RU2286584C2 - Method for independent instantaneous determination by users of co-ordinates of location, velocity vector components, angular orientation in space and phase of carrier phase of radio signals of ground radio beacons retransmitted by satellites - Google Patents

Abstract

FIELD: satellite radio navigation, geodesy, communication, applicable for independent instantaneous determination by users of the values of location co-ordinates, velocity vector components of the antenna phase centers of the user equipment, angular orientation in space and bearing.

SUBSTANCE: the method differs from the known one by the fact that the navigational information on the position of the antenna phase centers of ground radio beacons, information for introduction of frequency and time corrections are recorded in storages of the user navigational equipment at its manufacture, that the navigational equipment installed on satellites receives navigational radio signals from two and more ground radio beacons, and the user navigational equipment receives retransmitted signals from two satellites.

EFFECT: high precision of navigational determinations is determined by the use of phase measurements of the range increments according to the carrier frequencies of radio signals retransmitted by satellites.

3 dwg, 1 tbl

Description

The present invention relates to the field of satellite radio navigation, geodesy, communication, and can be used for offline instant determination by users of the coordinates of the location of the components of the velocity vector of the phase centers of the antennas of satellite sources of radio emission, location coordinates and components of the velocity vector of the phase centers of the antenna of user equipment, angular orientation in space and bearing, as well as for the integration of currently operating narrow-target satellite systems appointments to the multipurpose global integrated satellite system (GISS), creating a global information space for providing users with navigation, geodesy, communication, monitoring, control and a number of other services in real time, at any time, anywhere in the world and on the highest level.

There is a method of determining location coordinates, components of the velocity vector of navigational artificial Earth satellites (NIE) and users of satellite radio navigation systems (SRNS), implemented, for example, in SRNS of the second generation of the American Global Positioning System (GPS) [1].

Each GPS satellite, and they are in system 24, continuously emit radio signals and transmit their own navigation messages containing service information, information about time, ephemeris, parameters for introducing corrections, about the components of the satellite velocity vector, etc. Navigation equipment of users (NAP) simultaneously receive navigation radio signals from four NESA, measure the pseudorange between navigating users and NIEA and make the calculations necessary to solve the navigation problem.

The formation of arrays of navigation information, as well as their loading into the memory of the electronic computing means of the corresponding NESS, is carried out by ground control stations (CS) that control the orbits of the NIE, the divergence of the NISS time scales with the system time and the ephemeris of each NIE.

Using the information of navigation messages received by the NAP and pseudorange measurements of up to four selected NISS, the functional relationships are established between the known values of the NISS coordinates and the unknown values of the coordinates of the SRNS users. Determining the coordinates of users comes down to solving systems of four navigation equations with four unknowns.

As a result of solving the system of navigation equations, four unknowns are determined: three coordinates of the user's location (X _P , Y _P , Z _P ) and an amendment to his time scale (correction to his clock).

The geometric equivalent of the final algorithm for solving the navigation problem of this known method is the construction of four position surfaces with respect to the NIE used, the intersection point of which is the desired position of the users.

,

,

) и поправку к частоте местного эталона частоты.Similarly, using the results of measurements, but already quasi-velocities, three components of the user velocity vector are determined (

,

,

) and an amendment to the frequency of the local frequency standard.

The disadvantages of this method are:

- the need to be in the radio visibility zone of the navigating user at the same time four NIZZ;

- the need for content in the ARNS 24 and more NIH;

- the presence of a ground network of CS, determining the coordinates of the location of the NESZ (ephemeris);

- forecasting and laying on board the ephemeris of each NISS;

- low accuracy of navigation definitions.

There is also a method for determining the location coordinates, components of the velocity vector of the phase centers of the antennas of satellite sources of navigation signals and phase centers of the antennas NAP SRNS (RF Patent No. 2210788) [2], in which the navigation equipment installed on each satellite is received continuously emitted by ground navigation radio beacons (NNRM) navigation radio signals modulated by navigation information, rangefinding codes and containing the coordinates of the location of the phase centers NNRM, time and information for making corrections in frequency, time, is measured on measured intervals of distance, the difference of distances between phase centers of antennas of LNRM and phase centers of antennas on NISS, measure the rate of change of range in the middle and at the edges of measured intervals, the difference of navigation speeds signals, then the carriers of the received navigation signals are modulated with the measured information, amplify them and relay in the direction of the Earth, which receive the NAP installed on the SRNS users, measure at the edges in the middle of the measured ranges of the distance, the difference of the distances between the phase centers of the NISS antennas and the phase centers of the NAP, the rate of change of the ranges, the difference of the rates of the change of ranges, information is provided on the coordinates of the location of the phase centers of the antennas of the NNRM, on the corrections to the frequencies and delays, the time and the measured, allocated Information is determined by:

- modules of the position vector of the phase center of the receiving antenna ON NISS;

- modules of the position vector of the phase center of the antenna of the source of the navigation radio signal (ANN) NISS;

- the value of the cosine of the angle between the vectors of the bases connecting the beginnings and ends of the measured intervals, and the distance vectors connecting the positions of the phase center of the antenna ННРМ and the position of the phase center of the receiving antenna ON NISS;

- values of the cosine of the angle between the vectors of the bases connecting the beginning and the ends of the measured intervals, and the distance vectors connecting the positions of the phase center of the NAP antenna and the position of the phase center of the antenna of the ANN NISS;

- base vector modules;

- modules of the position vector of the phase center of the antenna of the NNRM;

- modules of the position vector of the phase center of the antenna NAP SRNS;

- the values of the angles between the range vector connecting the position of the phase center of the antenna of the NNRM and the position of the phase center of the antenna of the NISS, and the position vector of the phase center of the antenna of NNRM;

- the values of the angles between the distance vector connecting the position of the phase center of the NAP SRNS antenna and the position of the phase center of the ANN NISS antenna and the position vector of the phase center of the NAP antenna, then establish the system of functional dependencies between the known values of the coordinates of the phase centers of the NNRM antennas and the unknown coordinates of the phase centers of the antennas ON NISS, determine the values of the coordinates and components of the velocity vector of the phase centers of the antennas NA, ANN NISS, and then establish the system of functional dependencies between the known values of the coordinates that make up the velocity vector of the phase centers of the antennas of the ANN NISS antenna and the unknown values of the coordinates that make up the velocity of the phase centers of the phase centers of the NAP antennas and determine the location coordinates that make up the velocity vectors of the phase center of the antennas of the NAP antennas of SRNS users by solving the system of navigation equations.

The disadvantages of this method, taken as a prototype, are:

- low accuracy of navigation measurements and definitions, reliability and reliability due to satellites relaying navigation information and ranging codes of ground navigation radio beacons (NNRM);

- it is impossible to navigate to users using the carrier frequencies of the radio signals of other satellite systems;

- it is impossible to determine by users their orientation in space, bearing when receiving satellite radio signals on one weakly directed antenna;

- It is difficult to integrate narrow-purpose satellite systems into multi-purpose ones.

The known method (prototype) is characterized by the following set of actions:

- navigation radio signals, the carriers of which are modulated by rangefinding codes and navigation information, as well as information for introducing corrections in frequency and time, emit NRM;

- navigation equipment installed on the satellites receive the radiated HHM radio signals, measure using rangefinder distance codes, the distance difference between the phase centers of the HHHM antennas and the phase centers of the antennas of the navigation equipment mounted on the satellites, and also measure using the carrier tracking system (CCH) range increment values due to Doppler frequency shifts, Doppler frequency values, range change rates, range change rate differences, modulate changes With the help of information provided, carriers of relayed radio signals amplify them and radiate in the direction of the Earth;

- NAP SRNS receive navigation radio signals relayed by satellite sources of navigation signals (SINS), measured using rangefinder range codes, range difference between phase centers of SINS antennas and phase centers of NAP antennas, and also using SSN values of range increments due to Doppler frequency shifts, values of Doppler frequencies, speed of range change, difference of speed of range change provide navigation information about the coordinates of the phase location NNRM centers antennas, information on frequency-time corrections to the frequency, delay, and time information measured by SNA and then measured for the selected NAM information SRNS define:

- modules of the position vector of the phase center center of the SNA antenna as the ratio of the geocentric gravitational constant to the product of the square of the speed of light and the difference between the unit and the ratio of the square of the frequency of the navigation radio signal received by the SNA to the square of the frequency of the navigation radio signal emitted by the NRM multiplied by the square of the sum of the unit and the ratio of the radial the speed of the phase center of the SNA antenna in the middle of measured intervals relative to the phase center of the HHP antenna to the speed of light;

- modules of the position vector of the phase center of the antenna of the satellite source of the navigation radio signal as the ratio of the geocentric gravitational constant to the product of the square of the speed of light and the difference between the unit and the ratio of the square of the frequency of the navigation radio signal received by the NAP to the square of the frequency of the navigation radio signal emitted by the SINS multiplied by the square of the difference between the unit and the ratio of the radial velocity of the phase center of the SINS antenna in the middle of the measured intervals relative to the phase center NAP antenna to the speed of light;

- values of the cosine of the angle between the vectors of the bases connecting the beginning and ends of the measured intervals, and the distance vectors connecting the positions of the phase center of the HHP antenna and the position of the phase center of the SNA antenna, as well as the angle as the ratio of the products of the radial velocity values of the phase center of the SNA antenna located in the middle of measured intervals relative to the phase center of the HHM antenna by the frequency of the navigation radio signal emitted by HHHM and the product of the speed of light by the square root of the difference the square of the value of the unit and the ratio of the radial velocity of the phase center of the SNA antenna located in the middle of the measured intervals relative to the phase center of the HHP antenna to the speed of light and as the arcsine of relations, respectively;

- the cosine of the angle between the vectors of the bases connecting the beginning and ends of the measured intervals, and the distance vectors connecting the positions of the phase center of the NAP antenna and the position of the phase center of the SINS antenna, as well as the values of its angle as the ratio of the products of the radial velocity values of the phase center of the SINS antenna located in the middle of the measured intervals relative to the phase center of the NAP antenna, by the frequency of the navigation radio signal emitted by SINS, by the product of the speed of light by the square root of the difference squares of the values of the frequency of the navigation radio signal emitted by SINS and squares of the values of the frequency of the navigation radio signal received by the NAP multiplied by the square of the difference between the unit and the ratio of the radial velocity of the phase center of the SINS antenna located in the middle of the measured intervals relative to the phase centers of the NAP antennas and the speed of light and as arccosine relations respectively;

- base vector modules as the product of the relationship of the distance difference between the phase center of the HHP antenna and the phase center of the SNA antenna at measured intervals, multiplied by the speed of light to the radial speed of the phase center of the SNA antenna, relative to the phase center of the HH antenna, multiplied by the value of the frequency of the navigation radio signal emitted by the HH antenna , the square root of the difference of the square of the values of the frequency of the navigation radio signal emitted by the HHM and the square of the values of the frequency of the navigation radio signal received by the SNA, and the square sum of one unit and the ratio of the radial velocity of the phase center of the SNA antenna located in the middle of the measured intervals, relative to the phase center of the HHP antenna, to the speed of light;

- base vector modules as a product of the relationship of the distance difference between the phase center of the SINS antenna and the phase center of the NAP antenna at measured intervals times the speed of light to the radial speed of the phase center of the SINS antenna relative to the phase center of the NAP antenna multiplied by the frequency value of the navigation radio signal re-emitted by the SINS , to the square root of the difference of the square of the values of the frequency of the navigation radio signal re-emitted by the satellite and the square of the values of the frequency of the navigation radio signal, take of NAP, multiplied by the difference between the square of unity and values of the ratio of the radial velocity of the antenna phase center Sins, sitting in the middle dimensional intervals, with respect to the phase center of the antenna NAP to the speed of light;

- the distance difference between the phase centers of the NNRM antennas and the phase centers of the SNA antennas, as well as the difference of the distances between the phase centers of the SINS antennas and the phase centers of the NAP antennas by extracting information about the phase increments of the carrier radio navigation signals due to Doppler frequency shifts in order to control the frequencies of the generators controlled by the voltage of the CCH in SNA and NAP;

- the distance between the phase center of the SINS antenna and the phase center of the NAP antenna as the ratio of the products of the radial velocity values of the phase center of the SINS antenna in the middle of measured intervals relative to the phase center of the NAP antenna, measured with the NAP, and the square of the base vector module determined by the measured interval, to the product of the difference radial velocities at the edges of measured intervals by the difference in distances, multiplied by the square of the sine of the arc cosine of the ratio of the values of the differences of distances, measured by extracting information information on the increments of the phases of the carrier of the navigation radio signals due to Doppler frequency shifts in the control circuit of the generator controlled by the voltage of the CCN NAP to the values of the base vector module;

- the distance between the phase center of the HHP antenna and the phase center of the SNA antenna as the ratio of the products of the radial velocity values of the phase center of the SNA antenna in the middle of the measured intervals relative to the phase center of the HH antenna, measured with the SSS of the SNA, and the square of the base vector module determined by the measured interval, to the product differences of radial velocities at the edges of measured intervals by a difference of distances multiplied by the square of the sine of the arc cosine of the ratio of the values of the differences of ranges, measured by highlighting inf rmatsii of carrier phase increments navigation signals caused by the Doppler frequency shift in the control circuits of generators, voltage controlled CCH CHA, to the values of the base module of the vector;

- the distance between the phase center of the HHP antenna and the phase center of the SNA antenna as the ratio of the distance difference between the phase center of the HH antenna and the phase center of the SNA antenna, measured with the help of the CCH as the increment of the distance on the measured interval, multiplied by the square of the speed of light, to the difference in the rate of change of ranges by the measured interval multiplied by the square of the frequency value of the navigation radio signal emitted by the NNRM, and the difference of ranges, multiplied by the difference of the squares of the frequency values of the navigation radio signal, rad of the studied NRM, and the squares of the values of the frequency of the navigation radio signal received by the SNA, multiplied by the square of the sum of one and the ratio of the radial velocity of the phase center of the SNA antenna to the speed of light, multiplied by the sine of the arc cosine of the ratio of the products of the values of the radial speed of the phase center of the SNA antenna by the frequency of the navigation of the radio signal emitted by the NNRM to the products of the difference of the ranges and the speed of light, multiplied by the square root of the difference of the square of the values of the navigation frequency the radio frequency signal emitted by the NRM and the square of the frequency values of the navigation radio signal received by the SNA, multiplied by the square of the sum of unity and the ratio of the radial velocity of the phase center of the SNA antenna to the speed of light;

- the distance between the phase center of the SINS antenna and the phase center of the NAP antenna as the ratio of the difference in the distances between the phase center of the SINS and the phase center of the NAP antenna, measured using CCH, as increments of the distance on the measured interval, multiplied by the square of the speed of light, to the difference in the rate of change of ranges on the measured interval, multiplied by the squares of the values of the frequency of the navigation radio signal emitted by SINS, and the difference of ranges, multiplied by the difference of the squares of the frequency value of the navigation radio signal, rad of the obtained SINS, and the squares of the frequency values of the navigation radio signal received by the NAP, multiplied by the square of the difference from unity and the ratio of the radial velocity of the phase center of the SINS to the speed of light, multiplied by the sine of the arc cosine of the product of the values of the radial speed of the phase center of the SINS by the frequency of the navigation of the radio signal emitted by SINS to the products of the difference of the ranges and the speed of light multiplied by the square root of the difference of the square of the values of the frequency nav NAVIGATION radio signal emitted Sins, and the square of the frequency values of navigation signal received NAP multiplied by the squared difference from unity and the ratio of the radial velocity Sins antenna phase center to the speed of light;

- establish systems of functional dependencies between the known coordinate values of the phase centers of the HH antenna antennas, as well as the known coordinates of the location of the beginning of the rectangular geocentric coordinate system and the unknown coordinate values of the phase centers of the SINS antennas, determine the coordinates and components of the velocity vector of the phase centers of the SINS antennas by solving systems of navigation equations, then establish systems of functional dependencies between the known values of the coordinates that make up the vector the speed of the phase centers of the SINS antennas, the known coordinates of the location of the beginning of the rectangular geocentric coordinate system and the unknown values of the coordinates that make up the velocity vector of the phase centers of the NAP antennas and determine the location coordinates that make up the velocity vector of the phase center of the NAP SRNS antennas by solving the corresponding systems of equations.

The technical task (goal) of the present invention is an autonomous instant determination by users of the coordinates of their location of the components of the velocity vector, the angular orientation in space and the bearing of the phase of the carrier radio signals of ground beacons relayed by satellites.

The goal is achieved through a new set of actions and the use of new algorithms for solving the navigation problem.

A geometric interpretation of the essence of the proposed method is illustrated in figures 1, 2, 3.

The figure 1 shows a geometric diagram illustrating navigation measurements and determining the coordinates of the phase center of the satellite antennas by phase of the carrier radio signals emitted by two ground beacons.

Figure 2 is a geometric diagram illustrating navigation measurements and determining the coordinates of the phase center of user antennas by phase of the carrier signals of ground-based radio beacons relayed by two satellites.

The figure 3 shows a geometric diagram illustrating the relationship of the measured azimuths using a compass and satellites with course correction in the coordinate system associated with the vessel,

where DP - directional bearing;

N is the true north direction;

N _to - direction to the north, measured by a compass;

X ^T , Y ^T , Z ^T - axis of a topocentric coordinate system.

The essence of the proposed method is as follows.

A network of simple automatic radio beacons located on the Earth's surface in such a way that in the radio visibility zone of each satellite there are continuously two beacons continuously emitting radio signal carriers. As beacons, for example, existing existing, stationary terminals of connected satellite systems or beacons continuously emitting carriers of radio signals can be used.

Main requirements: continuously emitted radio signals of beacons radiated sufficient carrier power for reliable reception of satellite transponders by receiving devices; the relayed signals had information about the belonging of the signals to the corresponding beacons, and the coordinates of the location of the beacons (phase centers of the antennas) were known with sufficient accuracy, which are recorded in their storage devices during the production of user equipment (AP).

The receivers of satellite transponders (MSSR) are continuously receiving carriers of radio signals from two or more radio beacons located in the radio visibility zone, and information about changes in the received carrier frequencies available in the generator frequency control circuits controlled by the voltage of the carrier tracking circuits (CCH) at the edges and in the midpoints of the same measured intervals in the satellite's time reference systems, the carriers of the radio signals are modulated, amplified and then radiated (relayed) in the direction of the Earth. At the same time, signals by radio beacons can be emitted in one frequency range, and relayed by satellites in another.

To determine the coordinates and speed, navigating users simultaneously receive, but already relayed beacon signals from two satellites, information on the belonging of the signals to the corresponding beacons and information on the changes in the received carrier signals of the ISSR is highlighted, and information on changes in the values of the carriers at the edges and in the middle of the measured data is recorded intervals available in the control circuits of voltage-controlled generators (VCO) SSN AP.

The extracted and recorded information in the AP allows us to calculate the navigation parameters, which in turn allow us to establish navigation dependencies between the known values of the direction cosines of the radio beacon position vectors and the unknown values of the direction cosines of the satellite position vectors. As a result of solving the system of navigation equations in the subscribers' equipment, the values and the directing cosines of the satellite position vectors are determined. Then, functional relationships are established between the known values of the guide cosines of the satellite position vectors and the unknown values of the guide cosines of the user position vectors. Next, the coordinates of the location of users without knowledge of the coordinates of the satellites are determined using only the known coordinates of the beacons recorded in the storage devices of the AP in the manufacture of the equipment.

When applying the proposed method for subscribers to independently determine their location, it is no longer necessary to transmit their own messages by each satellite, on the basis of which the navigation problem is being solved in the current NAP.

The proposed method for the autonomous location of satellites and users is based on a differential radial-velocity technique for measuring phase increments due to Doppler frequency shift. The modern radial-speed differential technique is based on measurements of Doppler frequency shifts that acquire radiated fluctuations of the nominal frequency on the propagation path between the end points in relative motion using satellite linear interferometers and tracking systems for carrier frequencies of signals received by receivers of satellites and satellite users systems.

, получим значение разности дальностей за время мерного интервала Т_M.In measurements using a differential radial velocity technique, the measuring interval is relatively small (units of seconds) and during T _{M the} measurement of phase increments (range increments) due to Doppler frequency shift can be considered linear. Dividing the result of measurements of phase increments by T _M , we obtain the value of the Doppler frequency (radial velocity) proportional to the instantaneous value, and dividing by the wave number

, we obtain the value of the difference of the ranges during the measuring interval T _M.

The classic representation of the principle of operation of the interferometer is the measurement of the phase difference of the oscillations received by two antennas spaced in space (direction finder). However, reception can be carried out on one antenna, but then the radiation of the received signal should be carried out by diversity antennas (phase beacon). A demonstration of the operation of the interferometer based on the second principle is the reception by users of satellite systems at measured intervals of radio signals emitted by moving satellites. The distance traveled by the satellite’s antenna (phase center) over the measuring interval is called the base (base distance d). Users of satellite systems are far from the centers of bases at distances many times greater than d. In this case, the directions of arrival of the satellite signals at measured intervals can be considered parallel and the distance difference can be written in the form [3]:

i = 1,2, ...,

where α _{t *} is the angle between the direction toward the user (phase center of the AP antenna) and the normal to the base passing through its center; π = 3.1415 ....

The user-satellite direction is determined by the steering angle θ _{t *} , measured relative to the base. The direction is often also characterized by the value cosθ _{t *} , which is called the directing cosine [4], [5].

Knowing the magnitude of the base and measuring the distance difference ΔR in one way or another, we can determine the direction to the direction finding satellite (radiation source).

In the phase method, the phase difference Δφ of the oscillations is measured. If the wavelength of the received oscillations is equal to λ, then

носит название крутизны пеленгационной характеристики или чувствительности [3].Where

is called the steepness of the direction-finding characteristic or sensitivity [3].

Since the phase difference Δφ is proportional to the directing cosine of the wave arrival angle, determining the direction by the phase method reduces to measuring the phase difference (range difference).

Thus, the sensitivity of the satellite interferometer, and therefore the direction finding accuracy, and the accuracy of measuring the radio navigation parameters increase with increasing d / λ ratio (increasing the measuring interval).

To reduce errors caused by phase fluctuation due to the medium in which the radio waves propagate, as well as due to phase readings, it is necessary that the size of the base exceed the effective radius of correlation of the inhomogeneities of the medium.

The geometric interpretation of measurements of radio navigation parameters using satellite linear interferometers and radial-velocity differential methods of the proposed method is illustrated in figures 1, 2.

Position surfaces for radial velocity are cones whose equations [5]

,

,

,

- радиальные скорости и линейные скорости кругового движения спутников, измеренные с применением информации ГУН ССН ПУСР и ГУН ССН АП об изменении несущих частот принимаемых сигналов соответственно.Where

,

,

,

- radial velocities and linear velocities of circular motion of satellites, measured using information from the VCO SSN PUSR and VCO SSN AP on changes in the carrier frequencies of the received signals, respectively.

The axes of these cones are directed along the satellite velocity vector, and the vertices at the moment of measuring the radial velocity are located in the phase centers of the satellite antennas. As the satellites approach the user, the radial velocity, while remaining negative, decreases in value, the angle θ increases (the cone “turns around”). At the moment of maximum approach of the satellites to the user, the angle θ = 90 ° the cone degenerates into a plane. Then the radial velocity becomes positive, θ> 90 ° (the cone is “turned inside out”).

Spatial sighting using satellite phase radio beacons (linear interferometers) allows you to indicate the angular position of the line connecting the phase center of the radio beacon antennas and the phase center of the satellite antennas, as well as the phase center of the satellite antennas and the phase center of the user antennas. The spatial direction finding process corresponds to many surfaces with which sight lines can be combined. In this case, position surfaces can only be those that have linear generators — ruled surfaces, for example, conical surfaces.

It is convenient to define the lines of sight with the guiding angles α, β, γ enclosed between these lines and coordinate axes. Instead of angles, it is possible to use the values of their cosines (cosα, cosβ and cosγ), which is convenient for finding the corresponding coordinate components along the axes through these direction cosines. Of the guide angles, only two are independent, and the third is determined through them.

One of the types of navigation measurements is the method of measuring the phase increments of the carrier navigation radio signals using a radial-velocity differential technique.

To measure the radionavigation parameter (the phase incursion of the carrier frequencies of the radio signals due to the Doppler frequency shift) using the radial-speed differential technique for processing phase measurements, SSN PUSR and SSN AP are used.

CCHs are designed to track the phase of carriers, extract information, and measure Doppler frequency shifts. To ensure fast carrier synchronization, a digital phase-locked loop (DFCA) is used. A phase-locked ring monitors the frequency variation of the input signal. Information about changing the frequency of the input signal is available in the frequency control circuit of the tuned VCO, with which the frequency of the signal generated by it is maintained equal to the frequency of the input signal.

The CFAPC ring is relatively simple and with high accuracy to measure the incidence of the non-cyclic phase of the output oscillation (i.e., a phase that varies within a range not limited to an interval of length 2π) on the measured interval. This makes it possible to apply relatively simple quasi-optimal algorithms for measuring phase increments from a signal masked by noise [6].

и ССН АП

включают в себя как основную (рабочую) составляющую фазы

обусловленные эффектом Доплера, так, дополнительную составляющую фазы

,

, вызванные рассогласованием временных шкал в радиолиниях «радиомаяки спутники», «спутники - пользователи» соответственноMeasured phase incursion using SSR PUSR

and CCH AP

include as the main (working) component of the phase

due to the Doppler effect, so, an additional component of the phase

,

caused by the mismatch of timelines in the radio beacons satellites, satellites - users, respectively

In the radial-speed differential mode of measurements, it can be considered that unknown phase increments caused by the instability of the frequencies of the reference generators of the terminal points of the radio measuring traces are kept constant during the measurement session and they are mutually compensated during the phase difference measurements. Therefore, in the expressions defining the values of the measured phase differences (phase increments), they are absent.

набега фаз на первой и на второй половинах мерного интервала и образования затем их разностей (двойных разностей фаз).In order to more significantly reduce the dispersion of phase measurements, the technology for measuring the phase incursion using the technique under consideration also provides for secondary averaging close to optimal. Secondary averaging of measurements is carried out by measuring averaged values

the phase incursion in the first and second halves of the measuring interval and then their differences (double phase differences) are formed.

In this case, in the measured values of the differences in the phase incursion, given that the unknown differences in the time scales are kept constant during the measurement session, they are mutually compensated and will also be absent in the final measured values of the radio navigation parameter.

Thus, the considered differential radial-velocity method for measuring the difference in the phase incursion of the oscillations of the carrier frequencies of navigation radio signals with double averaging over measured intervals makes it possible to almost instantly perform high-precision measurements of the current values of radio navigation parameters, which are the basis at first for determining navigation parameters, and then establishing functional navigation dependencies (algorithms) solutions to the navigation problem.

The main advantage of the high-speed differential radial method for measuring navigation parameters is the absence of systematic errors, errors due to the discrepancy between the time scales and frequencies of the beacon generators - satellites, satellites - users (subscribers).

в радиолинии «радиомаяк - спутник» и второй раз измеряется

в радиолинии «спутник - пользователь»The algorithm for estimating Doppler frequency shifts (phase difference of carrier frequencies due to Doppler frequency shift) is used twice in measuring navigation parameters. First time measured

in the radio beacon-satellite radio link and is measured for the second time

in the satellite - user radio link

спутниковой аппаратурой и аппаратурой пользователей соответственно будут определяться выражениямиThe actual measured values of the increments of ranges ΔR ^pr.s , ΔR ^pr.s , radial velocities

satellite equipment and user equipment will respectively be determined by the expressions

where f _0i is the oscillation frequency of the radio signals emitted by beacons; f _i - the frequency of oscillations of the radio signals relayed by satellites; c is the speed of light.

Using the measured values of the radio navigation parameters using satellite navigation equipment and user equipment, the navigation parameters themselves are calculated directly, which determine both the navigation determination algorithms and the proposed method as a whole.

The method of autonomous instant determination by users of subscribers of the location coordinates, components of the velocity vector, the angular orientation in space and the bearing by phase of the carrier signal of the radio signals of terrestrial beacons relayed by satellites, is based on the sequential measurement of navigation parameters expressing the distances between the phase centers of the beacon antennas - the phase centers of the satellite antennas and distances between phase centers of satellite antennas - phase centers of user antennas, as well as in measurement modules of the position vectors of satellites and users (distances from the location point of the origin of the geocentric coordinate system to the phase centers of the satellite antennas and phase centers of the user antennas) and the determination of the values of the directional cosines from the corresponding measurements. They can be implemented in the case when there are two beacons in the radio-visibility zone of each satellite, and two satellites in the radio-visibility zone of each user, the distances to which are measured simultaneously with appropriate consideration for the measured interval of their relative motion.

The proposed method allows you to implement two algorithms for solving the navigation problem: rangefinder and goniometric.

The initial data for solving the navigation problem of the proposed method are the coordinates of the beacons (phase centers of the antennas), the values of which do not change and are recorded in the storage devices of each set of APs during their manufacture and information on the change in the received frequencies of the carrier beacons and satellite repeaters available in the VCO control circuits SSN PUSR and AP. The corresponding navigation parameters then calculated allow us, in turn, to establish systems of navigation equations between the known values of the direction cosines of the local geocentric radius vectors and the unknown values of the direction cosines of the geocentric radius vectors. In the process of solving systems of equations, the values of the directing cosines of the radius position vectors of the satellites or the coordinates of the phase centers of the satellite antennas are determined directly. Next, the systems of navigation equations are established between the already known values of the directional cosines of the geocentric radius vectors (position vectors of the satellites) and the unknown values of the directional cosines of the radius vector of the position of the user.

To determine the values of the guiding cosines of the geocentric radius vectors, the systems of equations have the form

Where

X _M1 , Y _M1 , Z _M1 , ... X ^** _M3 , Y _M3 ^** , Z ^** _M3 - the coordinates of the first and second and third (in the radio-visibility zone of the satellite can be other beacons) reference ground beacons, respectively;

where cosA ₁ , cosA ₂ , cosA ₃ ^** , cosA ₄ ^** are the values of the cosines of the angles between the geocentric radius vector (R ₃ + Н _i ) ^etc. with local geocentric radius vectors (R ₃ + h ₁ ), ( R ₃ + h ₂ ), (R ₃ + h ₃ ) ^**, respectively; H ₁ , H ₂ - satellite heights; h ₁ , h ₂ , h ₃ ^** are the heights of the phase centers of the beacon antennas above the Earth's surface.

By the sine theorem

To determine the values of the directional cosines of the local geocentric radius vector and the coordinates of the location of users when users receive radio signals from two satellites using the known values of the directional cosines of geocentric radius vectors, systems of navigation equations are established

where cosB ₁ , cosB ₂ are the values of the cosines of the angles between the geocentric radius vectors (R ₃ + H ₁ ) ^a.s. , (R ₃ + H ₂ ) ^a.s. and the local geocentric vector R ₃ + h _P

As a result of solving systems of equations (5), (6), the values of the guide cosines of the user position vector and the location coordinates X _P , Y _P , Z _{P are} determined.

Equation 1, 2 of system (6) individually is an equation of a plane in space, and in aggregate, equations 1, 2 are a straight line. Therefore, the geometric equivalent of solving the system of equations as a whole is the point of intersection of a straight line with a spherical surface of radius (R ₃ + h _P ), the coordinates of which are the coordinates of the location of the phase center of the user’s antenna.

The system of equations (6) is the implementation of the algorithm of the range-finding method for solving the navigation problem, and the system of equations (5) is the goniometric method.

In accordance with the algorithm of the goniometric method for solving the navigation problem, the values of X _P , Y _P , Z _P can be determined using the known values of the directing cosines of the local geocentric radius vector (R ₃ + h _P ).

Similarly, using the known values of the direction cosines of the satellite position vector, you can determine the coordinates of the satellites

The components of the linear velocity vector, as well as the components of the angular velocity and angular acceleration vectors of the satellites relative to the axes of the geocentric coordinate system, are determined respectively from the expressions

The values of the direction cosines of the topocentric vectors are determined from the expressions

The values of the components of the user velocity vector are determined from the solution of the system of equations obtained after differentiating the equations of system (6).

As can be seen from the solution of the navigation problem to determine the coordinates of users, to find them it is enough to know the value of the coordinates of the phase centers of the antennas of the NNRM. The coordinates of the satellites are not explicitly applied. They are indirectly present in the values of the directing cosines of the satellite position vectors. Therefore, there is no need to determine them not only by ground-based means and transmit them to users using satellite radio links, but also to define them in general.

Thus, the proposed method allows to determine the location of user subscribers using both the ranging method and the goniometer method without knowing the coordinates of the location of the centers of the antennas of the sources of radiation of satellite radio signals.

In the differential radial-speed mode of measuring radio navigation parameters with double averaging of measurements, unknown phase increments due to the instability of the frequencies of the generators of the terminal points of the radio measuring traces, as well as additional phase components caused by the mismatch of the time scales in the radio beacon-satellite and user-satellite radio lines, will be preserved during measurement sessions lasting about several seconds, constant and in the process of measuring double phase differences they are almost mutually compensated. Therefore, in phase measurements on the carrier frequency, the mutual time reference of satellite radio signals of the orbital constellation is not required. Only the clock (time scales) of the satellites are synchronized. The navigation task is solved in the users timeline.

The determination of the values of the guiding cosines of the position vector of the satellites and the values of the guiding cosines of the position vector of the users are spaced in time on the time scale of users by no more than a few seconds. To bring them to a single time (the moment of solving the navigation problem), the guide cosines of the satellites are predicted in the AP, i.e. their current values are calculated at the time the user coordinates are determined. The law of satellite motion over a time interval of several seconds can be considered linear.

At the same time, the results of navigational measurements and determinations using the goniometric method make it possible to determine the components of linear velocity, the components of the angular velocity and angular acceleration vectors of the satellites relative to the axes of the geocentric coordinate system (8).

Some users, along with knowledge of the coordinates and components of the velocity vector, need to know the orientation of their own axes in space. Determining the orientation of the longitudinal axis of moving users relative to the direction to the true north comes down to measuring the true course, the longitudinal axis relative to the horizon - measuring the trim or tangent, the transverse axis relative to the horizon - measuring the course. All these quantities are necessary for sea and air navigation, some for topographic and geodetic work.

If the users have a gyroscopic or magnetic heading system, measuring the true orientation of the longitudinal axis according to satellite systems and comparing these results with the gyrocompass or magnetic compass data will allow you to lay a route and control it. Three-dimensional orientation in space is also needed for satellites, rocket systems, and launching devices for rocket systems.

To orient users in space using satellite systems, the measured navigation parameters are the angles between the user axes and the straight line connecting specific points of users and satellites (phase centers of AP antennas and antennas of satellite navigation radio signals).

To obtain information on the orientation of users of satellite systems in space, direction finding of satellites (users) is required.

In the process of direction finding using the proposed algorithms, the direction cosines of the angles α, β and γ of the geocentric and local geocentric vectors are determined, the values of which are associated with the movement of the user, the rotation of the Earth and the movement of satellites.

Rectangular coordinates and components of the velocity vector, for example, of a user in a geocentric equatorial coordinate system, are associated with geographical φ, γ and angular coordinates by known relations [3]:

- направляющие косинусы вектора положения пользователя; ψ - геоцентрическая широта;

,

- скорости изменения геоцентрической широты и долготы.where (R ₃ + h _P ) is the module of the local geocentric vector (user position vector);

- guide cosines of the user position vector; ψ - geocentric latitude;

,

- the rate of change of geocentric latitude and longitude.

Geocentric latitude is associated with geographical latitude by the expression:

where e is the eccentricity of the earth's ellipsoid.

The known values of the directing cosines of the user position vectors in the geocentric coordinate system, in turn, make it possible to find the values of the angles ψ, λ from the solution of the system of equations, and then the rate of change of the geocentric latitude and longitude by differentiating the expressions determining their values

- скорости изменения угловых параметров местного геоцентрического вектора, определяемые выражениями (5) после их дифференцирования.Where

- the rate of change of the angular parameters of the local geocentric vector, determined by expressions (5) after their differentiation.

в геоцентрической системе координат в значения в топоцентрической системе координат в соответствии с выражениями [7].Using the transition formulas from the geocentric coordinate system to the topocentric, recalculate the values of the direction cosines of the vectors

in a geocentric coordinate system into values in a topocentric coordinate system in accordance with the expressions [7].

In the same time

The joint solution of the equations allows us to find the values of the azimuth angles α _P and the places β _{P of} users in a topocentric coordinate system.

The condition of the user's direction finding by a moving satellite requires continuous compensation in one way or another of the deviation of the direction-finding plane. The violation of direction-finding conditions occurs due to disturbing rotational and translational movements of users and the movement of satellites in the celestial sphere.

One of the options for continuous compensation of direction finding conditions (errors) caused by rotational and translational movements of users by the phase characteristics of the antennas used, the underlying surface are, for example, technical solutions published in [8].

Knowing the values of the guiding cosines of the user position vector in the geocentric coordinate system and in the user coordinate system allows you to determine the angles between the unit vectors of the two systems. A knowledge of the values of the angles, for example, between the orts of the ship's coordinate system with the origin in the center of mass, directed along the starboard side, bow and up, and the orts of the geocentric coordinate system with the beginning in the center of mass of the Earth, directed north and vertically up the meridian, respectively relative to the Earth’s surface, is practically exhaustive information for determining the user's orientation in space. The calculated values of the directing cosines of the position vectors of the satellites and users at the same time make it possible to determine not only spatial orientation, but also the components of their angular velocities and accelerations by differentiating their defining expressions, as well as solving the course guidance problem.

In order to determine the course of the vessel with the required error, it is necessary to determine (check) the compass correction. We agree that by compass amendment we mean the angle in the horizontal plane between the plane of the true meridian and the axis of any (magnetic, gyroscopic, etc.) ship's direction keeper.

Heading correction using the goniometer algorithm is determined by comparing the measured values of α _P related to one moment of measurement using, for example, the navigation radio signals of GPS satellites of the frequency range L1 or L2 and the measured values of α _k using a compass.

Compass correction is determined from the expression

A geometric interpretation of the definition of the course correction for the navigation radio signals of GPS satellites is illustrated in figure 3.

The resulting error of user navigation definitions depends on many factors, the full accounting of which is hardly possible.

To a large extent, the error is determined by the type of signal used in the navigation system, and mainly the error of the ephemeris, the environment in which the navigation signals propagate, and the error of measuring the navigation parameters directly by the PUSR and AP equipment.

The basis for calculating the increments of ranges, radial velocities, linear velocities of circular motion of satellites, modules of topocentric, geocentric and local geocentric vectors of base distances, values of angular velocities of base distances, cosines of angles between radial motion of satellites and linear velocity vector are phase measurements, measurements of Doppler values frequency equipment PUSR and AP on the increments of the phases of the carriers of the navigation radio signals of beacons and satellites. Phase increments are measured using a radial-velocity differential technique. The measurement mode using SSN equipment PUSR and AP phase increments is equivalent to the measurement mode of the double differences of the path of the radio signals between the phase centers of the beacon antennas, the AP and the two positions of the phase centers of the satellite antennas by a satellite linear interferometer, creating at the ends of the measured intervals two sources of radiation signals spaced in time and in space. Therefore, the estimation of errors in navigation measurements and determinations should be made from the calculation of errors in phase measurements by a satellite interferometer.

The errors in phase measurements by a satellite interferometer of phase increments in the general case are due to inaccuracies in determining the frequencies of radio signals received by the PUSR and AP equipment (Doppler frequency shifts), errors in resolving the ambiguity of phase measurements, instability of the received frequencies, multipath propagation of signals, the influence of the ionosphere, troposphere and errors in the angles of sight of satellites due to the computational process, as well as the characteristics of the ISM and AP.

Measurements of phase increments by a satellite interferometer are an implementation of the relative measurement mode, the positive feature of which is that in their measurements, errors that are systematic in nature are mutually compensated. Essentially, relative measurements are one of the varieties of the differential mode of using interferometric measurements to determine navigation parameters, during the implementation of which, by compensating for systematic errors, high accuracy of phase measurements is ensured.

Compensation efficiency depends on the output characteristics of the digital tracking systems of the receiving devices of satellites and APs, in particular, on the characteristics of digital CCHs, since it is the noise error that limits the effect of compensation for highly correlated errors.

The measurement of the values of the Doppler frequency shift of navigation radio signals in modern domestic and foreign receiver indicators of satellite systems is based on measurements of the phase increments of the carrier frequencies using digital CCH systems, which make it possible to very easily and relatively accurately measure the incidence of the non-cyclic phase of the output oscillations (i.e., a phase that varies within not limited to 2π). Therefore, there is no problem of resolving the ambiguity of phase measurements. This makes it possible to apply relatively simple quasi-optimal phase measurement algorithms for the values of the Doppler frequency shift from a signal masked by noise [6]. The root-mean-square error of the tracking tracking systems, for example, at American GPS frequencies having a tracking band of 20 Hz, due to the spectral density of phase noise, is not more than 0.1 radian [9].

The instability of the received frequencies (instability of phase increments) in the PUSR and AP equipment can be represented as the sum of the constant during the measurement session (but unknown) and fluctuation components. The first upon the formation of the second phase differences is practically eliminated, the proportion of the second is reduced to a value of the order of 0.1 radian [10].

Errors due to multipath are also reduced to insignificant values, both due to the use of directional antennas with right circular polarization, as a result of which the reflected signals are received at low elevation angles with lower gain and mainly have left polarization, and due to the compensation of systematic errors in the process of navigation measurements and measurement processing.

The influence of the ionospheres and the troposphere, as well as the telling effect on the satellite’s motion, the drag and the anomalies of the gravitational field are insignificant, since the phase increments due to the propagation conditions of the radio waves at measured intervals differ little and most of them are compensated in the process of measuring phase differences. The use of primary and secondary averaging of phase measurements allows a large part of both the noise error and the remaining parts of the errors associated with the influence of propagation conditions (ionosphere, troposphere, multipath), with the influence of drag on satellite motion, the instability of phase shifts in receivers, the effect of accelerations and gravitational fields of satellites and AP to minimize.

- шумовая погрешность.By their origin, the causes of errors can be very different, but the most significant is the error due to the energy potential of the radio line, the ratio

- noise error.

можно использовать выражение для дисперсии фазы (ε² _ф) схем ССН [11].To assess the noise error of measuring increments of ranges (σ _ΔR ), the values of Doppler frequency shifts (σ _Ωd ), radial velocity

one can use the expression for the phase dispersion (ε ² _f ) of the CCH schemes [11].

The root mean square values of the error in the measurements of the phase increments are determined by the expression

where _CCH is the bandwidth of the carrier tracking system.

дБГц и B_CCH=20 Гц на несущей частоте (λ=19 см) составит 0.079 радиан. Погрешность измерения приращений дальностей как приращений фаз несущей за определенный интервал времени увеличивается в

раз. Поэтому среднеквадратическая погрешность измерения приращений дальностей по фазе несущей, обусловленной шумом σ_ΔRш=0,34 см.RMS error of the measurement of increments of ranges, for example, in GPS

dBHz and B _CCH = 20 Hz at the carrier frequency (λ = 19 cm) will be 0.079 radians. The error in measuring increments of ranges as increments of the phases of the carrier for a certain time interval increases in

time. Therefore, the standard error of the measurement of the increments of ranges in the phase of the carrier, due to noise σ _ΔRш = 0.34 cm.

см/с.Radial velocity measurement is also based on measurements of phase increments at the carrier frequency. If the time interval during which the increment of the phase of the carrier is measured is equal to one second, and the phase is expressed in terms of the wavelength, then the error in measuring the radial velocity will be

cm / s.

The quantization errors of the measured range increments in the digital implementation of SSN under the assumption of their uniform distribution (σ _ΔRkv ) are 0.25 cm [11].

Sources of errors in the computational process in PUSR and AP are the limited capacity of the process, mathematical approximations and approximation of the execution of commands with a time delay. Using calculators capable of performing calculations with double accuracy and floating point, it is possible to obtain the standard error of processing increments of ranges of no more than (σ _ΔRv ) 0.3 cm.

Thus, as a first approximation, it can be argued that noise-type interference and receiver intrinsic noise, errors due to quantization and the computational process have a dominant influence on the accuracy of measurements of radio navigation parameters using phase measurements by a satellite interferometer.

The resulting error in measuring increments of ranges is determined by quadratic summation of the components according to the formula

Let us consider the errors of navigation measurements as applied to the considered differential radial-velocity technique for measuring the radio navigation parameters of expressions (2), (3) of double phase differences.

,

,

,

,

,

выражений (1), (2) получим для конечных приращенийIn accordance with the formula of the total differential of the measured values

,

,

,

,

,

expressions (1), (2) we obtain for finite increments

Errors in the measurements of double phase differences can be caused by both errors in the tracking of SSNs and errors in determining wavelengths and measured intervals.

Поэтому среднеквадратические значения погрешностей измерений радионавигационных параметров с использованием радиально-скоростной методики можно найти по формуламTypically, the random measurement errors on the radio beacon satellites and user satellites are independent, and their mean square values are the same

Therefore, the root mean square values of the measurement errors of the radio navigation parameters using the radial velocity technique can be found by the formulas

[3] с учетом (1) среднеквадратическая погрешность углов визирования θ_t* оценивается какIn accordance with the formula for the full differential of the expressions of the determined quantities

[3] taking into account (1) the standard error of the viewing angles θ _{t *} is estimated as

Thus, the error in direction finding by a satellite interferometer decreases with an increase in the signal-to-noise ratio, the length of the measured interval, and with a decrease in the tracking band of the CCH.

спутниковым фазовым интерферометром, например, на частотах GPS составит не более 0,123 угл. с. (на односекундном мерном интервале d≈4 км). Соответственно, на мерном интервале, равном 10 с, погрешность составит 0,0123 угл. с.Given the above information about the standard error of the phase measurements, equal to 0.079 radians in the one-second measured interval, the standard error of the viewing angles

satellite phase interferometer, for example, at GPS frequencies will be no more than 0.123 angles. from. (on a one-second measured interval d≈4 km). Accordingly, on a measured interval equal to 10 s, the error will be 0.0123 angles. from.

Consider the errors in measuring ranges and the errors in the navigation definitions of satellites, users, for example, using a GPS radio signal using a radial-speed differential method of phase measurements of navigation parameters.

,

вычисляются по приращениям

,

и значениям

,

,

, которые в свою очередь косвенно измеряются по одним и тем же фазовым измерениям на несущих частотах. Поэтому их случайные погрешности зависимы и равны между собой.Range Values

,

incremented

,

and values

,

,

, which, in turn, are indirectly measured by the same phase measurements at carrier frequencies. Therefore, their random errors are dependent and equal to each other.

Applying the principles of equal influence of phase measurement errors on the mean square values of range measurement errors, the errors of the latter can be determined using the expression [12]

раз. Чтобы учесть все неучтенные и остаточные погрешности фазовых измерений, увеличим среднеквадратическую погрешность измерения дальностей еще в два раза.The error in measuring ranges as an error due to phase increments of the carrier frequency for certain measured intervals also increase in

time. To take into account all the unaccounted and residual errors of phase measurements, we increase the standard error of the range measurement by a factor of two more.

Then

If the carrier wavelength is equal to λ ^a.s. = λ ^a.s. = 19 cm, the root-mean-square error of determining the distances between the phase centers of the antennas of beacons-satellites, satellite-users is 1.2 cm. Correspondingly, the limiting value of the error of measuring ranges (3 σ _R ) is 3.6 cm.

The root-mean-square error of the navigation definitions when applying the range-finding technique is defined as the product of the limiting values of the standard error of the measurement of the navigation parameter (range) by the corresponding value of the geometric factor (GF). Assuming a nominal GF value of 3-5, the marginal root-mean-square error of the navigation definitions of users when using the rangefinder method will accordingly be (10.8-18) cm (without taking into account the errors of determination, the location coordinates of the phase centers of satellite antennas).

раз.In the case of applying the same range-finding technique for determining the coordinates of satellites, the limiting value of the error in determining the location of users will accordingly be (15.23 ÷ 25.4) cm, i.e. will increase in

time.

Measurements of phase increments (range increments) in the AP using digital CCHs are performed using a differential (radial-velocity) measurement processing technique. Therefore, in the navigation systems of equations there are no errors due to the discrepancy of the time scales of users and satellites. Therefore, to determine the location coordinates that make up the speed vector of GPS users using autonomous functioning algorithms, it is sufficient that at least one or three satellites are in the radio visibility zone of each user, and at least one or three radio beacons are located in the radio visibility zone of each satellite.

(отношение мощности сигнала к мощности шума) и уменьшать полосу слежения систем слежения за несущими навигационных радиосигналов В_ССН.To reduce the random components of the errors in the navigation definitions and the errors caused by noise, it is necessary to increase the sizes of the base distances d (measured intervals) and the ratio

(the ratio of signal power to noise power) and reduce the tracking band of tracking systems for tracking radio navigation signals in the _SSN .

The global defect of increasing the vertical component of the error in determining the location of users in the algorithm of the goniometric method (26) is eliminated by using the measured value of the local geocentric radius vector (R ₃ + h _P ) in the system of equations.

Consider the question of the sources of errors and errors in the navigation definitions of the algorithms of the goniometric method.

Differentiating expressions (5), (6), (7) and passing to finite increments, we obtain expressions that determine the errors in determining the location of users and satellites, as well as the errors in determining the components of the angular velocity vector and the components of the angular acceleration of satellites relative to the axes of the geocentric coordinate system.

выражение (9) и составляют на мерных интервалах 1 с и 10 с 5,975·10^-7 и 5,975·10^-8 радиан соответственно. Допуская, что вычислительный процесс значений направляющих косинусов геоцентрического радиус-вектора (R₃+Н) и радиус-вектора положения пользователей (R₃+h_П) вносит дополнительную погрешность, равную

. Тогда средние среднеквадратические значения погрешностей определения углов

и

,

,

на мерных интервалах 1 с и 10 с соответственно составят 8,42·10^-7, 8,42·10^-8 и 1,19·10^-6, 1,19·10^-7 радиан. Это значит, что с такими средними погрешностями привязаны соответствующие радиус-вектора к осям геоцентрической системы координат, в том числе и к меридиану, направленному на север. Т.е. среднеквадратическое значение погрешности определения направления истинного меридиана с использованием спутниковых линейных интерферометров составит 1,19·10^-6 радиан (0,258 угл. с) на 1 с мерном интервале и 1,19·10^-7 радиан (0,0258 угл. с) на 10 с мерном интервале. Следовательно, предельная погрешность определения поправки курсоуказания спутниковыми интерферометрами с использованием приема приемоиндикатором спутниковых радиосигналов на одну антенну на мерном интервале, равном 1 с составит 1 угл. с. Соответственно, на мерном интервале, равном 10 с предельная погрешность поправки курсоуказания составит 0,1 угл. с.The errors in establishing the functional dependences of the equations of systems (3), (4) are determined by the measurement errors by satellite linear interferometers of sight sites

expression (9) and are at measured intervals 1 s and 10 s 5.975 · 10 ^-7 and 5.975 · 10 ^-8 radians, respectively. Assuming that the computational process of the values of the guiding cosines of the geocentric radius vector (R ₃ + H) and the radius vector of the user position (R ₃ + h _P ) introduces an additional error equal to

. Then the mean square errors of the angles

and

,

,

at measured intervals 1 s and 10 s, respectively, they will amount to 8.42 · 10 ^-7 , 8.42 · 10 ^-8 and 1.19 · 10 ^-6 , 1.19 · 10 ^-7 radians. This means that with such average errors the corresponding radius vectors are tied to the axes of the geocentric coordinate system, including the meridian directed to the north. Those. the root-mean-square error of determining the true meridian direction using satellite linear interferometers will be 1.19 · 10 ^-6 radians (0.258 angular s) per 1 measurement interval and 1.19 · 10 ^-7 radians (0.0258 angular s) per 10 with a measured interval. Consequently, the marginal error in determining the correction of the course guidance by satellite interferometers using the reception of satellite radio signals by one transceiver on one antenna at a measured interval of 1 s will be 1 angle. from. Accordingly, on a measured interval equal to 10 s, the marginal error of the correction of the course guidance will be 0.1 angle. from.

As can be seen from the systems of equations (3), (4), (5), in order to determine the coordinates of the location of users using the goniometric method of solving the navigation problem, the determination (value) of the coordinates of the satellites is not required.

- отношении мощности сигнала к спектральной плотности мощности шума приведена в таблице.Average values of marginal errors of navigation definitions using the algorithm of the goniometric method for

- the ratio of signal power to spectral density of noise power is given in the table.

Table. Average values of marginal errors of navigation definitions using the developed algorithm of the goniometric method with the ratio

.

.

Values of measured intervals Characteristics (t _{i + 1} -t _i ) [s] and the values of the tracking bandwidth of the CCH (V _CCH ) [Hz], respectively one; twenty one; 2 10; twenty 10; 2 one 2 3 four 5

с использованием дальномерного метода (6):Errors in determining the coordinates of the location of users (3σ) X _П , Y _П , Z _П and components of the velocity vector (3σ)

using the rangefinder method (6): coordinates, m 0.25 0,025 0,025 0.0025 speed, m / s 0.01 0.001 0.001 0.0001 Errors in determining the coordinates of the location of users (3σ) X _P , Y _P , Z _P and components of the velocity vector (3σ)

using the algorithm of the goniometric method (5): coordinates, m 16 1,6 1,6 0.16 speed, m / s 0.01 0.001 0.001 0.0001 Errors in determining the angular velocity and acceleration of satellites relative to the geocentric coordinate system (3σ): speed

10 ^-4 10 ^-5 10 ^-5 10 ^-6 acceleration

10 ^-8 10 ^-9 10 ^{-9 10-10} Errors in determining the angular velocity of users (3σ) relative to the geocentric coordinate system,

10 ^-2 10 ^-3 10 ^-3 10 ^-4 Errors in determining the correction of the user guidance (3σ),

. one 0.1 0.1 0.01

The technical task (goal) is achieved due to the new sequence and set of actions on emitted HHM signals, on received signals by the receivers of satellite relays, on relayed and on received NAP relayed satellites radio signals, by applying new algorithms for navigation measurements and solving navigation problems, which are distinctive features of the proposed method:

- navigation information in the coordinates of the location of the phase centers of the NNRM antennas, time and information for making corrections in frequency, time, as well as information on belonging to a specific NNRM are not transmitted as part of the emitted NNRM signals and are not relayed by relay satellites, but recorded in memory NAP devices in manufacturers at its manufacture;

- determine the values of the distances between the phase centers of the antennas of the NNRM and the phase centers of the satellite antennas of the receiving devices of the relay satellites (PUSR) as the product of the ratio of the squares of the values of the radial velocity of the phase centers of the satellites of the receiving antennas to the accelerations of the radial velocity by the squares of the values of the angles between the radial motion and the velocity vector of the satellites ;

- determine the values of the distances between the phase centers of satellite antennas relaying the HPHM signals and the phase centers of the NAP antennas as the product of the ratio of the squares of the values of the radial speed of the phase centers of the satellite antennas relaying the HRHM signals to the accelerations of the radial velocity by the squares of the values of the angles between the radial motion and the vector satellite speeds;

между радиальным движением фазового центра антенны ПУСР и вектором скорости спутников к значениям модулей векторов положения фазовых центров антенн ННРМ;- determine the values of the cosines of the angles between the geocentric radius vectors (position vectors of the satellites (R ₃ + H _i ) ^pr.s ) and the local geocentric radius vectors (position vectors of the phase centers of the NNRM antennas (R ₃ + h _i )) as arcsines of the product relations the values of the distances between the phase centers of the antennas and the phase centers of the antennas and the values of the cosines of the angles

between the radial motion of the phase center of the PUSR antenna and the satellite velocity vector to the values of the modules of the position vectors of the phase centers of the NNRM antennas;

между радиальным движением и векторами скорости спутников к значениям модуля вектора положения фазового центра антенны НАП;- determine the values of the cosines of the angles between the position vectors of the satellites and the position vector of the phase center of the NAP antenna as the arcsines of the relations of the products of the distance values between the phase centers of the satellite antennas through which the NRM signals are relayed, and the phase centers of the NAP antennas and the cosines of the angles

between radial motion and satellite velocity vectors to the values of the module of the position vector of the phase center of the NAP antenna;

- establish a system of functional dependencies (a system of navigation equations) between the known values of the directional cosines of the position vectors of the phase centers of the HHPM antennas and the unknown values of the directional cosines of the geocentric radius vectors (3), (4);

- determine the values of the guiding cosines of the geocentric radius vectors (R ₃ + H _i ) ^pr.s by solving systems of equations (3), (4);

- establish a system of functional dependencies (a system of navigation equations) between the known values of the directional cosines of the geocentric radius vectors and the unknown values of the directional cosines of the position vector of the phase center of the NAP antenna;

- determine the values of the guide cosines of the position vector of the phase center of the NAP antenna by solving the system of equations (5);

- using expressions connecting the known values of the directional cosines of the position vector of the phase center center of the PAP antenna with geographical longitude λ and latitude ψ, determine the values of λ and ψ, and then determine the values of the sines, cosines of the angles λ as sines, cosines of the arc tangents of the ratios of the projections of the position vectors of the position of the phase centers NAP antennas on the OY axis to the values of the projections of the position vectors of the phase center antennas on the OX axis on the same measured interval, as well as the sines, cosines of the angles ψ on the same measured interval as whiskers, cosine inverse cosine square roots of the sums of the squares relationship projection position vectors phase centers NAP antennas on the axis OX, OY geocentric coordinate system to their modules;

- using the transition formulas from the geocentric coordinate system to the topocentric one, recalculate the values of the directional cosines of the distance vectors between the phase centers of the antennas of the satellite radio signal sources and the phase centers of the NAP antennas into the values of the directional cosines in the topocentric coordinate system, determine the azimuth angles and elevation angles of the true meridian as arcsines the roots of their square sums of squares of the relations of the projections of the position vectors of the phase centers of the NAP antennas on the axis OX ^T , OY ^T of the topocentric coordinate system to their modules and as arctangents of the ratio of the projection values of the position vectors of the phase centers of the NAP antennas on the OY ^T axis to the values of the projections of the position vectors of the phase centers of the NAP antennas on the OX ^T axis, and then determine the course correction values in the topocentric coordinate system by comparing the one moment of measurement of the measured values of the azimuth angles using radio signals from satellites and the measured values of the azimuth angles using a compass by mutual subtraction.

The positive effect of using the proposed technical solution is as follows.

A satellite positioning strategy (ephemeris) is a key issue in creating any satellite navigation system. Therefore, the ability to navigate by users with high accuracy using navigation measurements of the carrier phase of the radio signals of ground beacons relayed by satellites and the coordinates of the location of the phase centers of the LNRM antennas without knowledge of the ephemeris, and also to determine the angular parameters with high accuracy by receiving the radio signal satellites on one NAP antenna, are great advantages of the proposed method.

In addition to accuracy, the number of important output parameters of the proposed method include reliability and reliability.

Reliability is understood as the ability of the system to detect its malfunction and notify users about this in order to exclude the use of this system in cases where its operational parameters are outside the established tolerances.

Reliability is understood as the probability that, during a certain time interval at any point in space, the navigation system provides users with information sufficient to determine the location with the required accuracy.

Reliability is ensured by the fact that navigation information is not determined and is not laid by ground-based monitoring and measuring stations (CIS) on board each satellite, is not relayed to users by satellites and rangefinding codes are not used, and reliability is ensured by monitoring the levels of satellite radio signals received by NAP directly during the navigation session.

The proposed technical solutions open up real possibilities for integrating currently used narrow-purpose satellite systems into multi-purpose GISS navigation, geodesy, communications, monitoring and control and solving the issue of efficient use of satellite systems of an irreplaceable world resource, which are the radio frequency spectrum and satellite orbits.

At the same time, the proposed method allows to simplify ground facilities and solve the problem of autonomous functioning of satellite systems.

The high cost of satellite systems is especially due to the high cost of the ground segment, its high operating costs. Autonomous operation of systems will reduce the economic costs of managing satellite systems. Thus, the economic effect of the application of the proposed method is achieved by reducing operating costs.

The needs of human life and activity, as well as competition, are forcing mobile operators to aggressively struggle to expand the range of services provided, including positioning using satellite systems.

Moreover, the relevance of the provision of navigation services using satellite systems is increasing every year. So, for example, on February 19, 2003, the Moscow authorities found a means to combat traffic jams. In the capital, the first stage of the program to introduce a satellite navigation system has started. So far, we are talking about 140 regular buses and 20 ambulances. The city authorities are also going to offer satellite navigation services to all comers from Moscow. Consequently, not only in foreign countries, but also in Russia, an order has almost been formed to provide users with navigation services using satellite systems. Therefore, the proposed method meets the requirements of "industrial applicability".

Thus, the proposed method for the autonomous instant determination by users of the coordinates of their location, components of the velocity vector, the angular orientation in space, and the bearing by phase of the carrier signal of the radio signals of terrestrial beacons relayed by satellites, meets the criteria of novelty, inventive step, industrial applicability and gives a positive effect when used consisting in increasing the accuracy of navigation measurements and definitions, reliability, reliability and the use of radio frequency spectrum and satellite orbits, and to reduce the operating costs of satellite systems.

LITERATURE

1. B.C. Shebshaevich. Network satellite radio navigation systems. - M .: Radio and communications, 1993.

2. A.N. Armizonov. A method for determining the location coordinates of the velocity vector of the phase centers of the antennas of satellite sources of navigation signals and phase centers of the antennas of navigation equipment of the SRNS users. Patent No. 2210788 (IPC G 01 S 5/00), 2001

3. Yu.M. Kazarinov, Yu.A. Kolomensky et al. Radio engineering systems. - M.: Soviet Radio, 1968.

4. P. A. Agadzhanov, N. M. Barabanov and others. Space trajectory measurements. - M .: Soviet Radio, 1969.

5. B.C. Volosov, Yu.S. Dubinko et al. Ship satellite navigation systems. - Leningrad, Shipbuilding, 1976.

6. Digital radio receiving systems. Handbook edited by M.I.Zhodzishsky. - M .: Radio and communications, 1990.

7. B.C. Shebshaevich. Introduction to the theory of space navigation. - M .: Radio and communications, 1971.

8. N.E. Armizonov, A.G. Kozlov. Phase characteristics and phase centers of the antennas of navigation equipment for users of satellite radio navigation systems. // Radio engineering. - 2000. - No. 5.

9. Global satellite system GLONASS. Interface control document. - M.: KNITS, 2002 (fifth edition).

10. A.P. Manin, L.M. Romanov. Methods and means of relative definitions in the NAVSTAR system. Foreign electronics number 1. - M.: Radio and Communications, 1989.

11. B.C. Shebshaevich et al. On-board satellite navigation devices. - M .: Transport, 1988.

12. G.A. Burmistrov. The basics of the least squares method. - M.: Publishing house of literature on geology and mineral protection, 1963.

Claims (1)

The method of autonomous instant determination by users of the coordinates of their location, components of the velocity vector, angular orientation in space and direction-finding bearing on the phase of the carrier signals of ground-based radio beacons relayed by satellites, according to which ground-based navigation beacons (NNRM) continuously emit navigation radio signals, and navigation equipment (ON) installed on each satellite receive the radiated NNRM radio signals, with information about the change in the frequencies of received The carriers modulate the carriers of the emitted radio signals, amplify them and relay them in the direction of the Earth, receive relayed signals from the navigation equipment of users (NAP) determine: the values of the distances between the phase centers of the NNRM antennas and the phase centers of the satellite antennas, the distances between the phase centers of the satellite antennas and the phase center of the NAP antennas , then install the system of functional dependencies, characterized in that the navigation information about the position of the phase centers of the antennas NNRM, information A correction on the frequency of administration, the time is recorded in the storage device NAP during its manufacture; ON installed on the satellites, receive navigation radio signals from two or more NNRM, and NAP receive relayed signals from two satellites and determine: the distances between the phase centers of the HHP antennas and the phase centers of the satellite antennas as the product of the ratio of the squares of the values of the radial velocity of the phase centers of the satellite receiving antennas to the accelerations of the radial velocity by the squares of the values of the angles between the radial motion and the satellite velocity vector; the distances between the phase centers of the satellite antennas and the phase center of the NAP antennas as the product of the ratio of the squares of the values of the radial velocity of the phase centers of the satellite antennas relaying the signals of the NNRM to the radial velocity accelerations by the squares of the angles of tangent angles between the radial movement and the satellite velocity vector; the values of the cosines of the angles between the position vectors of the phase centers of the satellite antennas and the position vectors of the phase centers of the HHP antennas as arcsines of the relations of the products of the distances between the phase centers of the HHH antennas and the phase centers of the satellite antennas and the cosines of the angles

between the radial motion of the phase centers of the satellite antennas and the satellite velocity vector to the values of the moduli of the position vectors of the phase centers of the HHPM antennas; the values of the cosines of the angles between the position vectors of the phase centers of the satellite antennas and the position vector of the phase center of the NAP antenna as the arcsines of the relations of the products of the distances between the phase centers of the satellite antennas through which the NRM signals and the phase centers of the NAP antennas relay and the cosines of the angles

between the radial movement of the phase centers of satellite antennas emitting radio signals and the linear velocity vector of the satellites to the values of the module of the position vector of the phase center of the NAP antenna; establish two systems of functional dependencies between the unknown values of the directional cosines of the position vectors of the phase centers of the antennas of two satellites and the known values of the directional cosines of the position vectors of the phase centers of the antennas of two LPRs, as the sum of the products of the values of the directional cosines of the angles α, β, γ of the position vector of the phase center of the antenna of the first satellite and the values of the guide cosines of the corresponding nodes of the position vector of the phase center of the antenna of the first HHP equal to the cosine of the angle between them, as the sum of the products of the values of the directional cosines of the angles α, β, γ of the position vector of the phase center of the antenna of the first satellite and the values of the directional cosines of the corresponding angles of the position vector of the phase center of the antenna of the second NNRM, equal to the value of the cosine of the angle between them, as the sum of the squares of the values of the directional cosines of the angles α, β, γ of the position vector of the phase center antenna of the first satellite, equal to unity, the first and as the sum of the products of the values of the direction cosines of the angles α, β, γ of the position vector of the phase the center of the antenna of the second satellite and the values of the directional cosines of the corresponding angles of the position vector of the phase center of the antenna of the first NNRM, equal to the value of the cosine of the angle between them, as the sum of the products of the values of the directional cosines of the angles α, β, γ of the position vector of the phase center of the antenna of the second satellite and the values of the directional cosines of the corresponding angles the position vector of the phase center of the antenna of the second HHM, equal to the cosine of the angle between them, as the sum of the squares of the values of the guiding cosines of the angles α, β, γ vect ra phase center of the antenna of the second satellite, is equal to unity, and a second solution by the first and second systems determine the values of the direction cosines of the angles α, β, γ of the position vector of the phase centers of the antennas of the first and second satellites; establish a system of functional dependencies between the known values of the directional cosines of the position vectors of the phase centers of the antennas of the first and second satellites and the unknown values of the directional cosines of the position vector of the phase center of the user’s antenna as the sum of the products of the values of the directional cosines of the angles α, β, γ of the position vector of the antenna center phase center of the first satellite and the values guide cosines of the corresponding angles of the position vector of the phase center of the user’s antenna, equal to the value the sine of the angle between them, as the sum of the products of the values of the directional cosines of the angles α, β, γ of the position vector of the phase center antenna of the second satellite and the values of the directional cosines of the corresponding angles of the position vector of the phase center of the user’s antenna, equal to the cosine of the angle between them and as the sum of the squares of the values of the directional cosines angles α, β, γ of the position vector of the phase center of the user’s antenna equal to unity, and by solving the system, the values of the direction cosines of the angles α, β, γ of the polo vector are determined the center of the user’s antenna, the known values of the directing cosines of the position vectors of the phase centers of the NAP antennas determine: User location coordinates user velocity vector components; values of longitude λ and latitude ψ of the location of the phase center of the NAP antenna, recalculate the known values of the guide cosines of the position vectors of the phase center of the NAP antenna into the values of the direction cosines of the vectors in the topocentric coordinate system and determine azimuth and elevation angles of the user in a topocentric coordinate system; the angular orientation of the user in space, calculating the course correction values by mutually subtracting the azimuth angles measured using radio signals from satellite navigation systems and the azimuth angles measured using a compass in a topocentric coordinate system.

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