RU2750228C1 - Method for determining orthogonal components of velocity vector and method for determining space vehicle coordinates using earth stations - Google Patents

Abstract

FIELD: cosmonautics.SUBSTANCE: inventions group relates to the field of cosmonautics, namely to the technique of performing trajectory measurements, determining the coordinates and orthogonal components of the spacecraft velocity vector, and can be used on ground and onboard spacecraft flight control systems to accurately determine the current parameters of the spacecraft movement. The method for determining the velocity vector of the main spacecraftincludes: measuring in the ground radio technical station (GRTS) K values of the nominal frequenciesof the received radio signals of n-th earth stations (3C) Inafter their retransmission by the main S1and adjacent S1spacecraft, respectively, calculation of the coordinates of the main spacecraft х1, у1, z1, calculation of the orthogonal components of the velocity vector of the main spacecraftThe method for determining the coordinates of the main spacecraft х1, у1, z1includes: measuring in the GRTS K for each n-th 3C Invalues of the time delays Δtnbetween the received radio signals after their retransmission by the main S1and adjacent spacecraft S2, respectively, calculating the coordinates of the main spacecraft x1, y1, z1.EFFECT: increases accuracy of determining the coordinates and orthogonal components of the spacecraft velocity vector.4 cl, 7 dwg, 2 ex

Description

The claimed objects are united by a single inventive concept and the claimed method for determining the coordinates of a spacecraft (SC) using earth stations (ES) is intended to implement a method for determining the orthogonal components of the spacecraft velocity vector using ES.

The inventions relate to the field of cosmonautics, namely, to the technique of performing trajectory measurements and determining the parameters of the spacecraft orbit, and can be used on ground and on-board spacecraft flight control systems to accurately determine the current parameters of spacecraft motion.

A known method for determining the orthogonal components of the spacecraft velocity vector [1]. To implement this method, the following steps are sequentially performed:

placed at positions with known coordinates of the NRTS and at least three PORS;

receive and record the spacecraft radio signals together with time stamps using the NRTS and the indicated PORS at time t ₀ ;

the recorded radio signals of the spacecraft together with time stamps are transmitted from each PORS to the NRTS;

using correlation processing measure the values of frequency shifts between the radio signals recorded by the NRTS and each of the PORS;

calculate the difference between the radial velocities of the spacecraft relative to the NRTS and each of the POR;

calculate the components of the spacecraft velocity vector using the indicated differences in radial velocities.

The disadvantages of the method [1] include:

long time for determining the orthogonal components of the spacecraft velocity vector, due to the need to place at least three PORS at positions with known coordinates;

the relatively low accuracy of determining the orthogonal components of the spacecraft velocity vector, due to the need for synchronous recording of spacecraft radio signals using the NRTS and at least three PORS.

A known method for determining the orthogonal components of the spacecraft velocity vector [2]. To implement this method, the following steps are sequentially performed:

placed at positions with known coordinates of the NRTS and at least two PPORs;

at time t _0, test radio signals are synchronously emitted with the help of the NRTS and the specified PPORs;

receive and record test radio signals after their retransmission by the spacecraft using the NRTS and the specified PPORs;

using correlation processing measure the values of frequency shifts between the transmitted and received radio signals for the NRTS and each of the PPORS;

calculate the radial speeds of the spacecraft relative to the NRTS and each of the PPORs;

the calculated value of the radial velocity is transmitted from each PPORS to the NRTS;

calculate the orthogonal components of the spacecraft velocity vector using the calculated radial velocities.

The disadvantages of the method [2] include:

a long time for determining the orthogonal components of the spacecraft velocity vector, due to the need to place at least two PPORs at positions with known coordinates;

the relatively low accuracy of determining the orthogonal components of the spacecraft velocity vector, due to the need for synchronous radiation and recording of test radio signals of the spacecraft using the NRTS and at least two PPORs.

Of the known methods, the closest analogue (prototype) of the proposed method in technical essence is a method for determining the orthogonal components of the spacecraft velocity vector [3]. To implement this method, the following steps are sequentially performed:

a ground radio technical station (NRTS) and at least two emitting reference reference stations (IORS) are placed at positions with known coordinates;

at time t _0, test radio signals are synchronously emitted with the help of NRTS and said IORS;

receive and record test radio signals after their retransmission by the spacecraft using the NRTS;

using correlation processing measure the values of frequency shifts between the transmitted and received radio signals for the NRTS and each of the IORS;

calculate the sum of the radial velocities of the spacecraft relative to the NRTS and each of the IORS;

calculate the components of the spacecraft velocity vector using the indicated sums of radial velocities.

The disadvantages of the prototype method [3] are:

long time for determining the orthogonal components of the spacecraft velocity vector, due to the need to place at least two IORS at positions with known coordinates;

relatively low accuracy of determining the orthogonal components of the spacecraft velocity vector due to the need for synchronous emission of test radio signals using the NRTS and at least two IORS.

A known method for determining the coordinates of the spacecraft [1]. To implement this method, the following steps are sequentially performed:

a ground radio technical station (NRTS) and at least three receiving reference reference stations (PRS) are placed at positions with known coordinates;

receive and record the spacecraft radio signals together with time stamps using the NRTS and the indicated PORS at time t ₀ ;

the recorded radio signals of the spacecraft together with time stamps are transmitted from each PORS to the NRTS;

using correlation processing, measure the values of the mutual time delays between the radio signals recorded by the NRTS and each of the PORS;

the spacecraft coordinates are calculated using the indicated range differences.

The disadvantages of the method [1] include:

long time for determining the coordinates of the spacecraft, due to the need to place at least three PORS at positions with known coordinates;

relatively low accuracy in determining the coordinates of the spacecraft, due to the need for synchronous recording of spacecraft radio signals using the NRTS and at least three PORS.

A known method for determining the coordinates of the spacecraft [2]. To implement this method, the following steps are sequentially performed:

they are placed at positions with known coordinates of the NRTS and at least two receiving and transmitting reference reference stations (PPORS);

at time t _0, test radio signals are synchronously emitted with the help of the NRTS and the specified PPORs;

receive and record test radio signals after their retransmission by the spacecraft using the NRTS and the specified PPORs;

using correlation processing, measure the values of the mutual time delays between the transmitted and received radio signals for the NRTS and each of the PPOR;

the distances from the spacecraft to the NRTS and each of the PPORs are calculated;

the calculated value of the range is transmitted from each PPORS to the NRTS;

calculate the coordinates of the spacecraft using the calculated ranges.

The disadvantages of the method [2] include:

a long time for determining the coordinates of the spacecraft, due to the need to place at least two PPORs at positions with known coordinates;

the relatively low accuracy of determining the coordinates of the spacecraft, due to the need for synchronous radiation and recording of test radio signals of the spacecraft using the NRTS and at least two PPORs.

Of the known methods, the closest analogue (prototype) of the proposed method in technical essence is the method for determining the coordinates of the spacecraft [3]. To implement this method, the following steps are sequentially performed:

placed at positions with known coordinates of the NRTS and at least two emitting reference reference stations (IORS);

at time t _0, test radio signals are synchronously emitted with the help of NRTS and said IORS;

receive and record test radio signals after their retransmission by the spacecraft using the NRTS;

using correlation processing measure the values of the mutual time delays between the transmitted and received radio signals for the NRTS and each of the IORS;

the sums of the ranges from the spacecraft to the NRTS and each of the IORS are calculated;

calculate the coordinates of the spacecraft using the indicated sums of ranges.

The disadvantages of the prototype method [3] are:

long time for determining the coordinates of the spacecraft, due to the need to place at least two IORS at positions with known coordinates;

relatively low accuracy in determining the coordinates of the spacecraft due to the need for synchronous emission of test radio signals using the NRTS and at least two IORS.

The aim of the proposed technical solutions is to reduce the time spent on determining the coordinates and orthogonal components of the spacecraft velocity vector and to improve the accuracy of determining the coordinates and orthogonal components of the spacecraft velocity vector.

в момент времени t₀ на основе частотных сдвигов радиосигналов, известных координат НРСТ и ОРС, предварительно заданной частоте сдвига рабочей частоты основного

а также вычисленных координат основного КА x₁, y₁, z₁, дополнительно выбирают смежный КА S₂ с известными значениями координат х₂, y₂, z₂, и ортогональных составляющих вектора скорости

в момент времени t₀ и заданной частотой сдвига

рабочей частоты, а в качестве ОРС используют выбранные ЗС I_n, размещенные на земной поверхности на позициях с известными координатами

где n=1…N-номер 3C, N≥3.The stated goal in the claimed method for determining the orthogonal components of the spacecraft velocity vector using the ZS is achieved by the fact that in the known method for determining the orthogonal components of the spacecraft velocity vector (according to patent No. 2652603) including: placing the NRTS K at a position with known coordinates x _K , y _K , z _K , reception at time t ₀ by means of NRTS K radio signals transmitted by reference reference stations (OPC) and relayed by the main spacecraft S ₁ , calculation of coordinates x ₁ , y ₁ , z _{1 of the} main spacecraft S ₁ at time t ₀ , calculation of orthogonal components of the velocity vector of the main spacecraft

at time t ₀ based on the frequency shifts of the radio signals, the known coordinates of the NRST and OPC, the preset frequency of the shift of the operating frequency of the main

as well as the calculated coordinates of the main spacecraft x ₁ , y ₁ , z ₁ , additionally select the adjacent spacecraft S ₂ with known values of coordinates x ₂ , y ₂ , z ₂ , and orthogonal components of the velocity vector

at time t ₀ and a given shift frequency

operating frequency, and the selected ES I _n are used as the OPC, located on the earth's surface at positions with known coordinates

where n = 1 ... N-number 3C, N≥3.

Calculate the coordinates of the main spacecraft x ₁ , y ₁ , z ₁ .

и

принятых радиосигналов после их ретрансляции основным КА S₁ и смежным КА S₂ соответственно. На основе известных координат НРТС x_K, y_K, z_K, координат x₂, y₂, z₂ и ортогональных составляющих вектора скорости

смежного КА S₂ в момент времени t₀, координат не менее трех ЗС

рассчитывают значения радиальных скоростей

смежного КА S₂ относительно каждой из n-й ЗС I_n и НРТС K соответственно.For each n-th ЗС I _{n is} measured in NRTS K due to correlation processing of radio signals the values of the nominal frequencies

and

the received radio signals after their retransmission by the main spacecraft S ₁ and the adjacent spacecraft S _2, respectively. Based on the known coordinates of the NRTS x _K , y _K , z _K , coordinates x ₂ , y ₂ , z ₂ and orthogonal components of the velocity vector

adjacent spacecraft S ₂ at time t ₀ , coordinates of at least three ES

calculate the values of radial velocities

adjacent spacecraft S ₂ relative to each of the n-th _{ES I n} and NRTS K, respectively.

принятых радиосигналов n-х ЗС после их ретрансляции смежным КА S₂, рассчитанные доплеровские сдвиги частот на входе

и на выходе

смежного КА S₂ за счет его сближения или удаления с или от n-й ЗС I_n и НРТС K, заданную частоту сдвига рабочей частоты смежного КА

вычисляют значения номиналов частот излучаемых каждой n-й ЗС f_n.Using the measured values of the nominal frequencies

of the received radio signals of the n-th ES after their retransmission by the adjacent spacecraft S ₂ , the calculated Doppler frequency shifts at the input

and at the exit

adjacent spacecraft S ₂ due to its approach or removal from or from the n-th _{ES I n} and NRTS K, the given frequency of the shift of the operating frequency of the adjacent spacecraft

calculate the values of the nominal frequencies emitted by each n-th ES f _n .

и вычисленных координат основного КА х₁, y₁, z₁ в момент времени t₀ рассчитывают расстояния

от и n-х ЗС I_n и НРТС K до основного КА S₁.Based on the known coordinates of the NRTS x _K , y _K , z _K , the coordinates of the ZS

and the calculated coordinates of the main spacecraft x ₁ , y ₁ , z ₁ at time t _{0, the} distances are calculated

from and n-x ZS I _n and NRTS K to the main spacecraft S ₁ .

по известным координатам НРТС x_K, y_K, z_K, координатам ЗС

и координатам смежного КА х₂, у₂, z₂, известным ортогональным составляющим вектора скорости смежного КА

заданной частоте сдвига рабочей частоты основного КА

рассчитанным значениям номиналов частот излучаемых каждой n-й ЗС f_n, расстояниям

от и n-х ЗС I_n и НРТС K до основного КА.Calculate the orthogonal components of the velocity vector of the main spacecraft

by the known coordinates of the NRTS x _K , y _K , z _K , the coordinates of the ZS

and the coordinates of the adjacent spacecraft x ₂ , y ₂ , z ₂ , the known orthogonal components of the velocity vector of the adjacent spacecraft

the given frequency of the shift of the operating frequency of the main spacecraft

the calculated values of the nominal frequencies emitted by each n-th ES f _n , distances

from and n-x ЗС I _n and НРТС K to the main spacecraft.

имел одинаковые участки с диапазоном частот на линии "вверх" основного КА

а зона покрытия смежного КА Ω₂ пересекалась с зоной покрытия основного КА Ω₁.The adjacent spacecraft S _{2 is} selected so that its frequency range on the "up" link

had the same sections with the frequency range on the "up" line of the main spacecraft

and the coverage area of the adjacent spacecraft Ω ₂ intersected with the coverage area of the main spacecraft Ω ₁ .

и смежного КА

Каждая ЗС I_n находится в зонах покрытия как основного КА Ω₁, так и смежного КА Ω₂, при этом взаимные расстояния

между n-й и m-й ЗС, где m=1…N, m≠n максимальны.ЗС I _n are chosen such that the values of the nominal values of the radiated frequencies f _n are included in the frequency ranges on the "up" line of the main spacecraft

and adjacent spacecraft

Each ES I _n is located in the coverage areas of both the main spacecraft Ω ₁ and the adjacent spacecraft Ω ₂ , while the mutual distances

between the n-th and m-th ES, where m = 1… N, m ≠ n are maximum.

в момент времени t₀, а также ЗС I_n, размещенных на земной поверхности на позициях с известными координатами

достигается цель изобретения: снижение времени определения ортогональных составляющих вектора скорости КА, а также повышение точности определения ортогональных составляющих вектора скорости КА.Thanks to the listed new set of essential features, due to the use of NRTS K at a position with known coordinates x _K , y _K , z _K , adjacent spacecraft S ₂ with known values of coordinates x ₂ , y ₂ , z ₂ , and orthogonal components of the velocity vector

at time t ₀ , as well as ZP I _n , located on the earth's surface at positions with known coordinates

the aim of the invention is achieved: reducing the time of determining the orthogonal components of the spacecraft velocity vector, as well as increasing the accuracy of determining the orthogonal components of the spacecraft's velocity vector.

The goal in the claimed method for determining the coordinates of the spacecraft using the ZS is achieved by the fact that in the known method for determining the coordinates of the spacecraft (according to patent No. 2652603) including: placing the NRTS K at a position with known coordinates x _K , y _K , z _K , choosing the initial values of parameters orbit of the main spacecraft S ₁ , reception at time t ₀ by means of the NRTS K radio signals transmitted by reference reference stations (ORS) and retransmitted by the main spacecraft S ₁ , calculation based on the time delays of radio signals of the coordinates of the main spacecraft x ₁ , y ₁ , z ₁ in time t ₀ , additionally select the adjacent spacecraft S ₂ with known coordinates x ₂ , y ₂ , z ₂ at time t ₀ , and the selected SZ I _{n is} used as the OPC,

где n=1…N-номер ЗС, N≥3.placed on the earth's surface at positions with known coordinates

where n = 1 ... N-number of the ЗС, N≥3.

For each n-th ES, I _{n is} measured in the NRTS due to the correlation processing of radio signals, the value of the time delay Δt _n between the received radio signals after their retransmission by the main and adjacent spacecraft, respectively.

траекторий

на основе известных координат ЗС

смежного КА х₂, y₂, z₂ и НРТС x_K, y_K, z_K.Calculate N lengths

trajectories

based on the known coordinates of the ST

adjacent spacecraft x ₂ , y ₂ , z ₂ and NRTS x _K , y _K , z _K.

траекторий

а также измеренные временные задержки Δt_n рассчитывают длины

траекторий

Using lengths

trajectories

and also the measured time delays Δt _n calculate the lengths

trajectories

траекторий I_nS₁K, известных координат НРТС x_K, y_K, z_K, ЗС

и смежного КА х₂, y₂, z₂.Calculate the coordinates of the main spacecraft x ₁ , y ₁ , z ₁ based on the calculated lengths

trajectories I _n S ₁ K, known coordinates of the NRTS x _K , y _K , z _K , ЗС

and adjacent spacecraft x ₂ , y ₂ , z ₂ .

где n-1…N - номер ЗС, N≥3 достигается цель изобретения: снижение времени определения координат КА, а также повышение точности определения координат КА.Thanks to the listed new set of essential features, due to the use of NRTS K at a position with known coordinates x _K , y _K , z _K , an adjacent spacecraft S ₂ with known coordinates x ₂ , y ₂ , z ₂ , at time t ₀ , as well as ЗС I _n , located on the earth's surface at positions with known coordinates

where n-1 ... N is the ZS number, N≥3 the aim of the invention is achieved: reducing the time for determining the coordinates of the spacecraft, as well as increasing the accuracy of determining the coordinates of the spacecraft.

The claimed inventions are illustrated by drawings, which show: FIG. 1 is a block diagram of a subsystem for determining the orthogonal components of the velocity vector of the main spacecraft using the ES;

in fig. 2 is a diagram of an algorithm for calculating the orthogonal components of the velocity vector of the main spacecraft using three ES;

in fig. 3 - block diagram of the subsystem for determining the coordinates of the main spacecraft using the ES;

in fig. 4 is a diagram of the algorithm for calculating the coordinates of the main spacecraft using three ES;

in fig. 5 is a diagram of the ES selection taking into account the frequency ranges on the uplink of the main SC and the adjacent SC, as well as the nominal values of the radiated frequencies of the ES;

in fig. 6 is a diagram of the ES selection taking into account the coverage areas of the main and adjacent spacecraft;

in fig. 7 is an example of a topology scheme for placing three ES.

The theory of spacecraft flight, or, as it is also called, astrodynamics, celestial mechanics, space ballistics, is based on the laws of I. Kepler and the law of universal gravitation of I. Newton.

In the first approximation, the spacecraft motion is presented as unperturbed - such a motion that would occur only under the influence of the Earth's gravitational force according to Newton's law, i.e. exactly corresponds to the problem of two bodies (Earth - SC) in celestial mechanics. This motion is called motion along the Kepler orbit, since it obeys three Kepler's laws [4].

The advantage of the Kepler orbit is the simplicity of calculating the coordinates and the velocity vector of the spacecraft at the predicted moment in time. This predetermined the widespread use of the elements of the Kepler orbit. In the present invention, the elements of the Kepler orbit of the spacecraft act as a priori data about the spacecraft. With the help of these elements, the receiving antennas of the NRST are oriented to the spacecraft. In addition, the elements of the Kepler orbit of the spacecraft serve to eliminate the ambiguity of determining the coordinates of the spacecraft.

The disadvantage of the Kepler orbit is the relatively low accuracy of determining the coordinates and the velocity vector of the spacecraft, which is insufficient for performing a number of applied tasks, for example, for correcting the spacecraft motion.

More precisely, the spacecraft motion is described using a perturbed orbit [4, 5], which is specified:

в начальный момент времени t₀,the canonical parameters of the spacecraft, including the spacecraft coordinates x ₁ , y ₁ , z ₁ and the orthogonal components of the vector of its velocity

at the initial moment of time t ₀ ,

factors that lead to deviations of the spacecraft from the ideal (Keplerian) orbit and are called perturbing factors.

For example, for a geostationary spacecraft, it is sufficient to take into account only three factors that lead to deviations of the spacecraft from the ideal (Keplerian) orbit - the influence of the Sun, the Moon, and the noncentrality of the Earth's gravitational field.

When predicting the coordinates of spacecraft located in other (not geostationary) orbits, a number of factors are additionally taken into account that lead to deviations of the spacecraft from the ideal (Kepler) orbit. Such factors, for example, for spacecraft in low orbits are: the influence of the resistance of the Earth's atmosphere, light pressure, the attraction of planets, etc.

в начальный момент времени t₀ с высокой точностью является важной задачей, которая решена в заявленных технических решениях.Thus, the determination of the spacecraft coordinates x ₁ , y ₁ , z ₁ and the orthogonal components of its velocity vector

at the initial moment of time t ₀ with high accuracy is an important problem, which is solved in the stated technical solutions.

в момент времени t₀ содержит НРТС K, смежный КА S₂ с известными координатами х₂, у₂, z₂, и ортогональными составляющими вектора скорости

в момент времени t₀, а также N≥3 выбранных ЗС I_n, n=1…N (см. фиг. 1) на позициях с известными координатами

излучающие радиосигналы в направлении основного и смежного КА.Subsystem for determining the orthogonal components of the velocity vector of the main spacecraft

at the moment of time t ₀ contains the NRTS K, adjacent spacecraft S ₂ with known coordinates x ₂ , y ₂ , z ₂ , and orthogonal components of the velocity vector

at time t ₀ , as well as N≥3 of the selected ZS I _n , n = 1 ... N (see Fig. 1) at positions with known coordinates

emitting radio signals in the direction of the main and adjacent spacecraft.

- расстояние между основным КА S₁ и первой ЗС I₁;

- расстояние между основным КА S₁ и НРСТ K;

- расстояние между смежным КА S₂ и первой ЗС I₁;

- расстояние между смежным КА S₂ и НРСТ K,

- радиальная скорость основного КА S₁ в направлении первой ЗС I₁,

- радиальная скорость основного КА S₁ в направлении НРСТ K,

- радиальная скорость смежного КА S₂ в направлении первой ЗС I₁,

- радиальная скорость смежного КА S₂ в направлении НРСТ K,

- векторы скорости основного и смежного КА соответственно,

- углы между направлением на НРТС и векторами

соответственно;

- углы между направлениями на первую ЗС и векторами

соответственно.FIG. 1 introduced the following notation:

- the distance between the main spacecraft S ₁ and the first _{ES I 1} ;

- the distance between the main spacecraft S ₁ and NRST K;

- the distance between the adjacent spacecraft S ₂ and the first _{ES I 1} ;

- the distance between the adjacent spacecraft S ₂ and NRST K,

- radial speed of the main spacecraft S ₁ in the direction of the first ES I ₁ ,

- radial speed of the main spacecraft S ₁ in the direction of NRST K,

- the radial speed of the adjacent spacecraft S ₂ in the direction of the first ES I ₁ ,

- radial speed of the adjacent spacecraft S ₂ in the direction of NRST K,

are the velocity vectors of the main and adjacent spacecraft, respectively,

- the angles between the direction to the NRTS and vectors

respectively;

- the angles between the directions to the first ZS and vectors

respectively.

- радиальная скорость основного КА S₁ в направлении n-ю ЗС I_n,

- радиальная скорость смежного КА S₂ в направлении n-ю ЗС I_n,

- углы между направлениями на n-ю ЗС и векторами

соответственно.For each n-th ES it is possible to enter the designations:

- radial speed of the main spacecraft S ₁ in the direction of the n-th ES I _n ,

- the radial speed of the adjacent spacecraft S ₂ in the direction of the n-th ES I _n ,

- the angles between the directions to the n-th ES and vectors

respectively.

по предлагаемому способу.FIG. 1 shows three ESs as the minimum required number of ESs for unambiguous one-step determination of the orthogonal components of the velocity vector of the main SC

according to the proposed method.

принятых радиосигналов после их ретрансляции основным КА S₁ и смежным КА S₂ соответственно для каждой из выбранных ЗС I_n.The fundamental premise of the present invention is the presence, in addition to the main spacecraft S ₁ , through which a communication channel between earth stations is organized, an adjacent spacecraft S ₂ , which is capable of retransmitting the same radio emissions as the main spacecraft, but with greater attenuation and a different transfer frequency. Thus, due to the correlation processing of radio signals, it is possible to obtain, due to the correlation processing of radio signals, the values of time delays Δt _n between radio signals received from the main S ₁ and adjacent spacecraft S ₂ , as well as the values of the nominal frequencies

the received radio signals after their retransmission by the main SC S ₁ and the adjacent SC S _2, respectively, for each of the selected ES I _n .

в момент времени t₀ используют значения номиналов частот

принятых радиосигналов после их ретрансляции основным КА S₁ и смежным КА S₂ соответственно, обусловленные различными радиальными скоростями основного и смежного КА относительно каждой из п-й ЗС I_n и НРСТ K [6].To determine the orthogonal components of the velocity vector of the main spacecraft

at time t ₀ use the values of the nominal frequencies

the received radio signals after their retransmission by the main spacecraft S ₁ and adjacent spacecraft S _2, respectively, due to different radial velocities of the main and adjacent spacecraft relative to each of the n-th _{ES I n} and NRST K [6].

смежного КА S₂ в момент времени t₀, координат ЗС

рассчитывают значения радиальных скоростей

смежного КА S₂ относительно каждой из n-й ЗС I_n и НРТС K соответственно.Based on the known coordinates of the NRTS x _K , y _K , z _K , coordinates x ₂ , y ₂ , z ₂ and orthogonal components of the velocity vector

adjacent spacecraft S ₂ at time t ₀ , the coordinates of the ZS

calculate the values of radial velocities

adjacent spacecraft S ₂ relative to each of the n-th _{ES I n} and NRTS K, respectively.

смежного КА S₂ относительно каждой из n-й ЗС I_n и НРТС K, значения номиналов частот

принятых радиосигналов после их ретрансляции смежным КА S₂, значение заданной частоты сдвига рабочей частоты смежного КА

вычисляют значения номиналов частот излучаемых каждой n-й ЗС f_n.Using the values of the radial velocities

adjacent spacecraft S ₂ relative to each of the n-th _{ES I n} and NRTS K, the values of the nominal frequencies

of the received radio signals after their retransmission by the adjacent spacecraft S ₂ , the value of the set frequency of the shift of the operating frequency of the adjacent spacecraft

calculate the values of the nominal frequencies emitted by each n-th ES f _n .

по известным координатам НРТС x_K, y_K, z_K, координатам ЗС

и координатам смежного КА х₂, у₂, z₂, известным ортогональным составляющим вектора скорости смежного КА

заданной частоте сдвига рабочей частоты основного КА

рассчитанным значениям номиналов частот излучаемых каждой n-й ЗС f_n, расстояниям

от и n-х ЗС I_n и НРТС K до основного КА.Calculate the orthogonal components of the velocity vector of the main spacecraft

by the known coordinates of the NRTS x _K , y _K , z _K , the coordinates of the ZS

and the coordinates of the adjacent spacecraft x ₂ , y ₂ , z ₂ , the known orthogonal components of the velocity vector of the adjacent spacecraft

the given frequency of the shift of the operating frequency of the main spacecraft

the calculated values of the nominal frequencies emitted by each n-th ES f _n , distances

from and n-x ЗС I _n and НРТС K to the main spacecraft.

For one-step and unambiguous determination of the orthogonal components of the velocity vector of the main spacecraft, it is necessary to use three ES. A further increase in the number of ES will lead to an increase in the accuracy of determining the orthogonal components of the velocity vector of the main spacecraft.

в момент времени t₀. Подсистема определения координат основного КА х₁ у₁, z₁ в момент времени t₀ содержит НРТС K, смежный КА S₂ с известными координатами х₂, у₂, z₂ в момент времени t₀ и N≥3 выбранных ЗС I_n, n=1…N (см. фиг. 3) на позициях с известными координатами

излучающие радиосигналы в направлении основного S₁ и смежного КА S₂.As an example, Appendix A presents an algorithm for determining the orthogonal components of the main spacecraft velocity vector using three ESs. The output results of the presented algorithm are the components of the velocity vector of the main spacecraft

at time t ₀ . The subsystem for determining the coordinates of the main spacecraft x ₁ y ₁ , z ₁ at the time t ₀ contains the NRTS K, the adjacent spacecraft S ₂ with the known coordinates x ₂ , y ₂ , z ₂ at the time t ₀ and N≥3 of the selected ES I _n , n = 1 ... N (see Fig. 3) at positions with known coordinates

emitting radio signals in the direction of the main S ₁ and adjacent spacecraft S ₂ .

- расстояние между основным КА S₁ и первой ЗС I₁;

- расстояние между основным КА S₁ и НРСТ K;

- расстояние между смежным КА S₂ и первой ЗС I₁;

- расстояние между смежным КА S₂ и НРСТ K.FIG. 3 introduced the following designations:

- the distance between the main spacecraft S ₁ and the first _{ES I 1} ;

- the distance between the main spacecraft S ₁ and NRST K;

- the distance between the adjacent spacecraft S ₂ and the first _{ES I 1} ;

is the distance between the adjacent spacecraft S ₂ and NRST K.

- расстояние между основным КА S₁ и n-й ЗС I_n;

- расстояние между смежным КА S₂ и n-й ЗС I_n.For each n-th ES it is possible to enter the designations:

- the distance between the main spacecraft S ₁ and the n-th ES I _n ;

- the distance between the adjacent spacecraft S ₂ and the n-th ES I _n .

FIG. 3 shows three ES as the minimum required number of ES for unambiguous one-step determination of the coordinates of the main spacecraft x ₁ , y ₁ , z ₁ according to the proposed method.

The fundamental premise of the present invention is the presence, in addition to the main spacecraft S ₁ , through which a communication channel between earth stations is organized, an adjacent spacecraft S ₂ , which is capable of retransmitting the same radio emissions as the main spacecraft, but with greater attenuation and a different transfer frequency. Thus, it is possible to obtain, due to the correlation processing of radio signals, the value of time delays Δt _n between the radio signals received from the main S ₁ and the adjacent spacecraft S ₂ for each of the selected ES I _n .

и

траекторий

[6] для каждой n-й ЗС.To determine the coordinates of the main spacecraft x ₁ , y ₁ , z ₁ at time t ₀ , time delays Δt _{n are used} , due to the difference in lengths

and

trajectories

[6] for each n-th ES.

траекторий I_nS₂K рассчитывают длины

траекторий I_nS₁K.Based on measured time delays Δt _n and calculated lengths

trajectories I _n S ₂ K calculate the lengths

trajectories I _n S ₁ K.

траекторий I_nS₁K ставят в соответствие поверхность положения (ПП) которая является поверхностью второго порядка - эллипсоидом вращения с фокусами, совпадающими с НРТС K и ЗС I_n соответственно.Each of the lengths

trajectories I _n S ₁ K put in correspondence the surface of position (PP) which is a surface of the second order - an ellipsoid of revolution with foci coinciding with the NRTS K and ZS I _n, respectively.

The coordinates of the intersection point of at least three PPs correspond to the required spacecraft coordinates x ₁ , y ₁ , z ₁ at time t ₀ . Thus, for an unambiguous one-time determination of the coordinates of the main spacecraft x ₁ , y ₁ , z _1, it is necessary to have at least three ZP I _n . A further increase in the number of ES will lead to an increase in the accuracy of determining the coordinates of the spacecraft x ₁ , y ₁ , z ₁ .

As an example, Appendix B presents an algorithm for determining the coordinates of the main spacecraft x ₁ , y ₁ and z ₁ using three ES F ₁ ... F ₁₁ . The output results of the presented algorithm are the coordinates of the main spacecraft x ₁ , y ₁ , z ₁ at time t ₀ .

и смежного КА

а также диапазонов частот ЗС F₅…F₁₂, расположенных в районах зон покрытия основного КА

и смежного КА

По оси абсцисс на фиг. 5 отложены частоты f, по оси ординат - амплитуды А.FIG. 5, as an example, a scheme for selecting an ES is presented, taking into account the frequency ranges on the "up" link of the main SC.

and adjacent spacecraft

as well as the frequency ranges of the ZS F ₅ ... F ₁₂ located in the areas of coverage of the main spacecraft

and adjacent spacecraft

The abscissa in FIG. 5 shows the frequencies f, along the ordinate - the amplitudes A.

входят диапазоны частот ЗС F₁…F₁₁, а в диапазон частот на линии "вверх" смежного КА

входят диапазоны частот F₅…F₁₂ ЗС. Таким образом, одновременно в диапазоны частот на линии "вверх" основного КА

и смежного КА

входят диапазоны частот ЗС F₅…F₁₁. На схеме (фиг. 5) введены обозначения указанных ЗС - I₁…I₇, а также значений номиналов их излучаемых частот - f₁…f₇.Analysis of the circuit (Fig. 5) shows that in the frequency range on the "up" link of the main SC

includes the frequency ranges of the ZS F ₁ ... F ₁₁ , and the frequency range on the "up" line of the adjacent spacecraft

includes the frequency ranges F ₅ … F ₁₂ ЗС. Thus, simultaneously in the frequency ranges on the "up" line of the main spacecraft

and adjacent spacecraft

includes the frequency ranges ЗС F ₅ … F ₁₁ . The diagram (Fig. 5) introduces the designations of the indicated ZS - I ₁ ... I ₇ , as well as the values of the nominal values of their radiated frequencies - f ₁ ... f ₇ .

FIG. 6, as an example, a scheme for selecting an ES is presented, taking into account the coverage areas of the main Ω ₁ and adjacent spacecraft Ω ₂ .

Analysis of the circuit (Fig. 6) shows that in the coverage area of the main spacecraft Ω _{1 there} are _{ES I 1} , I ₂ , I ₃ , I ₄ and I ₆ , and in the coverage area of the adjacent spacecraft Q. _{2 there} are _{ES I 1} , I ₂ , I ₃ , I ₄ and I ₇ . Thus, at the same time in the coverage areas of the main Ω ₁ and the adjacent spacecraft Ω _{2 there} are _{ES I 1} , I ₂ , I ₃ and I ₄ .

When choosing an ES, the topology of the location of all ES I _{n is} taken into account, on which the accuracy of determining the coordinates x ₁ , y ₁ , z ₁ and the orthogonal components of the spacecraft velocity vector depends

между n-й и m-й ЗС, где m=I…N, m≠n, которые должны быть максимальными.The topology of the ZP I _n location is understood as their relative position on the Earth's surface. At the same time, mutual distances are important indicators when choosing an ES.

between the n-th and m-th ES, where m = I… N, m ≠ n, which should be maximum.

выбирают ЗС I₁, I₂ и I₃.Comparing FIG. 5 and FIG. 6 to determine the coordinates x ₁ , y ₁ , z ₁ and the orthogonal components of the spacecraft velocity vector

select ЗС I ₁ , I ₂ and I ₃ .

были максимальными.FIG. 7, as an example, the topology diagrams of the arrangement of three ESs I ₁ , I ₂ and I _{3 are} presented. The indicated ES were chosen so that the mutual distances

were maximum.

в 5…10 раз, а также повышения точности определения координат х₁, у₁, z₁ и ортогональных составляющих вектора скорости КА

по сравнению со способом прототипом на 10…20%.Simulation modeling based on computer programs [7, 8] of the claimed methods has shown the possibility of reducing the time for determining the coordinates x ₁ , y ₁ , z ₁ and orthogonal components of the spacecraft velocity vector

5 ... 10 times, as well as increasing the accuracy of determining the coordinates x ₁ , y ₁ , z ₁ and orthogonal components of the spacecraft velocity vector

in comparison with the prototype method by 10 ... 20%.

Information sources

1. Agievich S.N., Bespalov V.L., Dedovskaya E.G., Matyukhin A.S., Podyachev P.A., Sevidov V.V. Method for determining the orbit parameters of an artificial Earth satellite using receiving reference reference stations. Patent No. 2702098 IPC G01S 5/00 (2006.01). Bul. No. 28 dated 10/04/19. Application No. 2018127491 dated 25.07.18.

2. Agievich S.N., Vatutin V.M., Matyukhin A.S., Modin M.I., Sevidov V.V. A method for determining the orbit parameters of an artificial Earth satellite using transceiving reference reference stations. Patent No. 2708883. IPC G01S 5/00 (2006.01). Bul. No. 35 dated 12.12.19. Application No. 2018134855 dated 01.10.18.

3. Balabanov V.V., Bespalov V.L., Kelyan A.Kh., Ponomarev A.A., Sevidov V.V., Chemarov A.O. A method for determining the parameters of the orbit of an artificial earth satellite. Invention patent No. 2652603, publ. 04/27/2018 Bul. No. 12.

4. Mashbits L.M. Computer cartography and satellite communication zones, - 2nd ed., Revised and enlarged. - M .: Hot line - Telecom, 2009 .-- 236 p.

5. Volkov R.V., Malyshev S.R., Simonov A.N., Sevidov V.V. Determination of the canonical parameters of relay satellites by radio signals of reference reference stations. Proceedings of the V.V. A.F. Mozhaisky. 2016. Issue. 655.S. 88-92.

6. Volkov R.V., Sayapin V.N., Sevidov V.V. Model for measuring the time delay and frequency shift of the radio signal received from the relay satellite when determining the location of the earth station // T-Comm: Telecommunications and transport. 2016. Volume 10. No. 9. S. 14-18.

7. Volkov R.V., Sayapin V.N., Sevidov V.V. Model of motion of an artificial Earth satellite // Computer programs. Database. Topologies of integrated circuits. 2016. No. 2. P. 112.

8. Sevidov V.V. Determination of coordinates and parameters of motion of a radio emission source on the basis of difference-time and difference-Doppler measurements // Computer programs. Database. Topologies of integrated circuits. 2015. No. 11. P. 2.

Appendix A

Algorithm for determining the orthogonal components of the velocity vector of the main spacecraft using three ES

возможно использовать НРТС K, смежный КА S₂ с известными координатами х₂, у₂, z₂, и ортогональными составляющими вектора скорости

в момент времени t₀, а также не менее трех выбранных ЗС I_n, (см. фиг. 1), размещенных на позициях с известными координатами

излучающие радиосигналы в направлении основного и смежного КА.To determine the orthogonal components of the velocity vector of the main spacecraft

it is possible to use NRTS K, adjacent spacecraft S ₂ with known coordinates x ₂ , y ₂ , z ₂ , and orthogonal components of the velocity vector

at time t ₀ , as well as at least three selected ZS I _n , (see Fig. 1), located at positions with known coordinates

emitting radio signals in the direction of the main and adjacent spacecraft.

As an example, this appendix presents a variant with three ES (n = 1 ... 3) as the minimum required number of ES for unambiguous one-step determination of the velocity vector of the main SC

It is assumed that the coordinates of the main spacecraft x ₁ , y ₁ , z ₁ are calculated in accordance with the algorithm presented in Appendix A.

принятых радиосигналов n-х ЗС I_n после их ретрансляции основным и смежным КА.Using the correlation processing of radio signals in the NRTS K, the values of the nominal frequencies are measured

of the received radio signals of the n-th ES I _n after their retransmission by the main and adjacent spacecraft.

справедливы аналитические выражения:For frequency ratings

the analytical expressions are valid:

where f _n - values of the nominal frequencies emitted by each n-th ES I _n ;

- доплеровские сдвиги частот на входе основного и смежного КА соответственно за счет его сближения (удаления) с (от) n-й ЗС I_n;

- Doppler frequency shifts at the input of the main and adjacent spacecraft, respectively, due to its approach (removal) with (from) the n-th ES I _n ;

- заданные частоты сдвига рабочих частот основного и смежного КА соответственно;

- доплеровские сдвиги частот на выходе основного и смежного КА соответственно за счет его сближения (удаления) с (от) НРТС K.

- the specified frequencies of the shift of the operating frequencies of the main and adjacent spacecraft, respectively;

- Doppler frequency shifts at the output of the main and adjacent spacecraft, respectively, due to its approach (removal) with (from) the NRTS K.

It is assumed that the instability of the spacecraft frequency generator is known and compensated. The influence of other effects on the change in frequency, for example, gravitational and relativistic effects in the framework of the considered problem, is negligible and therefore is not taken into account.

с использованием трех ЗС разработан алгоритм, схема которого представлена на фиг. 2.To calculate the orthogonal components of the main spacecraft velocity vector

using three ESs, an algorithm was developed, the diagram of which is shown in Fig. 2.

смежного КА S₂ в момент времени t₀, координаты трех ЗС

значения частот сдвига рабочих частот

основного и смежного КА соответственно; значения номиналов частот

принятых радиосигналов n-х ЗС I_n после их ретрансляции основным и смежным КА соответственно.At stage 1, the initial data are entered, which are: the time of measurement t ₀ , the coordinates of the NRTS x _K , y _K , z _K ; coordinates of the main spacecraft x ₁ , y ₁ and z ₁ ; coordinates х ₂ , y ₂ , z ₂ and orthogonal components of the velocity vector

adjacent spacecraft S ₂ at time t ₀ , coordinates of three ES

frequency shift of operating frequencies

main and adjacent spacecraft, respectively; frequency ratings

of the received radio signals of the n-th ES I _n after their retransmission by the main and adjacent spacecraft, respectively.

смежного КА S₂ относительно каждой из n-й ЗС I_n и НРТС К соответственно. Для значений радиальных скоростей

смежного КА S₂ возможно записать формулы:At stage 2, the values of the radial velocities are calculated

adjacent spacecraft S ₂ relative to each of the n-th _{ES I n} and NRTS K, respectively. For values of radial velocities

adjacent spacecraft S _2, it is possible to write down the formulas:

According to the theorem on the scalar product of vectors [6], the following equalities hold:

равен:Modulus of the velocity vector of the adjacent spacecraft

is equal to:

and the distances from and n-th ES and NRTS to the adjacent spacecraft are calculated as

Equations (B.3) and (B.4) taking into account (B.5) ... (B.9) are converted to the form:

At stage 3, the values of the nominal frequencies f _n emitted by each n-th ES I _{n are} calculated.

и на выходе

смежного КА S₂ за счет его сближения (удаления) с (от) n-й ЗС I_n и НРТС K возможно представить в виде:Doppler input frequency shifts

and at the exit

adjacent spacecraft S ₂ due to its approach (removal) with (from) the n-th _{ES I n} and NRTS K can be represented in the form:

To calculate the values of the nominal frequencies emitted by each of the ES f _n expressions (A.2), taking into account equations (A.10) and (A.11), are converted to the form:

от и n-х ЗС I_n и НРТС K до основного КА S₁ по формулам:Step 4 calculates distances

from and n-x ЗС I _n and НРТС K to the main spacecraft S ₁ according to the formulas:

At step 5, the orthogonal components of the velocity vector of the main spacecraft are calculated

и на выходе

основного КА S₁ за счет его сближения (удаления) с (от) n-й ЗС I_n и НРТС K возможно представить в виде:Doppler input frequency shifts

and at the exit

the main spacecraft S ₁ due to its approach (removal) with (from) the n-th _{ES I n} and NRTS K can be represented as:

основного КА S₁ возможно записать формулы:For values of radial velocities

of the main spacecraft S ₁ it is possible to write down the formulas:

According to the theorem on the scalar product of vectors [6], the following equalities hold:

равен:The module of the velocity vector of the main spacecraft

is equal to:

Equations (A.14) and (A.15) taking into account (A.12), (A.13), (A.16) ... (A.20) are converted to the form:

Expressions (A.1), taking into account equations (A.12) ... (A.22) for a particular case, when n = 1 ... 3, are converted into a system of linear equations:

where the coefficients of the variables and the free terms are equal:

The system of three linear equations with three unknowns (A.23) is solved by one of the known methods, for example, the Cramer method. The result of solving the system of equations (A.23) are the orthogonal components of the velocity vector of the main spacecraft

в момент времени t₀.At step 6, the results are output, which are the orthogonal components of the velocity vector of the main spacecraft

at time t ₀ .

остается прежним, с той лишь разницей, что система уравнений (А.23) будет содержать более трех уравнений. Тогда такую систему уравнений решают, например, методом наименьших квадратов.In the general case, when the number of ES N> 3, the algorithm for determining the orthogonal components of the spacecraft velocity vector

remains the same, with the only difference that the system of equations (A.23) will contain more than three equations. Then such a system of equations is solved, for example, by the least squares method.

Appendix B

Algorithm for determining the coordinates of the main spacecraft using three ES

основан на том, что каждой из временных задержек Δt_n соответствует разности длин

траекторий

Algorithm for determining the coordinates of the main spacecraft x ₁ , y ₁ , z ₁ using the ES I _n , where n-1 ... N is the number of the ES, N≥3 located at positions with known coordinates

is based on the fact that each of the time delays Δt _n corresponds to the difference in lengths

trajectories

As an example, this appendix presents a variant with three ES (n = 1 ... 3) as the minimum required quantity for unambiguous one-time determination of the coordinates of the main spacecraft x ₁ , y ₁ , z ₁

траекторий I_nS₂K вычисляют по формулам:Lengths

trajectories I _n S ₂ K are calculated by the formulas:

траекторий I_nS₂K, а также измеренные временные задержки Δt_n рассчитывают длины

траекторий I_nS₁K:Using lengths

trajectories I _n S ₂ K, as well as the measured time delays Δt _n, calculate the lengths

trajectories I _n S ₁ K:

where c = 3 × 10 ⁸ m / s is the speed of light in vacuum.

траекторий I_nS₁K ставят в соответствие поверхность положения (ПП) основного КА S₁, которая является поверхностью второго порядка - эллипсоидом вращения с фокусами, совпадающими с НРТС K и ЗС I_n соответственно.Each of the lengths

trajectories I _n S ₁ K put in correspondence the surface of position (PP) of the main spacecraft S ₁ , which is a surface of the second order - an ellipsoid of revolution with foci coinciding with NRTS K and ZS I _n, respectively.

The coordinates of the point of intersection of the three PPs correspond to the sought coordinates of the main spacecraft x ₁ , y ₁ , z ₁ at time t ₀ . Thus, for an unambiguous one-time determination of the coordinates of the main spacecraft x ₁ , y ₁ , z ₁ , at least three ES are required.

To calculate the spacecraft coordinates x ₁ , y ₁ , z ₁ using three ES, an algorithm was developed, the diagram of which is shown in Fig. four.

и

временные задержки между радиосигналами принятыми от основного и смежного КА для каждой из выбранных ЗС

порог точности δ₀ расчета координат основного КА.At stage 1, the initial data are entered, which are: the time of measurement t ₀ ; coordinates of NRTS x _K , y _K , z _K coordinates of the adjacent spacecraft x ₂ , y ₂ , z ₂ ; coordinates of three ES

and

time delays between radio signals received from the main and adjacent spacecraft for each of the selected ES

accuracy threshold δ ₀ for calculating the coordinates of the main spacecraft.

траекторий I_nS₁K по формулам (Б.1, Б.2).Stage 2 calculates the lengths

trajectories I _n S ₁ K according to formulas (B.1, B.2).

как первое приближение к координатам основного КА.At stage 3, based on the elements of the Kepler orbit of the main spacecraft, the coordinates of the reference point are selected

as the first approximation to the coordinates of the main spacecraft.

траекторий

при условии равенства координат основного КА координатам опорной точки

по формулам:In step 4, the lengths are calculated

trajectories

provided that the coordinates of the main spacecraft are equal to the coordinates of the reference point

by the formulas:

- расстояния от опорной точки

до n-й ЗС I_n,

- расстояние от опорной точки

до НРТС K,Where

- distance from the reference point

to the n-th ЗС I _n ,

- distance from reference point

to NRTS K,

в свою очередь рассчитываются по формулам:Distances

in turn are calculated by the formulas:

траекторий

и длинами

траекторий I_nS₁K, определенными на этапе 2 соответственно:At step 5, the residuals k ₁ , k ₂ and k ₃ are calculated as the differences between the lengths determined at step 4

trajectories

and lengths

trajectories I _n S ₁ K determined at stage 2, respectively:

At stage 6, corrections to the coordinates of the main spacecraft Δх ₁ , Δу ₁ , Δz _{1 are} determined.

с точностью до первых членов:To determine the corrections to the coordinates of the main spacecraft Δx ₁ , Δу ₁ , Δz ₁ , a system of linear equations is preliminarily formed when the functions are expanded in the Taylor series

up to the first terms:

where partial derivatives are calculated according to the expressions

Solving the system of linear equations (B.3) using one of the known methods, for example, the Cramer method, corrections to the coordinates of the main spacecraft Δх ₁ , Δу ₁ , Δz ₁ are obtained.

At step 7, the coordinates of the new reference point are calculated

Steps 4-7 collectively make up the first iteration. Then the iterations are repeated, each time using a new reference point obtained at the previous iteration. The number of required iterations depends on the required accuracy of determining the spacecraft coordinates. _{The iteration step d w} is directly related to the accuracy of determining the spacecraft coordinates.

At step 8, the iteration step d _w is determined as the distance between the current and previous reference points:

At stage 8, d _{w is} compared with the threshold δ ₀ set at stage 1.

The required number of iterations, as a rule, is 2 ... 4. The coordinates of the main spacecraft x ₁ , y ₁ and z ₁ are selected as the coordinates of the reference point at the last iteration, the output of which is carried out at step 10.

In the general case, when the number of ES N> 3, the algorithm for determining the coordinates of the main spacecraft remains the same, with the only difference that the system of equations (B.3) will contain more than three equations. Then such a system of equations is solved, for example, by the least squares method.

Claims (4)

1. A method for determining the orthogonal components of the velocity vector of a spacecraft (SC) using earth stations (ES), which consists in placing a ground radio technical station (NRTS) K at a position with known coordinates x _K , y _K , z _K , take in time t ₀ using NRTS K radio signals transmitted by reference reference stations (OPC) and relayed by the main spacecraft S ₁ calculate the coordinates x ₁ , y ₁ , z _{1 of the} main spacecraft S ₁ at time t ₀ , based on the frequency shifts of radio signals, known coordinates of NRST and ORS, a predetermined frequency of the shift of the operating frequency of the main spacecraft

calculate the orthogonal components of the velocity vector of the main spacecraft

at time t ₀ , characterized in that the adjacent spacecraft S ₂ with known values of coordinates x ₂ , y ₂ , z ₂ and orthogonal components of the velocity vector is additionally selected

at time t ₀ and a given shift frequency

operating frequency, and the selected ES I _n are used as the OPC, located on the earth's surface at positions with known coordinates

, where n = 1 ... N is the number of the ES, N≥3, the coordinates of the main SC x ₁ , y ₁ , z ₁ are calculated, for each n-th ES I _{n is} measured in the NRTS K due to the correlation processing of radio signals the values of the nominal frequencies

of received radio signals after their retransmission by the main spacecraft S ₁ and adjacent spacecraft S _2, respectively, based on the known coordinates of the NRTS x _K , y _K , z _K , coordinates x ₂ , y ₂ , z ₂ and orthogonal components of the velocity vector

adjacent spacecraft S ₂ at time t ₀ , coordinates of at least three ES

calculate the values of radial velocities

adjacent spacecraft S ₂ relative to each of the n-th _{ES I n} and NRTS K, respectively, using the measured values of the nominal frequencies

of the received radio signals of the n-th ES after their retransmission by the adjacent spacecraft S ₂ , the calculated Doppler frequency shifts at the input

and at the exit

adjacent spacecraft S ₂ due to its approach or removal from or from the n-th _{ES I n} and NRTS K, the given frequency of the shift of the operating frequency of the adjacent spacecraft

calculate the values \ u200b \ u200bof the nominal frequencies emitted by each n-th ES f _n , based on the known coordinates of the NRTS x _K , y _K , z _K , the coordinates of the ES

and the calculated coordinates of the main spacecraft x ₁ , y ₁ , z ₁ at time t _{0, the} distances are calculated

from and n-th _{ES I n} and NRTS K to the main SC S ₁ , and the orthogonal components of the velocity vector of the main SC

calculated by the known coordinates of the NRTS x _K , y _K , z _K , the coordinates of the ZS

and the coordinates of the adjacent spacecraft x ₂ , y ₂ , z ₂ , the known orthogonal components of the velocity vector of the adjacent spacecraft

the given frequency of the shift of the operating frequency of the main spacecraft

the calculated values of the nominal frequencies emitted by each n-th ES f _n , distances

from and n-x ЗС I _n and НРТС К to the main spacecraft. 2. The method according to claim 1, characterized in that the adjacent spacecraft S _{2 is} selected such that its frequency range on the uplink

had the same sections with the frequency range on the "up" line of the main spacecraft

and the coverage area of the adjacent spacecraft Ω ₂ intersects with the coverage area of the main spacecraft Ω ₁ . 3. The method according to claim 1, characterized in that such ES I _n are selected, the values of the nominal values of the radiated frequencies f _{n of} which are included in the frequency ranges on the uplink of the main spacecraft

and adjacent spacecraft

and each ES I _n must be located in the coverage areas of both the main spacecraft Ω ₁ and the adjacent spacecraft Ω ₂ , while the mutual distances

between the n-th and m-th ES, where m = 1… N, m ≠ n are maximum. 4. A method for determining the coordinates of a spacecraft (SC) using earth stations (ES), which consists in placing a ground radio technical station (NRTS) K at a position with known coordinates x _K , y _K , z _K , select the initial values of the orbit parameters of the main spacecraft S ₁ , receive at time t ₀ using the NRTS K radio signals transmitted by reference reference stations (OPC) and relayed by the main spacecraft S ₁ , based on the time delays of the radio signals of the system, the coordinates of the main spacecraft x ₁ , y ₁ , z _{1 are calculated} time t ₀ , characterized in that the adjacent spacecraft S ₂ with known coordinates x ₂ , y ₂ , z ₂ at the time t _{0 is} additionally selected, and the selected earth stations (ES) I _n located on the earth's surface are used as the OPC at positions with known coordinates

where n = 1 ... N is the number of the ES, N≥3, for each n-th ES I _{n is} measured in the NRTS due to the correlation processing of radio signals the values of the time delay Δt _n between the received radio signals after their retransmission by the main and adjacent spacecraft, respectively, N values are calculated lengths

trajectories I _n S ₂ K based on the known coordinates of the ES

adjacent spacecraft x ₂ , y ₂ , z ₂ and NRTS x _K , y _K , z _K , using the lengths,

trajectories I _n S ₂ K, as well as the measured time delays Δt _n, calculate the lengths

trajectories I _n S ₁ K, the coordinates of the main spacecraft x ₁ , y ₁ , z _{1 are} calculated based on the calculated lengths

trajectories I _n S ₁ K, known coordinates of the NRTS x _K , y _K , z _K , ЗС

and adjacent spacecraft x ₂ , y ₂ , z ₂ .

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