плоскость ПЗС-матрицы вдоль оптической оси на расстояние f_п от фокуса телескопа, в результате чего плоскость ПЗС-матрицы в точке О_п будет касаться сферы радиусом f_п с центром в точке фокуса телескопа О_з, который лежит в плоскости экватора Земли.To determine the angular coordinates (α _ρ , δ _ρ ) of the vector

in the second equatorial coordinate system, we transfer the plane of the CCD matrix along the optical axis to a distance f _p from the telescope focus, as a result of which the plane of the CCD matrix at the point O _p will touch a sphere of radius f _p centered at the focal point of the telescope O _z that lies in Earth equator planes.

Because the telescope optical axis is perpendicular to the plane of the CCD, the linear coordinate _ρ x, y _ρ can be counted in terms of the projection angle of deviation ρ 'on a _straight axis x, y _ave (point K and M in Figure 1) from the optical axis of the telescope

, проходящего через точку ρ', от направления оптической оси телескопа равноand the deviation of the direction of the vector

passing through the point ρ 'from the direction of the optical axis of the telescope is

, в котором лежит вертикальная плоскость приборной системы координат (оси d_пр, y_пр),

, в котором лежит горизонтальная плоскость приборной системы координат (оси d_пр, x_пр),

, в котором лежат векторы

и

.By translating the linear coordinates (x _ρ , y _ρ ) into the angular values γ _ρ , β _ρ , Θ _ρ , further calculations can be performed on the sphere of unit radius using the formulas of spherical trigonometry to calculate the elements of spherical triangles formed by the intersection of the arcs of large circles on the surface of the unit sphere radius. To do this, draw arcs of large circles

, in which lies the vertical plane of the instrument coordinate system (axis d _pr , y _pr ),

, in which lies the horizontal plane of the instrument coordinate system (axis d _pr , x _pr ),

in which the vectors lie

and

.

большого круга обозначена буковой ρ", а точки М и К спроецируются на дуги

и

в виде точек М', К' (на фиг.1 не показаны). Точка О_п лежит на дуге

. Соединив точку ρ" с точками О_п и М' дугами больших кругов, получим прямоугольный сферический треугольник О_пМ'р", в котором известными элементами являются три стороны (О_пρ"=Θ_ρ,О_пМ'=β_ρ, ρ"М'=γ_ρ) и угол О_пМ_ρ"=π/2.The projection of the point ρ onto the arc

the large circle is marked with beechen ρ ", and the points M and K are projected onto arcs

and

in the form of points M ', K' (not shown in FIG. 1). Point O _p lies on an arc

. Connecting the point ρ "with the points O _n and M 'by arcs of large circles, we obtain a right-angled spherical triangle O _n M'r" in which the known elements are three sides (O _n ρ "= Θ _ρ , O _n M' = β _ρ , ρ "M '= γ _ρ ) and the angle O _p M _ρ " = π / 2.

By the sine theorem in a right-angled spherical triangle O _n M'ρ "we have

and by the cosine theorem of the parties

which allows you to determine the angle of rotation of the arc O _p Mρ "relative to the vertical plane of the instrument coordinate system (arc 1,2) x _ρ in the range [0,2π].

From the spherical triangle О _п Рρ ", in which two sides are known (РО _п = π / 2-δ _о ; О _п ρ" = Θ _ρ ) and the angle (φ _ρ + x _ρ ), by the cosine theorem of the sides we have

или

or

sin δ _ρ = sinδ _o cosΘ _ρ + cosδ _o sinΘ _ρ · cos (f _p + x _υ ),

во второй экваториальной системе координат определяется по формулеwhere is the declination of the vector

in the second equatorial coordinate system is determined by the formula

By the sine theorem in the same spherical triangle, we obtain

откуда

where from

во второй экваториальной системе координат равноFrom the geometric relationships in figure 1 it follows that the right ascension of the vector

in the second equatorial coordinate system is equal

Thus, a direct recalculation of the linear coordinates (x _ρ , y _ρ ) from the instrument coordinate system to the angular coordinates (α _ρ , δ _ρ ) of the second equatorial coordinate system was performed.

Optoelectronic device operates as follows.

At the time of measurements, the space object ρ is fixed on the photodetector (CCD matrix) in the form of a point, the linear coordinates (x _ρ , y _ρ ) are determined in the instrument coordinate system О _п x _пр y _пр d _пр (Fig. 1), which is rigidly connected with A CCD, the plane of which is set at a distance f _p from the focus of the telescope 1, is perpendicular to its optical axis. Together with KO, at the moment of measurements, stars (S ₁ , S ₂ , S ₃ , Fig. 1) are recorded on the CCD matrix, including catalogs whose coordinates are known.

которого подается на вход блока 7 деления. На вторые входы блоков 7, 8 и 9 деления поступает сигнал, пропорциональный f_п, с выхода блока 14. На выходе блоков 7, 8 и 9 деления образуются сигналы пропорциональныеThe linear coordinates x _ρ , at _ρ KO from the two outputs of the telescope 1 (CCD matrix) are fed to the inputs of the quadrants 3 and 4, to the first inputs of the blocks 8 and 9 of the division, respectively. The signals proportional to x _ρ ² and y _ρ ² from the output of the squared 3 and 4 are fed to the two inputs of the adder 5. The output signal of the latter, proportional to x _ρ ² + y _ρ ² , is fed to the input of the square root extracting unit 6, the output signal

which is fed to the input of block 7 division. The second inputs of the blocks 7, 8 and 9 of the division receives a signal proportional to f _p from the output of block 14. At the output of the blocks 7, 8 and 9 of the division, proportional signals are generated

;

;

,

;

;

,

respectively, which are input to the blocks 10, 11 and 12 computing arctangent. At the output of the latter, signals are proportional

respectively. These signals are fed to the inputs of the block 13 for determining the elements of a spherical triangle, to the other inputs of which signals proportional to α _o , δ _o and φ _ρ are supplied from the outputs of the corresponding blocks 15 and 16.

In block 13, the angular coordinates of the TO are determined in the second equatorial coordinate system:

All blocks used to implement the claimed optoelectronic device are known or can be implemented on the basis of known blocks by known methods.

Thus, the proposed method and device in comparison with prototypes and other technical solutions of a similar purpose provide an increase in the accuracy of determining the coordinates of a moving space object against a starry sky using optoelectronic equipment installed on an orbital meter. This is achieved by linking the space object to catalog stars, the coordinates of which are known with high accuracy in the second equatorial coordinate system.

At the same time, for the indicated binding, a method is proposed for directly converting the linear coordinates obtained in the measuring system of the optoelectronic device into the angular coordinates of the second equatorial coordinate system.

The proposed direct method for converting linear coordinates to angular coordinates compared to the classical method of conversion based on successive multiplication of transition matrices in accordance with the rules for transforming coordinates in space is free of a large number of calculations and a high risk of obtaining erroneous values of angular coordinates in the process of multiplying transition matrices.

Claims (1)

A method for determining the coordinates of a space object, which consists in determining the angular coordinate of a space object and then recalculating the obtained value into a stabilized coordinate system, characterized in that the second equatorial coordinate system is used as a stabilized coordinate system, the linear coordinates x _ρ and y _{ρ of the} image of the space object are additionally determined in the instrument coordinate system, rigidly connected with the CCD matrix of the telescope, the plane of which is established by transferring l telescope's optical axis at a distance f _n of the telescope focal perpendicular to its optical axis, the right ascension of α _o and declination δ _of the optical axis of the telescope in the second equatorial coordinate system and the angle of rotation φ _p between the plane of the circle declination optical axis and the vertical plane of the instrument coordinate system linear coordinates _ρ x, y _ρ converted into deviation angles γ _{ρ, ρ} β projection space object image on the x-axis, _{etc., etc.} in the instrument coordinate system on the optical axis of the telescope is determined by vector direction deviation

to a space object from the direction of the optical axis of the telescope, right ascension α _ρ and declination δ _{ρ of the} vector

to a space object in the second equatorial coordinate system, using the formulas of spherical trigonometry to calculate the elements of spherical triangles formed by the intersection of arcs of large circles on the surface of a sphere of unit radius.

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