RU2723199C1 - Method and system for determining orientation of spacecraft in space with autonomous correction of light aberration effect - Google Patents

Abstract

FIELD: space equipment.SUBSTANCE: group of inventions relates to space engineering, namely to a method and system for determining orientation of a spacecraft (SC) with autonomous correction of the effect of light aberration by observing stars. System includes at least three stellar sensors (SS) mounted on a common base in such a way that the optical axes of the sensors are not pair-wise parallel to each other with given angles between their optical axes determined by the location of the SS on the base, a unit for processing data received from stellar sensors. Each SS in the unit is configured to determine the direction of the viewing axis SS in the inertial coordinate system by determining the coordinates of the field of view of the sensors and the angle of rotation of the field of vision around its center to obtain preliminary parameters of the orientation of SC. Method includes simultaneous measurement of coordinates of centers of field of view of sensors during movement of SC, determination of angles between centers of field of view of not less than three pairs of sensors, determination of deviation of measured angles from given, determination of space velocity vector SC, after which the effect of light aberration is determined and taken into account when determining spatial orientation SC.EFFECT: method is proposed to determine orientation of spacecraft in space with autonomous correction of light aberration effect.8 cl, 8 dwg

Description

Technical field

The invention relates to space technology, and in particular to a method for determining the orientation of a spacecraft (SC) in space with autonomous correction of the effect of light aberration arising from the movement of the spacecraft in space, distorting the indications of stellar sensors (ZP) orientation.

The claimed invention can also be used for autonomous determination of the spacecraft velocity vector in an inertial coordinate system.

State of the art

Determining the orientation of the spacecraft in space relative to the selected coordinate system is necessary to perform most actions in outer space. The most reliable and accurate devices for determining the orientation of the spacecraft today are stellar orientation sensors. Errors of stellar sensors commercially available today are units of angular seconds, prototypes of products with subarsecond accuracy appear. However, the readings of stellar sensors are distorted by the effect of light aberration; the systematic errors caused by them are ten times higher than the accuracy of modern stellar sensors.

From the prior art, the effect of light aberration is known - a change in the visible direction of radiation propagation during the transition from one reference system to another. In astronomical observations, light aberration leads to a change in the apparent position of stars in the celestial sphere due to the movement of the observer together with the Earth and the solar system [1]. The effect depends only on the speed of the observer relative to the reference frame of reference, which was taken as motionless. During observations from the Earth, one-year, daily, and secular aberrations are distinguished. Annual aberration is associated with the movement of the earth around the sun. Daily - due to the rotation of the Earth around its axis. Century-old aberration takes into account the effect of the movement of the solar system around the center of the galaxy. For spacecraft, there is an aberration of light associated with their orbital motion.

The annual aberration of light due to the motion of the Earth at a speed of 30 km / s in an almost circular orbit around the Sun leads to a displacement of stars with an amplitude of up to 20 ``, but this is a slow displacement, with a period of one year. For spacecraft in low Earth orbit, which move at a speed of about 8 km / s, the amplitude of light aberration can reach 5 '', but the direction of the effect changes rapidly and depends on the orientation and parameters of the spacecraft's orbit.

Modern star sensors [2] consist of a lens, a matrix photodetector (CCD or CMOS sensor) and an electronics unit. The lens and the matrix photodetector, as well as some additional parts of the star sensor (housing, lens hood, etc.) are combined into the optical head of the sensor. The stellar orientation sensor operates as follows: the lens builds on a matrix photodetector an image of a portion of the starry sky falling within the sensor’s field of view. The exposure of the matrix photodetector is made and a frame with an electronic image of this part of the sky is read from it. Images of stars are highlighted in the frame and their coordinates are determined in the coordinate system associated with the matrix radiation receiver. The resulting star pattern is compared with the on-board catalog of stars, while some of the stars in the frame are identified with the navigation stars from the on-board catalog. For the identified stars, the coordinates were measured in the coordinate system of the matrix photodetector and the celestial coordinates (most often, equatorial) from the on-board catalog of stars are known. The presence of these two sets of coordinates makes it possible to determine the rotation of the coordinate system of the star sensor relative to the inertial coordinate system associated with the stars, and calculate the orientation parameters in the expected form (Euler angles, 3D rotation matrix, rotation quaternion, etc., the listed orientation representations are equivalent each other).

The effect of light aberration leads to the fact that the direction determined by the stellar orientation sensor is different from the true one - measured by a similar stellar sensor, stationary relative to the reference frame of reference. To compensate for this effect in a low orbit around the Earth, it is necessary to set the spacecraft velocity vector every 30-60 s, which creates a large computational load on the spacecraft onboard systems and require knowledge of the spacecraft's orbital speed with high accuracy.

To correct the effect of light aberration, it is necessary to determine the spacecraft spatial velocity vector relative to, for example, the barycenter of the solar system. Currently, there are several methods for determining the spatial velocity vector; each of them has its own disadvantages and limitations.

The first method is determining the orbit of the spacecraft from its observations from the Earth or from other spacecraft. Moreover, for spacecraft orbiting the Earth, positional observations in the visible range are more often used [3], and for interplanetary spacecraft - radio interferometry [4]. Knowing the orbit of the spacecraft, it is possible to calculate its speed at any exact time and at any time. This method is not autonomous - the observations and their processing are carried out using external infrastructure, and the received data (about speed or orbit) are transmitted onboard the spacecraft via communication channels.

The disadvantages of this method include the need for communication with the Earth and the availability of an extensive infrastructure (network of ground or space observation stations) to obtain data on the orbits of the spacecraft.

The remaining methods described below are autonomous.

The second method is the determination of spatial velocity by signals from a satellite global positioning system, similar to GPS or GLONASS [5]. However, this method only works in the vicinity of the Earth, covered by GPS or GLONASS systems. In addition, it requires constant updating of the almanac of a satellite positioning system containing information about the orbits of the system’s satellites.

The third method is pulsar navigation, the speed is determined by highly periodic pulses coming from natural objects — X-ray or radio pulsars (see, for example, patent RU 2453813). This method works throughout the solar system and even beyond. The disadvantage of this method is associated with the properties of reference objects, a systematic change in their periods and irregular periods - the so-called "glitches". Another drawback is the low level of the received signal - it requires expensive and complex equipment to register it - antennas with a diameter of several meters when working in the radio range or detectors with an area of several square meters in the x-ray range. Such equipment can not be installed on any spacecraft.

There is a fourth method and a device that implements it for autonomous navigation in long-distance space flights using the Sun as a guideline by determining the orbit of a spacecraft based on observations of the Sun using devices located on the device (patent US 6622970 B2). The device has a directional sensor to the Sun, as well as a radial (radial) velocity meter of the device relative to the Sun, based on the Doppler effect. This solution involves the use of a special direction sensor on the Sun, which determines this direction not only relative to the spacecraft, but also relative to the stars (i.e., relative to the inertial coordinate system associated with the stars). A series of observations carried out simultaneously by these two devices allows us to determine the orbit of the spacecraft around the Sun and, accordingly, its speed in space. The disadvantage of this solution is the very high complexity of the second instrument used to determine radial velocity: to obtain it with the necessary high accuracy, it is necessary to use a spectrometer (spectrograph) of a sufficiently high resolution, which usually requires accurate (not worse than 0.5) pointing to the Sun, analysis of the solar spectrum etc., which significantly increases the cost of implementing the proposed technical solution, reduces its reliability (due to the presence of moving parts in the structure). In addition, part of the device for determining radial velocity relative to the Sun has a large mass and dimensions. This method does not allow to determine the speed of the spacecraft from one observation, but only after a series of observations.

There is also known a method and device for the autonomous determination of speed (patent US 5109346, prototype), according to which at the same time observe the direction to the Sun, the Moon and the center of the Earth, which allows an autonomous way to determine the position of the spacecraft in near-Earth space. This invention has a number of disadvantages: when using wide-angle optical systems for observing the aforementioned celestial objects, covering a substantial part of the celestial sphere (ideally, the entire celestial sphere), the measurements of the visible positions of these objects will be carried out with low accuracy, and accordingly, navigation accuracy will also be low. If more precise optical systems with narrow fields of view are used for observation, then additional mechanisms will be required to direct these optical systems to objects and to keep objects within the fields of view of optical systems all the time the observations are made. This leads to a complication of the design of the apparatus, an increase in its mass, dimensions and cost, as well as a decrease in reliability. In addition, the result of the application of this invention is the determination of the position of the spacecraft in space. Its speed is not directly determined. To obtain it, it is necessary to conduct several measurements of the position of the spacecraft and divide the resulting displacement by the time between observations. Such a procedure can be time-consuming and leads to large errors in determining the velocity at small time intervals between measurements.

A common drawback of all these autonomous methods for determining the spatial velocity of the spacecraft is that for their implementation on board the spacecraft, it is necessary to install additional equipment.

The technical problem is the determination of the spacecraft’s orientation in space with the possibility of autonomous (based only on the readings of stellar sensors installed onboard the spacecraft without the use of ground-based measuring equipment, as well as additional equipment onboard the spacecraft) to determine and account for the effect of light aberration.

Determining the orientation of the spacecraft in space relative to the selected coordinate system is necessary to perform most of the actions during its functioning. Modern commercially available stellar sensors determine the orientation with an error of 1 '' - 3 '', samples of stellar sensors of the next generation appear with an accuracy of 0.2 '' - 0.5 ''. The effect of light aberration introduces a systematic error several times greater than their random error into the readings of modern sensors (for sensors of the next generation, this error will be several tens of times larger than their error).

To take into account light aberration, it is necessary to know with high accuracy the value and speed of the spacecraft in space and update these values with a sufficiently high frequency. The procedures for periodically calculating the current values of the spacecraft speed with high accuracy falls on the spacecraft onboard resources and causes their noticeable load.

Failure to take into account the effect of light aberration or its incomplete accounting (due to the low accuracy or frequency of calculating the current speed of the spacecraft) reduces the accuracy of determining the orientation of the stellar sensor to 10 '' - 20 ''. Thus, the use of a stellar sensor with small random errors becomes impractical.

Disclosure of invention

The technical result is an increase in the accuracy of determining the orientation of the spacecraft in space, the ability to maintain high accuracy in determining the orientation of the spacecraft far from the earth or in the absence of communication with the earth.

The technical result is achieved through the use of a system for determining the spatial orientation of a spacecraft with autonomous correction of the effect of light aberration, the vector of space velocity of a spacecraft, including a block of star sensors installed on board the spacecraft — at least three, fixed on a common base so that the optical axes of the sensors are not pairwise parallel to each other with predetermined (known) angles between their optical axes, determined by the location of the stellar sensors on the base, and the data processing unit received from the stellar sensors, equipped with power supplies, where

the stellar sensor unit (ST) is configured to simultaneously measure the stellar sensors included in it, each of the stellar sensors in the unit is configured to determine the direction of the optical axis (sight axis) of the ST in the inertial coordinate system by determining the coordinates of the centers of the field of view of the sensors and the angle of rotation of the field of view around its center with obtaining preliminary parameters of the orientation of the spacecraft;

the processing unit is configured to determine from the simultaneously measured preliminary parameters of the spacecraft orientation of the angles between the optical axes of the ZD in the inertial coordinate system of at least three pairs of ZD, comparing the obtained angles with the given (known) values of the angles between the optical axes of the ZD with the subsequent determination of the spatial vector spacecraft velocity in an inertial coordinate system, determining the effect of light aberration and taking it into account when determining the spatial orientation of a spacecraft.

When using three star sensors, the determination of the spacecraft spatial velocity vector in the inertial coordinate system in the processing unit can be implemented by fulfilling the following conditions:

where V _x , V _y , V _z are the spatial velocity components in the coordinate system of the device, (x ₁ , y ₁ , z ₁ ) are the coordinates of a unit vector directed along the axis of sight of the 1st star sensor (optical head) in the coordinate system of the device , (x ₂ , y ₂ , z ₂ ) - the same for the 2nd star sensor, (x ₃ , y ₃ , z ₃ ) - the same for the 3rd star sensor, B ₁₂ = 1-cosψ ₁₂ , a ψ ₁₂ is the angle between the viewing axes of the 1st and 2nd star sensors in the coordinate system of the device, B ₁₃ = 1-cosψ ₁₃ , and ψ ₁₃ is the angle between the viewing axes of the 1st and 2nd star sensors in the coordinate system of the device , B 1 = _{23-cosψ 23,} a ψ ₂₃ - the angle between the axes of sight of the 2nd and 3rd star sensors in the device coordinate system, D ₁₂ = cosψ _'12 -cosψ' _12, a ψ _'12 - the angle between the apparent (determinable) directions of the axes of sight of the 1st and 2nd star sensors, D ₁₃ = cosψ _'13 -cosψ ₁₃ and ψ' ₁₃ - the angle between the visible (determined by) the directions of the axes of sight of the 1st and 3rd star sensors, D ₂₃ = cosψ _'23 -cosψ _23, and ψ _'23 - the angle between the visible (determined by) the directions of the axes of sight of the 2nd and 3rd star sensors, c - velocity of light.

When using more than three stellar orientation sensors, the determination of the spacecraft spatial velocity vector in the inertial coordinate system in the processing unit can be realized by fulfilling the following condition:

where V _x , V _y , V _z are the spatial velocity components in the coordinate system of the device, (x _i , y _i , z _i ) are the coordinates of a unit vector directed along the axis of sight of the i-th star sensor (optical head) in the coordinate system of the device , B _ij = 1-cosψ _ij , a ψ _ij is the angle between the viewing axes of the i-th and j-th star sensors in the coordinate system of the device, D _jj = cosψ ' _ij -cosψ _ij , and ψ' _ij is the angle between the visible ( defined) directions of the axes of sight of the i-th and j-th star sensors, c - the speed of light.

Correction of the preliminary parameters of the orientation of the spacecraft can be carried out according to the formula:

- видимое направление оси визирования i-го звездного датчика, искаженное эффектом аберрации света,

- истинное направление оси визирования этого датчика,

- вектор пространственной скорости КА, с - скорость света, знаком «×» обозначено векторное произведение векторов.Where

- the visible direction of the axis of sight of the i-th star sensor, distorted by the effect of light aberration,

- the true direction of the axis of sight of this sensor,

is the spacecraft spatial velocity vector, c is the speed of light, the sign “×” denotes the vector product of vectors.

The technical result is also achieved by using the method for determining the spatial orientation of the spacecraft, using the system described above, which includes the simultaneous measurement of the coordinates of the centers of the field of view of the sensors during the motion of the spacecraft, which determine the angles between the centers of the field of view of at least three pairs of sensors, and then determine the deviations of the measured angles from the set, which determine the spatial velocity of the spacecraft, then determine the effect of light aberration and take it into account when determining the spatial orientation of the spacecraft.

The device for determining the orientation of a spacecraft in a space with autonomous correction of light aberration includes a mechanical base on which three or more autonomous stellar orientation sensors or optical heads of stellar orientation sensors are mounted, and a control unit. The axes of the optical systems of stellar sensors (optical heads) should not be parallel to each other in any pair of sensors.

The star sensors in the device are autonomous devices and consist of an optical system (lens), a matrix radiation detector located in the focal plane of the optical system and an electronics unit that receives and executes commands for controlling the star sensor (coming from the onboard spacecraft systems), matrix control photodetector, reading and digitizing the image received by the photodetector, processing the image and calculating the orientation parameters of the structural coordinate system relative to the inertial coordinate system. The on-board catalog of navigation stars, service data and algorithms for processing images of the starry sky are stored in the permanent memory of the electronics module of the star sensor.

Star sensors are autonomous, all necessary actions from receiving an external command to measure orientation to issuing orientation parameters relative to the inertial coordinate system are carried out inside the star sensor by its own means. Unlike a standalone orientation sensor, the optical head contains the minimum necessary set of electronic components for controlling the photodetector, reading and digitizing the resulting sky image, which cannot perform the more complex functions listed above. In this case, the electronic components necessary to perform these more complex operations are included in the control unit of the device.

The device for determining the orientation in space with autonomous correction of the effect of light aberration has its own control unit, which performs joint processing of the readings of stellar sensors. When using in the device not autonomous star sensors, but optical heads, all or the most complex functions performed by the electronics blocks of autonomous star sensors are transferred to the control unit of the device.

The operation of the device is as follows. The control unit of the device simultaneously gives commands to conduct orientation determination to star sensors (or optical heads). Star sensors perform exposure of sections of the starry sky falling into their fields of view, process the obtained images, calculate the orientation parameters of each of the sensors and transmit them to the control unit. The device control unit receives and together processes the readings of all stellar sensors. As a result of processing these data, the directions of the axes of sight of stellar sensors corrected for the influence of the light aberration effect are obtained in an inertial coordinate system. Additionally, the following quantities can be obtained explicitly: the absolute value (module) of the spatial velocity of the device (and spacecraft) relative to the barycenter of the Solar system; the direction of this speed in the inertial coordinate system and in the structural coordinate system of the device. Additional values are determined and transmitted to the consumer of the device, if necessary (at his request).

Perhaps a slightly different construction of the claimed device. The device includes a mechanical base on which three or more optical heads are mounted, and a control unit. The optical axis of the optical heads should not be parallel to each other. An optical head differs from a stellar sensor in that it contains a minimal set of electronics (electronic components), which provides control of a matrix photodetector, reads and digitizes the received image, and then transfers it to the control unit. In this embodiment of the device’s design, that part of the stellar sensor electronics blocks that handled the received frames after digitizing them and calculating orientation parameters is now included in the device’s control unit.

A variant of the device with optical heads can be cheaper, while in the first embodiment, you can use standard, industrial, star sensors, which simplifies the design and manufacture of the device.

Brief Description of the Drawings

The invention is illustrated by drawings.

The positions in the drawings indicate: 1, 2, 3 and 4 - star sensors (in some illustrations there are only 3 ZD with numbers 1, 2 and 3), 5 - a mechanical base, 6, 7, 8 and 9 - rectangular coordinate systems connected with ZD designated positions 1, 2, 3 and 4, respectively, 10 - a rectangular coordinate system of the device as a whole, connected with a mechanical base, 11 - connecting cables.

In FIG. 1 is an illustration of the occurrence of a light aberration effect. For a fixed stellar sensor, the star is in position (A), a ray of light from it forms an angle θ with a horizontal line. The sensor begins to move horizontally to the right with a speed ν. During the passage of light the distance from the sensor lens to the photodetector, equal to h, the sensor moves horizontally at a distance (ν / s) ⋅h. For a moving sensor, the same star will be visible in the direction (B), which forms an angle ϕ smaller than θ with the horizontal, i.e. moves in the direction of motion of the sensor. The displacement angle δθ = θ-ϕ is proportional to the ratio of the velocity ν to the speed of light c.

In FIG. Figure 2 shows the Hydra star sensor with three optical heads manufactured by Sodern (France).

, i=1…3 совпадают с векторами, направленными в центры полей зрения этих датчиков. Если устройство движется со скоростью

, то направления в центры полей зрения звездных датчиков

, i-1…3 смещаются в сторону вектора скорости

под действием аберрации света. Каждая тройка векторов

и

лежит в одной плоскости, причем вектор

лежит между векторами

и

. Угол между векторами

и

зависит от модуля скорости

и от угла между векторами

и

в соответствии с формулой (1.1).In FIG. Figure 3 shows an illustration of the effect of light aberration on a device with three star sensors (optical heads). In a stationary device, unit vectors directed along the axes of sight of stellar sensors

, i = 1 ... 3 coincide with the vectors directed to the centers of the field of view of these sensors. If the device is moving at a speed

, then the directions to the centers of the field of view of stellar sensors

, i-1 ... 3 are shifted towards the velocity vector

under the influence of light aberration. Each triple of vectors

and

lies in one plane, and the vector

lies between the vectors

and

. The angle between the vectors

and

depends on speed module

and from the angle between the vectors

and

in accordance with formula (1.1).

) на чертеже показаны толстыми сплошными стрелками. С каждым из звездных датчиков связана собственная система координат: с датчиком (1) - система координат (6) с осями (

), с датчиком (2) - система координат (7) с осями (

), с датчиком (3) - система координат (8) с осями (

). Оси этих систем координат показаны более тонкими пунктирными стрелками. Все системы координат являются ортогональными и правыми. Номера систем координат на чертеже не показаны.In FIG. 4 illustrates the relationship between parts of a device and associated coordinate systems. The drawing shows the mechanical base (5) and three star sensors (or optical heads) (1), (2) and (3) attached to the mechanical base (5). Each of these parts of the device has its own coordinate system. A single coordinate system of the device (10) is connected with the mechanical base (5). Its coordinate axis (

) are shown in the drawing by thick solid arrows. Each of the star sensors has its own coordinate system: with the sensor (1), the coordinate system (6) with the axes (

), with a sensor (2) - coordinate system (7) with axes (

), with a sensor (3) - coordinate system (8) with axes (

) The axes of these coordinate systems are shown by thinner dashed arrows. All coordinate systems are orthogonal and right. The numbers of the coordinate systems are not shown in the drawing.

In FIG. 5 shows a device with four star sensors on a rigid mechanical base, illustrating a 1st embodiment of the device. The numbers on the drawing indicate the following elements of the device: (5) - a rigid mechanical base, star sensors - (1), (2), (3) and (4). (The last digit of the number in the figure corresponds to the number of the star sensor.) Connecting cables in FIG. 5 are not shown.

In FIG. 6 shows a control unit illustrating a 1st embodiment of a device. This control unit is leaky, it is installed on the outer side of the spacecraft.

In FIG. 7 shows a device with three star sensors on a mechanical base, illustrating a 2nd embodiment of the device. The numbers on the drawing indicate the following elements of the device: (5) - the mechanical base, star sensors - (1), (2) and (3) (the last digit of the number in the figure corresponds to the number of the star sensor.), (11) - connecting cables.

In FIG. 8 is a control unit illustrating a 2nd embodiment of the device. This control unit is installed in a sealed internal spacecraft compartment filled with gas.

The implementation of the invention

The star sensor determines its orientation from observations of stars whose celestial coordinates stored in the on-board catalog of navigation stars are specified in a known coordinate system (the equatorial celestial coordinate system is most often used). During the operation of a stellar sensor, its orientation is determined relative to the coordinate system in which the coordinates of the stars are specified. The sensor orientation is described by three independent parameters. One of the possible representations of the orientation parameters is to specify three angles, two of which are the celestial (angular) coordinates of the center of the field of view of the star sensor, and the third sets the magnitude of the rotation of the star sensor around the axis of sight directed to the center of the field of view relative to a certain direction (for example, directions to the north pole of the world for the equatorial coordinate system).

With the same spatial orientation, the center of the image in the field of view of the stellar sensor will be shifted relative to the center of the image in the field of view of a similar and also oriented but fixed stellar sensor (see Fig. 1). This displacement is called the light aberration effect and is associated with the finiteness of the speed of light.

The displacement of the images of stars under the effect of light aberration is described by the following formula

here ν is the speed of the instrument, c is the speed of light, θ is the angle between the velocity vector and the direction to the observed star, δθ is the change in the angle θ due to light aberration, a minus sign means that the angle θ decreases - the star shifts forward in the direction of speed .

The methods of autonomous correction of the effect of light aberration and determination of the spacecraft spatial velocity vector are as follows. They receive readings from three or more star sensors mounted on board the spacecraft (SC), aimed at various points in the celestial sphere. The angles between the visible positions of the centers of the field of view of at least three pairs of stellar sensors are calculated. Physical angles between the axes of sight of the same pairs of stellar sensors are known from the geometry of the design of the device.

When the device is stationary, the angles between the centers of the field of view of the stellar sensors, up to measurement errors, will coincide with the angles between the visible directions of the corresponding pairs of sight axes. If the device moves, then the images in the field of view of each of the sensors under the influence of the aberration of light is shifted in the direction of motion of the spacecraft. The displacements will be different - the speed of movement has the same value for all sensors of the device, but the angles between the axes of sight of the sensors and the direction of speed are different. As a result of this, the angles between the centers of the field of view, calculated from the simultaneous readings of stellar sensors, will differ from the physically measured angles between their axis of sighting known from the geometry of the device’s design. Knowing the differences between these angles and the direction of the axes of sight of stellar sensors in the structural coordinate system, you can determine the velocity vector of the device in the structural coordinate system. The knowledge of the spacecraft orientation obtained by the same stellar sensors makes it possible to calculate the spacecraft velocity vector in an inertial coordinate system. Knowing the magnitude of the spacecraft speed and the angles between it and the axis of sight of the stellar sensors makes it possible to determine the deviations caused by the light aberration effect and take them into account in the readings of each of the stellar sensors.

As a result of joint processing of simultaneously obtained readings of three or more stellar sensors, the following values can be obtained: the absolute value of the spatial velocity of the device relative to the barycenter of the Solar system, the direction of this speed in the inertial coordinate system and in the structural coordinate system of the device, the direction of the axes of sight of the stellar sensors taking into account and without taking into account the effect of light aberration in the inertial and structural coordinate systems, the orientation of the device is uniform in all axes relative to the inertial coordinate system taking into account the effect of light aberration. At the request of consumers, not all of the listed values can be calculated and displayed.

The structure of the device that implements the method of autonomous correction of the light aberration effect and the method of determining the spacecraft spatial velocity vector includes a mechanical base on which three or more autonomous stellar orientation sensors or optical heads of stellar orientation sensors, a control unit, as well as a power source and connecting them are attached cables. The axes of the optical systems of stellar sensors (optical heads) should not be parallel to each other in any pair of sensors.

Below is a more detailed description of the essence of the claimed invention.

, N≥3 (N - число звездных датчиков или оптических головок в устройстве), должны быть не параллельны друг другу. Подобное устройство с тремя оптическими головками показано на фиг. 2.To determine the velocity vector of a spacecraft moving in space, a device is needed in which three or more star sensors (or a star sensor with three or more optical heads and a common electronics unit) are installed on a common base. In this case, the optical axis of the sensors, which are set in the structural coordinate system of the device by unit vectors

, N≥3 (N is the number of stellar sensors or optical heads in the device) should not be parallel to each other. A similar device with three optical heads is shown in FIG. 2.

The physical angles between the axes of sight of the sensors ψ _ij (i, j = 1 ... N) in the device are known from the geometry of the device structure (its base) and are supported by the mechanical rigidity of the structure. If the mechanical rigidity of the structures is insufficient, then the angles can be measured in real time by devices to control the geometry.

When the device is stationary, the angles between the centers of the field of view of stellar sensors (optical heads), up to measurement errors, will coincide with the physical angles between the corresponding pairs of sight axes.

If the device is moving, then the images in the field of view of each of the sensors (or optical heads) are shifted according to formula (1.1) and the centers of the fields of view determined by the stellar sensors will be shifted in the direction of the spacecraft's motion (see Fig. 3). The displacements will be different - the speed of movement v has the same value for all sensors of the device, but the angles between the axes of sight of the sensors and the direction of speed are different.

Moreover, the angles between the centers of the field of view ψ ' _ij , (i, j = 1 ... N), calculated from the simultaneously obtained readings of stellar sensors, will differ from the physically measured angles ψ _ij , (i, j = 1 ... N) between their axes sights.

, а также значения углов ψ_ij и ψ'_ij, определяют вектор скорости движения устройства

в конструкционной системе координат. Для этого решают систему трех линейных алгебраических уравнений, неизвестными в которой являются компоненты вектора скорости V_x, V_y, V_z в конструкционной системе координат. В правой части этой системы уравнений стоят разности углов ψ_ij и ψ'_ij, а коэффициенты перед неизвестными выражаются через компоненты векторов

.Knowing the “physical” directions of the axes of sight of stellar sensors in the structural coordinate system

, as well as the values of the angles ψ _ij and ψ ' _ij , determine the velocity vector of the device

in the structural coordinate system. To do this, solve a system of three linear algebraic equations, unknown in which are the components of the velocity vector V _x , V _y , V _z in the structural coordinate system. On the right side of this system of equations are the differences of the angles ψ _ij and ψ ' _ij , and the coefficients in front of the unknowns are expressed in terms of the components of the vectors

.

A single simultaneous measurement with three stellar sensors with pairwise non-parallel optical axes allows you to determine the following values:

=(V_x,V_y,V_z) в инерциальной системе координат, в конструкционной системе координат устройства, а также в любой системе координат, переход к которой от конструкционной системы координат устройства известен (например, в системе координат, связанной с КА);is the spatial velocity vector of the instrument (and the spacecraft on which it is installed)

= (V _x , V _y , V _z ) in the inertial coordinate system, in the structural coordinate system of the device, as well as in any coordinate system, the transition to which from the structural coordinate system of the device is known (for example, in the coordinate system associated with the spacecraft);

- the visible (distorted by light aberration) direction of the optical axes of stellar sensors in an inertial coordinate system;

- the true (corrected for the effect of light aberration) direction of the optical axes of stellar sensors in an inertial coordinate system;

- orientation parameters of the device relative to the inertial coordinate system from which the influence of the effect of light aberration is excluded.

с различными индексами и пометками относятся к величинам, заданным в системе координат устройства (10), а вектора

- к величинам, заданным в инерциальной системе координат.)Thus, the method for autonomously determining the spatial velocity and eliminating the influence of light aberration using the device includes the following steps. (The coordinate systems are illustrated in Fig. 4. The numbering of parts of the device corresponds to Figs. 4, 5, and 6. Below are the vectors

with various indices and marks refer to the values specified in the coordinate system of the device (10), and the vectors

- to the values specified in the inertial coordinate system.)

, (i=1…N), где N - число звездных датчиков в устройстве. Единая система координат связана с устройством, реализующим способ автономного определения скорости, например, с основанием этого устройства.1) The initial positions of each of the stellar sensors (11), (12), (13), (14) with respect to the coordinate system of the device (10) are described by the known unit vectors of the direction of their axes of sight

, (i = 1 ... N), where N is the number of star sensors in the device. A single coordinate system is associated with a device that implements a method of autonomous determination of speed, for example, with the base of this device.

считаются известными из конструкции звездных датчиков и устройства.Vectors

considered to be known from the design of stellar sensors and devices.

декартовой системы координат совпадала с его оптической осью (осью визирования), т.е.

The coordinate axes of the stellar sensors are selected so that each stellar sensor (or optical head) has an axis

Cartesian coordinate system coincided with its optical axis (axis of sight), i.e.

вычисляют углы ψ_ij между парами этих векторов по формуле2) Based on known vectors

calculate the angles ψ _ij between pairs of these vectors by the formula

here the sign "×" means the scalar product of vectors.

и угла ϕ_i разворота датчика вокруг оси визирования относительно заданного направления (например, на северный полюс мира), здесь i - номер звездного датчика. (Выбранное представление ориентации в виде направления и угла поворота вокруг него математически эквивалентно другим возможным представлениям ориентации, но более удобно для дальнейшего рассмотрения.)3) At the same time, at a given point in time t receive measurements using all stellar sensors. These measurements can be represented by the direction to the center of the field of view (the direction of the axis of sight) in the inertial coordinate system, distorted by the effect of light aberration, in the form of a unit vector

and the angle ϕ _{i of} the sensor’s turn around the axis of sight relative to a given direction (for example, to the north pole of the world), here i is the number of the star sensor. (The selected representation of the orientation in the form of the direction and angle of rotation around it is mathematically equivalent to other possible representations of the orientation, but it is more convenient for further consideration.)

, полученных в результате этих измерений по формуле4) Based on measurements made by stellar sensors, the angles ψ ' _ij , which are the angles between unit vectors, are calculated

obtained as a result of these measurements by the formula

here the sign "×" means the scalar product of vectors.

=(V_x,V_y,V_z) в системе координат устройства. Для чего решают систему линейных уравнений. Составить такую систему можно двумя способами.5) Find the components of the velocity vector

= (V _x , V _y , V _z ) in the coordinate system of the device. Why solve a system of linear equations. There are two ways to create such a system.

5.1) Of the N star sensors in the device, select three and assign them temporary numbers 1, 2 and 3. Only for these three sensors make up a system of three linear equations (temporary numbers are used in the indices):

- координаты единичных векторов направления осей визирования в системе координат устройства (10), D_ij=cosψ'_ij-cosψ_ij, B_ij=1-cosψ_ij, с - скорость света.Here

are the coordinates of the unit vectors of the direction of the axis of sight in the coordinate system of the device (10), D _ij = cosψ ' _ij -cosψ _ij , B _ij = 1-cosψ _ij , s is the speed of light.

If no pair of viewing axes of the selected stellar sensors is parallel to each other, then this system of equations is non-degenerate and has a unique solution. To solve the resulting system of equations, any known method for solving linear systems of equations can be used.

5.2) Make up a system of equations including all pairs of stellar sensors

If there are N star sensors in the system, the system of equations will contain N (N-1) / 2 equations, of which N are linearly independent. For N = 3, the resulting system of equations will coincide with that given in Section 5.1 above and is solved by the same methods. For N> 3, an overdetermined system of equations is obtained, which is solved by one of the following methods: least squares method, maximum likelihood method, SVD (singular decomposition method) or similar methods [6]. The solution of the overdetermined system of equations allows us to independently evaluate the error of the solution found.

и векторы

вычисляюм направления осей визирования звездных датчиков

в системе координат устройства (10) для которых устранено влияния аберрации света по следующей формуле:6) Knowing the speed

and vectors

I calculate the directions of the axes of sight of stellar sensors

in the coordinate system of the device (10) for which the influence of light aberration is eliminated according to the following formula:

here c is the speed of light.

и

- одна и та же тройка единичных (но не ортогональных) векторов, представленных в инерциальной системе координат и в конструкционной системе координат, соответственно. Эти тройки можно совместить с помощью трехмерного поворота. Матрицу этого поворота Q можно найти несколькими способами, например, следующим: а) тройки единичных векторов

и

превращаются в правые тройки взаимно ортогональных единичных векторов

и

, таким образом, чтобы первыми векторами в тройках были, соответственно, вектора

и

, вторые вектора в тройках лежали, соответственно, в плоскостях

,

и

,

, а третьи вектора были этим плоскостям ортогональны и дополняли соответствующие пары векторов до правых троек;7)

and

- the same triple of unit (but not orthogonal) vectors represented in the inertial coordinate system and in the structural coordinate system, respectively. These triples can be combined using three-dimensional rotation. The matrix of this rotation Q can be found in several ways, for example, in the following: a) triples of unit vectors

and

turn into right triples of mutually orthogonal unit vectors

and

, so that the first vectors in triples are, respectively, vectors

and

, the second vectors in triples lay, respectively, in the planes

,

and

,

, and the third vectors were orthogonal to these planes and complemented the corresponding pairs of vectors to right triples;

b) from the coordinates of the vectors of orthogonal triples, we compose the orthogonal matrices A and O:

c) the desired three-dimensional rotation matrix is calculated by the following formula Q = A × O ^T.

The matrix Q contains complete information about the orientation of the device relative to the inertial coordinate system. The matrix Q can be transformed into any other orientation representation: Euler angles, Tate-Brian angles, rotation axis, orientation quaternion.

8) The matrix Q allows you to calculate the velocity vector in an inertial coordinate system

9) Knowing the orientation matrix Q, you can (if necessary) determine the direction of the axis of sight in an inertial coordinate system:

- с устраненным эффектом аберрации света, или

- with the eliminated effect of light aberration, or

- без устранения эффекта аберрации света.

- without eliminating the effect of light aberration.

This invention allows: 1) to determine the orientation parameters of the spacecraft, adjusted for the effect of light aberration; 2) determine the space velocity of the spacecraft (in the inertial coordinate system or in the coordinate system of the device). The invention allows to determine the spatial velocity vector of the device, i.e. both magnitude and direction of speed. The speed of movement is determined relative to the coordinate system to which the coordinates of the stars in the celestial sphere are contained in the on-board catalogs of stellar sensors. Usually the coordinates of celestial objects lead to a coordinate system associated with the barycenter of the solar system - this is the closest to the inertial reference system that exists in the solar system (it does not take into account only the movement of the solar system around the center of the galaxy and the motion of our galaxy relative to other galaxies).

The advantages of the proposed method for determining orientation with autonomous correction of the effect of light aberration are:

- ease of measurement - to achieve the result, it is necessary to conduct a single simultaneous orientation measurement with three star sensors;

- autonomy of measurements - the elimination of the effect of light aberration is carried out only on the basis of the results of measurements performed in the device itself (i.e., on board the spacecraft);

- installation of additional instruments on board the spacecraft is not required - to obtain the result, only the readings of stellar sensors are used, which are then corrected;

- the device will work at very large distances from the Sun - until the coordinates of the stars in the on-board catalogs of stellar sensors are distorted by parallactic displacements, i.e. the device will remain operational at a distance of at least 100 parsecs (300 light years) from the Sun;

- as an intermediate result, the device allows you to determine the spatial velocity of the spacecraft (both the magnitude and direction of the velocity are determined; the speed of motion is determined relative to the coordinate system that includes the coordinates of the stars contained in the on-board catalogs of star sensors - usually this is the coordinate system associated with the barycenter Solar system).

It should be noted that the correction of the effect of light aberration always turns out to be consistent with the accuracy of the stellar sensors themselves, since it is determined based on their readings.

From the above description of the method for determining the orientation of a spacecraft with autonomous correction of the effect of light aberration, it is sufficient for its implementation to have three star sensors in the device (see paragraph 5). However, under the conditions of space exploitation, the star sensor can be exposed to direct solar radiation or it can be blocked by a celestial object (for example, the Earth). In this case, the choice of three sensors that have remained operational, from a larger number of installed ones, allows the device to continue functioning (see paragraph 5.1). The excessive number of stellar sensors allows the device to maintain operability when one of the sensors fails, i.e. increases its reliability. At the same time, the simultaneous use of all stellar sensors of the device, if there are more than three, can improve the accuracy of determining orientation and spatial speed and, at the same time, independently evaluate its error (see clause 5.2).

Implementation examples.

Confirmation of the possibility of implementing the invention with the achievement of the claimed technical result was obtained when conducting two model experiments in which the situations of a spacecraft flight from the Earth to Mars and a spacecraft in a low Earth orbit in a circular orbit of which medium and high accuracy missiles were installed were considered. For modeling, the software product MatLab was used.

Example 1. The method and device for determining the orientation in space with autonomous correction of the effect of light aberration.

A device for determining the orientation of a spacecraft in space with autonomous correction of the aberration effect installed on board an interplanetary spacecraft carrying out an Earth-Mars flight along an economical Hohman trajectory was simulated. The device uses standard stellar sensors with random errors equal to σ = 1 ''.

, максимальная величина аберрации достигается, когда угол θ между направлением скорости движения космического аппарата и осью визирования звездного датчика составляет 90°, соответственно максимальная величина аберрации будет изменяться от δθ(33 км/с)=22,6'' до δθ(21,5 км/с)=14,7'', что в 15-22 раза больше случайной погрешности звездных датчиков, которая составляет σ=1''.When moving along the Hohman trajectory, the speed of the interplanetary spacecraft relative to the barycenter of the Solar system changes during the flight from 33 km / s to 21.5 km / s. At these speeds, the maximum aberration values will be

, the maximum aberration value is achieved when the angle θ between the direction of the spacecraft’s speed of motion and the axis of sight of the star sensor is 90 °, respectively, the maximum aberration value will change from δθ (33 km / s) = 22.6 '' to δθ (21.5 km / s) = 14.7``, which is 15-22 times more than the random error of stellar sensors, which is σ = 1 ''.

The device for autonomous determination of the spacecraft orientation in space with autonomous correction of the light aberration effect includes four serial autonomous stellar orientation sensors mounted on a mechanical base (Fig. 5), a control unit mounted on the outer surface of the spacecraft (Fig. 6), and connecting cables .

The mechanical base (5) is a regular truncated quadrangular pyramid, the base of which is a square, and the side faces are the same trapezoid with angles of 60 ° with the larger side adjacent to the base of the pyramid.

The faces of the pyramid are rigidly interconnected. The mechanical rigidity of the base is sufficient to maintain the position of the axes of sight of the stellar sensors with an accuracy better than the error in determining the orientation of the sensors.

, где

- единичный вектор видимого направления оси визирования звездного датчика, ϕ_i - угол разворота звездного датчика вокруг оси визирования, i - номер датчика, характеризующий разворот конструкционных систем координат датчиков (6), (7), (8) или (9) относительно инерциальной системы координат.The lower face of the mechanical base (5) has holes for attachment to the spacecraft; star sensors (1), (2), (3), (4) are installed on the side faces. All star sensors are connected to the control unit by cables. (Cables pass inside the base. The connecting cables and the control unit are not shown in Fig. 5). The indications of star sensors (1), (2), (3), (4) are orientation parameters, for example, in the form of a pair

where

is the unit vector of the visible direction of the axis of sight of the star sensor, ϕ _i is the angle of rotation of the star sensor around the axis of sight, i is the number of the sensor characterizing the turn of the structural coordinate systems of sensors (6), (7), (8) or (9) relative to the inertial coordinates.

The coordinate system of the device (10) is connected with the mechanical base (5). The origin, coordinate O, is located in the center of the lower edge of the base. The axis OZ is perpendicular to the lower edge of the base, it passes through the point of origin O and the top of the pyramid. The OX axis lies in the plane of the lower edge of the base, it passes through the O point and the middle of the lateral edge on which the sensor No. 1 is installed, with the last point lying on the positive part of the OX axis. The OY axis is perpendicular to the OX and OZ axes, and its direction is chosen so that the OX, OY, and OZ axes form the right triple (see Fig. 5).

Coordinate systems (6), (7), (8), (9) are also associated with sensors. The origin of these coordinate systems O _i (i = 1 ... 4, i = 1 corresponds to the first stellar sensor, i = 2 to the second, i = 3 to the third, i = 4 to the fourth) are located at the centers (points of intersection of the diagonals) of the corresponding side faces mechanical base (5). Axes O _i X _{i are} directed along the external normal to the faces of the base and coincide with the axis of sight of the optical systems of the sensors. O _i Y _i lie in the plane of the side faces, they pass through the points O _i and the center of the base of the trapezoid of the face. The axes O _i Z _{i are} perpendicular to the axes O _i X _i and O _i Y _i , and their directions are chosen so that the axes O _i X _i , O _i Y _i and O _i Z _i form the right triple of vectors.

имеют вид:With this geometry of the mechanical base (5) and the indicated choice of coordinate systems, unit vectors

have the form:

the angles between the axes of sight of the pairs of stellar sensors are

ψ ₁₂ = ψ ₂₃ = ψ ₃₄ = ψ ₁₄ ≈70.5 °, ψ ₁₃ = ψ ₂₄ ≈109.5 °

a, the transition matrices R _i from the coordinate system of the i-th sensor to the coordinate system of the mechanical base are:

в инерциальной системе координат.At time t, measurements are simultaneously taken by all stellar sensors; the result of the measurements has the form

in an inertial coordinate system.

According to the readings of stellar sensors, we calculate the measured (observed) angles between the centers of the field of view of stellar sensors

here the sign "×" means the scalar product of vectors.

Of the four star sensors, we select three that are not illuminated by the Sun, for example, the 1st, 2nd and 3rd, and compose a system of equations:

Here V _X , V _Y , V _Z are the components of the velocity vector in the coordinate system of the device (10), and c is the speed of light. The system of equations is not degenerate, we solve it and get the spatial velocity vector

и направления осей визирования

(все эти вектора заданы в системе координат устройства (10)) находим углы между ними

По формуле (1.1) находим поправки для этих углов

(а для векторов

- по формуле (1.2)). Вычитая поправки из соответствующих углов θ_i (или векторов

), устраняем эффект аберрации света.Knowing the spatial velocity vector

and directions of the axis of sight

(all these vectors are specified in the coordinate system of the device (10)) we find the angles between them

By the formula (1.1) we find corrections for these angles

(and for vectors

- by the formula (1.2)). Subtracting corrections from the corresponding angles θ _i (or vectors

), eliminate the effect of light aberration.

According to the testimony of one or more star sensors, it is possible to determine the Q matrix of the transition from the coordinate system of the device to the inertial coordinate system. This matrix allows you to calculate the velocity vector in an inertial coordinate system

Depending on the orientation of the star sensors axes relative motion velocity vector of the spacecraft (which may be arbitrary) angle difference ₁₂ δψ = ψ _'12 -ψ _12, δψ ₁₃ = ψ' ₁₃ -ψ _13, δψ ₂₃ = ψ _'23 -ψ ₂₃ will vary within the limits: 0``≤δψ ₁₂ , δψ ₁₃ , δψ ₂₃ ≤22.6 '', and only one of the difference in angles can take on zero or close to zero, the other two must exceed 7 ''.

The error in determining the speed according to the system of equations (2.1) on average for all possible orientations of the spacecraft relative to the direction of its motion is σ _V = с⋅σ≈1.5 km / s, and the error in determining the aberration is σ _ab ≈1.4 ''. Thus, the residual error corrected for the influence of light aberration is comparable with the accuracy of stellar sensors used in the device and is 6% -10% of the maximum aberration value (depending on the orbital speed of the spacecraft), i.e. the accuracy of determining the orientation of the device is increased by 10-16 times.

Thus, the claimed invention ensures the achievement of the claimed technical result:

1) the orientation of the spacecraft with respect to the inertial coordinate system is determined;

2) the corrections δθ _i needed to correct the effect of light aberration are found;

3) the accuracy of determining the orientation increases by 10-16 times;

(в системе координат устройства или

(с инерциальной системе координат).4) the spatial velocity vector is determined

(in the coordinate system of the device or

(with inertial coordinate system).

5) the error in determining the velocity σ _V = 1.5 km / s.

Example 2. The method and device for determining the orientation in space with autonomous correction of the effect of light aberration.

A device for determining the orientation of the spacecraft in space with autonomous correction of the aberration effect installed onboard the spacecraft in an equatorial circular near-earth orbit with a height of h = 400 km was simulated. The device uses high-precision star sensors with random errors equal to σ = 0.3 ''

, максимальная величина аберрации достигается, когда угол θ между направлением скорости движения космического аппарата и осью визирования звездного датчика составляет 90°, соответственно максимальная величина аберрации будет изменяться от δθ(22 км/с)=15'' до δθ(38 км/с)=26'', что в 50-87 раз больше случайной погрешности звездных датчиков, которая составляет σ=0,3''.The speed of the spacecraft around the Earth in a circular orbit with an altitude of 400 km is 7.9 km / s, respectively, the speed of the spacecraft relative to the barycenter of the Solar System varies from 22 km / s to 38 km / s, depending on the position of the device in Earth orbit. At these speeds, the maximum aberration values will be

, the maximum aberration value is achieved when the angle θ between the direction of the spacecraft’s speed of movement and the axis of sight of the star sensor is 90 °, respectively, the maximum aberration value will vary from δθ (22 km / s) = 15 '' to δθ (38 km / s) = 26 '', which is 50-87 times more than the random error of stellar sensors, which is σ = 0.3 ''.

Does the device for autonomous determination of the spacecraft speed in space include connecting cables? three stellar orientation sensors (1), (2), (3) of increased accuracy mounted on a mechanical base (5) (see Fig. 7) and a control unit (Fig. 8) installed inside the airtight compartment of the spacecraft. The mechanical base (5) for three ZDs is a regular triangular pyramid, the base of which is a regular triangle, and the side faces are identical isosceles right-angled triangles with 90 ° angles at the top of the pyramid (thus, the side faces of this pyramid are mutually perpendicular).

, где

- единичный вектор видимого направления оси визирования звездного датчика в инерциальной системе координат, ϕ_i - угол разворота звездного датчика вокруг оси визирования, i - номер датчика. Эти параметры характеризуют разворот конструкционной системы координат каждого из датчиков (6), (7) или (8) относительно инерциальной системы координат.The lower face of the mechanical base (5) is attached directly to the spacecraft, the three side faces are attached to the bottom. The star sensors (1), (2), (3) are connected to the control unit by cables (11). Cables pass inside the base. The indications of star sensors (1), (2) and (3) are orientation parameters, for example, in the form of a pair

where

is the unit vector of the visible direction of the axis of sight of the star sensor in the inertial coordinate system, ϕ _i is the angle of rotation of the star sensor around the axis of sight, i is the number of the sensor. These parameters characterize the turn of the structural coordinate system of each of the sensors (6), (7) or (8) relative to the inertial coordinate system.

The coordinate system of the device (10) is connected with the mechanical base (5). The origin of coordinates O is in the center of the lower edge of the base. The axis OZ is perpendicular to the lower edge of the base, it passes through point O and the top of the pyramid. The OX axis lies in the plane of the lower edge of the base, it passes through the O point and the middle of the lateral edge on which the sensor No. 3 is installed, the last point lying on the positive part of the OX axis. The OY axis is perpendicular to the OX and OZ axes, and its direction is chosen so that the OX, OY, and OZ axes form a right triple (see Fig. 7).

Coordinate systems (6), (7) and (8) are also associated with star sensors (1), (2), (3), respectively. The origin of these coordinate systems O _i (i = 1 ... 3 are the numbers of stellar sensors) are located at the centers (points of intersection of the medians) of the corresponding lateral faces of the mechanical base. Axes O _i X _{i are} directed along the external normal to the faces of the base and coincide with the axis of sight of the optical systems of the sensors. O _i Y _i lie in the plane of the lateral faces, they pass through the points O _i and the center of the hypotenuse of the corresponding face. The axes O _i Z _{i are} perpendicular to the axes O _i X _i and O _i Y _i , and their directions are chosen so that the axes O _i X _i , O _i Y _i and O _i Z _i form the right triple.

имеют вид:With this geometry of the mechanical base (5) and the indicated choice of coordinate systems, unit vectors

have the form:

and the angles between the axes of sight of the pairs of stellar sensors are

ψ ₁₂ = ψ ₂₃ = ψ ₁₃ = 90 °.

в инерциальной системе координат.At time t, measurements are simultaneously taken by all stellar sensors; the result of the measurements has the form

in an inertial coordinate system.

According to the readings of stellar sensors, we calculate the measured (observed) angles between the centers of the field of view of stellar sensors

here the sign "×" means the scalar product of vectors.

We compose a system of equations for determining the speed. The system has the form:

в системе координат устройства (10).Here V _X , V _Y , V _Z are the components of the velocity vector in the coordinate system of the device (10), and c is the speed of light. The system of equations is not degenerate. We solve it and get the spatial velocity vector

in the coordinate system of the device (10).

и направления осей визирования

(все эти вектора заданы в системе координат устройства (10)) находим углы между ними

По формуле (1.1) находим поправки для этих углов

(а для векторов

- по формуле (1.2)). Вычитая поправки из соответствующих углов θ_i (или векторов

), устраняем эффект аберрации света.Knowing the spatial velocity vector

and directions of the axis of sight

(all these vectors are specified in the coordinate system of the device (10)) we find the angles between them

By the formula (1.1) we find corrections for these angles

(and for vectors

- by the formula (1.2)). Subtracting corrections from the corresponding angles θ _i (or vectors

), eliminate the effect of light aberration.

According to the testimony of one or more star sensors, it is possible to determine the Q matrix of the transition from the coordinate system of the device to the inertial coordinate system. This matrix allows you to calculate the velocity vector in an inertial coordinate system

Depending on the orientation of the star sensors axes relative motion velocity vector of the spacecraft (which may be arbitrary) angle difference ₁₂ δψ = ψ _'12 -ψ _12, δψ ₁₃ = ψ' ₁₃ -ψ _13, δψ ₂₃ = ψ _'23 -ψ ₂₃ will vary within the limits: 0``≤δψ ₁₂ , δψ ₁₃ , δψ ₂₃ ≤26 '', and only one of the angle differences can take on zero or close to zero, the other two must exceed 8 ''.

The error in determining the velocity according to the system of equations (2.2) on average over all possible orientations of the spacecraft relative to the direction of its motion is σ _V = с⋅σ≈0.45 km / s, and the error in determining the aberration is σ _ab ≈0.42 ''. Thus, the residual error corrected for the influence of light aberration is comparable to the accuracy of the stellar sensors used in the device and is 1.6% -2.8% of the maximum aberration value (depending on the orbital speed of the spacecraft), i.e. the accuracy of determining the orientation of the device increases by 30-60 times.

The technical result is achieved:

1) the orientation of the spacecraft with respect to the inertial coordinate system is determined;

2) the corrections δθ _i needed to correct the effect of light aberration are found;

3) the accuracy of determining the orientation increases by 30-60 times;

(в системе координат устройства или

(с инерциальной системе координат).4) the spatial velocity vector is determined

(in the coordinate system of the device or

(with inertial coordinate system).

5) the error in determining the velocity is σ _V = 0.45 km / s.

Bibliography.

1. V.E. Zharov Spherical astronomy // Fryazino: Century-2. 2006.480 s.

2. Woodpeckers S.A., Bessonov R.V. Survey of stellar orientation sensors of spacecraft // Mechanics, Control and Informatics, 2009. No. 1. S. 11-31.

3. Emelyanov N.V. Practical celestial mechanics // Moscow: Faculty of Physics, Moscow State University, 2018. ISBN 978-5-9600218-1-7. 270 s

4. Ivanov N.M., Lysenko L.N. Ballistics and navigation of spacecraft // M .: URSS, 2016 / 3rd edition. 680 s ISBN 978-5-7038-4340-6.

5. Serapinas BB Global positioning systems // M .: IKF "Catalog", 2002. 106 p.

6. J. Forsyth, M. Malcolm, K. Mowler Machine Methods of Mathematical Computing // M.: Mir. 1980.280 s.

Claims (22)

1. A system for determining the spatial orientation of a spacecraft with autonomous correction of the effect of light aberration, spacecraft’s spatial velocity vector, including a set of star sensors installed on board the spacecraft — at least three, mounted on a common base so that the optical axes of the sensors are not paired with each other given angles between their optical axes, determined by the location of the stellar sensors on the base, and the data processing unit received from the stellar sensors, equipped with power supplies, where the stellar sensor unit (ST) is made with the possibility of simultaneous measurements by the stellar sensors included in it, while each of the stellar sensors in the unit is configured to determine the direction of the optical axis of the ST in an inertial coordinate system by determining the coordinates of the centers of the field of view of the sensors and the angle of rotation of the field of view around its center with obtaining preliminary parameters of the spacecraft orientation; the processing unit is configured to determine from the simultaneously measured preliminary parameters of the spacecraft orientation of the angles between the optical axes of the ZD in the inertial coordinate system of at least three pairs of ZD, comparing the obtained angles with the given (known) values of the angles between the optical axes of the ZD with the subsequent determination of the spatial vector spacecraft velocity in an inertial coordinate system, determining the effect of light aberration and taking it into account when determining the spatial orientation of a spacecraft. 2. The system according to claim 1, characterized in that when using three stellar sensors, the determination of the spacecraft spatial velocity vector in the inertial coordinate system in the processing unit is implemented by fulfilling the following condition:

where V _x , V _y , V _z are the spatial velocity components in the coordinate system of the device, (x ₁ , y ₁ , z ₁ ) are the coordinates of a unit vector directed along the axis of sight of the 1st star sensor (optical head) in the coordinate system of the device , (x ₂ , y ₂ , z ₂ ) - the same for the 2nd star sensor, (x ₃ , y ₃ , z ₃ ) - the same for the 3rd star sensor, B ₁₂ = 1-cosψ ₁₂ , a ψ ₁₂ is the angle between the viewing axes of the 1st and 2nd star sensors in the coordinate system of the device, B ₁₃ = 1-cosψ ₁₃ , and ψ ₁₃ is the angle between the viewing axes of the 1st and 2nd star sensors in the coordinate system of the device , B 1 = _{23-cosψ 23} and ψ ₂₃ - the angle between the axes of sight of the 2nd and 3rd star sensors in the device coordinate system, D ₁₂ = cosψ _'12 -cosψ ₁₂ and ψ' ₁₂ - the angle between the apparent ( determinable) directions of the axes of sight of the 1st and 2nd star sensors, D ₁₃ = cosψ _'13 -cosψ ₁₃ and ψ' ₁₃ - the angle between the visible (determined by) the directions of the axes of sight of the 1st and 3rd star sensors, D ₂₃ = cosψ '-cos ₂₃ ψ _23, a ψ _'23 - the angle between the visible (determined by) lines of sight axes of the 2nd and 3rd star sensors, c - velocity of light. 3. The system according to claim 1, characterized in that when using more than three stellar orientation sensors, the determination of the spacecraft spatial velocity vector in the inertial coordinate system in the processing unit is implemented by fulfilling the following condition:

where V _x , V _y , V _z are the spatial velocity components in the coordinate system of the device, (x _i , y _i , z _i ) are the coordinates of a unit vector directed along the axis of sight of the i-th star sensor (optical head) in the coordinate system of the device , B _ij = 1-cosψ _ij , and ψ _ij is the angle between the viewing axes of the i-th and j-th star sensors in the coordinate system of the device, D _ij = cosψ ' _ij -cosψ _ij , and ψ' _ij is the angle between the visible ( defined) directions of the axes of sight of the i-th and j-th star sensors, c - the speed of light. 4. The system under item 1, characterized in that the adjustment of the preliminary parameters of the orientation of the spacecraft is carried out according to the formula:

Where

- the visible direction of the axis of sight of the i-th star sensor, distorted by the effect of light aberration,

- the true direction of the axis of sight of this sensor,

is the spacecraft spatial velocity vector, c is the speed of light, the sign “×” denotes the vector product of vectors. 5. A method for determining the spatial orientation of a spacecraft using the system according to claim 1, including the simultaneous measurement of the coordinates of the centers of the field of view of the sensors during the motion of the spacecraft, which determine the angles between the centers of the field of view of at least three pairs of sensors, and then determine the values of the deviations of the measured angles from given by which the spacecraft spatial velocity vector is determined, after which the light aberration effect is determined and taken into account when determining the spacecraft’s spatial orientation. 6. The method according to p. 5, characterized in that when using three stellar sensors, the spacecraft spatial velocity vector in an inertial coordinate system is determined from the system of equations:

where V _x , V _y , V _z are the spatial velocity components in the coordinate system of the device, (x ₁ , y ₁ , z ₁ ) are the coordinates of a unit vector directed along the axis of sight of the 1st star sensor (optical head) in the coordinate system of the device , (x ₂ , y ₂ , z ₂ ) - the same for the 2nd star sensor, (x ₃ , y ₃ , z ₃ ) - the same for the 3rd star sensor, B ₁₂ = 1-cosψ ₁₂ , a ψ ₁₂ is the angle between the viewing axes of the 1st and 2nd star sensors in the coordinate system of the device, B ₁₃ = 1-cosψ ₁₃ , and ψ ₁₃ is the angle between the viewing axes of the 1st and 2nd star sensors in the coordinate system of the device , B 1 = _{23-cosψ 23,} a ψ ₂₃ - the angle between the axes of sight of the 2nd and 3rd star sensors in the device coordinate system, D ₁₂ = cosψ _'12 -cosψ ₁₂ and ψ' ₁₂ - the angle between the apparent ( determinable) directions of the axes of sight of the 1st and 2nd star sensors, D ₁₃ = cosψ _'13 -cosψ _l3, a ψ' ₁₃ - the angle between the visible (determined by) the directions of the axes of sight of the 1st and 3rd star sensors, D ₂₃ = cosψ '-cos ₂₃ ψ ₂₃ and ψ _'23 - the angle between the visible (determined by) the directions of the axes of sight of the 2nd and 3rd star sensors, c - velocity of light. 7. The method according to p. 5, characterized in that when using more than three stellar orientation sensors, the spacecraft spatial velocity vector is determined from the system of equations:

where V _x , V _y , V _z are the spatial velocity components in the coordinate system of the device, (x _i , y _i , z _i ) are the coordinates of a unit vector directed along the axis of sight of the i-th star sensor (optical head) in the coordinate system of the device , B _ij = 1-cosψ _ij , and ψ _ij is the angle between the viewing axes of the i-th and j-th star sensors in the coordinate system of the device, D _ij = cosψ ' _ij -cosψ _ij , and ψ' _ij is the angle between the visible ( defined) directions of the axes of sight of the i-th and j-th star sensors, c - the speed of light. 8. The method according to p. 5, characterized in that the account for the effect of aberration in determining the spatial orientation of the spacecraft is produced by the formula:

Where

- the visible direction of the axis of sight of the i-th star sensor, distorted by the effect of light aberration,

- the true direction of the axis of sight of this sensor,

is the spacecraft spatial velocity vector, c is the speed of light, the sign “×” denotes the vector product of vectors.

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