RU2304549C2 - Self-contained onboard control system of "gasad-2a" spacecraft - Google Patents

Abstract

FIELD: astro-navigation, control of attitude and orbital position of spacecraft.

SUBSTANCE: proposed system includes control computer, star sensor, Earth sensor, storage and timing device, processors for control of attitude, processing angular and orbital data, inertial flywheels and spacecraft orbit correction engine plant. Used as astro-orienters are reference and navigational stars from celestial pole zone. Direction of spacecraft to reference star and direction of central axis of Earth sensor to Earth center are matched with plane formed by central axes of sensors with the aid of onboard units. Shift of direction to reference star relative to central axis of Earth sensor is considered to be latitude change in orbital position of spacecraft. Turn of navigational star around reference star read off sensor base is considered to be inertial longitude change. Point of reading of longitude is point of spring equinox point whose hour angle is synchronized with the board time. This time is zeroed upon completion of Earth revolution. Stochastic measurements by means of static processing are smoothed-out and are converted into geographic latitude and longitude parameters. Smoothed inertial parameters are compared with parameters of preset turn of spacecraft orbit found in storage. Revealed deviations of orbit are eliminated by means of correction engine plant.

EFFECT: enhanced accuracy of determination of spacecraft attitude and orbital position; automatic elimination of deviation from orbit.

44 dwg

Description

The invention relates to navigation and control of the angular orientation and orbital location of a spacecraft (SC) and is intended for use on an autonomously functioning spacecraft.

As means of navigation, radio-technical ground-based measuring points (NPCs) are widely known and traditionally used. NPCs are geographically separated in longitude-latitude so as to cover as much space as possible. This arrangement of NPCs is due to the fact that sessions of measuring distances to the spacecraft, azimuth and elevation are realized only in those areas where the radio visibility conditions between the NPC and the spacecraft are fulfilled. And, nevertheless, during the spacecraft circulation period, for example, about one and a half hours from 15-16 daily turns, at least 6 pass outside the radio visibility zones from the territory of the former USSR. In addition, there is a limitation due to the fact that each NPC needs some time to prepare for further work. Restrictions related to the impossibility of the simultaneous operation of two different NPCs may also be imposed on navigation measurements.

Thus, there is a mismatch between the global need for measurements and existing capabilities. In addition, the requirements for the accuracy of measuring the motion parameters of the spacecraft are combined with the cost of the NIP equipment and with the cost of servicing the number of measuring points involved.

Another well-known navigation tool is the space system, which consists of a combination of navigation satellites and a ground-based measuring complex. The ability to use measurements relative to this system depends on the relative position of the navigation satellites and the spacecraft. There is an uncertainty in the implementation of navigation measurements in given or any areas of space, since their possibility is associated with the waiting time for the appearance of at least one navigation satellite and the waiting time for different spacecraft is different. In other words, in different subspaces of the scope of the satellite navigation system, the probability of navigation definitions is different. In this case, one can speak about globality as the maximum value of the ratio of the subspace maintained by the system to the entire near-Earth space intended for navigation, only conditionally. In the same restrictive sense, we should talk about the continuity of navigation definitions, since continuity is due to the simultaneous geometric visibility of several satellites, which is not always consistently available. Also, one should not speak in the absolute sense of efficiency.

Meanwhile, both in the case of using NPCs and when using the space navigation system, the continuity of measurements is the means that provides the necessary accuracy indicators of navigation definitions.

At the same time, accurate sequential data on the location of the spacecraft in space are the source material that serves to calculate the sequential angular orientation of the spacecraft, for example, relative to the Earth. Note that, among the measurements by the parameters considered by the means, there is no determination of the spatial position of the direction “SC - the center of the Earth”, with respect to which essentially the angular control of the SC is performed for any of its target functioning. In general, the purpose of navigation definitions should be precisely this parameter. However, with the adopted approach, it is not directly observable. Therefore, to determine it, additional navigational aids, in particular celestial landmarks, are involved. In essence, this means that in addition to the artificial navigation system, a second navigation system is also used - a system of natural supporting astro-orientations. Different systems with different reference systems split a single motion of the spacecraft into two movements - spatial and angular. It must be recognized that such a mediated technique, designed not initially, but at the very end of the navigation process to characterize the motion of the spacecraft as angular, generates not only additional volumes of work, but also accuracy orientation errors.

Thus, the spacecraft navigation problem is traditionally solved independently of the spacecraft angular control task, and in practice, the spacecraft navigation and angular orientation control algorithms are initially independent of each other.

As a result of the review of the level of traditionally used equipment, it should be recognized that there is a problem of providing in real time and on a global scale the most accurate, continuous and direct measurements of such navigation variables that could directly correspond to control variables and would facilitate the synthesis of control and navigation algorithms in one autonomous spacecraft onboard control system.

A characteristic feature of this problem is that for its solution it is necessary to go beyond the known methods. It should be solved from those points of view that allow us to consider the navigation and management process as something unified and whole.

The well-known "Autonomous onboard control system for the spacecraft" GASAD "[application 93007754 (patent 2033949), 1993], which does not claim to solve this problem, however, indicates some methods for obtaining and processing astronomical measurements. This system contains: the Earth sensor, the sensor of the North Star and the navigation star (star sensor), a computer, a memory device, a temporary device and actuators. Wherein:

- the outputs of the Earth sensor, star sensor, storage device are connected to the inputs of the computer on the corresponding signals; the output of the temporary device is also connected to the temporary input of the calculator, and the input of the executive bodies is connected to the output of the calculator;

- the storage device contains the parameters of the base of inertial longitude, and these parameters are the right ascension of the North Star and the angle relative to the common sensitivity plane of the Earth sensor and the star sensor, equal to the angle between the plane containing the directions "center of the Earth - North Star" and "center of the Earth - pole world ", and a plane containing the directions" the center of the Earth - the North Star "and" the center of the Earth - the navigation star ";

- the computer is configured to determine the latitude of the spacecraft by the angle "center of the Earth - spacecraft - the North Star";

- the computer is configured to generate a control signal for the angular orientation of the spacecraft along the yaw channel based on the measured corresponding angular mismatches to combine the common sensitivity plane of the Earth sensor and the star sensor containing the longitudinal axis of the spacecraft with a plane containing the center of the Earth, the spacecraft and the Polar star;

- the calculator is configured to determine the inertial longitude of the spacecraft’s location by the azimuthal angle of rotation of the navigation star around the direction of the spacecraft — the Polar Star ”, counted in the corresponding field of view from the base angular position of the plane containing the directions“ spacecraft - the navigation star ”and“ spacecraft - the polar star ".

Consider whether this system, based on the totality of its features, can serve as a prototype of the invention. But first, note the following. It is strange, of course, to talk about what goes without saying. So, the choice of a ground measuring station or the choice of a navigation satellite as an artificial reference point are not equivalent. This choice is usually justified by the peculiarity of a particular case. For example, the features of the problem being solved, the orbit used, etc.

Of similar importance is the choice of a polar star as a natural reference point.

To ensure the global space of navigational definitions, the continuity and accuracy of astronomical measurements, the reference star should be:

1) is observable from any point of the used orbit;

2) relatively motionless (a change in the star’s right ascension should be as minimal as possible for the spacecraft’s active existence).

We note here that, due to the precession of the earth's axis, the polar region of stars is generally a zone of special right ascents.

In this case, it becomes obvious that, while ensuring global space and the continuity of navigational measurements, the features of a particular orbit used impose restrictions on the freedom to choose a star from the zone of the north pole of the world or from the zone of the south pole of the world. So, when the spacecraft moves in the perigee zone of the orbit of the Lightning type, the Polar Star is obscured by the Earth. At the same time, a reference star from the region of the south pole is observable from any points of the same orbit. In addition, the change in the direct ascent of the North Star over 10 years is 4.3 minutes, which in terms of degrees is 1 ° 4.5 '(4.3 _min × 15' / _min ). It is not necessary to speak about high accuracy indicators in this case. It should be noted that the Polar Star surpasses all the stars in both the northern and southern polar zones in the "instability" of its relative location in space.

True, the coordinate changes of the North Star can be periodically updated in the on-board computational algorithms by correcting their current actual coordinates. Given that the change of coordinates in time is known, it is possible to implement such a correction due to a significant complication of the on-board software. Of course, in the presence of other options to complicate the software is irrational.

It must be recognized that the global, continuity and accuracy of navigation measurements when using the North Star in this case is not provided. The system in question was originally intended to work in conjunction with traditional navigation aids and is designed to solve a limited narrow task. This also follows from the fact that it did not provide for the location of the spacecraft with respect to the geographic latitude-longitude grid of the Earth. Moreover, the system is not intended to ensure that the parameters of the real orbit correspond to the parameters given and does not contain means for processing the measured angular data in order to obtain their high-precision values.

Essentially, all the features of the system under consideration are based on the use of the North Star as a fundamental navigational reference. In addition, these signs also contain the following uncertainties and disadvantages:

1) The stated task - to determine the latitude of the spacecraft by the angle "center of the Earth - spacecraft - the Polar Star" is not solved due to the fact that the correction is not taken into account, which is due to the polar distance of the Polar Star and the value of which depends on inertial longitude.

2) The zero instrument base of the inertial longitude reference, corresponding to the external zero reference base, relative to which the time is counting, is not defined.

3) The moment of zeroing of the onboard time is not determined.

4) The longitudinal axis of the spacecraft is contained in the general plane of the sensitivity of this system, which does not allow the axis to be reoriented to the set target points of the Earth, without interrupting the navigation session.

Thus, the features of the considered system are not the closest to the features of the invention, and therefore this system cannot be recognized as a prototype of the invention.

An analogue of the invention can also be a typical spacecraft orientation and stabilization control system, which includes mainly a traditional computer, an Earth sensor, a star sensor, and inertial flywheels.

Such a system is designed to solve the problems of angular orientation and stabilization.

In these modes, stars falling into the field of view of the sensor are identified and tracked, and stabilization is also carried out, which can also be attributed to the features common with the invention.

The technical problem is the basis of the invention - to create an onboard control system for the spacecraft, which would make it possible to provide autonomous control of the angular orientation, autonomous determination of the angular and location of the device relative to the latitudinal-longitude grid of the Earth, autonomous determination of the mismatches of the real orbit from the given one and their autonomous elimination .

The technical result boils down to:

- the exclusion of the use of ground-based navigation and spacecraft control infrastructure;

- ensuring the globalization of the space of navigational measurements carried out by spacecraft;

- the implementation of the synthesis of control and navigation algorithms;

- the implementation of direct and continuous measurements of the parameters of the orbital motion in accordance with each other orientation and navigation angles;

- real-time determination of the angular and location of the device both in inertial space and in relation to the latitude-longitude grid of the Earth;

- ensuring high accuracy of the parameters of the angular and location of the spacecraft for the current and forecasted interval;

- identification of evolutionary changes in orbital parameters relative to a given orbit and the implementation of their automatic elimination.

The technical result, which boils down to several results, at the level of functional generalization can be represented as autonomy, spacecraft independence from ground-based and space-based complexes, i.e. from external artificial means of navigation and control.

The structural composition of the proposed control system includes, in addition to the control computer, several processors designed to simultaneously perform each function, as well as inertial flywheels and pulse correction engines as executive bodies.

All devices of the system, including the Earth sensor, star sensor, storage device and a temporary device are connected by communication lines in an appropriate manner and by corresponding signals.

The technical result is achieved due to:

I. AUTONOMOUS ANGULAR ORIENTATION:

(involved: position control processor, Earth sensor, star sensor, inertial flywheels and corresponding algorithms)

one). The system of astro-orientations is formed from two stars of the polar zone: the reference and navigation and (center) of the Earth.

2). A plane containing the direction of the central axis of the Earth’s sensor to the center of the Earth and the direction from the spacecraft to the reference star is constantly aligned in the process of orbital motion with a rigid plane formed by the central axes of the sensors and coordinated in the coordinate system of the star sensor.

II. OFFLINE DETERMINATION OF INERTIAL LENGTH:

(involved: star sensor, angular data processor and related algorithms)

3). The rotation of the navigation star (due to the orbital motion of the spacecraft) around the reference star in the field of view of the star sensor is recorded in the coordinates of the star sensor as an inertial-longitudinal change in the orbital position of the spacecraft.

III. FIXING ONBOARD POINT OF REPORT OF INERTIAL LONGITUDE:

(involved: design calculations, angular data processor and related algorithms)

four). In design calculations, the base inertial longitude of the spacecraft is determined by the direct ascension of the reference star in degree terms at that time of orbital motion, when the base angle between the rigid plane of the sensors and the plane of directions from the spacecraft to both stars in the field of view of the star sensor corresponds to the moment of the culmination of the reference star.

5). The onboard zero reference point of inertial longitude is coordinated in the coordinates of the stellar sensor as the position of the directional plane from the spacecraft to both stars at the moment when the projected inertial longitude is zeroed, and the range of the base angle changes reaches the value of the base inertial longitude.

IV. FIXING THE EXTERNAL POINT OF INERTIAL LONGITUDE AND TIME:

(temporary device involved)

6). As the external reference point of inertial longitude, the point of the vernal equinox becomes (see paragraphs 4, 5).

7). The spacecraft onboard time is synchronized with the hourly angle of the vernal equinox relative to the Greenwich meridian and is reset to zero after the time the Earth has completely turned.

V. OFFLINE DETERMINATION OF GEOGRAPHICAL LENGTH:

(involved: star sensor, angular data processor, temporary device and related algorithms)

8). The geographic longitude of the spacecraft is determined by the corresponding mathematical dependencies, taking into account the speed of rotation of the Earth, current time and the measured inertial longitude.

VI. OFFLINE DETERMINATION OF LATITUDE LOCATION:

(involved: design calculations, Earth sensor, star sensor, processor for processing angular data, storage device and corresponding algorithms)

9). In design calculations, the angle between the direction from the satellite to the reference star and the Earth's axis is determined by the polar distance of the reference star at the moment when the base inertial longitude of the satellite corresponds to the right ascension of the reference star in degree calculation. The values of the specified angle for other values of inertial longitude are determined by a known mathematical dependence and are presented in read-only memory (ROM).

10) The geographic latitude of the spacecraft is determined by converting the measured angle between the central axis of the Earth’s sensor, directed to the center of the Earth, and the direction from the spacecraft to the reference star (coordinated by a stellar sensor) and taking into account the angle between the direction from the spacecraft to the reference star and the Earth’s axis, presented in storage device with a value corresponding to that inertial longitude value at which latitude is determined.

VII. AUTONOMOUS DETERMINATION OF REAL ORBIT AND PRECISE ANGULAR ORIENTATION:

(involved: angular data processor, position control processor, storage device, temporary device, inertial flywheels and corresponding algorithms)

eleven). The orbit in inertial space is determined by a set of points formed at each time cycle by inertial-longitudinal and inertial-latitudinal measurements.

12). The accuracy level of a stellar sensor (in the light of the incompatibility of the error values of both sensors) is interpreted as the base level, and therefore the error of angular measurements is related to the error of the Earth sensor.

13). The measurement error is interpreted in the form of an imaginary error in the nature of the orbital motion.

fourteen). The parameters of the real and essentially “smooth” motion of the spacecraft are determined by statistical processing of stochastic inertial-longitudinal and inertial-latitudinal measurements using the corresponding software module (neural network) and are presented as they are processed by writing to random access memory (RAM).

fifteen). With this processing, errors in measurements are eliminated and the values of inertial-longitudinal and inertial-latitudinal angles are predicted several clock steps in advance to realize the subsequent updated angular orientation of the spacecraft.

Viii. AUTONOMOUS DETERMINATION OF NON-COMPATIBILITY OF THE REAL ORBIT PARAMETERS TO THE PARAMETERS OF THE SET ORBIT.

(involved: design calculation, storage device (ROM and RAM), orbital data processor and corresponding algorithms)

16). On board the spacecraft, by writing to the read-only memory (ROM), the specified orbital turn is presented (corresponding to the requirements of the target function of the spacecraft) with its traditional parameters and in the form of inertial-longitudinal and inertial-latitudinal angles for each time cycle.

17). According to the corresponding mathematical dependencies and directly from the available data, the period, semi-major axis, eccentricity, perigee argument, inclination and right ascension of the ascending node of the real one represented in the orbital orbit RAM are determined.

eighteen). By comparing the parameters of the real orbit and the parameters of the given orbit presented in the ROM, the desired deviations are determined.

19). According to the known dependencies and the revealed deviations, the following are determined: the sequence of corrective actions, the type of corrective impulse, the point of its application, the value of the speed impulse, the value of energy consumption and the operating time of the propulsion system (ДУ).

IX. OFFLINE IMPLEMENTATION OF CORRECTION.

(involved: position control processor, temporary device, inertial flywheels, correction engines and corresponding algorithms)

twenty). According to the point and direction of application of the pulse, the angular turns of the spacecraft relative to the coordinate system modeled on board are determined and implemented, which provide the necessary direction of the vector of the correcting pulse, and according to the pulse duration, the operating time of the remote control.

X. AUTOMATIC CONTROL OF TECHNICAL PROCESS.

(involved: host computer and peripherals)

21) In the multitasking mode of operation, the control computer cyclically interrogates and evaluates the current status of peripheral devices, updates the data of the internal database and receives the necessary exposure commands for the purpose of the process.

It should be noted that the totality of the above features relates to a group of inventions that are interconnected by a single concept - a single autonomous onboard spacecraft synthesized in terms of navigation and control.

Figure 1 presents a hierarchical structural diagram of an autonomous on-board control system; figure 2 is a schematic representation of astronomical spatial and temporal relationships as the basis of navigation definitions; figure 3 - a spacecraft in Earth orbit with a diagram of the measured angles, stabilized relative to the direction to the center of the Earth and the direction to the reference star; figure 4 is a table of stars from the vicinity of the north pole of the world; figure 5 is a table of stars from the vicinity of the south pole of the world; figure 6 - a spacecraft with an extended field of view of the stellar sensor and the ability to orient the longitudinal axis to any point on the Earth; 7 is a diagram of the shading by the Earth of stellar landmarks in various orbits; on Fig - a spherical triangle, designed to determine the angle between the plane containing the direction to the reference and navigation stars, and the plane containing the direction to the reference star and the pole of the world; Fig.9 is a diagram for determining the onboard reference point of inertial longitude; figure 10 is a diagram of determining the angle between the direction from the SC to the reference star and the axis of the Earth; figure 11 is the orbit formed by points that are coordinated by inertial-longitudinal and inertial-latitudinal angles; 12 is a diagram illustrating the relative position of the values of geographical longitude and inertial longitude; Fig.13 is a diagram of the construction of a geocentric vertical using 4 scanning sensors; on Fig - diagram of the geometry of the measurements in determining the geocentric vertical; on Fig - a monoblock astronomical sensors KA, its "rigid" plane and the coordination of the axes of the sensors in the monoblock; on Fig is a diagram of the differences of systematic and random errors; 17 and 18 are diagrams illustrating errors in the angular spatial position of the spacecraft in the plane of the longitudinal channel and in the plane of the latitudinal channel, respectively; on Fig - diagrams illustrating the real and imaginary orbits at the moments of measurement of the latitudinal angle; in Fig.20 is a diagram illustrating the real and imaginary position of the spacecraft at the moments of measurement of the latitudinal angle; on Fig is a block diagram of the statistical processing of the measured data; on Fig - time dependence of stochastic latitudinal and longitude data intended for training a neural network - a software processing module; in Fig.23 is a table of the results of processing the measurement information in the orbital section from 500 to 559 seconds; in Fig.24 is a graphical time dependence of the real, measured and predicted inertial longitude neural network in the orbital section from 500 to 559 seconds; on Fig - graphical dependence on time of the real, measured and predicted by the neural network latitudinal equivalent in the orbital section from 500 to 559 seconds; in Fig.26 is a table of the results of processing the measurement information in the orbital section from 2999 to 3058 sec; on Fig is a graphical time dependence of the real, measured and predicted by the inertial longitude neural network in the orbital section from 2999 to 3058 sec; on Fig - graphical dependence on time of the real, measured and predicted by the neural network latitudinal equivalent in the orbital section from 2999 to 3058 sec; on Fig - graphical dependence on time of the real and predicted neural network of inertial longitude in the interval of a full turn from 0 to 5402 seconds; on Fig - graphical dependence on time of the real and predicted by the neural network latitudinal equivalent in the interval of a full turn from 0 to 5402 seconds; on Fig - comparative table of parameters processed by various methods - a linear trend and a neural network in the orbital section from 3049 to 3058 sec; on Fig is a graph of comparisons of longitudinal parameters predicted by a linear trend and a neural network in the orbital section from 3049 to 3058 sec; on Fig is a graph comparing latitudinal parameters predicted by a linear trend and a neural network in the orbital section from 3049 to 3058 sec; on Fig - a given orbit and the actual orbit and the elements characterizing each of the orbits; not Fig. 35 is a table of parameters of three orbits, explaining the definition of apogee and perigee; on Fig - travel time curves of two orbits with zones and points of apogee and perigee; on Fig - orbit and the corresponding axis of change of inclination, argument perigee and right ascension of the ascending node under the action of lateral corrective forces; on Fig - orbit and lateral impulse, which in the General case, changes all three elements that determine the orientation of the orbit; Fig. 39 is a diagram explaining the dependence of the lateral impulse and the angle value characterizing the direction of the impulse depending on the angle of rotation of the orbit plane; on Fig is a diagram of a direct turn of the plane of the orbit to change its inclination; Fig. 41 is a diagram explaining a change in the in-plane elements of the orbit under the influence of a tangential force; on Fig is a diagram illustrating the correction of the position of the perigee (perigee argument) under the influence of a tangential impulse; on Fig - orbit and its points at which changes in the semimajor axis, eccentricity and perigee argument under the influence of tangential force have extreme values; on Fig - table, which shows the equations of the increments of the orbital elements under the action of a tangential or lateral force.

On the presented figures are marked: 1 - Earth, 2 - celestial sphere, 3 - direction to the pole of the world, 4 - direction to the reference star, 5 - direction to the navigation star, 6 - equator, 7 - sky equator, 8 - Greenwich meridian, 9 - the celestial meridian of the absolute reference point 0, γ, 10 - the plane of the Greenwich meridian, 11 - the meridian of the reference star, 12 - the first plane, 13 - the second plane, 14 - the spacecraft, 15 - the star sensor, 16 - the Earth sensor, 17 - the plane sensitivity, 18 - geocentric vertical, 19 - orbit, 20 - solution of the field of view of stellar sensors Ikov, 21 - a monoblock of astro devices, 22 - a two-stage drive of a monoblock of astro devices, 23 - the longitudinal axis of the spacecraft, 24 - a propulsion system, 25 - the center of the Earth, 26 - the point of contact of the horizon with the line of sight of the Earth sensor, 27 - horizon, 28 - instantaneous field of view, 29 — scanning area by instantaneous field of view, 30 — on-board reference system for measuring the Earth’s sensor, 31 — CO ₂ layer, 32 — shadow region of the orbit, 33 — first tangent at the apex of λ, 34 — second tangent at the apex of λ, 35 — scale inertial longitude.

The figures also show: γ is the vernal equinox, “0” is the instrument base, 0 is the absolute direction to the external reference point at t = 0, formed by the intersection of the plane of the celestial equator by the Greenwich meridian plane, α is the right ascension of the reference star, μ is the polar distance of the reference star, t is the hourly angle of the vernal equinox relative to the Greenwich meridian, t _m is the time scale of the complete rotation of the Earth, the flight time scale, σ is the angle of the triangle, the vertex of which is the poles pa, ρ is the angle of the triangle whose apex is the navigation star, β is the polar distance of the navigation star, ε is the angular distance between the stars, x, y, z are the coordinate axes of the Earth’s sensor, x ₀ , y ₀ , z ₀ are the coordinate axes of the stellar sensor, ω is the angle between the central axis of the Earth’s sensor and the direction “KA is the reference star”, ω ₀ is the angular relationship between the coordinate systems of the star sensor and the Earth’s sensor, λ is the angle between the first and second planes, ψ is the angle fixing the instrument base relatively rigid plane of the sensors, φ is the angle between the first plane and the absolute reference direction, the angle between the rigid plane of the sensors and the absolute reference direction, the angle between the rigid plane of the sensors and the Greenwich meridian plane, which at t = 0 coincides with the right ascension of the reference star, A is the apogee of the orbit, P is the perigee, B is the ascending node, H is the descending node, Ω is the right ascension of the ascending node, i is the inclination of the orbit, ∈ coincides with the right ascension of the reference star, A is the apogee of the orbit, P is the perigee, B is the ascending node, H is the descending node, Ω is right ascension of the descending node, i is the inclination of the orbit, ∈ is the argument of the perigee, u is the argument of the AC, ϑ is the true anomaly of the AC, 2α is the distance between the perigee and the apogee of the orbit, e is the eccentricity, F is the focus of the orbit, D and D ₁ are the points of intersection of the orbit with a minor axis, ι is the inertial longitude, ∂ is the geographic longitude, η is the latitude, ζ is the longitude error, ξ is the latitudinal error, Z is the angle measured by the sensor between the airborne reference system and the direction to the visible horizon of the Earth, ∑ is the angle measured by the sensor to direction of the horizon to the opposite side, ΔV - pulse rate, V _η - ransversalnaya speed, Δχ - angle of rotation of the plane of the orbit, j - angle characterizing the impulse direction ΔV.

The internal spacecraft means, which are schematically depicted in figure 1, are structurally and functionally divided into three levels:

- at the level of local control, the parameters of the external process of orbital motion, which proceeds in the form of angular changes, are measured by means of a star sensor and the Earth sensor, and by means of inertial flywheels and correction engines, impacts on this process are carried out in order to change its parameters;

- at the level of controlling the spacecraft’s angular and location by means of the position control processor, laws are developed for controlling the spacecraft’s angular position, its orbital location according to the results of comparing (in the processor for processing orbital data) the parameters of the real orbit with the parameters of the given (presented in the storage device) and the results of statistical processing of the measured data (in a corner data processor, which also converts inertial parameters to geographic e);

- at the level of strategic management in real time and a multitask sequential-parallel mode of operation, the control computer cyclically (using the frequency grid of the temporary device) polls and evaluates the current status of peripheral devices, updates the data of the internal database and receives the necessary action commands for the purpose of the proper process .

Consider the astronomical basis of the navigation and control process and for this we turn to figure 2, which presents a schematic representation of the astronomical spatial and temporal relationships.

Pay attention to the following circumstances:

1) the vernal equinox and the poles of the world in the sky are not marked by anything, these are abstract points;

2) the angles α, μ, t are subject to varying degrees.

The reason for the change in α is that the vernal equinox (the point of intersection of the celestial equator with the ecliptic) shifts relative to fixed stars due to precession.

The reason for the change in μ is that the pole of the world (the axis of rotation of the Earth) moves due to precessions around the pole of the ecliptic, continuously changing the equatorial coordinates of the stars.

Note that the effect of precession is much stronger for stars close to the pole of the world.

The reason for the change in t is that the point (the point of intersection of the celestial equator with the celestial meridian), which does not take part in the diurnal rotation of the celestial sphere, is taken as the origin of the reference angles.

The situation, captured by certain angular relations at the time of the vernal equinox, at the next moment will “unfreeze”.

Nevertheless, we will set ourselves the goal of connecting the situation (reference system) with new angular relations so that the indicated abstract points (the point γ and the world pole) are already contained in the planes, that is, we specify the situation.

Actually, if we look at any system in isolation, this does not mean that it exists in isolation and the point here is to determine the connections of the system. We draw attention to the fact that direction 3 and direction 4 are contained in the plane 12, in which the reference star is at the moment 0 ^{h of} Greenwich Mean Time, in its upper culmination, and directions 4 and 5 are contained in the second plane 13, which is unchanged in inertial space. These planes intersect at an angle λ.

We emphasize the following circumstance - the second plane 13 fixes the first plane 12 in space through the angle λ, which contains the direction “the center of the Earth is the north pole of the world”. In this case, the pole of the world is fixed in space not only by this plane, but also by the polar distance μ.

In turn, the first plane 12 thus fixed in inertial space, by means of an angle measured from it and equal in degree terms to the right ascension of the reference star 4, fixes in space the position of the meridian of the vernal equinox γ, which is also not marked in the sky.

Further determination of the external relations of the landmark system is associated with the manifestation of the angular relations of the first plane 12 to the plane of the Greenwich meridian.

Greenwich stellar time is the hourly angle of the vernal equinox relative to the Greenwich meridian, that is, t in degree measurement. The position of the vernal equinox γ relative to the first plane 12 is determined above by the right ascension of the reference star, that is, the angle α. Obviously, the first plane 12 and the Greenwich meridian plane 10 intersect at an angle equal to α-t. At t = 0, the Greenwich meridian plane coincides with the direction to the vernal equinox γ, i.e. at this moment, the plane 12 and the plane of the Greenwich meridian 10 intersect at an angle equal to the right ascension α of the reference star.

Recall that in astronomical yearbooks the Greenwich hour angles of the vernal equinox γ and, accordingly, time intervals are determined.

This spatial situation, which includes such geometric elements as directions 0, 3, 4, 5 and planes 12, 13 and 10, is characterized by a decrease in the level of abstraction and certain angular ratios.

Of particular importance here is point 0, which coincides at the given moment with point γ. The particular importance of this point is due to the fact that it is intended to be a zero base for counting time and longitude.

At t = 0, point 0 becomes the zero base of the time measure of the hour angle.

As for the zero base for reading longitude values, the matter here is somewhat more complicated.

The question is as follows. The point γ shifts along the ecliptic to the west at a speed of 50.3 '' per year, so it must be correlated to the moment at which the coordinates of the stars belong to the equinox.

Of course, the coordinates of the stars in our case should be attributed to a certain era.

It should be noted here that only in equatorial stars the annual increment of their right ascensions is equal to the annual shift of the vernal equinox γ. The annual increments of the direct ascents of the polar stars are not subject to such a correspondence.

The polar zone of stars is a zone of special right ascents, where the annual increments of right ascensions can be positive, negative, and even very close to zero.

Since stellar day is the time interval between two successive climaxes of the same point γ, it is obvious that the shift of the point γ by 0 '', 133 = 0 ^s , 0084 per day leads to a mismatch between the duration of the stellar day and the period of the complete rotation of the Earth and, thus, the stellar day becomes shorter.

If the coordinates of the stars are attributed to a certain epoch (frozen) and at the same time their annual (daily) increments of right ascensions correspond to the annual (daily) shift of the point γ, then there is no problem here and the stellar day will turn out to be equal to the period of the complete rotation of the Earth.

In this regard, those polar stars whose annual increments of right ascensions are equal to (or close to) the annual shift of the point γ are preferred for use as landmarks.

At t = 0, point 0 through each complete rotation of the Earth will be fixed in space by the plane of the Greenwich meridian and, thus, the subsequent situation will repeat the previous one.

In this case, the values of geographical longitudes will coincide with the values of right ascensions of stars (for example, equatorial).

Thus, point 0, the direction to which is formed by the intersection of the plane of the celestial equator by the plane of the Greenwich Meridian, becomes the absolute zero point of reference not only for time, but also for longitude.

In general, the precession changes not only the values of the direct ascents of stars, but also their polar distances.

For engineering applications, a spatial reference system in which coordinate changes are negligible is preferable.

Figure 3 schematically shows a spacecraft in Earth orbit with a diagram of the measured angles, stabilized relative to the direction to the center of the Earth and the direction to the reference star.

The question arises: how can the detected astrometric bases become useful for our purpose?

It is known that utility means the relation of an object, considered as a part, to a certain relationship of objects, considered as a whole.

The whole, in our case, is the interconnection of spacecraft onboard devices with the spatial structure of the external environment.

A common characteristic feature of each astrometric base, that is, of each particular subject, be it a reference system, an absolute reference point, inertial longitude, or the relationship of longitudes, is an angular measure, calculated depending on necessity and in time.

Consequently, the benefit may lie in the identified angular relationships.

As material reference points, we use a reference star 4, a navigation star 5, and the center of the Earth.

Note that the reference and navigation stars are displayed in the star sensor with their corresponding coordination with respect to the instrument axes.

The center of the Earth is implemented by the Earth's sensor as the estimated location of a point relative to the airborne reference base. The direction to this point is treated as a geocentric vertical.

The plane that contains the central axis of the star sensor and the Earth sensor, as well as the display of the reference star and the center of the Earth, will be called the sensitivity plane 17.

To use the coordinate relationships of the astronomical base, we “freeze” the spacecraft’s location at the orbital point belonging to the first plane 12, so that the sensitivity plane 17 is aligned with the first plane 12, in which the reference star is in its upper culmination, and the geocentric vertical coincides with the direction "KA is the center of the Earth."

Obviously, in this case, the sensitivity plane 17 will become the first plane 12, and the plane formed by the directions “KA - reference star” and “KA - navigation star” - the second plane 13 and these planes intersect at an angle λ.

At this moment, the spacecraft, similarly to the reference star 4, culminates in the first plane 12 and its right ascension is equal to the right ascension of the reference star or, in degree terms, equal to the angle φ, that is, equal to the inertial longitude, which at zero hour angle of the point γ relative to the Greenwich meridian corresponds to the geographical longitude.

Knowing the coordination of the sensitivity plane 17 in the axes of the stellar instrument and the value of the angle φ, it is not difficult to calculate the position of the zero instrument base of the inertial longitude reference corresponding to the absolute reference point 0 in the axes of the stellar sensor.

By the value of the hourly angle of the point γ relative to the Greenwich meridian, the airborne stellar time is scaled to zero every 24 hours.

In addition to the angles φ and λ, the polar distance of the reference star μ is also used to coordinate the Earth in space. This angle serves to coordinate the Earth in the first plane. Obviously, the angle "the center of the Earth - the SC - the reference star", designated ω, serves a similar purpose - it coordinates the position of the SC in the sensitivity plane 17.

Note that the first plane 12, which contains the center of the Earth, the world pole and the reference star, in the considered fixed moment is combined with the sensitivity plane 17, formed by the central axis of the earth sensor and the central axis of the star sensor, and in which the directions to the center of the Earth and the reference star are coordinated .

If you “unfreeze” the situation and keep the sensitivity plane in orbital motion aligned with the plane containing the directions “KA - reference star” and “KA - center of the Earth”, then the effect of rotation of the sensitivity plane of the KA around the direction to the reference star 4 will occur.

This effect is due to the orbital motion of the spacecraft and is supported by the corresponding angular control of the spacecraft in space.

Both bringing the spacecraft to the specified angular position, and maintaining this position in time is impossible without the implementation of the controlled motion of the spacecraft.

Consider this issue in more detail.

Controlled is such a movement in which, under the influence of a controlling force, the spacecraft passes from a certain initial state to a given final state.

The nature of the controlled movement is thus determined by the features of the initial and final states.

In the general case, the angular position of the spacecraft can be determined by the relative position of two coordinate systems, the direction of the axes of one of which sets the desired orientation, and the other, which is rigidly connected with the device, the actual orientation of the device.

The first of these coordinate systems is called the basic reference system, the second - the associated coordinate system.

Since in the general case the axes of the coupled and the base systems do not coincide, the spacecraft orientation problem can be defined as the problem of combining the axes of the connected coordinate system with the axes of the base.

It is clear that to solve this problem, the movement of the apparatus around its own center of mass should be controlled. Such control allows the spacecraft to give any desired position in space and maintain this position when various disturbing moments act on the spacecraft. In this case, two characteristic control modes can be distinguished. The first corresponds to the process of bringing the axes of the associated coordinate system to the axes of the base reference system. If we consider this regime from the moment the spacecraft is separated from the launch vehicle, then it includes:

- braking (damping) of the initial angular velocity;

- search for physical landmarks used for the technical reproduction of the basic reference system;

- rotary maneuver in order to combine the axes of the base and associated coordinate systems.

The second mode, usually called the stabilization mode, is designed to maintain the required orientation of the spacecraft with a given accuracy.

The position of the coordinate axes of the coupled system in the base coordinate system is determined by the roll, yaw, and pitch angles.

In our case, the system of two directions “KA - center of the Earth” 28 and “KA - reference star” 4, the mutual angular position of which varies depending on the location of the spacecraft in space, is taken as the basic coordinate system. As the third, we use the direction connecting the images in the star sensor of the reference and navigation stars, that is, we use the projection of the plane 13, which is formed by the directions “KA - reference star” 4 and “KA - navigation star” 5. The angular position of this direction relative to the reference plane, formed by the first two directions, also varies depending on the location of the spacecraft in space.

To conduct orientation operations in order to ensure the considered alignment, it is first necessary to extinguish the angular velocity of the spacecraft.

When separated from the launch vehicle, the spacecraft acquires a significant kinetic moment, arbitrarily located in space.

The quenching mode of initial angular velocities is implemented by the well-known control algorithm for the signals of the angular velocity meter of the spacecraft and with the help of the corresponding control moment of the executive bodies.

Then the spacecraft is oriented to the sun. This mode is necessary to provide spacecraft service systems with energy and to obtain a certain spatial orientation of the associated spacecraft axes. The capture of the Sun, bringing and keeping it in the field of view of the solar sensor is carried out by the traditional method using the signals of the solar sensor, angular velocity meter and control moments of the executive organs through the channels of roll, yaw and pitch.

According to well-known algorithms, the search for Earth 1 is also carried out using the direction “KA - Sun”, the subsequent capture of a landmark by the Earth sensor 16 and the construction of a geocentric vertical.

Corresponding rotational maneuvers of the spacecraft with a change in the coordination of the Sun in the solar sensor, the field of view of the star sensor 15 is oriented to that region of the celestial sphere in which the reference star 4 is located.

It should be noted that the orientation of the field of view of the star sensor to the vicinity of the reference star can be carried out before the search and capture of the Earth by turning the spacecraft around the direction "spacecraft - the sun."

At the end of this mode, the television camera of the stellar sensor registers images of stars falling into its field of view on the CCD matrix. As a result of processing the obtained video data, the position of the stars in the instrument coordinate system is determined. The stellar sensor memory (in the on-board star catalog) stores data on the position of stars in the stellar coordinate system.

A comparison of the instrumental and catalog coordinates of the same stars makes it possible to determine the mutual orientation of the instrumental and stellar coordinate systems. The stars registered on the CCD matrix are recognized by the criterion for the same angular distances between them in both of these coordinate systems.

In this way, the reference star 4 is recognized, the direction of which is then aligned with the plane formed by the central axes of the star sensor and the Earth sensor.

When the spacecraft moves in orbit 19, the position control processor, based on the continuous readings of the star sensor 15, generates settings designed to eliminate the angular mismatch between the specified plane and the direction to the reference star. To eliminate the mismatch, the executive bodies and the roll control channel are involved.

Pitch and yaw channels are controlled by an Earth sensor designed to realize the geocentric vertical.

The dynamic processes in the implementation of these modes are theoretically well developed and in practice do not cause insurmountable problems.

Recall that the state of a spacecraft as a dynamic system is generally defined as a set of variable states at time t ₀ , from which it is possible to predict the behavior of a dynamic system at any other time t> t ₀ .

The set of such variables is represented as a state vector.

It is known that not only the traditional oblique range, azimuth, elevation angle and their derivatives, but also equivalent parameters can form a state vector, moreover, the missing parameters can be supplemented with mathematical dependencies, which make it possible to obtain values of unmeasured parameters.

Consider the state vector of the spacecraft formed by equivalent parameters.

As already mentioned, in the process of functioning, the spacecraft is constantly oriented in such a way that in the plane of sensitivity materialized by the sensitive elements of the stellar sensor, there always appear two directions: the direction to the center of the Earth of the central axis of the Earth’s sensor and the direction “KA - reference star”.

Note that the coordinate fixation for each time step of the position in the star sensor of the plane containing directions to the stars is made relative to the instrument base of reference “0”, which is discussed in the subsequent material. Here we only say that relative to the instrument base of the reference “0”, the inertial longitude of the spacecraft is calculated by the on-board processor.

The position of the direction “KA - reference star” relative to the central axis of the Earth’s sensor is also calculated by the onboard processor, and when the correction, depending on the values of inertial longitude, is taken into account, the inertial latitude of the KA is determined.

According to the results of these measurements, not only the angular distances traveled in latitude and longitude are determined, but also the corresponding speeds that can be decomposed along the control axes of the spacecraft, as well as in the case of vector addition, the orbital velocity.

Thus, the angular and location of the spacecraft in inertial space become known, and with a transformation that takes into account the speed of rotation of the Earth and the current onboard time, the projection of the location of the spacecraft relative to the latitude-longitude grid of the Earth, i.e., the spacecraft’s path, is known.

In general, to realize the spatial and angular motion of the spacecraft from the state at time t ₀ to the state at time t> t ₀ , a set of state variables is needed that would characterize not only the initial angular and location of the spacecraft relative to the latitude-longitude grid of the Earth, but also the subsequent angular and location of the spacecraft.

Moreover, the state at time t> t ₀ must correspond to the desired state with reliable accuracy.

In this regard, the following circumstance should be noted: measurements of inertial-latitudinal and inertial-longitude angles are processed onboard the spacecraft by a special software module for statistical processing.

The purpose of statistical data processing is to identify the trend component in the stochastic input data array and to obtain the predicted values of inertial-latitudinal and inertial-longitude angles by a number of clock steps after the input values.

As a result of the implementation of this procedure, the angles that determine the position of the SC axes relative to the direction to the center of the Earth, as well as relative to the latitude-longitude grid of the Earth, acquire values of increased accuracy.

Moreover, high-precision values of these angles are predicted from the last measurements several steps forward, which allows controlling the angular and location of the spacecraft in space with increased accuracy.

It should be noted here that determining the angular position of the spacecraft and determining the location of the spacecraft in space are not two separate modes.

The high-precision mode for determining the angular position of the SC axes relative to the direction to the center of the Earth and relative to the latitudinal plane of the Earth containing the sub-satellite point is at the same time a high-precision mode for determining the spacecraft in space.

From the foregoing, it follows that the set of spacecraft state variables at time t _{0 is} sufficient to predict the behavior of a dynamic system at time t> t ₀ .

It should also be noted that the parameters required for the formation of the spacecraft state vector are determined independently on board the spacecraft. If necessary, the traditionally used parameters can be calculated onboard the spacecraft according to the corresponding mathematical relationships, which will be discussed in subsequent materials.

In the above materials, it is noted that the correct choice of reference stars is of particular importance.

Figures 4 and 5 show tables of stars from the environs of the north and south poles of the world, respectively. It has already been noted that the polar region of stars is a zone of special right ascents, where the annual increments of right ascensions can be positive, negative, and even very close to zero.

We relate the coordinates of the stars in our case to the 2000 era, and to compare coordinate increments, we present data from the 1950 era.

For the indicated epochs, the data, including, in addition to coordinates, also the designations of stars and magnitudes, are summarized in two tables: in table 4, we present the coordinates of stars from the vicinity of the north pole, in table 5, the coordinates of stars from the vicinity of the south pole.

The choice of a star as a reference or navigation one is determined by the permissible value of its coordinate change, as well as by the capabilities of the stellar sensor's detecting ability and the size of its field of view.

The magnitudes should correspond to the detection ability of the sensor. The sensors mastered by the industry are capable of detecting stars up to 7-8 magnitude. The stars presented in the tables satisfy this condition.

As for the issue of coordinate changes in stars, this issue needs to be considered in more detail.

Based on the fact that the point γ shifts at a speed of 50 '', 24 per year and over 50 years, its displacement will be 2512 '' or 168 ^s (2 ^m 48 ^s ), then over the same 50 years the right ascension of a fixed star should increase on the same 2 ^m 48 ^s . However, as already mentioned, the polar region is a zone of special direct ascents of stars and their increment over 50 years, as shown by the coordinates presented in the tables, vary in a rather wide range.

With an increment of the star’s right ascension of 2 ^m 48 ^s , equal to the displacement of the point γ, it is fair to assume that the star is stationary, and with an increment of 00 ^m 00 ^{s, the} star is conventionally shifted by 2 ^m 48 ^s over 50 years.

For our case, from the northern polar region, we select 1642 as a reference star, and 454 as a navigation star, 3983 as a reference, and 4583 as a navigation star. The increments of the direct ascents of these stars are close to the indicated value in 2 ^m 48 ^s .

This choice is due to the following consideration.

The stellar days are considered to be the time interval between the first culmination of the point γ and the subsequent culmination of the same point of the same point, which shifts during this period. Therefore, the stellar day is shorter (by the amount of displacement) of the Earth's rotation period. In order for the time interval between the first culmination of a star and the subsequent culmination of the same star to become equal to the full period of the Earth’s rotation, the selected star, unlike the point γ, must be motionless, that is, the increment of its right ascension should be at least close to a value of 2 ^m 48 ^s .

It is appropriate to note here that the increments of the declination of stars from the northern zone (-16 37.56 and -16 40.01) should be close to each other, as well as the increment of stars from the southern zone (+16 42.22 and +16 38.67).

It is also advisable that the polar distances of the reference stars (1642 and 3983) be as small as possible, and the angular distance between the reference and navigation stars fit into half the smallest field of view of the star sensor (the field of view of modern sensors are in the range from 8 ^° × 8 ^° to 13 ^° × 13 ^° , and the astrosystem for recognition of the constellation of the development of MBB and CIRA has a field of view of three optical heads - 30 ^° × 40 ^° ).

In some specific cases, stars can also be selected using a milder criterion with respect to coordinate increments.

Also in some specific cases, there may be different requirements for the size of the field of view of the stellar sensor.

Obviously, (except for a stationary orbit), the required range of the latitudinal angular solution of the field of view of the stellar sensor must be increased depending on the latitudinal locations of the spacecraft in orbit.

The star sensors mastered by the industry do not have a latitude plane of field of view sufficient for our purposes.

The required angular latitudinal solution of the field of view of the stellar sensor can be provided with an appropriate set of several optical heads and / or using a drive that implements two fixed positional positions.

When using a two-position drive, it will require certain logic for switching the fixed positions of the optical head to control it. For example, a command to switch from the first position to the second can be formed upon the fact that the image of the reference star falls into some limit coordinate zone of the sensor field of view.

The option of increasing the field of view through a set of optical heads can be implemented in a single monoblock together with the Earth sensor.

Compared to the on-off option, the monoblock version is more preferable due to the lack of positioning logic and the elimination of possible backlash errors in fixing the position of the optical head.

One or another variant of expanding the field of view of the star sensor, one or another size of its latitudinal solution depends on the inclination of the used orbit (on which it is planned to provide latitudinal measurements in full) and is determined by the requirements of each specific project.

True, a general option is also possible, providing the maximum latitudinal field of view by a set of optical sensor heads, as well as a general version of one sensor optical head, which “holds” the reference star in the center of its field of view, tracking the angular position of the spacecraft relative to the direction through an external drive to the reference star. These options satisfy any inclination of the used orbit of a particular case, however, with unequal accuracy characteristics.

Note that the implementation of the target function of the spacecraft, which in some cases may require the angular reorientation of the target equipment, can affect the choice of the angle of the latitudinal solution.

With the active functioning of the spacecraft, it is often necessary to remove the central axis of the target equipment from the direction to the center of the earth and reorient it to a particular area of the earth’s surface to perform the target function.

In the absence of an appropriate drive for the target equipment, the implementation of this orientation leads to a mismatch of the materialized sensitivity plane of the astro sensors with the direction “KA - the center of the Earth” and to relocation in the onboard algorithms of the reference bases of inertial longitudes and latitudes of the spacecraft location.

Use for this purpose a special mat. collateral seems inappropriate.

The required angular orientation of the spacecraft with the target equipment rigidly mounted on it can be achieved by using a two-stage drive of a monoblock of astroprocessors.

Figure 6 presents a spacecraft with an extended field of view of the stellar sensor and the ability to orient the longitudinal axis to any point on the Earth through a two-stage drive 22.

Monoblock 21 with an extended field of view 20 in this case consists of two star sensors 15 and the Earth sensor 16.

With long-term tracking of the same area of the earth's surface - this is the best option.

True, in the predicted flight areas with relatively minimal time redirections, you can do without a special drive.

If the target equipment has the ability to differently orient its central axis relative to the longitudinal axis of the spacecraft, then the drive is also not necessary.

Obviously, in some situations, selected stars can be obscured by the Earth and therefore may not be available to spacecraft astro sensors in some areas of orbital motion.

Figure 7 presents: on the left - a variant in which stars from the vicinity of the north pole of the world are involved, on the right - stars of the south pole.

On the left are the low equatorial circular orbits 19, the middle circular orbit with some “optimal” inclination, and the orbit with “non-optimal” inclination.

It is clear that if the inclination of the circular low or circular middle orbit does not exceed a certain threshold value, then all points of the orbit have the visibility of the stars 4 and 5 of the northern polar zone involved. The orbital points are not visible by the stars involved when they are obscured by Earth 1, as in the shadow area 32 of the orbit with a "non-optimal" inclination.

In general, it should be noted that the duration of the shadow section (as well as its presence) is due to the diameter of the Earth, the value of the inclination of the orbit and the height of the orbit.

In this case, the geostationary orbit has a special position - its points are observed by both northern and southern stars involved.

The image on the right involves stars from the vicinity of the south pole of the world and presents: a low circular orbit, an average circular orbit and a Lightning orbit, the inclination of which is about 65 °.

What has been said for the variant with the northern stars involved is also true for the variant with the southern stars involved.

The following should be emphasized: in a highly elliptical orbit of the Lightning type, the perigee region is not observed by northern stars, while the apogee region, which is usually the target functioning spacecraft, is located in the northern hemisphere at a considerable height and therefore is observed by both northern and southern stars.

Circular polar orbits, unlike the considered ones, have the following features: due to the inadmissibility of the so-called “folding” of the control axes, they have areas in the polar regions where the passive spacecraft mode is implemented — the constant solar orientation (PSO) mode.

As already noted, the first plane 12 and the second plane 13 of the astronomical base coincide, respectively, at some point in the orbital motion of the spacecraft with its sensitivity plane 17 and its plane formed by the directions "spacecraft - reference star" and "spacecraft - navigation star".

The angle λ between these planes is determined in advance when designing from a triangle whose vertices on the celestial sphere are: the pole of the world, a reference star and a navigation star.

On Fig this triangle with the desired angle is depicted on the sphere. In this regard, the tangents 22 and 23 to its sides at the apex of the desired angle are shown. But since the radius of the celestial sphere is infinite in size, the following formulas of plane trigonometry are used to calculate the desired angle, which connect the sides and angles of the triangle:

1) cos ε = cos β cos μ + sin β sin μ cos σ;

2) cos β = cos μ cos ε + sin μ sin ε cos λ.

The angle λ determined in this way corresponds to the moment when the spacecraft is in the plane of the culmination of the reference star. At other points in time, the sensitivity plane containing the central axes of the sensors, due to the rotation effect, sweeps the celestial sphere over the orbital revolution, and the navigation star 5 (its display) moves in the star sensor 15 along a “closed” curve.

Let us turn to Fig. 9, which shows two characteristic positions of the spacecraft in orbit: the right one, coinciding with the plane in which the reference star culminates, and the left one, coinciding with the absolute reference direction 0.

The position in orbit 19 of the spacecraft 14, shown in the figure to the right, is characterized by the angle λ at which the inertial longitude of the spacecraft is equal to the right ascension of the reference star.

Obviously, at some moment of orbital motion, the inertial longitude of the spacecraft will become equal to 0 °. Since the plane 13, containing directions to the stars, is unchanged in space, any angular rotation of the spacecraft due to orbital motion will entail a change in the angle between this plane and the sensitivity plane 12. This happens continuously when the spacecraft moves in orbit, when the center of the Earth is 25 and the reference star 4 (their display) are held in the sensitivity plane.

When the spacecraft moves from the right orbital position to the left plane of sensitivity, it is combined with the absolute reference direction. The angle between the sensitivity plane and the display in the star sensor of plane 13 (the second plane of the astronomical base) takes on a value that fixes the instrument base of the inertial longitude reference and which corresponds to a zero value of inertial longitude.

We emphasize that the angle ψ fixing in the star sensor the instrument base of reference “0” relative to the sensitivity plane is determined in advance by calculation when zeroing the inertial longitude of the spacecraft equal to the right ascension of the reference star. This angle at any location of the reference star in the sensitivity plane has the same value, which is then taken into account in the inertial longitude calculation algorithms.

The inertial latitude of the spacecraft location is defined as the difference between the measured angle "the center of the Earth - the spacecraft is the reference star" and 90 °, however, it is also necessary to take into account the correction due to the polar distance of the reference star μ. See FIG. 10.

Taking this amendment into account provides essentially the determination of the angle “the center of the Earth - the SC - the pole of the world” at any orbital points, in which, of course, it has one or another value.

We note that the spatial positions of the spacecraft are characteristic in that the sensitivity plane coincides with the direction “center of the earth - the pole of the world” at the moments of alignment with the plane of the angle μ, that is, at the moments of passage of the plane in which the reference star is at the upper or lower climax.

Obviously, at these moments, the measured angle "the center of the Earth - the SC - the reference star" must be reduced by determining the latitude by the polar distance μ at the upper culmination of the star and increased by the same value at the lower culmination.

In orbital positions in which the spacecraft sensitivity plane is perpendicular to the same spacecraft sensitivity plane located in pos. 1, the correction due to the polar distance of the reference star takes zero values.

In general, the current correction value depends on the value of the current inertial longitude.

Each value of inertial longitude strictly corresponds to a certain correction value, which can be pre-calculated and presented in the on-board storage device.

The current correction is determined by the product of the polar distance of the reference star by the cosine of the angle, the value of which is equal to the difference between the values of the current inertial longitude and the angle between the first plane and the absolute reference direction.

To determine the latitude of the spacecraft, therefore, you should use the ratio:

η = (ω-90 °) -μ cos (ι-φ),

where η is the latitude, ω is the angle "the center of the Earth - the spacecraft is the reference star", μ is the polar distance of the reference star, ι is the inertial longitude, φ is the angle between the first plane 12 and the absolute reference direction.

The polar distance of the reference star also determines the oscillations of the spacecraft along the roll.

The retention of directions to the reference star and to the center of the Earth in the sensitivity plane of the airborne sensors leads to orbital motion of the spacecraft to oscillations of this plane along the roll channel with an amplitude equal to the polar distance of the reference star.

The angular position of the spacecraft relative to the north-south axis depends on the inertial longitude of the spacecraft.

Obviously, in the orbital positions of the spacecraft, when ι = φ and when ι = φ + 180 °, the plane of sensitivity of the spacecraft is combined with the plane of the angle μ and the north-south axis.

In the orbital positions of the spacecraft, when ι = φ + 90 ° and when ι = φ + 270 °, the plane of sensitivity deviates from the north-south axis by an angle equal to the polar distance of the reference star.

Each value of inertial longitude strictly corresponds to a certain angular position of the spacecraft relative to the north-south axis, which can be pre-calculated and presented in the on-board storage device.

The current angular position of the spacecraft is determined by the product of the polar distance of the reference star by the sine of the angle, the value of which is equal to the difference between the values of the current inertial longitude and the angle between the first plane 12 and the absolute reference direction.

The measurement scheme for the inertial longitude and latitude of the orbital location of the spacecraft is shown in Fig. 11, where it is indicated: 1 - Earth, 14 - spacecraft, 19 - orbit, 25 - center of the Earth, ι - inertial longitude, η - latitude.

Inertial longitude is the angle of absolute space in the range of changes from 0 to 360 °, measured in the direction of the Earth’s rotation on the plane of the celestial equator from the absolute reference point 0 and coinciding with geographic longitude after each period of the Earth’s complete rotation.

It should be explained here that right ascension coordinates fixed stars with respect to point γ, while inertial longitude coordinates a spacecraft moving against a background of fixed stars with respect to absolute reference point 0.

An angular data processor is used to convert inertial longitude to geographic.

The translation is as follows. The mutual relations of geographic longitude and inertial longitude at different moments of the 24-hour cycle (period of the Earth’s full rotation) are presented in options a) and b) in Fig. 12 (view from the North Pole of the world).

The following notation is used in this figure: 0 - absolute reference direction, 1 - Earth, 2 - celestial sphere, 8 - Greenwich meridian, ι - inertial longitude, ∂ - geographical longitude, t - time on Greenwich. Option a) illustrates the relative position of the values of geographic longitude and inertial longitude at 0 ^h on the Greenwich meridian. At the moment, the values of geographical longitude coincide with the values of inertial longitude. So, a value of inertial longitude of 30 ° (indicated by an arrow in the figure) corresponds to a geographical longitude of 30 °. Option b) illustrates the relative position of geographic longitude and inertial longitude at time t = 10 ^h . At the moment, like at other non-zero points in time, the values of geographical longitude do not coincide with the values of inertial longitude.

Consider two possible options in which the relationship between longitudes is determined differently.

1) Let us determine at a given moment the value of geographic longitude, which should correspond, for example, to 240 ° inertial longitude (indicated by an arrow in the figure).

At time t = 10 ^{h, the} Earth will rotate by an angle equal to 150 °. This angle is less than the inertial longitude of 240 °, their difference will be 90 °. In this case, an inertial longitude of 240 ° corresponds to a geographical longitude of 90 °.

2) Let us determine at the same moment in time t = 10 ^{h the} value of geographical longitude, which should correspond, for example, to an inertial longitude of 90 °.

The Earth’s rotation angle of 150 ° is not less, but greater than the value of inertial longitude and the difference between them will be 60 °. In this case, the geographical longitude will be equal to the difference of 360 ° and 60 °, i.e. 300 °.

Thus, geographical longitude and inertial longitude are related by the following dependencies:

1) λ _g = λ _u - (ω.t) for ω.t <λ _u ;

2) λ _g = 360 ° - [(ω.t) -λ _and ] for ω.t> λ _and ,

where the speed of rotation of the Earth ω = 15 ° / hour; λ _g - longitude; λ _and - inertial longitude; t is time.

As for the orientation of the axis of the spacecraft relative to the center of the earth, such an orientation is provided by the Earth's sensor.

The construction diagram of the geocentric vertical using four scanning sensors is presented in Fig.13.

The principle of determining the geocentric vertical 18 is based on measuring the angle between the direction to the Earth’s horizon 27, defined as the space-Earth boundary, and the SC axes at various points on the horizon.

The direction of the geocentric vertical is the bisector of the angle between two diametrically opposite points of the observed horizon 27.

The principle is based on the use of temperature contrast existing between the earth's surface and outer space. The sensors used for this should be sensitive to radiation in the range from 11 to 20 microns.

The fields of view of the sensors are arranged in pairs in two mutually perpendicular planes, while the angle of view of each sensor by scanning with an instant field of view 28 covers an area with an Earth-space boundary.

A radiant energy receiver captures the angular position of the Earth’s horizon as a sharp difference in energy brightness (optical contrast) between the edge of the Earth’s disk and the surrounding space.

The Earth sensor measures the position of the horizon in the onboard coordinate system of the spacecraft.

Two types of measurement errors are known:

1) instrumental errors;

2) errors caused by inconstancy of the phenomenon of the visible horizon (errors of the "phenomenon).

Instrumental errors of the sensor itself are electronic noise, quantization errors, and others.

Instrumental errors are represented as the sum of a Gaussian random process and errors of the bias type. Random errors - not correlated (white noise), permanent measurement errors (bias) can be considered errors with an infinite correlation time.

Errors of the “phenomenon” are caused by the uncertainty of the CO ₂ layer in the Earth’s atmosphere. Due to temporal and spatial fluctuations of the atmosphere, the horizon is determined by the position of the CO ₂ layer with a larger error than in the case of determining the horizon directly along the edge of the earth's disk (earth's limb).

Errors of the “phenomenon” are most pronounced at low altitudes of the spacecraft flight and quickly decrease with increasing altitude.

At high altitudes, instrumental errors prevail. In our case, we use a sensor consisting of four scanning devices: two of them measure in the sensitivity plane and two in the orthogonal plane.

On Fig presents a diagram of the geometry of the measurements when determining the geocentric vertical, which is "orthogonal" to the plane of sensitivity.

After the sensor 16 measures the angle Z between the on-board reference system 30 and the direction to the visible horizon of the Earth and the angle ∑ to the direction to the horizon in the opposite direction, a geocentric vertical 18 is determined, which should be in the sensitivity plane 17 and strictly oriented to the center of the Earth 25.

We note that the error ζ caused by the horizon uncertainty, electron noise, and bias, as well as the error ξ when measured in the sensitivity plane, generally speaking, complicates a strict orientation to the center of the Earth.

The measured angles are determined by the following relationships:

Z = Z _nom -ζ;

∑ = ∑ _nom + ζ,

where Z _nom , ∑ _nom are nominal angles.

Similarly, the angles in the sensitivity plane are determined. The angle between the on-board reference frame 30 and the direction to the center of the earth is defined as half the sum of the measured angles.

Note that the accuracy of the sensors used is disproportionate in value to each other. The high accuracy of the stellar sensor in 2-3 arc seconds is extremely important due to the fact that the angle between the central axis of the Earth’s sensor and the direction “KA - reference star” can be measured with almost equivalent accuracy if the connection between the Earth is carried out and certified coordinate systems of the star sensor and the Earth sensor.

In particular, this angular connection between the central axis x of the Earth sensor 16 and the sight axis y _{0 of the} star sensor 15 must be carried out and adjusted as possible in one block and so that the plane of two axes x ₀ , y _{0 of the} star sensor and the plane of two axes x , y of the Earth sensor formed one plane of sensitivity 17. See FIG.

The value of the angle ω ₀ measured in this case between the central axis of the Earth sensor and the sighting axis of the star sensor should be represented in the corresponding on-board algorithms.

Obviously, in this case, the angle in the field of view of the stellar sensor between the line of sight and the direction "KA - reference star" should be summed with an angle ω ₀ representing the above relationship.

Thus, it becomes possible to accurately measure the position in space of the central axis x of the Earth’s sensor relative to the direction of the spacecraft - reference star. Whether in this case the central axis of the sensor coincides with the direction to the center of the earth is another question. Only the most accurate knowledge of this situation is important here.

This high-precision knowledge relates to latitudinal angular communication in the sensitivity plane, in which the accuracy level of the stellar sensor is essentially a basic level.

A long-term measurement is realized in a plane perpendicular to the plane of sensitivity. But since the instrument base of the inertial longitude reference is fixed relative to the sensitivity plane with high calculated accuracy, it is obvious that the actual measurement of the longitudinal angle can also be carried out with an accuracy equivalent to the accuracy of a stellar sensor.

Thus, while providing high-precision angular communication between the coordinate systems of the sensors, the accuracy level of the stellar sensor is the basic level both in the latitudinal measurement and in the measurement of the longitudinal angle.

On Fig presents a diagram of the differences in systematic and random errors of the Earth sensor.

The center of each target represents the true value of the measured quantity, and each point is a measurement. The sum of measurements is characterized by bias and scatter. The first and third figures above show biased results. The standard deviation or spread of the results of individual measurements is a measure of the error. A sensor with good repeatability of the result (or a small random error) obviously has a good random error, but it does not necessarily give the correct output value, since the shift can significantly distort the result, i.e. the accuracy of the sensor is low. The measurement results in the second and fourth figures have a small error, but only the result shown in the fourth figure is accurate. In the diagrams on the right, the true value is represented by a straight line on which the measurement results are superimposed.

The accuracy of the measurement depends on both the offset and the spread:

- large displacement + large spread = low accuracy;

- small displacement + large spread = low accuracy;

- large displacement + small spread = low accuracy;

- low bias + small spread = high accuracy.

Under conditions of orbital motion, the coordinate system of the sensors is transformed into a navigation coordinate system associated with the longitudinal and latitudinal location of the spacecraft. There are a number of other transformations of the onboard coordinate systems that generate errors. Thus, to the instrumental errors of the sensor and to the errors caused by the inconstancy of the phenomenon of the visible horizon of the Earth, transformation errors are added. When constructing a geocentric vertical, measurements are made through two channels: in latitudinal, i.e. in the plane of sensitivity, and in longitudinal - orthogonal plane.

According to the results of measurements and subsequent transformations of coordinate systems, the central axis of the sensor is oriented to the center of the Earth with the indicated errors through the corresponding rotation of the satellite.

We agree to consider all errors irrespective of the nature of their origin in the longitude channel as one longitude error, and all errors in the latitudinal channel as one latitudinal error.

The angular spatial position of the spacecraft in the plane orthogonal to the plane of sensitivity, that is, in the plane of the longitudinal channel, is shown in Fig. 17.

Note that in the designation under the number 18 there is a geocentric vertical, although the direction from the sensor 16 to the center of the Earth 25 is deviated by the value of the longitudinal error ζ. Under the number 18, it would be more likely to represent the central axis of the Earth's sensor.

Obviously, if the central axis of the sensor were strictly oriented to the center of the Earth 25, then the inertial longitude ι would have a different meaning, namely, its value for the situation depicted in this figure would be less by the magnitude of the longitudinal error ζ.

These considerations are also true for the angular position of the spacecraft shown in Fig. 18 in the plane of the latitudinal channel.

In this figure, under the figure 18, similarly to the designation in the previous figure, a fictitious geocentric vertical appears, the difference between which and the true vertical is due to the presence of an error ξ. Obviously, when the latitudinal error ξ is eliminated, the angular positions of the spacecraft shown in the figure in the space of the northern and southern hemispheres of the Earth will correspond to the true latitude of its location.

Latitudinal and longitudinal errors lead the central axis of the sensor away from the direction of the attracting center of the Earth. However, whether these errors are present at the next measurement is unknown. But regardless of this uncertainty, it can be asserted with certainty that the spacecraft is at the actual point of the orbit at each moment of measuring latitude and longitude.

It is permissible, however, to imagine that the central axis of the sensor is always strictly oriented towards the center of the earth. True, with this assumption, the spacecraft at each moment of measurement should not be at a real orbital point, but at some imaginary point.

Turning to FIG. 19, two views of a) and B) are presented, illustrating the real and imaginary position of the spacecraft at the moments of measurement of the latitudinal angle, respectively.

In this figure, 1: Earth, 14 - KA, 4 - direction to a reference star, 6 - equator, 18 - geocentric vertical, 19 - orbit, 19 _f - imaginary orbit, 25 - attracting the center of the Earth, η - latitude, ξ - latitudinal error.

In the figure on the left (view A), the spacecraft 14 is at the actual orbital point. Also depicted are other real points at which the spacecraft is located at the moments of latitudinal angle measurements.

The latitudinal angle η is measured with an error ξ and, therefore, the central axis of the sensor is oriented away from the center of the Earth.

The figure on the right (view B) shows the imaginary position when the central axis of the sensor for the same errors ξ in latitudinal angles η coincides with the geocentric vertical 18, but the SC is at imaginary points forming an imaginary orbit of 19 _f .

It should be noted that everything related to imaginary points in the latitudinal measurement is also true for imaginary points in the longitudinal measurement.

In such an imaginary way, one can imagine the error of the Earth's sensor in the form of an error in the nature of the motion of the spacecraft.

Obviously, latitudinal and longitudinal angles, if they did not contain errors, would characterize the motion of the spacecraft, its orbit with high accuracy. It can be said in another way - the nature of the motion of the spacecraft, that is, its location in space, at different points in time determines certain latitudinal and longitudinal angles at the same time.

Thus, the latitudinal and longitudinal angles depend on the location of the spacecraft in space, on the one hand, and on measurement errors, on the other.

Referring to FIG. 20, this relationship is illustrated.

This figure marked 14 _on - the spacecraft in real point of the orbit at time zero, 14 _of ^m - SC in the imaginary point at the same point in time, 14 ₄ - SC in the real point at the time of 4 minutes, 14 ₄ ^m - SC at the imaginary point in the fourth minute, 3 - direction to the pole of the world, 18 - geocentric vertical, 19 - orbit, 25 - center of the Earth, η ₀ - latitudinal angle at zero time, η ₄ - latitudinal angle at four minutes, ξ ₀ - latitudinal error at time zero.

The imaginary points located in the figure along the orbit plane form a cloud of measured latitudinal data.

With a sufficient number of such points in the data cloud, their statistical processing is possible.

Obviously, in our case, the statistical processing of latitudinal and longitude data can be used to identify the nature of the motion of the spacecraft, i.e. to accurately identify the line along which the spacecraft is moving.

It is also obvious that according to the results of such processing, the central axis of the sensor should be oriented to the center of the Earth with high accuracy.

From a statistical point of view, the measured data should be attributed to a time series that can be processed in one way or another to repay unsystematic components.

The comparison of methods for solving the problem of approximating the curve along which the spacecraft moves reveals the advantage of a neural network, in particular, an RBF network (a network with radial basis functions).

Thus, it is better to use just such a software module for on-board statistical processing. On Fig presents a block diagram of the processing.

Note that due to perturbations of the orbital parameters, the spacecraft moves along an intricate line that is not located essentially in the same plane and is not closed at all.

In this regard, network training (its programming) is highly dependent on the set of training data presented to it during the training process. The training data should be typical of the task whose solution the network is learning. Such network programming can be carried out even before the launch of the spacecraft, but it is possible to train the network in real conditions.

To confirm the validity of using a neural network as an on-board processing software module, simulation of the spacecraft motion was performed.

Modeling was carried out on a personal computer using the neural network of the STATISTICA system.

Such a choice is dictated by the task of time series in which the relationships between the data in our case are close to linear in a limited section of the orbit and obviously non-linear - in relatively long sections, for example, at the full turn.

In modeling, the estimated inertial latitude and longitude were used as reference parameters, inertial-longitudinal and inertial-latitudinal measurements of stochastic nature were used as measured angles, and parameters processed by a neural network were used as filtered parameters.

The estimation at the corresponding time interval was the value of the mismatch between the calculated inertial, so-called real, parameters and the processed, filtered parameters.

Latitudinal and longitude data sets of stochastic nature were fed to the input of a neural network for training. It should be emphasized that the training data and the measured data (inertial longitude and latitude) have different fluctuations, as evidenced by the graphical dependencies shown in Fig.22. The processing of information was aimed at identifying the trend component in conditionally measured data.

On Fig presents a table of the results of processing by the neural network of conditionally measured information in the orbital section from 500 to 559 seconds.

Inertial latitude measurements (column 2), inertial longitude measurements (column 6) and the corresponding time (column 1) were used as input data for the neural network.

The resulting processing data is represented by the corresponding values for each time step in columns 3 and 7 of the table.

So, in column 3 the processed, that is, predicted by the neural network, inertial latitude values are presented, and in column 7 the predicted inertial longitude values are presented.

Columns 4 and 8 show the reference values of the real inertial latitude and real inertial longitude, respectively, which serve, as agreed, to compare the predicted values with them and determine the efficiency of the processing module.

By analyzing the errors presented in angular seconds in columns 5 and 9, it can be recognized that the data processed by the neural network, both inertial latitude and inertial longitude, have good convergence with the reference values.

On Fig and 25 presents the results of processing in graphical form. Graphical time dependences of real, measured and predicted information are presented in the section from 500 to 559 sec (from 0 to 60 sec). It can be seen from the graph that the sawtooth line (measurements) was transformed by processing into a smooth dashed line (forecast), which coincides with the solid line, with the real spacecraft motion line.

On Fig, 27 and 28 presents a table and graphical dependencies of the processing results of the neural network of conditionally measured information in another orbital section from 2999 to 3058 sec.

Interpretation of data and conclusions on the results of this processing are similar to the previous ones.

On Fig and 30 presents a graphical dependence on time of the results of processing conventionally measured information in full turn. The graphs indicate good convergence of the processed data with the reference values (with a dashed line).

On Fig presents a comparative table of parameters processed by a linear trend and a neural network in the orbital section from 3049 to 3058 sec.

In this table, columns 2 and 5 show the reference values of the real inertial latitude and real inertial longitude, intended to compare the processed predicted values with them.

The inertial latitude values processed by the linear trend and neural network are presented in columns 3 and 4, respectively.

The inertial longitude values processed by the linear trend and neural network are presented in columns 6 and 7, respectively.

Thus, the parameters of columns 3 and 4 and the parameters of columns 6 and 7 are subject to comparative analysis.

The result of the comparison is the degree of their approximation to the parameters presented in columns 2 and 5.

Obviously, the most preferred method for processing measurement data is a method based on the use of a neural network.

On Fig and 33 presents graphs comparing the parameters processed by various methods in the area from 3049 to 3058 sec. Obviously, the parameters processed by the neural network have the greatest convergence with the criterion.

Thus, modeling showed that the most preferable method of processing measurement data is a method based on the use of a neural network.

For a particular objective function of the spacecraft, the corresponding orbit is always selected.

Its spatio-temporal characteristics must satisfy all the conditions for solving the spacecraft task, be it a survey observation of a certain area of the earth’s surface, be it a survey of a specific ground object, Earth probing in the interests of economic activity, or communication between regions.

A specific orbit that is optimal for the target task is the basic environment in which the most complex interactions of various means of the space system are carried out in space corresponding to a specific time and in time corresponding to a specific space.

This is why maintaining the parameters of the calculated orbit in acceptable ranges is so important.

An orbital coil that meets the requirements specified by its traditional parameters and in the form of inertial-longitudinal and inertial-latitudinal values with a clock time step equal to the on-board measurement clock is displayed onboard the spacecraft by writing it to a read-only memory.

In orbit, as the measurement information is statistically processed, the next real turn is recorded in the random access memory for subsequent comparison with the set one.

Any orbit is uniquely determined by six independent Kepler’s motion parameters, four of which characterize the motion of the spacecraft inside the orbit plane and two characterize the orientation of the orbit plane in space. Elements of the orbit are called parameters that determine its position in space, size and shape. Turning to Fig. 34, which presents: a given orbit, a real orbit, and all the elements characterizing each of the orbits.

On this figure are indicated: 1 - Earth, 6 - equatorial plane, 19 ₁ , 19 ₂ - real orbit and given respectively, 0, γ - direction to the vernal equinox, B ₁ (B ₂ ) and H ₁ (Н ₂ ) - ascending and descending nodes of the real (given) orbit, Ω ₁ (Ω ₂ ) - right ascension of the ascending node of the real (given) orbit, P ₁ (P ₂ ) and A ₁ (A ₂ ) - the perigee and the apogee of the real (given) orbit, i ₁ (i ₂ ) is the inclination of the real (given) orbit, ∈ ₁ (∈ ₂ ) is the argument of the perigee of the real (given) orbit, 2α ₁ (2α ₂ ) is the distance between the perigee and the apogee of the real (given) orbit, ϑ is Mudstone anomaly of the spacecraft (spacecraft argument u = ϑ + ∈).

The parameters, as well as the characteristic orbital points of the real orbit, are determined on board the spacecraft as follows.

The orbital period T ₁ is measured as the time interval between successive passes of the spacecraft of two points at which the latitude is the same (for example, points of an ascending or descending node of the orbit).

When the inclination is 0 °, the period T ₁ is the time interval between successive passes of the spacecraft of two points at which the inertial longitude is the same.

, где k - гравитационный параметр, равный 3,986·10⁵ км³/с².The semimajor axis α ₁ is determined by the formula

where k is the gravitational parameter equal to 3.986 · 10 ⁵ km ³ / s ² .

The angular velocities at the perigee and apogee of the real orbit are known from the measurement results.

The point with maximum angular velocity becomes the point of perigee and is coordinated by the angles of latitude and inertial longitude. The apogee point is also defined and coordinated.

The ratio of the spacecraft flight speeds at perigee and apogee is inversely proportional to the ratio of the values of the radius vectors of these orbit points, i.e. V _p / V _a = r _a / r _p , where r _a , r _p are the distances from the center of the Earth to the apogee and perigee, respectively. Due to the fact that 2α = (r _a + r _p ), the ratio of velocities can be represented in the following form V _p / V _a = (2α-r _p ) / r _p , from where the radius vector of perigee is determined. And then from the formula 2α = (r _a + r _n) by substituting it r _{n and} r determined.

The eccentricity of the orbit becomes known from the following formula e ₁ = (r _a1 -r _p1 ) / (r _a1 + r _p1 ).

The ascending B ₁ (and descending H ₁ ) node of the orbit is defined directly as a point with a certain value of inertial longitude and with a zero value of latitude.

Knowing the coordinates of the point of perigee P ₁ and the ascending node B ₁ , the angle corresponding to the argument of perigee ∈ _{1 is} determined in the plane of the orbit.

Similarly, the CA argument u or the true CA anomaly ϑ is calculated.

The inclination i _{1 of the} real orbit is defined as the maximum latitude angle.

Thus, the following parameters of the real orbit become known: α ₁ , е ₁ , ∈ ₁ , Ω ₁ , i ₁ and u (or ϑ).

By comparing the parameters of the real orbit and the parameters of the given orbit presented in the memory, the desired deviations are determined.

So, comparing the values of inertial longitudes at the time of the passage of the spacecraft of the ascending nodes of each of the orbits (i.e., at the moment when both latitudes are equal to zero), we obtain the mismatch Δ Ω as the difference of the indicated longitudes.

Similarly, it is enough to compare the values of the inclinations i ₁ and i ₂ and their difference will reveal the magnitude of their inconsistencies Δi.

As a result of the corrections of the real orbit to eliminate the discrepancies Δ Ω and Δi, the plane of the real orbit will be combined with the plane of the given orbit.

It should be noted here that for the same value of Ω and for the same value of i, the sizes and shapes of two orbits lying in the same plane may not coincide.

The different orientation of the perigee of the two orbits indicates that the values of their arguments are different, and therefore Δ∈ quantitatively characterizes the indicated orientation, and the corresponding Δα and Δe quantitatively characterize the difference in size and shape.

It should also be noted the difference in the form of measurements of orbital speeds: the speed of the real orbit is presented in deg / sec, and the speed of a given orbit is in km / sec (and deg / sec).

The following formulas are known that make it possible to determine the speed in km / s of the real orbit at perigee and apogee:

V ² _n = (k / α) [(1 + e) / (1st)] and V ² _a = (k / α) [(1 + e) / (1 + e)].

A comparison of these velocities with angular velocities makes it possible to ensure their mutual convertibility in any orbital section.

This ensures the determination of deviations of the real orbit from the given one: Δα, Δe, Δ∈, Δi, Δ Ω, as well as the convertibility of speeds.

The data measured at the orbital turn, as shown above, is smoothed by the neural network for each time cycle with second errors. The data processed in this way are recorded in the onboard memory for use in determining the parameters of the orbit. The time step for a particular orbit is chosen optimal. In contrast to the three types of orbits considered below (see Fig. 35), we agree that in our case, when determining perigee and apogee, the time step will be 10 seconds. On Fig presents a summary table of the calculated parameters of the three orbits (three subtable). A high elliptical orbit with the values of the period, heights of perigee and apogee and eccentricity is also set with a time step of 1000 sec, measured by the angle in degrees and speed V '' / sec for each moment after the expiration of each step. With appropriate parameters, a “quasistationary” and a low elliptical orbit are specified. Note that according to the data presented in the memory, the angular distances traveled by the spacecraft for every 10 seconds are detected. For each of the three orbits, we determine the angular distances traveled over time steps and put the obtained values in the empty third columns of each subtable (the empty fourth columns of each subtable serve to fix the location zone of the perigee and apogee points). It is easy to verify from the sub-tables that the smallest angular distances, such as 1.86 °, 8.16 ° and 10.05 °, correspond to the zones of apogee points, and the largest angular distances correspond to the zones of perigee points. In the fourth columns of each subtable, these zones are marked with the letters A (apogee) and P (perigee). The range of zones is limited by such equal (or close) values of angular distances in a 10-second step (V '' / s × 10 s), which reliably differ in their values from intraband values at available accuracy. The ranges of the perigee zone (PZ) and apogee zone (AZ) for (tabular) orbits will be as follows:

- high PZ: ~ 1530``, 4 → ~ 2991 '', 6 ← ~ 1640``, 16 (1530 ''); AZ: ~ 80``, 028 → ~ 66 '', 96 ← ~ 79``, 92;

- stationary PZ: -150``, 84 → ~ 154 '', 08 ← ~ 150``, 84; AZ: ~ 150``, 12 → ~ 146 '', 88 ← ~ 150``, 12;

- low PZ: ~ 2309``, 4 → ~ 2325 '', 9 ← ~ 2301``, 8; AZ: ~ 1814``, 4 → ~ 1804 '', 3 ← ~ 1819``.

Note that for a quasistationary orbit, a step of more than 10 seconds is required. The median angular values of the ranges of zones determine the points of perigee and apogee. It should be borne in mind that points A and P are separated by an angular distance of 180 °. Fig. 36 illustrates the foregoing and presents hodographs of angular velocities of circular and highly elliptical orbits. The OR vectors here are equal to the angular velocity at successive instants of time.

When fixing the ascending node of the orbit and perigee according to the smoothed data, the argument of perigee is defined as the angle between the longitudes of the ascending node and perigee (in the direction of the spacecraft).

Thus, the apogee, perigee and its argument are determined, and from the following formulas - all the necessary parameters: T = 2π√α ³ / k, whence α; 2α = (r _a + r _p ), but since V _p / V _a = r _a / r _p , then V _p / V _a = (2α-r _p ) / r _p , whence r _p ;

r _a = (2α-r _p );

e = (r _a -r _p ) / (r _a + r _p );

r = α (1st ² ) / 1st cosφ, where φ is the angle measured from the axis of the ellipse, connecting the apogee with perigee.

Correction of the parameters of a real orbit in order to ensure their compliance with the parameters of a given orbit depends on the magnitude, point of application, and direction of the correction pulse.

In the direction of action, lateral and tangential pulses are known, under the action of which the deviations of the real orbit from the given one are eliminated.

It should be noted that in our case, corrective maneuvers must be carried out under the influence of impulse traction.

Let us consider what consequences arise when a lateral impulse is applied.

Referring to Fig. 37, where it is indicated: 1 - Earth, 10 - equatorial plane, 30 - orbit, VL nodes line - axis of change of inclination of orbit i, world axis F ₁ P - axis of change of right ascension of ascending node Ω, axis F ₁ Q is the axis of change of the argument of perigee ∈ (this axis is perpendicular to the plane of the orbit and also passes through the center of the Earth), γ is the direction to the vernal equinox, A is the apogee point, P is the perigee point.

Obviously, the lateral force changes i, Ω, ∈, i.e. orientation of the orbit plane in space, but does not change either the shape of the orbit or its size.

The point of application of lateral force during the maneuver for combining the orbit planes is one of two points on the line of intersection of the orbit planes (the point closest to the apogee).

Such a point is determined by comparing the real and given orbits as a point with common coordinates, i.e. like a point belonging to both orbits.

Consider Fig. 38, which shows the real orbit 30 ₁ with the ascending node B ₁ , with inclination i ₁ and argument perigee ∈ ₁ . The listed parameters of the real orbit do not correspond to the similar parameters В ₂ , i ₂ , ∈ _{2 of the} given orbit 30 ₂ . After applying the corresponding lateral impulse ΔV to the corresponding point _{in the} parameters of the real orbit, the values of the parameters of the given orbit will acquire.

Under the action of the lateral impulse, the velocity vector will turn around the axis passing through the point of application of lateral force (point M, Fig. 37) and the center of the earth (point F ₁ ).

When the spacecraft is flying in an elliptical orbit, the velocity vector at any point, except for perigee and apogee, does not coincide with the line of the local horizon. The projection of the velocity vector on the line of the local horizon is called the transversal velocity V _η and it is determined from the relation: V _η = VcosΘ, where the angle Θ = arctan [(1 + ecosϑ) / esinϑ]. Here e, ϑ, and V are known.

In a lateral maneuver at point M, the axis of the orbit is the axis M'M, passing through the point of application of lateral force and the center of the Earth. The vector of orbit Δχ is directed along this axis, i.e. the axis of rotation of the orbit does not coincide with any of the axes of variation of i, Ω and ∈. In this case, the increments of all three elements (Δi _in , Δ Ω _in , Δ∈ _in ) are determined by the projections of the vector of rotation of the orbit plane Δχ on the corresponding axis of change.

Changes in the inclination of the orbit, the right ascension of the ascending node and the perigee argument under the influence of a lateral impulse depend on the spacecraft argument u at the maneuver point (u = ϑ + ∈).

To change the right ascension of the ascending node, the lateral force impulse must be applied at points with an argument equal to 90 ° or 270 °. However, with inclinations of orbit i not equal to 90 °, the application of a lateral impulse at the points of the original orbit with u ₀ = 90 ° or u ₀ = 270 ° will cause a change in the perigee argument. Since u = ∈ + ϑ, a change in the argument of perigee ∈ will also lead to a change in the argument of CA u at the point of maneuver. Therefore, the spacecraft argument in orbit after the maneuver will no longer be 90 ° or 270 °. As a result, the lateral impulse will change not only the right ascension of the ascending node, but also the inclination of the orbit.

Turning to FIG. 39, it is indicated: 30 ₁ is the plane of the original orbit (plane of the real orbit), 30 ₂ is the plane of the orbit after the maneuver (plane of the given orbit), Δχ is the angle of the orbital plane, ΔV _в is the side impulse, V _η is the transverse velocity, j is the angle characterizing the direction of the vector ΔV _in .

The angle Δχ, the plane of which is perpendicular to the line of intersection of the planes of the real and given orbits, is defined as the maximum difference in the coordinates of the orbital points lying in the plane of the angle.

With the known Δχ, the required value of the pulse ΔV _in can be determined from the relation: ΔV _in = 2V _η sin0.5Δχ. In this case, the direction of the vector ΔV _in respect to the original plane of the orbit will be characterized by an angle of j = 90 ° + 0,5Δχ. For circular orbits, as you know, the velocity vector at any point in the orbit is perpendicular to the radius vector. Therefore, for circular orbits, V _η = V _cr .

For elliptical orbits, the transverse flight speed is a variable.

It has the maximum value at the perigee, the minimum at the apogee. Therefore, the magnitude of the momentum ΔV _in when turning the plane of a given orbit at the perigee will be maximum, and at the apogee - minimal.

If the lateral force is applied in one of the nodes of the orbit, the axis of rotation will coincide with the axis of change of inclination of the orbit. Consequently, the lateral force applied at the nodes of the orbit will cause a change only in the inclination of the orbit.

A diagram of the direct turn of the plane of the original orbit to change its inclination is shown in Fig. 40. In one of the nodes of the orbit on January ₃₀ applied pulse ΔV _in speed, under which there is a reversal of the orbital plane by an angle Δχ. As a result, the inclination of the orbit 30 ₂ will differ by an angle Δi = Δχ.

Let us consider what consequences arise when a tangential impulse is applied.

The direction of action of the tangential force either coincides with the direction of the flight velocity vector, or is opposite to it.

Therefore, the tangential force can only change the magnitude of the flight speed. The direction of speed under the action of tangential force does not change. The tangential force does not cause a change in the inclination of the orbit and the right ascension of the ascending node. To determine what changes in the orbit the tangential force will cause, we consider the equation V = √k [(2 / r) - (1 / α)]. Since k is a constant value, and r at the point of maneuver does not change, when maneuvering, an increase (decrease) in the velocity value will cause a change in α.

Consider Fig. 41. It shows an elliptical orbit 30 ₁ with foci F ₁ and F ₂ before maneuvering.

Suppose that at the moment of performing the pulse maneuver, the spacecraft was at point M with a true anomaly ϑ. The distance from this point to the first focus is r, and the distance to the second focus is r '.

As you know, an ellipse is the locus of points for which the equality r + r ₁ = 2a is valid. If the flight speed at point M is increased by ΔV _t , this will cause an increase in the semimajor axis by Δα _t .

Obviously, the distance to the second focus will increase and it will move from the point F ₂ to the point F ₂ '. The magnitude of this displacement is Δr '= 2Δα _t . It is also known that the tangent at any point of the ellipse is the bisector of the external angle formed by the radius vectors of this point. The velocity vector is directed tangent to the trajectory (to the ellipse at point M). Therefore, the angle τ = τ '. Since, after the maneuver, the directions of the velocity vector and the radius vector of the spacecraft do not change, then the angles τ and τ 'do not change either. This means that the direction to the second focus will be preserved and it will move along the radius vector r 'by 2Δα _t to the point F ₂ '. The movement of the second focus from the point F ₂ to the point F ₂ 'leads to a change in the focal length by 2Δс _t , which means that the eccentricity of the orbit e (e = c / α) will also change. Moving the second focus also leads to a rotation of the apse line by an angle Δ∈ _t , i.e. tangential force, changing the semimajor axis of the orbit, also changes the argument of perigee.

Turning to FIG. 42. If the perigee position is corrected due to the tangential impulse applied at one of the intersection points of the orbit with the minor axis (point D), then the magnitude of the major axis will also change.

The latter also causes a change in the circulation period. As a result, after such a single-pulse correction, it will still be necessary to carry out a correction of the magnitude of the semi-major axis. Therefore, in those cases when, when correcting the position of the perigee, a change in the semimajor axis is unacceptable, it is advisable to perform such a correction using two tangential pulses applied at points D and D '(Fig. 42). The magnitudes of these pulses must be the same, and the signs are different. In a two-pulse maneuver under the action of a positive impulse ΔV _t1 applied at point D, the perigee argument will change by Δ∈ _t1 and the semi-major axis will increase by Δα _t1 . Under the influence of a negative momentum ΔV _t2 applied at the point D 'of the intermediate orbit, the semi-major axis will decrease by Δα _t2 , and the argument of perigee ∈ will change in the same way as with the first impulse.

Note that the energy cost of performing the maneuver is determined not only by the selected orientation of the control pulse (for example, tangential or lateral), but also by the point of its application in orbit.

In orbit there are not only points at which one or another impulse of force does not cause changes in individual elements of the orbit, but also points at which this force provides the greatest change in a given element of the orbit.

Turning to FIG. 43.

The figure shows the points at which the changes in α, e, and ∈ under the influence of the applied tangential force have extreme values. In the equation Δα _t = (2Δα ² V / k) ΔV _{t the} semimajor axis α is a constant value for any point of this orbit. The variable in this equation is only the flight speed, the maximum value of which is at perigee, and the minimum is at apogee. Consequently, the same in magnitude and direction of action velocity impulse ΔV _t in the perigee will cause maximum changes in the semimajor axis, and in the apogee, the minimum.

The maximum changes in the eccentricity of the orbit under the influence of tangential force occur at the perigee and apogee of the orbit. However, it must be borne in mind that in order to increase the eccentricity of the orbit, the tangential momentum at the perigee must be positive, and at the apogee, negative.

The tangential force applied at the points of perigee and apogee does not cause a turn of the apse line. In these cases, the directions r and r 'coincide with the apse line and the second focus will move along this line. To correct the position of the perigee (apogee) of the orbit, when the magnitude of the major semiaxis is to be preserved, it is advisable to use two tangential pulses applied at the points (D, D ') of the intersection of the orbit with the minor semiaxis. In this case, the values of both pulses must be the same, and their signs are different.

The necessary changes in the orientation of the orbit plane are performed only under the influence of lateral force. To combine two orbital planes, a lateral control pulse is applied at one of the two points on the plane intersection line, which is closer to the apogee. When the right ascension of the ascending node changes, the application of lateral force at points with an argument equal to 90 ° and 270 ° also leads to a change in the inclination of the orbit.

To change the inclination of the orbit, a control pulse is applied in one of the nodes of the orbit.

When comparing the parameters of a real orbit with the parameters of a given orbit, the following discrepancies are determined: Δ Ω, Δi, Δ∈, Δα and Δе. To eliminate each of these discrepancies in the above materials, the type of the correcting impulse, its direction and the point of its application are revealed. Obviously, first of all, the plane of the real orbit must be aligned with the plane of the given orbit. Given that the correction of the longitude of the ascending node of the initial orbit leads to a change in the inclination i and the argument of perigee ∈, the result of the first corrective action should be to eliminate the mismatch Δ Ω. Therefore, the true mismatch Δ∈ can be detected only after eliminating Δ Ω. The second pulse should be aimed at eliminating Δi, that is, at the final combination of the orbit planes. Two of these impulses are lateral. Elimination of Δα and Δе is performed by tangential impulse applications. Correction of the position of perigee, i.e. correction ∈, in the case when the value of α must be preserved, is performed by two tangential pulses applied at the points of intersection of the orbit with the minor axis.

The equations of the increments of the elements of the orbit with one or another corrective pulse are presented in Fig. 44.

The elements of the real orbit, such as α, е, i, u, and also V _η entering into the equations, as shown above, are determined. The values of each of the increments are revealed by comparing the given and real orbits. The value of the increment of speed ΔV required for the implementation of each type of maneuver is determined from the presented formulas.

The cost of speed is associated with the cost of engine fuel by the formula of KE Tsiolkovsky ΔV = ω _e In (m ₀ / m ₀ -m _t ), where ω _e is the effective velocity of the gas outflow from the engine nozzle, m ₀ is the mass of the spacecraft before maneuver, m _t is the mass of fuel spent on maneuver. Solving it relative to the mass of fuel, we get

All the actions considered are deterministic, and therefore, with the corresponding on-board software, they can be implemented offline.

Claims (1)

An autonomous onboard spacecraft control system (SC) containing at least one star sensor, a temporary device, a memory device, actuators, and a position control processor, which determines the angular mismatches between the SC axes and the axes of the external coordinate system, and forms control signals to the specified Executive bodies to ensure a given relative position of these coordinate systems, characterized in that the processor and Inertial flywheels in the form of inertial flywheels ensure the direction of the reference star selected from the zone of the world’s pole with the target plane containing the central axis of the stellar sensor and the central axis of the Earth’s sensor with the direction to the center of the Earth, and in the sensitivity plane, given by the axes, determined by the indicated processor, the displacement of the reference star characterizes the change in the latitudinal angle of the spacecraft’s orbital position, and the rotation in the star sensor of the navigation star around reference star — inertial-longitudinal change in the orbital position of the satellite, the inertial longitude being measured from the onboard zero reference point, which is coordinated by the angle between the plane defined by the directions from the satellite to both of these stars and the sensitivity plane at the time of zeroing of the right ascension of the reference star measured on board the satellite the inertial longitude-dependent angle between the direction from the spacecraft to the reference star and the Earth axis is recorded in the storage device, and the spacecraft onboard time is synchronized with In the middle of the spring equinox, it is zeroed out in a temporary device after the time of a complete turn of the Earth, and the angular data processor with the program for statistical processing of stochastic inertial-longitudinal and inertial-latitudinal measurements has been introduced into the system, which is capable of determining trend components for each cycle measurements, their translation for recording in a storage device, the forecast of angular data several clock steps forward to implement the subsequent refined angular orientation of the spacecraft and providing, taking into account the Earth's rotation speed and current time, the conversion of the specified inertial longitude to geographic longitude and the conversion of the specified latitudinal angle to geographic latitude, taking into account the angle between the direction from the spacecraft to the reference star and the Earth's axis, the system is also introduced an orbital data processing processor that determines the period, semi-major axis, eccentricity, perigee argument, inclination and right ascension of the ascending node of the real orbital orbit taking into account the results of statistical smoothing data recorded in the storage device, and revealing, by comparing the indicated parameters with the parameters recorded in the storage device, deviations of the actual orbit parameters from the given ones and determining the form, application point, impulse value and sequence of corrective actions by means of the spacecraft propulsion system using the detected deviations while a control computer is also introduced into the system.

Images