RU2605457C1 - Method of user terminal locating using two relay satellites - Google Patents

Abstract

FIELD: communication equipment.

SUBSTANCE: invention relates to communication engineering and can be used to locate radio-frequency radiation sources when designing satellite communication system user terminal locating subsystem. To do so, method is based on time delays and frequency shifts measurement between transmitted and received system test signals. According to measurement results using network-to-network connection node known coordinates, relay satellites coordinates and motion parameters, user terminal velocity vector

module

azimuth α_UT and its height h_UT, relative to Earth's surface and predetermined frequency shifts f _g1, f _g2 of relay satellites operating frequencies to calculating user terminal coordinates.

EFFECT: technical result is increased accuracy of user terminal coordinates determining in wide range of its movement speeds due to more accurate system signals frequency shifts determination.

1 cl, 1 tbl, 15 dwg

Description

The claimed technical solution relates to the field of radio engineering, and in particular to methods for determining the location (WMD) of radio emission sources.

The claimed invention can be used in the construction of the subsystem OMP user terminals (PT) satellite communications system (CCC).

A known method of weapons of mass destruction using a global satellite radio navigation system GLONASS. This method is widely known and described, for example, in the book of V. Tyapkin. and Garina E.N. "Methods for determining the navigation parameters of vehicles using the GLONASS satellite radio navigation system." - Krasnoyarsk: Sib. Feder. Univ., 2012 .-- 260 p. At the same time, for the simultaneous weapons of mass destruction in space, the signals of at least four satellites are required. However, this analogue has disadvantages. So, the PT must have a separate receiver that receives signals from the GLONASS system. Another disadvantage is the increased requirements for computing resources of the PT, allowing you to calculate your coordinates from the signals of the GLONASS system.

There is also an analogue method for determining the location of a satellite communications earth station using a relayed signal from RF patent 2172495 IPC G01S 5/06 (2006.01) dated 06.05.00. This method is based on measuring the Doppler frequency shifts of the signals relayed by one repeater satellite (CP ₁ for several hours. This analogue also has significant drawbacks. The first drawback is associated with the unacceptably long time interval of the MSS of the PT necessary to observe the signals of the system. The second drawback - cumbersome calculations, which entail a significant increase in the cost of the system that implements it.

The closest in technical essence to the claimed method of OMP PT is the method of OMP PT described in RF patent 2256935 IPC G01S 5/02 (2006.01) from 09/26/1997. The prototype method, including the AT, at least two satellites with known locations and known speeds and the node internetworking (UMC) for communicating with the AT through the aforementioned satellites, comprising the step of determining the range parameter, which is the distance between one of the satellites and PT, the step of determining the distance difference parameter, which is the difference of the distances of one and the other satellite from the PT, the step of determining at least one of the following parameters: range, which is the radial speed of one of the satellites relative to the PT, the parameter of the difference in the speeds of range changes, which is the difference of the radial velocities of one and the other satellite relative to the PT, the step of determining the position of the PT on the Earth’s surface based on known locations and known CP speeds, as well as the indicated range parameter, range change rate parameter and at least one of the mentioned range difference parameters and range difference rate difference stey.

With this method, the high-speed performance of the weapons of mass destruction without significant complication of the equipment of the PT and UMC is ensured.

The disadvantage of the closest analogue (prototype) is the relatively low accuracy of determining the coordinates of the PT when changing the speed of the PT, due to the possibility of placing it on a wide class of moving objects (car, helicopter, plane, etc.).

The technical result when using the claimed solution is the development of a method of weapons of mass destruction using two CPs, which improves the accuracy of determining the coordinates of the points when changing the speed of its movement.

, азимута α_ПТ вектора скорости

пользовательского терминала и его высоты h_ПТ, относительно земной поверхности, с учетом координат CP₁, CP₂, векторов их скоростей

,

координат УМС и предварительно заданных частотных сдвигов

,

рабочих частот CP₁, СР₂, определяют расстояние

между первым CP₁ и ПТ, определяют расстояние

между вторым CP₂ и ПТ, определяют, по меньшей мере, один из параметров: радиальную скорость

перемещения первого CP₁ относительно ПТ, и/или радиальную скорость

перемещения второго СР₂ относительно ПТ, после чего с учетом координат CP₁, СР₂, векторов их скоростей

,

, определенных параметров

,

, а также радиальной скорости

и/или радиальной скорости

, вычисляют широту φ_ПТ и долготу λ_ПТ пользовательского терминала, дополнительно на основе известных модуля

, азимута α_ПТ вектора скорости

пользовательского терминала и его высоты h_ПТ относительно земной поверхности вычисляют в УМС доплеровские сдвиги частот

и

первого и второго узкополосных тестовых сигналов, обусловленные изменениями радиальных скоростей ПТ относительно CP₁ и CP₂, для чего предварительно определяют вероятные местоположения ПТ с учетом координат спутников-ретрансляторов CP₁, CP₂, определенных параметров

и

, а при определении по меньшей мере одного из параметров:

и/или

учитывают дополнительно доплеровские сдвиги частот

и

.The specified technical result in the claimed method of OMP PT is achieved by the fact that in the known method of OMP PT using two satellite transponders CP ₁ , CP ₂ and an interconnection node (UMC), which consists in the fact that based on measurements of time delays and frequency shifts between transmitted and received test signals of a system known to the module

, azimuth α _PT velocity vector

and the user terminal _UT its height h, with respect to the earth's surface, with the coordinates CP _1, CP _2, the vectors of their velocities

,

UMS coordinates and predefined frequency shifts

,

operating frequencies CP ₁ , CP ₂ , determine the distance

between the first CP ₁ and PT, determine the distance

between the second CP ₂ and the PT, at least one of the parameters is determined: radial velocity

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

the movement of the second CP ₂ relative to the PT, after which, taking into account the coordinates CP ₁ , CP ₂ , and their velocity vectors

,

defined parameters

,

as well as radial velocity

and / or radial velocity

calculate the latitude φ _PT and the longitude λ _{PT of the} user terminal, additionally based on known modules

, azimuth α _PT velocity vector

the user terminal and its height _hF relative to the earth's surface, the Doppler frequency shifts are calculated in the UMC

and

the first and second narrow-band test signals due to changes in 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 coordinates of the satellite transponders CP ₁ , CP ₂ , certain parameters

and

, and when determining at least one of the parameters:

and / or

additionally take into account Doppler frequency shifts

and

.

и

обусловлены изменениями радиальных скоростей ПТ относительно CP₁ и CP₂. При их вычислении предварительно определяют вероятные местоположения ПТ с учетом координат спутников-ретрансляторов CP₁, CP₂, определенных параметров

и

, известных модуля

, азимута α_ПТ вектора скорости

пользовательского терминала и его высоты h_ПТ относительно земной поверхности.Additional Doppler frequency shifts

and

due to changes in the radial speeds of the PT relative to CP ₁ and CP ₂ . When calculating them, the probable locations of the PTs are preliminarily determined taking into account the coordinates of the satellite transponders CP ₁ , CP ₂ , certain parameters

and

known module

, azimuth α _PT velocity vector

user terminal and its height h _PT relative to the earth's surface.

, в ПТ измеряют частоту

первого узкополосного тестового сигнала, излученного УМС на частоте

и ретранслированного через CP₁, передают результат измерения в УМС и рассчитывают доплеровский сдвиг частоты

первого сигнала, обусловленного изменением радиальной скорости CP₁ относительно УМС. Далее рассчитывают доплеровский сдвиг частоты

первого сигнала, обусловленного изменением радиальной скорости ПТ относительно CP₁ и вычисляют параметр

на основе первого сигнала, излучаемого на частоте

, предварительно заданной частоте сдвига

рабочей частоты CP₁, измеренной частоты

первого сигнала, принятого после прохождения им трассы УМС-CP₁-ПТ, рассчитанных доплеровских сдвигов частот

и

первого сигнала.To define a parameter

, in PT measure the frequency

first narrowband test signal emitted by the UMC at a frequency

and relayed through CP ₁ , transmit the measurement result to the UMC and calculate the Doppler frequency shift

the first signal due to a change in the radial velocity of CP ₁ relative to the UMC. Next, calculate the Doppler frequency shift

the first signal due to a change in the radial velocity of the PT relative to CP ₁ and calculate the parameter

based on the first signal emitted at a frequency

preset shear rate

operating frequency CP ₁ measured frequency

the first signal received after passing the UMS-CP ₁ -FET path, calculated Doppler frequency shifts

and

the first signal.

, в ПТ измеряют частоту

второго узкополосного тестового сигнала, излученного УМС на частоте

и ретранслированного через CP₂, передают результат измерения в УМС и рассчитывают доплеровский сдвиг частоты

второго сигнала, обусловленного изменением радиальной скорости CP₂ относительно УМС. Далее рассчитывают доплеровский сдвиг частоты

второго сигнала, обусловленного изменением радиальной скорости ПТ относительно СР₂ и вычисляют параметр

на основе второго сигнала, излучаемого на частоте

, предварительно заданной частоте сдвига

рабочей частоты СР₂, измеренной частоты

второго сигнала, принятого после прохождения им трассы УМС-CP₂-ПТ, рассчитанных доплеровских сдвигов частот

и

второго сигнала.To define a parameter

, in PT measure the frequency

the second narrowband test signal emitted by the UMC at a frequency

and relayed through CP ₂ , transmit the measurement result to the UMC and calculate the Doppler frequency shift

the second signal due to a change in the radial velocity of CP ₂ relative to the UMC. Next, calculate the Doppler frequency shift

the second signal due to a change in the radial velocity of the PT relative to SR ₂ and calculate the parameter

based on the second signal emitted at a frequency

preset shear rate

operating frequency SR ₂ measured frequency

the second signal received after passing the UMS-CP ₂ -PT path, calculated Doppler frequency shifts

and

second signal.

Alternatively, in case of weapons of mass destruction, various combinations of four parameters are used: 1) range, 2) range difference, 3) range change rate, 4) range change rate difference.

However, the joint use of parameters: ranges from one CP to PT and a difference in ranges from one and the other CP to PT is equivalent to using two range parameters: 1) ranges from CP ₁ to PT, 2) ranges from CP ₂ to PT. Similarly, the sharing of the parameters: rate of change in range of one CP relative to PT and the difference in the rates of change of distances of one and other CP relatively Fr, is equivalent to using two range-rate parameters: 1) the rate of change of range CP ₁ with respect to PT and 2) range rate SR ₂ relative to PT.

от CP₁ до ПТ, 2) дальность

от CP₂ до ПТ, 3) скорость

изменения дальности CP₁ относительно ПТ, 4) скорость

изменения дальности CP₂ относительно ПТ.At the same time, the preparation and solution of equations corresponding to the position parameters for ranges and speeds of range changes is much simpler than for the difference of ranges and speed difference of ranges, therefore, in the preferred embodiment of the present invention, the following position parameters are used: 1) range

from CP ₁ to PT, 2) range

from CP ₂ to PT, 3) speed

range changes CP ₁ relative to PT, 4) speed

range changes CP ₂ relative to PT.

In an alternative embodiment, projections of position lines on the Earth's surface are considered, thereby limiting the spatial location of the PT. In a preferred embodiment, projections of position lines onto a plane parallel to the surface of the Earth having an arbitrary known height h _{PT are considered} .

и

определяют на основе измерений временных задержек между переданными и принятыми тестовыми сигналами системы.Options

and

determined on the basis of measurements of time delays between transmitted and received test signals of the system.

и

определяют на основе частотных сдвигов между переданными и принятыми тестовыми сигналами системы. Сдвиги тестовых сигналов системы являются суммой предварительно заданных частотных сдвигов

,

рабочих частот CP₁, СР₂ и доплеровскими сдвигами частот, обусловленными суммарными радиальными скоростями соответствующего CP относительно ПТ и УМС.Options

and

determined based on the frequency shifts between the transmitted and received test signals of the system. System test signal offsets are the sum of predefined frequency offsets.

,

operating frequencies CP ₁ , CP ₂ and Doppler frequency shifts due to the total radial velocities of the corresponding CP relative to PT and UMC.

In an alternative embodiment, it is assumed that the PT does not move relative to the earth's surface. In real conditions, the AT can be placed on a wide class of moving objects (car, helicopter, airplane, etc.). The motion of the PT relative to the earth's surface introduces additional Doppler frequency shifts into the received test signals of the system. Such shifts can not be taken into account if the speed of CP relative to the earth's surface significantly exceeds the speed of the PT relative to the earth's surface. But when these speeds are comparable, then to calculate the parameters of the rate of change of range and the difference of the speeds of change of ranges, it is necessary to take into account additional Doppler frequency shifts of the test signals of the system due to the movement of the ground relative to the ground.

Table 1 shows the values of the characteristic velocities and the corresponding maximum Doppler frequency shifts introduced by some types of AT and CP at a carrier frequency of 10 GHz.

An analysis of the values given in the table allows us to conclude that, in many cases, when determining the total radial velocity, an important factor is taking into account the velocity of the surface. This is especially true for CCS in geostationary orbit (GSO).

и/или

, что в свою очередь ведет к повышению точности ОМП ПТ.Accounting for the speed of the PT leads to an increase in the accuracy of determining the parameters

and / or

, which in turn leads to an increase in the accuracy of weapons of mass destruction.

One of the advantages of the present invention is to improve the accuracy of OMP PT.

Another advantage of the present invention is the possibility of OMP FET at an arbitrary known height h _FET .

The claimed method is illustrated by drawings, which show:

- in FIG. 1 - a typical satellite communications system;

- in FIG. 2 - the geometric basis of a typical satellite communications system;

- in FIG. 3 is a diagram of the absence of the Doppler effect;

- in FIG. 4 is a diagram of the manifestation of the Doppler effect;

- in FIG. 5 - options for finding the mutual radial velocity of the moving receiver and transmitter;

;- in FIG. 6 - illustration of finding the line of position of the PT, as the intersection of the surface of the position of the range parameter with the plane

;

;- in FIG. 7 - illustration of finding the line of position of the PT, as the intersection of the surface of the position of the parameter of the rate of change of range with the plane

;

- in FIG. 8 - algorithm for determining the location of the user terminal;

- in FIG. 9 - determination of the probable locations of the user terminal using ranges as position parameters;

- in FIG. 10 - disambiguation principle for a fixed user terminal;

- in FIG. 11 is a disambiguation principle for a mobile user terminal;

- in FIG. 12 - refinement of the radius of the Earth;

- in FIG. 13 - determination of the coordinates of the velocity vector of the user terminal in a geocentric coordinate system;

- in FIG. 14 is an iterative method for increasing the accuracy of determining the coordinates of a user terminal;

- in FIG. 15 is a geometric basis for compiling a circular cone equation in a geocentric coordinate system.

The implementation of the claimed method is presented on the example of a typical satellite communication system shown in FIG. 1. It contains one gateway node (UMC), user terminals, which can be in stationary version 4 (see Fig. 1), or placed on moving objects: on car 5, on helicopter 6, on airplane 7 (see Fig. 1), etc., as well as two satellite transponders: CP ₁ and CP ₂ to provide communication between the UMC and PT.

Modern CCCs make it possible to provide communication services both to fixed-line vehicles and those located on a wide class of moving objects (car, helicopter, airplane).

As an example, to describe the invention consider PT placed on an airplane. The geometrical basis of the satellite link in this embodiment is disclosed in FIG. 2.

The UMC is stationary, its coordinates, or rather the coordinates of the optical foci of the antennas, are well known.

в плоскости

, параллельной горизонтальной плоскости Ω₀ (на нулевой высоте) и находящейся на высоте h_ПТ от нее. Азимутом движения самолета является угол γ_ПТ, отсчитываемый между направлением на север, обозначенным стрелкой Z′ и направлением движения самолета. В дальнейшем будем считать, что параметры

, h_ПТ и γ_ПТ известны, так как большинство самолетов оборудованы приборами, позволяющими измерить указанные параметры в любой момент времени.Fri placed on a plane that moves at speed

in the plane

parallel to the horizontal plane Ω ₀ (at zero height) and located at a height h _FR from it. The aircraft azimuth is the angle γ _PT , counted between the north direction indicated by the arrow Z ′ and the direction of the aircraft. In the future, we assume that the parameters

, h _PT and γ _{PT are} known, since most aircraft are equipped with devices that allow you to measure these parameters at any time.

An ideal GSO CP is characterized by the following parameters: the eccentricity of the orbit is equal to e = 0, the inclination of the orbit is i = 0 °, the period of revolution of CP is equal to the period of revolution of the Earth (stellar day, which is 23 hours 56 minutes 04 seconds), compensation of the effects of disturbing factors, such as the uneven gravitational field of the Earth, the attractive force of the Sun, Moon, and other space objects. In this case, the CP is “hanging” over a certain point on the earth’s surface, at a certain longitude, strictly above the equator, at an altitude of 35875 km above the Earth’s surface.

However, in practice, the conditions listed are unattainable. Relay satellites CP ₁ and CP ₂ are in the so-called quasi-stationary orbit, and their daily displacement, as a rule, is units of degrees. As a result of this, CPs are not “hanging” over certain points on the earth’s surface, but oscillate.

,

, обозначенных на фиг. 2 стрелками. Очевидно, что векторы скоростей

,

в течение суток меняют и модуль, и направление, однако на малом интервале времени, исчисляемом минутами, можно считать их постоянными. В дальнейших рассуждениях считают, что векторы

,

, равно как и координаты CP₁ и CP₂, известны в любой момент времени. Действительно, операторам-владельцам ССС должны быть известны эти параметры, существуют методики, с помощью которых либо измеряют, либо рассчитывают координаты CP и параметры их движения. Они описаны, например, в монографии Дубошина Г.Н. Небесная механика. Методы теории движения искусственных небесных тел. - М.: Наука. Главная редакция физико-математической литературы, 1983. - 352 с.The daily shift of CP ₁ and CP ₂ is the cause of the presence of velocity vectors

,

indicated in FIG. 2 arrows. Obviously, the velocity vectors

,

during the day, both the module and the direction are changed, however, over a small time interval, calculated in minutes, they can be considered constant. In further considerations, it is believed that the vectors

,

, as well as the coordinates CP ₁ and CP ₂ , are known at any time. Indeed, these parameters should be known to the operators-owners of CCCs, there are techniques with which they either measure or calculate the CP coordinates and their motion parameters. They are described, for example, in the monograph of Duboshin G.N. Heavenly mechanics. Methods of the theory of motion of artificial celestial bodies. - M .: Science. The main edition of the physical and mathematical literature, 1983. - 352 p.

At a particular point in time, the topology of the system is characterized by the distances of the relay satellites from the UMS and the AT indicated in FIG. 2 solid and dotted lines:

- расстояние между CP₁ и УМС,

- the distance between CP ₁ and UMC,

- расстояние между CP₂ и УМС,

- the distance between CP ₂ and UMC,

- расстояние между CP₁ и ПТ,

- the distance between CP ₁ and PT,

- расстояние между CP₂ и ПТ.

- the distance between CP ₂ and PT.

и

можно вычислить, основываясь на известных координатах УМС, CP₁ и CP₂.At any given time

and

can be calculated based on the known coordinates of the UMC, CP ₁ and CP ₂ .

и

являются параметрами положения, вычисление которых производится при использовании тестовых сигналов системы.Distances

and

are position parameters, the calculation of which is carried out using the test signals of the system.

,

,

и соответствующими направлениями:In FIG. 2 also shows the angular values between the velocity vectors

,

,

and relevant areas:

- угол между вектором

и направлением ПТ-CP₁,

is the angle between the vector

and direction PT-CP ₁ ,

- угол между вектором

и направлением ПТ-СР₂,

is the angle between the vector

and the direction of PT-SR ₂ ,

- угол между вектором

и направлением CP₁-ПТ,

is the angle between the vector

and direction CP ₁ -T

- угол между вектором

и направлением CP₁-УМС,

is the angle between the vector

and the direction of CP _1- UMS,

- угол между вектором

и направлением CP₂-ПТ,

is the angle between the vector

and direction CP ₂ -T

- угол между вектором

и направлением СР₂-УМС.

is the angle between the vector

and the direction of the SR _2- UMS.

,

,

с их проекциями на соответствующую ось. Такие проекции являются радиальными скоростями:These angular values relate the velocity vectors

,

,

with their projections on the corresponding axis. Such projections are radial velocities:

- радиальная скорость ПТ относительно CP₁ - проекция вектора

на ось ПТ-CP₁,

- the radial velocity of the PT relative to CP ₁ - the projection of the vector

on the axis PT-CP ₁ ,

- радиальная скорость ПТ относительно CP₂ - проекция вектора

на ось ПТ-CP₂,

- the radial velocity of the PT relative to CP ₂ - the projection of the vector

on the PT-CP ₂ axis,

- радиальная скорость CP₁ относительно ПТ - проекция вектора

на ось CP₁-ПТ,

- radial velocity CP ₁ relative to PT - vector projection

on the axis CP ₁ -F,

- радиальная скорость CP₁ относительно УМС - проекция вектора

на ось CP₁-УМС,

- radial velocity CP ₁ relative to the UMS - vector projection

on the axis CP _1- UMS,

- радиальная скорость CP₂ относительно ПТ - проекция вектора

на ось CP₂-ПТ,

- radial velocity CP ₂ relative to the PT - vector projection

on the axis CP ₂ -PT,

- радиальная скорость CP₂ относительно УМС - проекция вектора

на ось CP₂-УМС.

- radial velocity CP ₂ relative to UMS - vector projection

on the axis CP _2- UMS.

,

,

,

можно вычислить, основываясь на известных координатах УМС, CP₁ и CP₂, известных векторах

,

,

.At any given time, radial speeds

,

,

,

can be calculated based on the known coordinates of the UMC, CP ₁ and CP ₂ , known vectors

,

,

.

и

являются параметрами положения, вычисление которых производится при использовании тестовых сигналов системы.Radial speeds

and

are position parameters, the calculation of which is carried out using the test signals of the system.

и

определяют на основе измерений временных задержек между переданными и принятыми тестовыми сигналами системы. Измеренные временные задержки умножают на скорость распространения радиоволны, равную скорости света в вакууме: с=3×10⁸ м/с.Options

and

determined on the basis of measurements of time delays between transmitted and received test signals of the system. The measured time delays are multiplied by the speed of propagation of the radio wave, equal to the speed of light in vacuum: s = 3 × 10 ⁸ m / s.

и

определяют на основе частотных сдвигов между переданными и принятыми тестовыми сигналами системы. Сдвиги тестовых сигналов системы являются суммой предварительно заданных частотных сдвигов

,

рабочих частот CP₁, CP₂ и доплеровскими сдвигами частот, обусловленными суммарными радиальными скоростями соответствующего CP относительно ПТ и УМС.Options

and

determined based on the frequency shifts between the transmitted and received test signals of the system. System test signal offsets are the sum of predefined frequency offsets.

,

operating frequencies CP ₁ , CP ₂ and Doppler frequency shifts due to the total radial velocities of the corresponding CP relative to PT and UMC.

Let us consider in general terms the cause of the Doppler effect, its relationship with the radial velocity of the transmitter (receiver), as well as the procedure for calculating the mutual radial velocity during movement of both the transmitter and the receiver.

The Doppler effect in a certain sense is universal. Its manifestations can be traced both in mechanical (sound) waves and in electromagnetic waves both in the optical range and in the radio range. The Doppler effect can be explained using FIG. 3 and FIG. four.

равна частоте ПРД

:In FIG. 3 shows a transmitter (Rx) and a receiver (Rx). The concentric circles schematically depict the phase fronts of the radio waves emitted by the PRD, the distances between which correspond to the wavelength. In the absence of relative motion of the Tx and PfP, there is no Doppler effect: the PfP wavelength is equal to the PWM wavelength. From the last statement it follows that the frequency of PfP

equal to frequency

:

.

.

с углом θ_{ПРД-ПРМ} к направлению ПРД-ПРМ. Такое движение приводит к изменению длины волны в ПРМ по отношению к длине волны ПРД. Такое изменение называется эффектом Доплера. Частота ПРМ в этом случае изменяется на величину доплеровского смещения частоты

, относительно частоты ПРД:In FIG. 4 depicts a traveling speed

with an angle θ of the _Tx-Rx to the direction of the Rx-Rx. This movement leads to a change in the wavelength in the PFP with respect to the wavelength of the PFD. This change is called the Doppler effect. The frequency of the PFP in this case changes by the magnitude of the Doppler frequency shift

, relative to the frequency of the PRD:

The sign of this bias may be positive if the PfP and PfP are converging, and negative if the PfP and PWM are removed relative to each other.

The analytical expression for calculating the Doppler frequency shift without taking into account the relativistic effect is as follows:

- модуль вектора скорости ПРД,

- радиальная скорость ПРД относительно ПРМ - проекция вектора

на ось ПРД-ПРМ, θ_{ПРД-ПРМ} - угол между вектором

и направлением ПРД-ПРМ.Where

- module of the velocity vector

- radial velocity of the PRD relative to the PFP - projection of the vector

on the axis of the Rx-Rx, θ _Rx-Rx - the angle between the vector

and the direction of the PfP.

In some cases, in the movement can be both PRD and PFP. Then, finding the mutual radial velocity of the moving Rx and Rx is possible in two ways, as shown in FIG. 5.

и

, как проекции векторов

и

на ось ПРД-ПРМ, затем находят взаимную радиальную скорость движущихся ПРМ и ПРД

, как вектор суммы

и

.In the first embodiment, first determine the radial speed of the PRD and PFP

and

like projection vectors

and

on the axis of the Rx-Rx, then find the mutual radial speed of the moving Rx and Rx

as a sum vector

and

.

движущихся ПРМ и ПРД, как вектор суммы их скоростей

и

, затем находят взаимную радиальную скорость движущихся ПРМ и ПРД

, как проекцию вектора

на ось ПРД-ПРМ.In the second embodiment, the resulting relative velocity is first determined

moving Rx and Rx as a vector of the sum of their speeds

and

, then find the mutual radial velocity of the moving Rx and Rx

like a projection of a vector

on the axis of the PRD-PRM.

The above options are also valid for CCCs using a moving CP, with the only difference being that three radial speeds will be involved in calculating the mutual radial velocity of the moving Rx and Rx (see Fig. 5). In this case, it is advisable to use the first option to find the mutual radial velocity of the moving Rx and Rx.

от CP₁ до ПТ, 2) дальность

от СР₂ до ПТ, 3) скорость

изменения дальности CP₁ относительно ПТ, 4) скорость

изменения дальности CP₂ относительно ПТ.When OMP PT use the following position parameters: 1) range

from CP ₁ to PT, 2) range

from SR ₂ to PT, 3) speed

range changes CP ₁ relative to PT, 4) speed

range changes CP ₂ relative to PT.

These parameters can be characterized by position surfaces and position lines.

The position surface (of some position parameter) is the surface in space connecting all points having the same value of this parameter. In some cases, the surface of the Earth can serve as the position surface.

, параллельную земной поверхности (горизонтальной плоскости Ω₀ на нулевой высоте) и находящейся на известной высоте h_ПТ от нее.The position line (of any position parameter) is a curve on the surface of the Earth or on some other surface connecting all points having the same value of this parameter. The position lines of the considered position parameters are indicated by bold lines in the corresponding figures (see Fig. 6, 7). In an alternative embodiment, position lines are considered only on the earth’s surface, while the earth’s surface is approximated by a plane. In a preferred embodiment, consider the plane

parallel to the earth's surface (the horizontal plane Ω ₀ at zero height) and located at a known height h _FR from it.

- окружность, центр которой совпадает с подспутниковой точкой CP (см. фиг. 6). Рассмотрение в качестве CP поочередно CP₁ и СР₂ приводит к получению параметров положения

и

соответственно.The position parameter range R _CP-PT is the distance between CP and PT. The position surface of the range parameter is a sphere with a center coinciding with the optical center of the CP antenna and radius R _CP-PT . The position line of the range parameter on the plane

- a circle whose center coincides with the sub-satellite point CP (see Fig. 6). Consideration as CP alternately CP ₁ and CP ₂ leads to obtaining position parameters

and

respectively.

представляет собой относительную радиальную скорость между ПТ и СР. Поверхность положения параметра скорости изменения дальности - круглый конус (далее просто конус) с вершиной, совпадающей с оптическим центром антенны CP, с осью, совпадающей с вектором

и с углом вращения, равным θ_СР-ПТ. Линия положения параметра скорости изменения дальности на плоскости

- гипербола, симметричная относительно

(см. фиг. 7). Рассмотрение в качестве CP поочередно CP₁ и СР₂ приводит к получению параметров положения

и

соответственно.Position parameter Range change rate

represents the relative radial velocity between the PT and SR. The position surface of the rate of change of range parameter is a round cone (hereinafter simply a cone) with a vertex coinciding with the optical center of the CP antenna, with an axis coinciding with the vector

and with a rotation angle equal to θ _CP-PT . The position line of the parameter of the rate of change of range on the plane

- hyperbole symmetric with respect to

(see Fig. 7). Consideration as CP alternately CP ₁ and CP ₂ leads to obtaining position parameters

and

respectively.

In an alternative embodiment, it is assumed that the PT does not move relative to the earth's surface. In real conditions, the AT can be placed on a wide class of moving objects (car, helicopter, airplane, etc.). The motion of the PT relative to the earth's surface introduces additional Doppler frequency shifts into the received and transmitted test signals of the system. Such shifts can not be taken into account if the speed of CP relative to the earth's surface significantly exceeds the speed of the PT relative to the earth's surface. But when these speeds are comparable, then to calculate the parameters of the rate of change of range and the difference of the speeds of change of ranges, it is necessary to take into account additional Doppler frequency shifts of the test signals of the system due to the movement of the ground relative to the ground.

The sequence of stages of the implementation of the claimed method of weapons of mass destruction can be considered using the one shown in FIG. 8 algorithms.

,

, 4) частотные сдвиги

,

рабочих частот CP₁, CP₂, 5) модуль

, азимут γ_ПТ вектора скорости ПТ и его высота h_ПТ, 6)

- средний радиус Земли,

- радиус Земли на экваторе; е_З≈0,081819 - эксцентриситет эллипсоида Земли, 5) порог ξ - допустимое расстояние между истинными и определенными координатами ПТ.Stage 1. Input of initial data. The initial data, in accordance with the notation introduced above, are: 1) UMS coordinates (x ₀ , y ₀ , z ₀ ), 2) coordinates CP ₁ (x ₁ , y ₁ , z ₁ ) and CP ₂ (x ₂ , y ₂ , z ₂₎ and 3) velocity vectors

,

4) frequency shifts

,

operating frequencies CP ₁ , CP ₂ , 5) module

, azimuth γ _PT of the velocity vector of the PT and its height h _PT , 6)

- the average radius of the Earth,

- the radius of the Earth at the equator; e _З ≈0.081819 is the eccentricity of the Earth's ellipsoid, 5) the threshold ξ is the allowable distance between the true and certain coordinates of the PT.

Stage 2. Measurement of time delays and frequency shifts of the test signals of the system.

и

. Тестовыми сигналами при этом являются две известные псевдошумовые (ПШ) последовательности.Time delays between transmitted and received test signals of the system are used to determine position parameters

and

. The test signals in this case are two known pseudo-noise (PN) sequences.

To measure time delays perform the following operations:

и

.1. The UMC emits two known test signals, which are PN sequences, and remembers the radiation time of each of these signals

and

.

и

.2. The PT receives the first test signal through CP ₁ , the second test signal through CP ₂ and re-emits them immediately, or with known delays

and

.

и

и вычисляет задержки двусторонних распространений сигналов

и

, соответствующих траекториям УМС-СР₁-ПТ-CP₁-УМС и УМС-СР₂-ПТ-СР₂-УМС:3. The UMS receives the first test signal through CP ₁ , the second test signal through CP ₂ , measures the reception time of each of these signals

and

and calculates the delay of two-way signal propagation

and

corresponding to the trajectories of UMS-SR _1- PT-CP _1- UMS and UMS-SR _2- PT-CP _2- UMS:

,

,

.

.

и

. Тестовые сигналы, представляющие собой два узкополосных сигнала с центральными частотами

и

, передают УМС через СР₁, СР₂ и принимают ПТ. На траекториях УМС-СР₁-ПТ и УМС-CP₂-ПТ центральные частоты сигналов подвержены сдвигам, среди которых можно выделить:The frequency shifts between the transmitted and received test signals of the system are used to determine position parameters

and

. Test signals, which are two narrow-band signals with center frequencies

and

transmit UMS through CP ₁ , CP _2, and receive PT. On the trajectories of UMS-SR _1- PT and UMS-CP _2- PT, the central signal frequencies are subject to shifts, among which are:

,

рабочих частот CP₁, СР₂,- given frequency shifts

,

operating frequencies CP ₁ , CP ₂ ,

,

, обусловленные движением CP₁ и CP₂ относительно УМС,- Doppler frequency shifts

,

due to the movement of CP ₁ and CP ₂ relative to the UMC,

,

, обусловленные движением CP₁ и CP₂ относительно ПТ,- Doppler frequency shifts

,

due to the movement of CP ₁ and CP ₂ relative to the PT,

,

, обусловленные движением ПТ относительно CP₁ и CP₂.- Doppler frequency shifts

,

due to the movement of the PT relative to CP ₁ and CP ₂ .

The indicated shifts of the central frequencies of the test signals can be expressed analytically:

,

- значения центральных частот тестовых сигналов после прохождения обозначенных траекторий и соответствующих сдвигов.Where

,

- the values of the central frequencies of the test signals after passing the indicated trajectories and the corresponding shifts.

In the considered method, it is possible to measure the central frequencies of the test signals in the DT with the subsequent transfer of information about them to the UMC.

и

и частотные сдвиги

,

тестовых сигналов системы.Thus, during this stage, time delays are determined

and

and frequency shifts

,

test signals of the system.

и

.Step 3. Parameter Definition

and

.

и

в момент времени измерения временных задержек

и

используя выражения:The known coordinates CP ₁ , CP ₂ and UMS allow you to calculate distances

and

at time measurement of time delays

and

using expressions:

where x ₀ , y ₀ , z ₀ are the coordinates of the UMC, x ₁ , y ₁ , z ₁ are the coordinates of CP ₁ , x ₂ , y ₂ , z ₂ are the coordinates of CP ₂ .

и

можно рассчитать по формулам:Position Parameters

and

can be calculated by the formulas:

Stage 4. Calculation of coordinates of the probable position of the PT; PT) and PT ₂ .

During this stage, the coordinates of the transformer are calculated with a large error reaching 500 km and, as will be shown below, with ambiguity not resolved.

представляющим собой средний радиус Земли, что для приблизительных расчетов вполне допустимо.At this stage, a sphere with radius

representing the average radius of the Earth, which is acceptable for approximate calculations.

The task of calculating the coordinates of the probable position of the PT can be reduced to solving a system of three equations with three unknowns x, y, and z, which are the Cartesian geocentric coordinates of the PT:

третье выражение - уравнение сферы с центром, совпадающим с оптическим центром антенны СР₂ и радиусом

The system of equations (5) a first expression - the equation of a sphere whose center coinciding with the center of the Earth and a radius equal to the sum of the average Earth radius R _W and the height PT h _TP, the second expression - the equation of a sphere whose center coinciding with the optical center of the antenna CP ₁ and radius

the third expression is the equation of a sphere with a center coinciding with the optical center of the antenna CP ₂ and radius

In FIG. 9 schematically shows: L ₁ is the position surface corresponding to the first expression of the system of equations (5), L ₂ is the position line on the surface L ₁ corresponding to the second expression of the system of equations (5), L ₁ is the position line on the surface L ₁ corresponding to the third expression of the system of equations (5). Points S ₁ and S ₂ show sub-satellite points CP ₁ and CP ₂ .

Due to the geometrical features of constructing the CCS for CP in the geostationary orbit, the ambiguity of the results of the FGM OT occurs, since the position lines Z ₂ and L ₃ intersect at two points UT ₁ and UT ₂ , as shown in FIG. 9, while one point will be in the northern hemisphere of the Earth, the other in the southern.

и

являющихся декартовыми координатами точек ПТ₁ и ПТ₂, соответственно.The analytical solution to the system of equations (5) will be two triples of real roots

and

which are the Cartesian coordinates of the points PT ₁ and PT ₂ , respectively.

Stage 5. Disambiguation, selection of the starting point PT ₀ .

In most cases, hemispheric ambiguity can be eliminated even before the establishment of a PT communication session. It is also possible to use additional a priori information about the PT, for example, the probability of its simultaneous falling into the radio-visibility zones CP ₁ and CP ₂ .

и

В результате новыми линиями положения будут

и

(штриховые линии) и, как следствие, искомая точка ПТ₁ останется в том же месте, а ложная изменит свое положение на

Аналитически такая трансформация выразится в повторном составлении и решении системы уравнений (5) с новыми координатами CP₁ и СР₂, а также новыми параметрами положения

и

However, in the general case, in the UMC CCC there is no information about the location of the PT. In this case, a method of eliminating the arising ambiguity is used, the implementation of which for a fixed PT is shown in FIG. 10. The first part in FIG. 10, shown in solid lines, is similar to the figure in FIG. 9 and corresponds to the first moment in time. The second moment of time is characterized by the fact that as a result of their movement, CP ₁ and CP ₂ will shift, while the sub-satellite points also change their coordinates by

and

As a result, the new lines of position will be

and

(dashed lines) and, as a result, the desired point of PT ₁ remains in the same place, and the false one changes its position to

Analytically, such a transformation will be expressed in the re-compilation and solution of the system of equations (5) with new coordinates CP ₁ and CP ₂ , as well as new position parameters

and

и азимут α_ПТ вектора скорости ПТ позволяют рассчитать смещение ПТ, которое считают одинаковым для обеих вероятных точек. В качестве примера на фиг. 11 показано перемещение ПТ в северовосточном направлении, в результате чего точки ПТ₁ и ПТ₂ сместятся соответственно в точки ПТ₃ и ПТ₄. Процедура построения новых линий положений

и

(штриховые линии) через определенное время позволяет сделать выбор в пользу точек ПТ₁ и ПТ₃, исключив точки ПТ₂ и ПТ₄, тем самым устранив неоднозначности ОМП ПТ.In the case of the mobile AT shown in FIG. 11, the reasoning is similar with the difference that during the displacement CP ₁ and CP _{2 the} PT also moves. Famous module

and the azimuth α _PT of the velocity vector of the PT allows you to calculate the offset of the PT, which is considered the same for both probable points. As an example in FIG. 11 shows the movement of the PT in the northeastern direction, as a result of which the points of PT ₁ and PT ₂ will move to the points of PT ₃ and PT _4, respectively. Procedure for constructing new position lines

and

(dashed lines) after a certain time allows you to make a choice in favor of points PT ₁ and PT ₃ , excluding the points PT ₂ and PT ₄ , thereby eliminating the ambiguities of the PMF PT.

для поиска более точных координат ПТ итерационным методом с использованием параметров

и/или

Thus, for both a stationary and a moving vehicle, it is possible to eliminate the ambiguity of its WMD by the above method. In the presented options, the choice is made in favor of the coordinates of the northern hemisphere of the Earth - the point of PT. Further, the selected point acts as the starting point of PT ₀ with coordinates

to search for more accurate coordinates of the iterative method using parameters

and / or

Step 6. Is the ambiguity resolved?

и

Затем на этапе 4 повторно рассчитывают вероятные координаты ПТ и на этапе 5 устраняют неоднозначность. При следующем прохождении этапа 6 неоднозначность уже устранена и выполняют переход к следующему этапу.The essence of this stage is partially disclosed in the explanation of stage 5. So, if during the first passage of the algorithm there is no additional a priori information about PT, then the ambiguity cannot be eliminated. Then go to step 3, where after some time the parameters are re-determined

and

Then, in step 4, the probable coordinates of the PT are recalculated and in step 5 the ambiguity is eliminated. At the next step 6, the ambiguity is already eliminated and the transition to the next step is performed.

For a sufficient offset of CP ₁ and CP ₂ , a relatively short time is required - a few minutes. In addition, in order to save time, disambiguation must be performed when registering a subscriber in the network. Then, at the time of establishing the connection, the ambiguity will already be eliminated.

Step 7. Refinement of the coordinates of the PT ₀ .

в точке ПТ₀. Обозначим, полученную на этапе 5, исходную точку ПТ₀, как ПТ₀₁, а ее координаты

Точку с учетом корректировки по высоте обозначим ПТ₀₂, а ее координаты

At this stage, the coordinates of the starting point PT ₀ in height are adjusted taking into account the sphericity of the Earth, and also find the equivalent radius of the Earth

at the point PT ₀ . Denote, obtained in step 5, the starting point PT ₀ , as PT ₀₁ , and its coordinates

The point, taking into account the height adjustment, is denoted PT ₀₂ , and its coordinates

Вторая поверхность - эллипсоида вращения с центром в точке О, большой полуосью, равной радиусу Земли на экваторе

и эксцентриситетом e_З≈0,081819 (модель Земли - ПЗ.90.02). Третья поверхность - сфера с центром в точке О и радиусом, равным радиусу Земли

в точке ПТ.In FIG. 12 shows sections of three surfaces by a meridian plane passing through the center of the Earth — point O and PT ₀₁ . The first surface is a sphere centered at point O and a radius equal to the average radius of the Earth

The second surface is an ellipsoid of revolution centered at point O, with a semi-major axis equal to the radius of the Earth at the equator

and eccentricity e _З ≈0.081819 (Earth model - ПЗ.90.02). The third surface is a sphere centered at point O and a radius equal to the radius of the Earth

at point PT.

, и точка ПТ₀₂, расположенная на высоте h_ПТ от сферы с радиусом

Also in FIG. 12 shows point PT ₀₁ located at a height h of _PT from a sphere with radius

, and the point PT ₀₂ located at a height h of the _PT from a sphere with a radius

зависит от широты φ_ПТ и максимален на экваторе, где принимает значение

минимален на полюсах, где принимает значение

(радиус Земли на полюсе). В общем случае выражение для расчета

выглядит следующим образом:Sphere radius

depends on the latitude φ _PT and is maximum at the equator, where it takes on the value

minimum at the poles, where it takes on value

(radius of the Earth at the pole). In the general case, the expression for the calculation

as follows:

- радиус Земли на полюсе, вычисляемый по формуле:Where

- the radius of the Earth at the pole, calculated by the formula:

The geocentric latitude φ _PT and the geocentric longitude λ _{PT of the} starting point of PT _{01 are} calculated by the formulas:

- декартовы координаты точки ПТ₀₁,Where

- Cartesian coordinates of the point PT ₀₁ ,

The values of φPT and λ _{PT are} left unchanged for PT ₀₂ . Then the Cartesian coordinates of PT ₀₂ are equal to:

- декартовы координаты точки ПТ₀₂.Where

- Cartesian coordinates of the point PT ₀₂ .

В качестве земной поверхности используют сферу с центром в точке О и радиусом

Next, as the coordinates of the starting point of PT ₀ take the coordinates of PT ₀₂ and designate them as

As the earth's surface, use a sphere with a center at point O and a radius

и

Step 8. Parameter Definition

and

и

позволяют рассчитать радиальные скорости

и

показанные на фиг. 2.Known YMC location coordinates points (x _0, y _0, z _0), CP ₁ (x _1, y _1, z _1), SR ₂ (x _2, y _2, z _2), and the known coordinates of the vectors

and

allow you to calculate radial speeds

and

shown in FIG. 2.

равна:According to equation (1), the radial velocity

is equal to:

скорости CP₁ равен:Vector module

speed CP ₁ is equal to:

- декартовы координаты вектора

Where

are the Cartesian coordinates of the vector

From the scalar product of vectors theorem we have:

Substituting (7) and (8) in (6), we obtain:

Similarly calculate the radial velocity

- декартовы координаты вектора

.Where

are the Cartesian coordinates of the vector

.

рассчитывают радиальные скорости

и

Given the location of the point at the starting point of point ₀ with coordinates

calculate radial speeds

and

и

равны:According to equation (1)

and

equal to:

скорости ПТ известен.Vector module

PT speed is known.

Using the scalar product of vectors theorem, taking into account (9), we have:

- координаты вектора

скорости ПТ в декартовой геоцентрической системе координат при условии нахождении ПТ в начальной точке ПТ₀.Where

- vector coordinates

speed of a point in a Cartesian geocentric coordinate system, provided that the point is at the starting point of point ₀ .

In FIG. Fig. 13 shows the geocentric Cartesian coordinate system, where the origin is the point O coinciding with the center of the Earth, the OXY plane coincides with the equator plane, the OX axis lies in the plane of the zero (Greenwich) meridian, the OZ axis is directed along the Earth's rotation axis, the OY axis complements the system coordinates to the right.

в геоцентрической декартовой системе рассмотрим сначала местную топоцентрическую декартову систему координат Z′O′Y′X′, представленную на фиг. 13, начало которой - точка О′ - совмещена с точкой ПТ₀, а плоскость Z′O′Y′ совмещена с плоскостью

.To find the coordinates

in a geocentric Cartesian system, we first consider the local topocentric Cartesian coordinate system Z′O′Y′X ′ shown in FIG. 13, the beginning of which - the point O ′ - is aligned with the point PT ₀ , and the plane Z′O′Y ′ is aligned with the plane

.

скорости ПТ будут равны:Obviously, in the coordinate system Z′O′Y′X ′ the coordinates of the vector

PT speeds will be equal to:

- топоцентрические декартовы координаты вектора

скорости ПТ в системе координат Z′O′YX′.Where

- topocentric Cartesian coordinates of the vector

PT speeds in the coordinate system Z′O′YX ′.

к геоцентрическим декартовым координатам производится посредством поворота системы координат относительно осей O′Y′ и О′Х′ на углы φ_ПТ и λ_ПТ соответственно и смещения начала координат из точки О′ в точку О.Transition from topocentric Cartesian coordinates

to geocentric Cartesian coordinates by rotating the coordinate system relative to the axes O′Y ′ and O′X ′ by the angles φ _PT and λ _PT, respectively, and shifting the origin from point O ′ to point O.

The analytical expression of such transformations, taking into account (11), can be represented in matrix form:

The system of equations (2) taking into account (1) can be rewritten in the form:

и

которые можно выразить следующим образом:In the system of equations (12) only

and

which can be expressed as follows:

Step 9. Calculation of the current coordinates of the PT.

When calculating and refining the coordinates of the starting point PT ₀ (steps 3 ... 7), situations may arise in which there is a geometric factor in the decrease in accuracy due to the small angle between the lines of position L ₂ and L ₃ , as a result of which the error of the GSS of the PT reaches 500 km, which not acceptable for CCC.

и/или

призвано повысить точность ОМП ПТ. Схема реализации итерационного метода повышения точности ОМП ПТ представлена на фиг. 14. Сущность метода можно описать следующим алгоритмом:Using Position Parameters

and / or

Designed to improve the accuracy of weapons of mass destruction. A diagram of the implementation of the iterative method for improving the accuracy of the WMD of the PM is presented in FIG. 14. The essence of the method can be described by the following algorithm:

и/или

(этап 8) в плоскости

определяют линии положения L₃ и/или L₄;1) Based on calculated position parameters

and / or

(step 8) in the plane

determining the position lines L ₃ and / or L ₄ ;

2) According to the selected decision rule, using the positions of the lines L ₂ and L _3, and L ₃ and / or L ₄ define a point 36 (see. FIG. 14), which is the current point TP (x _PT, y _PT, z _PT ).

3) Since the true coordinates of the PT indicated in FIG. 14, point 35, the unknown and how close the current point 36 with the coordinates (x _PT, y _PT, z _Fr) to point to the true coordinates. However, indirectly, the approximation of a point with current coordinates to a point with true coordinates can be judged by the so-called step distance between the previous and current points of the PT coordinates, estimated by the inequality:

where ξ is the predefined (step 1) allowable distance between the true and certain coordinates of the PT.

и/или

(этап 8). На основе новых параметров положения

и/или

заново определяют соответствующие им линии положения, обозначенные на фиг. 14

и

Определяют точку 37 и проверяют неравенство (13).4) In the event that inequality (13) is true, the current coordinates of the PT are taken as the coordinates of PT ₀ . Then redefine the position parameters

and / or

(step 8). Based on new position parameters

and / or

redefine their corresponding position lines indicated in FIG. fourteen

and

Point 37 is determined and inequality (13) is checked.

и

получают координаты точки 38 и снова проверяют неравенство (13). Количество шагов (итераций), как правило, не превышает пяти.5) If the distance between points 36 and 37 is greater than ξ, that is, inequality (13) is again true, the procedures of paragraph 4 of the algorithm are repeated: the position lines indicated in FIG. fourteen

and

get the coordinates of point 38 and check inequality (13) again. The number of steps (iterations), as a rule, does not exceed five.

6) In the event that inequality (13) is incorrect, the iterative algorithm is completed, the coordinates of the current point are taken as the required coordinates of the PT.

Consider the analytical solution of the presented algorithm.

, представляет собой круглый конус, схематически изображенный на фиг. 15, с вершиной О′, совпадающей с оптическим центром антенны CP₁, направляющей осью Z″, совпадающей с вектором

скорости CP₁ и углом вращения

который можно рассчитать по формуле:Position surface corresponding to the position parameter

is a circular cone, schematically depicted in FIG. 15, with the vertex O ′ coinciding with the optical center of the antenna CP ₁ , the guiding axis Z ″ coinciding with the vector

speed CP ₁ and rotation angle

which can be calculated by the formula:

In FIG. Figure 15 shows the geocentric Cartesian coordinate system ZOXY, considered earlier, as well as the coordinate system Z′O′X′Y ′, obtained by parallel transfer of ZOXY to the origin, which coincides with the optical center of antenna CP ₁ .

The equation of the round cone in the coordinate system Z ″ O′X ″ T ″ (the axis O′X ″ and O′Y ″ in Fig. 15 are not shown, so as not to clutter up the picture) has the form:

where x ″, y ″ and z ″ are the coordinates in the coordinate system Z ″ O ″ X ″ Y ″, associated with the coordinates in the geocentric coordinate system ZOXY by the following relation in matrix form:

- угол между осью O′Z″ и осью O′Z′,

- угол между

и осью ОХ′,

- проекцией вектора

на плоскость O′X′Y′.Where

- the angle between the axis O′Z ″ and the axis O′Z ′,

- angle between

and axis OX ′,

- vector projection

to the plane O′X′Y ′.

и

рассчитывают по формулам:Angles

and

calculated by the formulas:

The equation of the round cone in the geocentric coordinate system ZOXY, taking into account (13) and (14), takes the form:

, имеет вид:Similarly, the circular cone equation in the geocentric coordinate system ZOXY, corresponding to the position parameter

has the form:

рассчитывают по формулам:where are the angular values

calculated by the formulas:

на радиус Земли

в точке ПТ, который был рассчитан на этапе 7.The implementation of the considered algorithm of the iterative method for increasing the accuracy of the WMD of the FS in the analytical form reduces to adding equations (15) and / or equations (16) to the system of equations (5) and solving the resulting system. In the new system of equations in the first expression, the value of the average radius of the Earth is replaced

on the radius of the earth

at the point PT, which was calculated in step 7.

The system of equations obtained in this way will consist of four or five equations and will include three unknowns x _PT , y _PT , z _PT . The calculation of the roots of such equations is possible using well-known numerical methods, for example, using the least squares method. The solution to the system of equations will be the coordinates of the PT in the Cartesian geocentric system.

Step 10. The distance between the points PT ₀ and PT greater than ξ?

The essence of this stage is disclosed when explaining the third point of the iterative method of increasing the accuracy of the WMD of the stage 9.

Step 11. As the coordinates of PT ₀ take the coordinates of the PT.

The essence of this stage is disclosed when explaining the 6th point of the iterative method for increasing the accuracy of the WMD of stage 9.

Step 12. Output the results.

The Cartesian coordinates of the PT (x _PT , y _PT , z _PT ) are the results of the considered algorithm, from which the polar coordinates are calculated - geocentric latitude and geocentric longitude according to the formulas:

Simulation of the claimed method of the OMP PT using two CPs showed an increase in the accuracy of determining the coordinates of the PT when changing the speed of its movement by 20 ... 50% (depending on the magnitude of the velocity vector of the PT), due to a more accurate determination of the frequency shifts of the system signals without significant complication of the PT equipment and UMS implementing it.

Claims (1)

The method for determining the location (OMP) of a user terminal (PT) using two satellite transponders (CP) CP ₁ , CP ₂ and a gateway node (UMC), which is based on measurements of time delays and frequency shifts between transmitted and received test signals of the system, taking into account the known coordinates CP ₁ , CP ₂ , their velocity vectors

,

, UMS coordinates and predefined frequency shifts

,

operating frequencies CP ₁ , CP ₂ , determine the distance

between the first CP ₁ and PT, determine the distance

between the second SR ₂ and PT, 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 CP ₂ relative to the PT, after which the latitude φ _PT and the longitude λ _{PT of the} user terminal are calculated, characterized in that to calculate the latitude φ _FR and the longitude λ _{PT of the} user terminal, the module is additionally measured

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

, and when determining at least one of the parameters:

and / or

additionally take into account Doppler frequency shifts

and

, moreover, to determine the parameter

in PT measure the frequency

first narrow-band test signal emitted by the UMC at a frequency

and relayed through CP ₁ with a signal shift frequency

transmit the measurement result to the UMC, determine the Doppler frequency shift

first signal due to the radial velocity CP ₁ relative YMC determine Doppler frequency shift

the first signal due to the radial velocity of the PT relative to CP ₁ , then calculate the parameter

, in addition, to determine the parameter

in PT measure the frequency

the second narrowband test signal emitted by the UMC at a frequency

and relayed through CP ₂ with a signal shift frequency

transmit the measurement result to the UMC, determine the Doppler frequency shift

the second signal due to the radial speed of SR ₂ relative to the UMC, determine the Doppler frequency shift

the second signal due to the radial velocity of the PT relative to SR ₂ , then calculate the parameter

.

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