RU2679890C1 - Method for determining location of user terminal by means of a satellite-repeater in a low near-earth orbit - Google Patents

Abstract

FIELD: radio engineering and communications.SUBSTANCE: invention relates to radio engineering, and in particular to methods for determining the location of radio frequency source (RFS), and can be used in navigation, direction-finding, location means for determining the location of a user terminal (UT) using radio signals received from a satellite transponder (ST) at low near-earth orbit. Method is based on the location of the complex electronic monitoring (CEM) and M≥2 emitting reference benchmark (ERBM) at positions with known coordinates, specifying the area of radio monitoring (ARM), radiation with the help of CEM equipment and m-s, where m=1…M, ERBM test radio signals at times t, where n=1…N, N≥3, receiving in a CEM of said test radio signals after their retransmission of ST, determining canonical parameters of ST at time t, choosing a sphere with a radius calculated on the basis of the average latitude of the ARM as the surface of the earth, and then determining the location of UT on the surface of the earth.EFFECT: improving the accuracy of determining frequency shifts of system signals.1 cl, 5 dwg

Description

The method relates to radio engineering, and in particular to methods for determining the location of radio emission sources, and can be used to determine the location of a satellite communications subscriber terminal (AT) by receiving and processing their signals from a relay satellite in low Earth orbit (CP).

,

, координат узла межсетевого сопряжения (УМС) и предварительно заданных частот конвертирования

,

рабочих частот СР₁ СР₂, вычисляют широту ϕ_ПТ и долготу λ_ПТ пользовательского терминала (ПТ).A known method for determining the location of a user terminal using two satellite transponders [1]. This method consists in the fact that based on measurements of time delays and frequency shifts between transmitted and received test signals of the system, taking into account the known coordinates of the first and second satellite repeaters CP ₁ , CP ₂ , and their velocity vectors

,

coordinates of the gateway node (UMC) and predefined conversion frequencies

,

operating frequencies CP ₁ CP ₂ , calculate the latitude ϕ _PT and longitude λ _PT user terminal (PT).

To implement the specified known method, the following steps are performed:

между первым CP₁ и ПТ;determine the distance

between the first CP ₁ and PT;

между вторым СР₂ и ПТ;determine the distance

between the second CP ₂ and PT;

, азимут α_ПТ вектора скорости пользовательского терминала и его высоту h_ПТ относительно земной поверхности;measure modulus

, azimuth α _PT of the user terminal velocity vector and its height h _PT relative to the earth's surface;

и

первого и второго узкополосных тестовых сигналов, обусловленные радиальными скоростями ПТ относительно CP₁ и СР₂, для чего предварительно определяют вероятные местоположения ПТ с учетом известных координат CP₁, СР₂ и определенных параметров

и

;Doppler frequency shifts are calculated in the UMC

and

the first and second narrow-band test signals due to the radial speeds of the PT relative to CP ₁ and CP ₂ , for which the probable locations of the PT are preliminarily determined taking into account the known coordinates of CP ₁ , CP ₂ and certain parameters

and

;

перемещения первого CP₁ относительно ПТ, и/или радиальную скорость

перемещения второго СР₂ относительно ПТ, с учетом доплеровских сдвигов частот

и

;determine at least one of the parameters: radial velocity

the movement of the first CP ₁ relative to the PT, and / or radial velocity

the movement of the second SR ₂ relative to the PT, taking into account Doppler frequency shifts

and

;

calculate the latitude ϕ _PT and longitude λ _PT PT.

The disadvantages of the method for determining the location of vehicles using two satellite transponders [1] are:

a long time for determining the coordinates of the ES, associated with the need for additional measurements of the module, the azimuth of the velocity vector of the PT and its height relative to the earth’s surface,

the need for reciprocal transmission of test signals from the PT, whose coordinates must be determined in the UMC through SR.

A known method for determining the location of an earth station for satellite communications [2], which consists in the fact that the coordinates of the earth station (AP) are determined based on an analysis of the propagation conditions of radio waves on the path ZS-SR. The fall in signal level is associated with attenuation during the passage of the ZS-SR route through the areas of volumetric distributed hydrometeors (OORG). Identify the similarity of fading amplitude between the desired and at least one of the reference ZS.

To implement the specified known method, the following steps are performed:

receive and measure the parameters of the relayed signals of earth stations (APs) of satellite communications at a satellite radio monitoring station (SSRK), at discrete points in time;

measure the levels of relayed signals from satellite reference earth stations (OSS) simultaneously operating through CP with known geographical coordinates and the desired ES;

register the measurement results in the form of sequences of discrete samples equal to the signal levels;

using a visual analysis of these dependencies, long-term cyclic repetitions of a drop in the signal level against the background of short-lived high-frequency components are revealed;

they associate the decrease in the level of signals with their attenuation during the passage of the ZS-SR routes through the OORG regions;

identify the similarity of signal level drops between the desired ES and at least one of the OZS;

The reason for this similarity is considered the passage of the tracks ZS-SR and OZS-SR through the same area of OORG with a limited size of the occupied space;

as a condition for the passage of different ZS-SR routes through the OORG with such characteristics, they take the territorial proximity of the ZS and OZS;

determine by binding to the geographic coordinates of the identified OZS the region of the most probable location of the desired AP;

carry out the final search and localization of the desired ES with respect to the identified OZS in the radius of the horizontal extent of the projection of the local homogeneous OORG on Earth.

The disadvantages of the method for determining the location of the satellite earth station [2] include:

a long time of determining the coordinates of the surroundings associated with the need for multiple measurements of the levels of relayed signals of the surroundings and many OZS, the search for probable OORG and mutual comparison of the measurement results;

the high cost of the device that implements the method, due to the need to place additional transmitters, receivers, as well as information processing equipment, on board the navigation CPs.

Of the known methods, the closest analogue (prototype) of the proposed method according to the technical essence is the method of determining the location using one satellite in low Earth orbit [3]. To implement this method, the following steps are performed sequentially:

measuring in AT the frequency of the first signal received from the nodal station (US) through CP;

send the result of measuring the frequency of the first signal to the CSS;

transmit the second signal from AT to the UE via CP;

measure in US the frequency of the second signal received from AT through CP;

the delay at the double passage of the signal transmitted from the UE to the AT through the CP and retransmitted from AT to the US through the CP is measured at the nodal station;

determine the range parameter - the distance between CP and AT;

dividing the frequency of the first signal by the nominal frequency of the first signal to obtain the first ratio, dividing the frequency of the second signal by the nominal frequency of the second signal to obtain the second ratio, and multiplying the sum of the first and second relations by half the speed of light;

determine the rate of change of range - the radial speed between CP and AT;

determine the location of AT on the surface of the Earth based on the known position and speed of CP, the mentioned range parameter and the rate of change of range.

The disadvantages of the prototype method are:

relatively low accuracy of determining the coordinates of AT;

the need for response transmission of test signals from AT, whose coordinates must be determined in the CRM through SR.

The aim of the invention is to develop a method for determining the location of AT using CP in low Earth orbit, providing higher accuracy in determining the coordinates of AT due to a more accurate determination of the frequency shifts of the signals of the system and at the same time eliminating the need for reciprocal transmission of test signals from AT.

в направлении на CP в момент времени t₁, измерение в КРМ НСЧ радиосигнала

, принятого от AT через CP в момент времени t₁, вычисление местоположения AT на поверхности земли на основании известных координат КРМ x_K, y_K, z_K, номинала частоты конвертирования /с, запомненных НСЧ

и

переданного тестового радиосигнала и принятого от AT через CP радиосигнала в момент времени t₁, дополнительно устанавливают на земной поверхности М≥2 излучающих опорных реперных станции (ИОРС) на позициях с известными координатами x_Im, y_Im, z_Im, где m=1…М - номер ИОРС.This goal is achieved by the fact that in the known method for determining the location of AT using CP in low Earth orbit, it includes: placing an ASM containing receiving and transmitting equipment at positions with known coordinates x _K , y _K , z _K , selecting electronic monitoring object CP with a known nominal frequency of conversion ƒ _G , radiation using the CRM equipment of a test radio signal with a nominal frequency of medium frequency (LF)

in the direction of CP at time t ₁ , the measurement in the CRM of the LSS of the radio signal

received from AT via CP at time t ₁ , calculating the location of AT on the earth’s surface based on the known coordinates of the RCM x _K , y _K , z _K , the nominal frequency of conversion / s, memorized NSC

and

The transmitted test radio signal and the radio signal received from AT via CP at time t ₁ are additionally installed on the Earth’s surface M≥2 of radiating reference reference stations (IORS) at positions with known coordinates x _Im , y _Im , z _Im , where m = 1 ... M - IORS number.

To select CP as the object of electronic monitoring, the radio monitoring area (RRM) is preliminarily set as the area on the surface of the earth in which it is necessary to determine the location of AT and the nth time instants t _n are chosen, where n = 1 ... N, N≥3, in which the illumination zone of the specified CP covers both the CRM, and the PBPM, and the positions of all M IORS.

,

,

и ортогональные составляющие вектора его скорости

,

,

на основе излучения тестовых сигналов КРМ и m-ми ИОРС в моменты времени t_n в направлении на CP и их последующего приема КРМ после переизлучения указанным CP,Determine the nth canonical parameters (CP) of CP including coordinates of CP

,

,

and orthogonal components of its velocity vector

,

,

based on the radiation of the test signals of the CRM and m IORS at times t _n in the direction of the CP and their subsequent reception of the CRM after re-emission of the specified CP,

, принятых от AT через CP в моменты времени t_n', где n'=2…N.Measured in the CRM of the NSC of the radio signals

received from AT via CP at times t _{n '} , where n' = 2 ... N.

Allocate as the reference g-e, where g = 1, ..., N KP CP for time t _g .

, где

,

.Form N-1 different from each other pairs of CP CP, in each of which the first CP CP correspond to time t _g , and the second CP CP correspond to time

where

,

.

для каждой сформированной пары КП CP на основе g-x и

КП CP, координат КРМ x_K, y_K, z_K, номинала частоты конвертирования ƒ_G, НСЧ радиосигналов

,

принятых от AT через CP в моменты времени t_g и

соответственно.Calculate N-1 radial velocity differences

for each formed pair of CP CPs based on gx and

CP CP, KPM coordinates x _K , y _K , z _K , nominal frequency of conversion ƒ _G , LF of radio signals

,

received from AT via CP at time t _g and

respectively.

, который рассчитывается на основе средней широты РВРМ ϕ_A.As the surface of the earth take a sphere with a radius

, which is calculated based on the average latitude of the PBPM ϕ _A.

и радиуса сферы поверхности земли

.The location of ATs on the surface of the earth is determined using n-th CP CP, N-1 radial velocity differences

and the radius of the sphere of the earth’s surface

.

To determine the n-th CP CP at time t _n , additionally perform the following procedures below.

в направлении на CP в моменты времени t_n'.Test signals from the low-frequency range are emitted using the KRM equipment

towards CP at time t _{n '} .

в направлении на CP в моменты времени t_n.Test signals from the LF emit m-mi IORS

towards CP at time t _n .

и

в моменты времени

и

соответственно.Receive re-emitted CP test signals from the NSC using Raman

and

at times

and

respectively.

от m-х ИОРС.Transmit test radio signals to the NSC

from m IORS.

,

между излученными и принятыми тестовыми радиосигналами.Time delays are measured.

,

between emitted and received test radio signals.

и до m-х ИОРС

соответствующие моментам времени t_n.Oblique ranges from CP to CRM are calculated.

and up to m-iors

corresponding time instants t _n .

,

,

в моменты времени t_n по известным координатам КРМ и m-х ИОРС, а также измеренным наклонным дальностям

, и

.Calculate CP coordinates

,

,

at time t _n according to the known coordinates of the CRM and m-x IORS, as well as the measured inclined ranges

, and

.

и m-х ИОРС

в моменты времени t_n на основе известных координат КРМ и m-х ИОРС, рассчитанных координат CP

,

,

, а также запомненных НСЧ переданных

,

и принятых

,

тестовых радиосигналов.Measure CP radial velocities relative to CRM

and m-iors

at times t _n based on the known coordinates of the CRM and m-x IORS calculated coordinates CP

,

,

as well as the memorized NSC transmitted

,

and adopted

,

test radio signals.

,

,

в моменты времени t_n используя известные координаты КРМ и m-х ИОРС, вычисленные координаты CP

,

,

и измеренные радиальные скорости

и

.The orthogonal components of the velocity vector CP are calculated

,

,

at time t _n using the known coordinates of the CRM and m-x IORS, the calculated coordinates CP

,

,

and measured radial velocities

and

.

,

,

и ортогональных составляющих вектора его скорости

,

,

в момент времени t_n.As n-x CP CP take the set of coordinates CP

,

,

and orthogonal components of its velocity vector

,

,

at time t _n .

Thanks to the above-mentioned new set of essential features, when using test radio signals M IORS at positions with known coordinates, the aim of the invention is achieved: to ensure high accuracy in determining the coordinates of AT due to more accurate measurement of the frequency shifts of the system signals, and eliminating the need for reciprocal transmission of test signals from AT.

The claimed method is illustrated by drawings, which show:

in FIG. 1 is a typical diagram of conducting radio monitoring for positions CP S ₁ , S ₂ and S _n at time t ₁ t ₂ and t _n ,

,

,

в моменты времени t_n,in FIG. 2 is a diagram of a subsystem for determining coordinates of CP

,

,

at times t _n ,

in FIG. 3 is a diagram of an algorithm for determining the coordinates of CP at times t _n when using two IORS,

in FIG. 4 is a diagram of a subsystem for determining the orthogonal components of the velocity vector CP at time instants t _n ,

figure 5 - the topology of the placement of the CRM and M IORS.

To implement the inventive method for determining the location of AT, one CP is used, and measurements are carried out at time moments t _n , where n = 1 ... N, and N≥3 is the number of the time reference corresponding to the position of CP, at which both CRM, and RRM, and position all M IORS would be in the radio visibility zone (SRV) of the specified SR.

,

и

- расстояния от КРМ до CP,

,

и

- расстояния от AT до CP,

,

,

- векторы скорости CP,

,

,

- радиальные скорости CP относительно КРМ (проекции векторов скорости CP

,

,

на оси

,

и

соответственно),

,

- радиальные скорости CP относительно AT (проекции векторов скорости CP

,

,

на оси

,

и

соответственно) в моменты времени t₁, t₂ и t_N. In FIG. 1 shows a typical radio monitoring system including positions CP S ₁ , S ₂ and S _N at time points t ₁ , t ₂ and t _N , KPM K, AT A. FIG. 1, the following notation is introduced:

,

and

- distance from CRM to CP,

,

and

- distances from AT to CP,

,

,

are the velocity vectors CP,

,

,

- radial velocities of CP relative to CRM (projections of CP velocity vectors

,

,

on axis

,

and

respectively),

,

- radial velocities of CP relative to AT (projections of CP velocity vectors

,

,

on axis

,

and

respectively) at times t ₁ , t ₂ and t _N.

CRM is stationary, its coordinates x _K , y _K , z _K , are considered known.

Assume that the AT is located in a pre-selected PBPM.

The claimed method for determining the location of AT is based on the use of CP CP at various points in time t _n , which imposes requirements on the accuracy of determining these CP CP.

CP flight theory, 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 a first approximation, the CP 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 two-body problem (Earth - CP) in celestial mechanics. This movement is called Kepler’s orbit, as it obeys the three Kepler laws [4].

The advantage of the Kepler’s orbit is the simplicity of calculating the coordinates and the velocity vector CP at the predicted time instants. This predetermined the widespread use of Kepler’s orbit elements. In the present invention, using these elements, CP is selected as the object of electronic electronic monitoring and the moments of time t _n corresponding to the position of CP are selected, at which both the CRM and the PBPM, and the positions of all M IORS would be in the SRV of the specified SR.

In addition, the elements of the Kepler’s orbit CP serve to orient the receiving and transmitting antenna of the CRM, as well as the transmitting antennas of all M IORS to the selected CP when transmitting and receiving test radio signals and receiving AT radio signals relayed by SR.

The disadvantage of the Kepler’s orbit is the relatively low accuracy of determining the coordinates and velocity vector CP, which in most cases is insufficient to implement the claimed method for determining the location of AT using one CP in low Earth orbit.

,

,

и ортогональные составляющие вектора его скорости

,

,

в моменты времени t_n, определяют по радиосигналам ИОРС, размещенных на позициях с известными координатами [5].More precisely, the canonical parameters (CP) of CP, including the coordinates of CP

,

,

and orthogonal components of its velocity vector

,

,

at time t _n , determined by radio signals IORC placed at positions with known coordinates [5].

,

,

и ортогональных составляющих вектора его скорости

,

,

в моменты времени t_n. Эти подсистемы состоят из КРМ и М≥2 ИОРС, размещенных на позициях с известными координатами

,

,

, где m=1…М - номер ИОРС.In FIG. 2 and FIG. 4 shows diagrams of subsystems for determining the coordinate CP

,

,

and orthogonal components of its velocity vector

,

,

at times t _n . These subsystems consist of CRM and M≥2 IORS placed at positions with known coordinates

,

,

where m = 1 ... M is the IORS number.

- расстояния между CP и КРМ,

- расстояния между CP и m-и ИОРС в моменты времени t_n.In FIG. 2 designations introduced:

- the distance between CP and CRM,

- the distance between CP and m-and IORC at time t _n .

- векторы скоростей CP,

- углы между векторами

и направлениями на КРМ,

- углы между векторами

и направлениями на m-ю ИОРС,

-радиальные скорости CP относительно КРМ;

- радиальные скорости CP относительно m-й ИОРС.In FIG. 4, the following notation is introduced:

are the velocity vectors CP,

- angles between vectors

and directions to CRM,

- angles between vectors

and directions to the mth IORS,

- Radial speeds CP relative to CRM;

- radial speeds CP relative to the m-th IORS.

The synchronous operation of the KRM and M IORS transmitters is ensured by the use of timestamps of a highly stable frequency generator.

To determine the CP CP at time t _n use time delays and frequency shifts of test radio signals [6].

и

соответственно. Далее принимают в КРМ переизлученные CP тестовые радиосигналы в моменты времени

и

с НСЧ

и

. Определяют в КРМ задержки во времени

,

между излученными и принятыми тестовыми радиосигналами:At time t _n synchronously emit test radio signals KRM and M IORS with nominal frequencies (LFN)

and

respectively. Next, the re-emitted CP test radio signals are received at the time points in the CRM

and

with NSC

and

. The time delay is determined in the CRM

,

between emitted and received test radio signals:

,

измеряют наклонные дальности от CP до КРМ

и наклонные дальности от CP до каждой из М ИОРС

для каждого момента времени t_n:Based on the received time delays

,

measure inclined ranges from CP to CRM

and slant ranges from CP to each of the M IORS

for each point in time t _n :

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

и

определяют координаты CP

,

,

в моменты времени t_n.Using the resulting slant ranges

and

determine CP coordinates

,

,

at times t _n .

,

,

в каждый момент времени t_n, необходимо и достаточно измерить минимум три наклонные дальности, например,

,

и

, следовательно, конфигурация подсистемы определения координат CP должна включать минимум две ИОРС I₁ и I₂.For simultaneous and unambiguous determination of CP coordinates

,

,

at each moment of time t _n , it is necessary and sufficient to measure at least three slant ranges, for example,

,

and

therefore, the configuration of the CP coordinate subsystem should include at least two IORS I ₁ and I ₂ .

,

,

в моменты времени t_n.As an example, for a special case when the number of IORS is two (M = 2), an analytical interpretation of the CP coordinate determination algorithm is presented in Appendix A

,

,

at times t _n .

A further increase in the number of IORS (M≥3) leads to an increase in the accuracy of determining the coordinates of CP and to a concomitant increase in the total cost of the device that implements the claimed method.

The algorithm for determining CP coordinates when using M≥3 IORS will be similar to the algorithm described in Appendix A, with the only difference being that the system (A.1), compiled in step 6 of Appendix A, will contain M + 1 (more than four) linear equations with three unknowns. Then system (A.1) is solved by one of the known numerical methods, for example, by the least squares method.

,

,

в каждый момент времени t_n, необходимо и достаточно измерить минимум три радиальные скорости, например,

,

и

, следовательно, конфигурация подсистемы определения ортогональных составляющих вектора скорости CP должна включать минимум две ИОРС I_\ и I₂.For the instantaneous and unambiguous determination of the orthogonal components of the velocity vector CP

,

,

at each moment of time t _n , it is necessary and sufficient to measure at least three radial velocities, for example,

,

and

therefore, the configuration of the subsystem for determining the orthogonal components of the velocity vector CP must include at least two IORS I _\ and I ₂ .

,

,

в моменты времени t_n.As an example, for a special case when the number of IORS is equal to two (M = 2), an analytical interpretation of the algorithm for determining the orthogonal components of the velocity vector CP is presented in Appendix B

,

,

at times t _n .

A further increase in the number of IORS (M≥3) leads to an increase in the accuracy of determining the orthogonal components of the velocity vector CP and to a concomitant increase in the total cost of the device that implements the claimed method.

The algorithm for determining the orthogonal components of the velocity vector CP when using M≥3 IORS will be similar to the algorithm described in Appendix B, with the only difference being that the system (B.8) compiled in step 3 of Appendix B will contain M + 1 (more four) linear equations with three unknowns. Then the system (B.8) is solved by one of the known numerical methods, for example, by the least squares method.

,

,

и ортогональные составляющие вектора его скорости

,

,

.As CP CP at time points take the coordinates CP

,

,

and orthogonal components of its velocity vector

,

,

.

, принятых от AT через CP в моменты времени t_n.To determine the location of the AT in the CRM, the LFM of the radio signals is measured

received from AT via CP at times t _n .

It is assumed that AT at times t _n radiates radio signals with a constant LEL equal to ƒ _A in the direction of CP, however, this LLL is not known in the CRM. The NSC of the AT radio signals at times t _n undergo the following shifts on the AT-SR-KRM path [7]:

за счет его сближения (удаления) с (от) AT;Doppler shifts of the LF AT radio signals at the input CP

due to its convergence (removal) from (from) AT;

the shift of the LF of the AT radio signals by a predetermined value of the nominal conversion frequency ƒ _G ;

за счет его сближения (удаления) с (от) K.Doppler shifts of the LF of the AT radio signals at the CP output

due to its convergence (removal) from (from) K.

It is believed that the instability of the frequency generator CP at times t _{n is} known and its compensation is possible. The influence of other effects on the frequency change, for example, the gravitational and relativistic effects in the framework of the method under consideration, is negligible and therefore not taken into account.

за счет его сближения (удаления) с (от) K, рассчитываются на основе известных координат КРМ x_K, y_K, z_K и КП CP определенных n-х КП СР.Doppler shifts of the LF AT radio signals at the CP output

due to its approach (removal) from (from) K, they are calculated on the basis of the known coordinates of KPM x _K , y _K , z _K and KP CP of certain n-x KP SR.

за счет сближения (удаления) CP с (от) AT используют для определения местоположения самого AT х_А, y_A и z_A. В условиях, когда НСЧ радиосигнала ƒ_А в КРМ не известен, рассчитывают разности указанных доплеровских сдвигов НСЧ радиосигналов AT на входе CP в различные моменты времени. Для этого предварительно выделяют в качестве опорных g-e, где g=1, ..., N, КП CP для момента времени t_g.In turn, the Doppler shifts of the LF AT radio signals at the input CP

due to the approach (removal) of CP from (from) AT is used to determine the location of the AT x _A , y _A and z _{A itself} . Under the conditions when the LFN of the radio signal ƒ _A is not known in the CRM, the differences of the indicated Doppler shifts of the LFN of the AT radio signals at the input CP at different times are calculated. For this, ge is preliminarily allocated as reference ge, where g = 1, ..., N, KP CP for the time t _g .

, где

,

. Всего получают N-1 таких пар.Then, CP CP pairs differing from each other are formed, in each of which the first CP CPs correspond to the time t _g , and the second CP CPs correspond to the time

where

,

. A total of N-1 such pairs are obtained.

на основе g-x и

КП CP, координат КРМ x_K, y_K, z_K, номинала частоты конвертирования ƒ_G, НСЧ радиосигналов

,

принятых от AT через CP в моменты времени t_g и

соответственно.For each formed pair of CP CP, the difference in radial velocities is calculated

based on gx and

CP CP, KPM coordinates x _K , y _K , z _K , nominal frequency of conversion ƒ _G , LF of radio signals

,

received from AT via CP at time t _g and

respectively.

, где a _З=6378136 м - большая полуось эллипсоида Земли;

- радиус Земли на полюсе;

- эксцентриситет эллипсоида Земли; λ_З=1/298,25784 - сжатие эллипсоида Земли, ϕ_A - средняя широта РВРМ.As a model of the Earth’s surface, we choose a sphere with a variable radius [8], which depends on latitude and is determined from the known relation, which in RRM will be equal to

where a _З = 6378136 m is the semimajor axis of the Earth's ellipsoid;

- the radius of the Earth at the pole;

- eccentricity of the ellipsoid of the Earth; λ _З = 1 / 298.25784 - compression of the ellipsoid of the Earth, ϕ _A - average latitude of the PBPM.

и радиус сферы поверхности земли

.At the final stage, the coordinates AT x _A , _{A A} , z _A are calculated using ne CP CP, N-1 radial velocity difference

and the radius of the sphere of the earth’s surface

.

, следовательно, требуется проведение измерений в три момента времени (N=3).For instant and unambiguous determination of the location of AT (calculation of coordinates AT x _A , _A , z _A ) using the claimed method, it is necessary and sufficient to calculate at least two radial velocity differences

therefore, measurements are required at three points in time (N = 3).

As an example of the implementation of the claimed method, Appendix B provides an analytical interpretation of the AT location algorithm using CP in low Earth orbit for N = 3, that is, for three time instants t ₁ , t ₂ , t ₃ . In this example, the first (g = 1) CP CP for the time t _{1 were} selected as reference.

A further increase in the number of measurements (N≥4) leads to an increase in the accuracy of determining the location of the AT and to a concomitant increase in the total cost of the device that implements the claimed method.

The algorithm for determining the AT location using CP in low Earth orbit for N≥4 measurement moments will be similar to the algorithm described in Appendix B, with the only difference being that the system of equations (B.14) will contain N (more than four) second-order equations with three unknowns. This in turn will lead to the fact that the subsequent system of linear equations (B.15) with three unknowns will include more than four equations. Then the system (B.15) is solved by one of the known numerical methods, for example, by the least squares method.

The accuracy of determining the location of AT using the claimed method is influenced by many factors, the main of which are:

the number of M IORS installed on the earth's surface;

topology of placement of CRM and m-x IORS;

accuracy of synchronization of CRM and m-x IORS emissions;

the number of measurements N;

,time intervals between times t _g and

,

measurement errors of the LSS of transmitted and received test radio signals and received radio signals from AT;

,

,

и ортогональных составляющих вектора скорости CP

,

,

в каждый момент времени t_n. Это в свою очередь способствует повышению точности определения местоположения AT.An increase in the number of IORCs installed on the earth’s surface leads to an increase in the accuracy of determining CP coordinates

,

,

and orthogonal components of the velocity vector CP

,

,

at every moment in time t _n . This in turn helps to improve the accuracy of determining the location of the AT.

, 2) величины углов

, образованных отрезками

и

. На фиг. 5, в качестве примера, представлена топология КРМ и М ИОРС, а также показаны расстояния

,

. и угол

. Для повышения точности определения местоположения AT необходимо увеличивать расстояния

и увеличивать углы

.Under the topology of the placement of the CRM and mx IORS is understood the totality of such parameters as 1) the distance between the CRM and m-m IORS

, 2) angles

formed by line segments

and

. In FIG. 5, as an example, the topology of the CRM and M IORS is presented, and the distances are also shown

,

. and angle

. To increase the accuracy of determining the location of AT, it is necessary to increase the distance

and increase the angles

.

The high accuracy of synchronization of the radiation of the Raman and m-x IORS and the low measurement error of the LFN of the transmitted and received test radio signals and the received radio signals from AT are ensured by the use of high-precision frequency generators in the Raman and m-x IORC.

решают противоречивую задачу: с одной стороны количество проводимых измерений необходимо увеличивать с целью повышения точности определения местоположения AT; с другой стороны увеличение проводимых измерений снижает производительность КРМ.When choosing the number of measurements N and the associated time intervals between time instants t _g and

solve a contradictory problem: on the one hand, the number of measurements must be increased in order to increase the accuracy of determining the location of AT; on the other hand, an increase in measurements reduces the performance of the CRM.

Simulated modeling of the claimed method for determining the location of the subscriber terminal using a single relay satellite in low Earth orbit and the prototype method using the developed computer programs [9, 10] with the same initial data was performed.

The simulation results indicate a significant increase in the accuracy of determining the location of the AT using the claimed method compared to the prototype method by 60 ... 80% (depending on the layout topology of the CRM and M IORS, as well as the number of measurements N), while eliminating the need for reciprocal transmission of test signals from AT, which indicates the possibility of achieving a technical result when using the claimed technical solution.

Information sources

1. Volkov RV, Sayapin VN, Sevidov VV A method for determining the location of a user terminal using two satellite transponders. Patent RU No. 2605457, publ. 12/20/2016 Bull. Number 35.

2. Basukinsky A.B., Kizima S.V., Lisitsa G.V., Mitchenkov S.G. A method for determining the location of a satellite earth station. Patent RU No. 2442996, publ. 02/20/2012 Bull. No. 5.

3. Levanon N. Positioning using a single satellite in low Earth orbit. Patent RU No. 2241239, publ. 11/27/2004 Bull. No. 33.

4. Abalakin V.K. Astronomical calendar. The permanent part. - M.: Science, 1981. - 704 p.

5. Volkov RV, Malyshev SR, Simonov AN, Sevidov VV Determination of the canonical parameters of satellite transponders from radio signals of reference reference stations // Transactions of the Military Space Academy named after A.F. Mozhaysky. 2016. Issue. 655.S. 88-92.

6. Kelyan A.Kh., Chemarov A.O., Volkov R.V., Sevidov V.V. Determination of aircraft motion parameters by a geolocation system from the radiation of a satellite communications station located on its board // Successes in modern radio electronics. 2016. No5. S. 10-14.

7. Volkov RV, Sayapin VN, Sevidov VV A model for measuring the time delay and frequency shift of a radio signal received from a repeater satellite when determining the location of an earth station // T-Comm: Telecommunications and transport. 2016. Volume 10. No. 9. S. 14-18.

8. Bogdanovsky S.V., Volkov R.V., Sevidov V.V., Teslevich S.F. A model of the Earth’s surface when determining the location of an earth station using signals from satellite transponders // High-tech. 2016. No. 12. S. 44-50.

9. Volkov RV, Sayapin VN, Sevidov VV A model of the motion of an artificial Earth satellite // Computer programs. Database. Topologies of integrated circuits. 2016. No2. C 112.

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

Appendix A

Algorithm for determining the coordinates of a relay satellite using two IORS

To calculate the coordinates of CP at times t _n in the particular case when the number of IORS is two (M = 2), an algorithm is developed, the scheme of which is shown in FIG. 3.

,

,

и

,

,

; временные задержки между излученными КРМ, двумя ИОРС и принятыми КРМ тестовыми радиосигналами

,

, и

, предварительно определенные в соответствии с формулами (1); порог точности δ₀ расчета координат СР.At stage 1, input data is entered, which are the coordinates of the CRM x _K , y _K , z _K ; coordinates of two IORS

,

,

and

,

,

; time delays between radiated CRM, two IORS and test radio signals received by CRM

,

, and

predefined in accordance with formulas (1); accuracy threshold δ ₀ for calculating CP coordinates.

,

и

по формулам (2).In step 2, the distances are calculated.

,

and

by formulas (2).

,

,

.At step 3, based on the elements of the Kepler’s orbit CP, the coordinates of the reference point

,

,

.

,

и

, при условии равенства координат CP координатам опорной точки

,

,

по формуламIn step 4, the distances are calculated.

,

and

, provided that the coordinates CP are equal to the coordinates of the reference point

,

,

according to the formulas

,

,

,

,

.

.

,

и

, рассчитанными на этапе 4, и расстояниями

,

и

, рассчитанными на этапе 2 и соответственноIn step 5, the residuals q ₁ , q ₂ and q ₃ are calculated as the differences between the distances

,

and

calculated in step 4 and distances

,

and

calculated in stage 2 and respectively

,

,

.

,

,

.

,

,

для чего предварительно формируют систему линейных уравнений путем разложении в ряд Тейлора функций

,

и

, с точностью до первых членов, где в качестве переменных выступают поправки к координатам CP

,

,

:In step 6, corrections to the CP coordinates are obtained.

,

,

why preliminarily form a system of linear equations by expanding the functions in a Taylor series

,

and

, up to the first terms, where the variables are corrections to the CP coordinates

,

,

:

from

where the partial derivatives, in turn, are calculated according to the expressions

,

,

Solve the system of linear equations (A.1) using one of the known methods, for example, the Cramer method, and obtain corrections to the CP coordinates

,

,

,

,

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

,

,

:

Stages 4 ... 7 together make up the first iteration. Next, the iterations are repeated, using each time the coordinates of the new reference point calculated at the previous iteration. The number of necessary iterations depends on the required accuracy of determining the coordinates of the SR. The accuracy of determining the coordinates of CP is directly related to the iteration step d _w.

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

In step 9, _br d compared with a threshold in step 1. δ _0, given by By comparison result or perform the next iteration (steps 4 ... 7) if d _w> δ _0, or proceeds to step 10, if d _w <δ _0. The required number of iterations, as a rule, is 2, ..., 4.

,

,

в качестве которых предварительно выбирают значения координат опорной точки на последней итерации.At step 10, the coordinates CP

,

,

as which the coordinates of the reference point at the last iteration are preselected.

Appendix B

Algorithm for determining the orthogonal components of the velocity vector of a repeater satellite using two IORS

To calculate the orthogonal components of the velocity vector CP at times t _n in the particular case when the number of IORS is two (M = 2), an algorithm has been developed whose main steps are described below.

,

и

,

; координаты CP

,

,

, рассчитанные в соответствии с алгоритмом, представленном в приложении А; НСЧ тестовых радиосигналов

,

,

переданных КРМ и двумя ИОРС и

,

,

принятых тестовых радиосигналов КРМ после их переизлучения CP; номинал частоты конвертирования CP ƒ_G.At stage 1, input data is entered, which are: coordinates of the CRM x _K y _K , z _K , the coordinates of two IORS

,

and

,

; CP coordinates

,

,

calculated in accordance with the algorithm presented in Appendix A; Low frequency test signals

,

,

transmitted by CRM and two IORS and

,

,

received test radio signals of the CRM after their re-emission of CP; nominal conversion frequency CP ƒ _G.

,

и

CP относительно КРМ, 1-й, 2-й ИОРС в моменты времени t_n.In step 2, the radial velocity values are calculated

,

and

CP relative to CRM, 1st, 2nd IORC at time t _n .

,

,

переданных тестовых радиосигналов КРМ и двумя ИОРС и

,

,

принятых тестовых радиосигналов КРМ после их переизлучения CP, имеют видNSC ratios

,

,

transmitted test radio signals KRM and two IORS and

,

,

received test radio signals of the CRM after their re-emission CP, have the form

,

и

- доплеровские сдвиги частот тестовых радиосигналов на входе CP за счет его сближения (удаления) с (от) КРМ, 1-й и 2-й ИОРС в моменты времени t_n,

,

и

- доплеровские сдвиги частот тестовых радиосигналов на выходе CP за счет его сближения (удаления) с (от) КРМ, 1-й и 2-й ИОРС в моменты времени t_n.where ƒ _G is the nominal conversion frequency CP,

,

and

- Doppler frequency shifts of the test radio signals at the CP input due to its convergence (removal) from (from) the CRM, the 1st and 2nd IORS at time t _n ,

,

and

- Doppler frequency shifts of the test radio signals at the output of CP due to its approach (removal) from (from) the CRM, the 1st and 2nd IORC at time t _n .

It is believed that the instability of the CP frequency generator is known and compensated. The influence of other effects on the frequency change, for example, the gravitational and relativistic effects in the framework of the method under consideration, is negligible and therefore not taken into account.

,

и

на входе CP и для доплеровских сдвигов частот тестовых радиосигналов

,

и

на выходе CP, с учетом того, что

,

и

, имеют следующие виды:Expressions for Doppler frequency shifts of test radio signals

,

and

at CP input and for Doppler frequency shifts of test radio signals

,

and

at the output of CP, given that

,

and

have the following types:

,

и

:From equalities (B.1) and (B.2) we obtain expressions for calculating radial velocities

,

and

:

,

,

.In step 3, the orthogonal components of the velocity vector CP are calculated

,

,

.

,

и

с векторами скоростей CP

, через углы

,

и

:The identities connecting the radial velocities are valid.

,

and

with velocity vectors CP

through the corners

,

and

:

According to the scalar product theorem of vectors

The modulus of the velocity vector CP is equal to:

,

,

рассчитывают какand distances from CRM, 1st, 2nd IORS to CP

,

,

calculated as

Expressions (B.1), taking into account equations (B.4) ... (B.7) for a particular case, when n = 1 ... 2, are transformed into a system of linear equations:

,

,

равны:where are the coefficients of the variables

,

,

equal to:

,

,

.A system of three linear equations (B.8) with three unknowns is solved by one of the known methods, for example, the Cramer method. The result of solving the system of equation (B.8) is the orthogonal components of the velocity vector CP

,

,

.

Appendix B

AT Low Position Orbit Algorithm for Low Earth Orbit for Three Measurement Moments

,

,

,

,

,

,

,

,

и ортогональные составляющие вектора его скорости

,

,

,

,

,

,

,

,

в моменты времени t₁, t₂ и t₃; радиус сферы поверхности земли

.The initial data of the developed algorithm are: coordinates of the CRM x _K , y _K , z _K ; CP CP - CP coordinates

,

,

,

,

,

,

,

,

and orthogonal components of its velocity vector

,

,

,

,

,

,

,

,

at times t ₁ , t ₂ and t ₃ ; Earth's surface radius

.

,

и

, принятых от AT через CP в моменты времени t₁, t₂ и t₃. Вместе с тем указанные НСЧ представляют в следующем виде:In CRM, the LFM of radio signals is measured

,

and

received from AT via CP at times t ₁ , t ₂ and t ₃ . However, these NSC are as follows:

,

,

- доплеровские сдвиги частот радиосигналов AT на входе CP за счет его сближения (удаления) с (от) AT в моменты времени t_n

,

,

- доплеровские сдвиги частот радиосигналов AT на выходе CP за счет его сближения (удаления) с (от) K в моменты времени t_n.where ƒ _G is the nominal frequency of the conversion,

,

,

- Doppler frequency shifts of the radio signals AT at the input CP due to its approach (removal) from (from) AT at time t _n

,

,

- Doppler frequency shifts of the radio signals AT at the output of CP due to its approach (removal) from (from) K at time t _n .

To compensate for the unknown LF radio signal AT ƒ _A based on the identities (B.1), the difference equations are compiled:

,

,

и

,

,

, то выражения для расчета доплеровских сдвигов частот имеют следующий вид:Since the inequalities are true

,

,

and

,

,

, then the expressions for calculating Doppler frequency shifts are as follows:

,

,

и

,

,

- радиальные скорости CP относительно AT и КРМ в моменты времени t₁, t₂, t₃.Where

,

,

and

,

,

- radial speeds CP relative to AT and CRM at time t ₁ , t ₂ , t ₃ .

,

,

в моменты времени t₁, t₂, t₃ по формулам:Calculate the values of the radial velocities CP relative to the Raman

,

,

at time t ₁ , t ₂ , t ₃ according to the formulas:

,

,

в моменты времени t₁, t₂, t₃:Identities for calculating the radial velocities of CP relative to AT

,

,

at time t ₁ , t ₂ , t ₃ :

where x _A , y _A and z _A are the desired coordinates of AT.

The difference equation (B.2), taking into account (B.4), (B.5), (B.7) and (B.8), takes the form:

Expression (B.10), containing three unknown variables x _A , y _A and z _A , is transformed to:

- разность радиальных скоростей CP относительно AT в моменты времени t₂ и t₁, которая вычисляется в соответствии с выражением:where is the coefficient on the right side

- the difference of the radial speeds CP relative to AT at time t ₂ and t ₁ , which is calculated in accordance with the expression:

Similarly transforming (B.3), taking into account (B.5), (B.6), (B.8) and (B.9), we obtain:

- разность радиальных скоростей CP относительно AT в моменты времени t₃ и t₁, которая вычисляется в соответствии с выражением:where is the coefficient on the right side

- the difference of the radial speeds CP relative to AT at time t ₃ and t ₁ , which is calculated in accordance with the expression:

Under the assumption that AT is located on the earth's surface, they make up another equation with the variables x _A , y _A and z _A :

Equations (B.11), (B.12) and (B.13) together form a system of equations

To solve the system of second-order equations (B.14), an iterative algorithm is used that includes the following steps:

Stage 1. Define arbitrary, but for fast convergence, the most plausible reference coordinates AT: x ' _A , y' _A , z ' _A.

,

и

системы уравнений (В.14) в точке с опорными координатами AT х'_А, у'_А, z'_A:Step 2: Determine Function Values

,

and

system of equations (B.14) at a point with reference coordinates AT x ' _A , y' _A , z ' _A :

Stage 3. The residuals q ₄ , q ₅ and q _{6 are} calculated using the formulas

,

,

.

,

,

.

,

и

в ряды Тейлора с точностью до первых производных:Stage 4. A system of three linear equations is composed, in which the corrections to the point with the reference coordinates AT Δх _A , Δу _A and Δz _A act as unknowns, based on the decompositions of the functions

,

and

in Taylor series up to the first derivatives:

where the values of the partial derivatives at the point with reference coordinates AT x ' _A , y' _A , z ' _A are:

,

,

от CP в моменты времени t₁, t₂, t₃ до точки с опорными координатами AT х'_А, у'_А, z'_A и радиальные скорости

,

,

CP в моменты времени t₁, t₂, t₃ относительно точки с опорными координатами AT x'_A, y'_A, z'_A равны:a, distance

,

,

from CP at times t ₁ , t ₂ , t ₃ to a point with reference coordinates AT x ' _A , y' _A , z ' _A and radial velocities

,

,

CP at times t ₁ , t ₂ , t ₃ relative to the point with the reference coordinates AT x ' _A , y' _A , z ' _A are:

Step 5. Solve the system of three linear equations (B.15), with three unknowns using one of the known methods, for example, the Cramer method.

,

,

The result of solving the system of equations (B.15) are corrections to the reference coordinates AT

,

,

,

,

:Step 6. Determine the new reference coordinates AT

,

,

:

;

;

.

;

;

.

Stages 1 ... 6 together form the first iteration. Next, the iteration is repeated, using each time the new reference coordinates AT obtained in step 6 of the previous iteration. The number of necessary iterations depends on the correct choice of the initial reference coordinates (step 1) and the required accuracy of determining the coordinates AT.

Finally, the coordinates of AT at the last iteration are taken as the coordinates AT x _A , y _A , z _A.

Claims (2)

1. A method for determining the location of a subscriber terminal (AT) using a satellite repeater (CP) in low Earth orbit, which consists in placing a radio-electronic monitoring complex (RCM) containing the receiving and transmitting equipment at a position with known coordinates x _K , y _K , z _K , select CP with a known nominal frequency of conversion ƒ _G as an object of electronic monitoring, emit a test radio signal with a nominal frequency rating (LFN) using the KRM equipment

in the direction of CP at time t ₁ , measured in the CRM of the LSS of the radio signal

received from AT via CP at time t ₁ , based on the known coordinates of the CRM x _K , y _K , z _K , the nominal frequency of the conversion ƒ _G , LF

and

The transmitted test radio signal and the radio signal received from AT via CP at time t ₁ calculate the location of AT on the surface of the earth, characterized in that it is additionally installed on the earth's surface M≥2 emitting reference reference stations (IORS) at positions with known coordinates x _Im , y _Im , z _Im , where m = 1 ... M is the IORS number, and to select CP as the object of electronic monitoring, the radio monitoring area (RRM) is preliminarily set as the area on the surface of the earth in which it is necessary to determine the location of AT, and select the nth time instants t _n , where n = 1 ... N, N≥3, at which the illumination zone of the specified CP covers both the CRM, and the RVRM, and the positions of all m-th IORCs, determine the nth canonical parameters (CP ) CP including CP coordinates

,

,

and orthogonal components of its velocity vector

,

,

at time t _n , based on the radiation of the test radio signals of the RRC and the m IORS in the direction of the CP and their subsequent reception of the RRC after re-emission by the indicated CP, the LSC of the radio signals is measured in the RSC

received from AT through CP at times

, where n '= 2 ... N, is distinguished as reference ge, where g = 1, ..., N, CP CP for time t _g , N-1 CP CP pairs differing from each other are formed, in each of which the first CP CPs correspond to time t _g , and second CPs correspond to time t ₁ , where l = 1 ... N, l ≠ g, N-1 radial velocity differences are calculated

for each formed pair of CP CPs based on gx and l-CP CPs, KPM coordinates x _K , y _K , z _K , nominal frequency of conversion ƒ _G , LF of radio signals

,

received from AT through CP at time t _g and t _l, respectively, as a surface of the earth take a sphere with a radius

, which is calculated on the basis of the average latitude of the PBPM ϕ _A , and the location of AT on the earth’s surface is determined using n-th CP CP, N-1 radial velocity differences

and the radius of the sphere of the earth’s surface

. 2. The method according to p. 1. characterized in that to determine the n-th CP CP at time t _n , test radio signals from the NSC are preliminarily emitted using the CRM equipment

towards CP at time points

emit m-mi IORS test radio signals with LFN

in the direction of the CP at time t _n , receive re-emitted CP test signals from the NSC with the help of the CRM

and

at times

and

accordingly, they transmit to the CRM the NSC test radio signals

from m-IORS, time delays are measured

between the emitted and received test radio signals, after which the slant ranges from CP to CRM are calculated

and up to m-iors

corresponding to points in time t _n , calculate the coordinates CP

,

,

at time t _n according to the known coordinates of the CRM and m-x IORS, as well as the measured inclined ranges

and

measure radial speeds CP relative to CRM

and m-iors

at times t _n based on the known coordinates of the CRM and m-x IORS calculated coordinates CP

,

,

as well as the memorized NSC transmitted

,

and adopted

,

test radio signals, calculate the orthogonal components of the velocity vector CP

,

,

at time t _n using the known coordinates of the CRM and m-x IORS, the calculated coordinates CP

,

,

and measured radial velocities

and

, and as the n-th CP CP take the set of coordinates CP

,

,

and orthogonal components of its velocity vector

,

,

at time t _n .

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