RU2713188C1 - Method for single-position determination of coordinates of sources of high-frequency radio waves during ionospheric propagation - Google Patents

Abstract

FIELD: radio engineering; radio navigation.

SUBSTANCE: invention is intended for use in radio engineering, radio navigation, as well as in research of ionosphere parameters and increases accuracy of determining coordinates of HF sources from one position. Technical result of invention is achieved due to single target approach, which includes detection and reception on known frequency of multibeam signal by phased antenna array, measurement with required accuracy according to known algorithms of spatial angles of arrival (azimuth, elevation angle) of each mode of received signal and evaluation of their energy parameters, formation of ionosphere model, corrected based on current data of vertical, inclined probing, using data of satellite tomography and magnetometers, as well as a radiophysical model of medium propagation of radio waves of the HF range, solving direct and inverse problems arising in single-position positioning and correction of the ionosphere model.

EFFECT: technical result is higher accuracy of single-position location of radio-frequency source.

1 cl, 3 dwg

Description

The invention relates to radio engineering, radio navigation, as well as for use in researching the parameters of the ionosphere and improves the accuracy of determining the coordinates of the sources of radio waves of the short-wave (KB) range from one position.

There is a method for single-point location of radio emission sources (IRI) after applying the "Smith" transmission of Smith to determine the location of radio emitters (Patent RU No. 2072524 C1, IPC G01S 3/02 - 01/27/1997). The algorithm provides for measuring the angles of arrival of the ionospheric wave in the vertical and horizontal planes, obtaining the ionosphere parameters by the method of vertical sounding (VZ), determining the increment of the median values of the ionosphere parameters between the direction-finding station and the area of reflection of the radio signal, calculating the longitudinal and transverse slopes of the reflecting layer of the ionosphere when using a flat model of the ionosphere in the area of reflection of the radio signal and the refinement of the position parameters of the IRI, according to the calculated amendments. The disadvantage of this method is that it does not take into account the shape of the profile of the electron concentration of the ionosphere. Correction according to B3 is linear in parameters without taking into account the spatio-temporal correlation dependences and errors in determining parameters by the WZ method. The use of reference IRI was reduced to correcting the longitudinal and transverse gradients of the slope of the ionospheric parameters in the region of reflection of the radio wave without taking into account the difference in the frequencies of the reference and direction finding IRI.

A known method of single-point ranging of electromagnetic radiation sources (Patent RU No. 2118836 C1, IPC G01S 13/95, G01S 5/02 - 09/10/1998). The method is based on measuring the received useful signal, the ionospheric reflection delay relative to the earth wave signal is determined in a known manner, the reference frequency of the signal is determined, the profile of the electron concentration of the ionosphere is restored using fixed-frequency signals from pulse-phase radio stations with known coordinates. From the obtained profile of electron concentrations, the reference frequency of the signal and the delay time of the ionospheric reflection, using the dependence of the delay time of the ionospheric reflection from the distance to the radiation source, determine the range. The disadvantage of the proposed method is its limited suitability in those cases when signals of surface and spatial waves are simultaneously observed, and the ionospheric (spatial) wave is formed by mode E (wave propagation upon reflection only from layer E). Correction of area E is linear according to the signals of reference sources.

The method according to the method of determining the sources of radio emission (Patent RU No. 2154281 C1, IPC G01S 3/02 - 08/10/2000, Bull. No. 22) is a development of patent RU No. 2072524 and provides for parabolic approximation instead of linear, and uses a quasiparabolic ionospheric model to calculate the trajectories of radio waves layer. The disadvantage of this method is the same as for patent RU No. 2072524, low accuracy of correction of ionospheric data, spatio-temporal correlation dependencies and errors in determining parameters by the VZ method are not taken into account. Reference sources are not used.

The traditional method for determining the coordinates of radio emission sources (IRI) is the triangulation method, which assumes the presence of a network of direction finding points united by a single control system (Patent RU No. 2490661 C1, IPC G01S 1/08 - 08/20/2013, Bull. No. 23). It is based on the simultaneous use of at least 2 HF direction finders. For high accuracy of IRI positioning, a separation of several hundred kilometers between the direction-finding points is necessary, which, when radio waves pass through the ionosphere, leads to a different nature of the propagation paths of radio waves having their own bearing measurement errors, up to the lack of radio signal reception, which makes it difficult and even impossible to solve the determination problem Iran coordinates. The disadvantage of this method is the ability to determine the coordinates only by a group of several (at least two) direction finders with the obligatory presence of a communication system between them.

The method of single-point location of the IRI (Patent RU No. 2523650 C2, IPC G01S 5/00 - 07/07/2014 Bull. No. 20) consists in modeling the propagation modes of signals from a range grid, determining by the angles of arrival of the modes of phase incursion in antenna elements (AE) with a circular antenna lattice (AR). Further, these phase incursions are subtracted from the signal from the AE, quadratically detected and averaged over the number of AE ARs. Bearing and range to Iran is determined by the minimum averaging results weighted in proportion to the number of rays. It is proposed to use the VZ station, which determines the heights and critical frequencies of ionospheric layers or monthly forecasts. The disadvantage of this method is the limited possibility of application, only for single-jump routes with elevation angles of more than 10 degrees, as well as the impossibility of correctly evaluating the received signal that it meets certain conditions and, as a result, there is a low probability of correct location of the IRI.

The closest in physical and technical nature to the proposed method is a one-position location method, which includes receiving at a given frequency a multipath transmitter signal by an array of antennas, synchronously converting an ensemble of signals received by antennas into digital signals and registering them synchronously at a given time interval (Patent RU No. 2285934 C1, IPC G01S 5/04 - 10/20/2006, Bull. No. 29). According to the invention, signals from individual arrival beams of the transmitter signal are extracted from digital signals and two-dimensional bearings of each beam are restored according to well-known algorithms, a model of the ionosphere corresponding to the frequency and time interval of reception of the signal is formed, and model feedback signals in the measured directions of arrival of the rays are determined, the paths of the reverse multi-hop propagation model signals and find the coordinates of the points of their arrival on the Earth’s surface, which are identified as the coordinates of of the assumed emission points of the transmitter signal, find the match of the received points, coincide the points combine and find the point whose coordinates are identified as the coordinates of the transmitter. The proposed method uses the IRI-2001 model in combination with radiation calculations in a three-dimensionally inhomogeneous ionosphere. The possibility of correction of the IRI-2001 model according to the data of the EO and NS of the ionosphere is indicated.

This invention is taken as a prototype.

Its main drawback is that the accuracy of determining the coordinates of the IRI is largely based on the use of a simplified version of the IRI-2001 ionosphere model and the method of its correction, the authors do not specify the settings for the model variants, therefore, use standard ones, which reduces the accuracy characteristics of the critical layer frequencies F2 (f0F2) and most importantly the heights of the maximum of the F2 (hmF2) layer, as well as the impossibility of correctly assessing the appearance of the F1 layer and the sporadic layer Es, in addition, the energy parameters of the rays and use a simplified approach to calculating the paths of propagation of radio waves near the point of beam rotation, which in most times of the daily-seasonal cycle leads to a systematic overestimation of altitude estimates and, consequently, range in radiation calculations.

All known methods of single-point location of IRI are based on simplified approaches to methods for the propagation of HF signals by ionospheric modes and the possibility of an accurate description of the ionospheric plasma using one or another of its corrections according to reference data, the results of airborne or (and) NS. None of the methods takes into account the energy and fluctuation characteristics of the propagating signals and the characteristics of the hardware of the IRI and direction finder. An example (Fig. 1) illustrates that none of the previously proposed methods is suitable for solving the problem of single-position location in most situations.

The task of the invention is to improve the accuracy of a single determination of the coordinates of the sources of radio waves of the HF range of radio waves during ionospheric propagation.

The technical result of the claimed invention is to improve the accuracy of single-position location of the IRI.

The technical result of the invention is achieved through a unified target approach, including the detection and reception of a multipath signal at a known frequency by a phased antenna array, measurement with the necessary accuracy according to known algorithms of spatial arrival angles (azimuth, elevation angle) of each mode of the received signal and estimation of their energy parameters, formation models of the ionosphere, corrected on the basis of current data of vertical, oblique sounding, using satellite tomography and magneto etrov and radiophysics medium model HF radio propagation range, direct and inverse problems arising in the course of single point positioning and ionospheric correction model.

The advantage provided by the given set of features is:

First, a more complete account of the propagation features of HF signals.

Secondly, taking into account the errors introduced by the knowledge of the ionosphere by calculating the propagation paths and measuring the angles of arrival by the direction finder.

In the linear approximation, the range error σ _R can be estimated by the formula:

- производная дальности по углу места;Where

- derivative of range in elevation;

- коэффициент учитывающий влияние относительной ошибки электронной концентрации на оценку дальности:

- coefficient taking into account the influence of the relative error of the electron concentration on the range estimate:

- СКО определения угла места;

- standard deviation for determining elevation angle;

δ _N is the relative error in estimating the electron concentration.

Formula (1) uses the assumption that the error in measuring the angles of arrival of signal modes and the knowledge of the spatial distribution of the electron concentration of the ionosphere are independent. Using the corollary of Martin's theorem after simple transformations for the coefficient of accounting for errors in determining the electron concentration, we can obtain:

- высота в точке поворота;Where

- height at the pivot point;

f is the frequency of the radio wave;

fo is the plasma frequency at the point of beam rotation.

и определение высоты точки поворота по формуле (2). Как и в патенте RU №2285934 основой при лучевых расчетах численно решается задача Коши для известной системы дифференциальных уравнений, однако вблизи точки поворота луча, где точное численное решение из-за ошибок вычислений невозможно применяется специальная аппроксимация позволяющая найти

с точностью недостижимой в указанном патенте.In (1), with one-position location, the errors in calculating the propagation paths of radio waves through the derivative of the distance-angle characteristic are also contained

and determining the height of the pivot point by the formula (2). As in RU patent No. 2285934, the basis for radiation calculations numerically solves the Cauchy problem for the well-known system of differential equations, however, near the beam turning point, where an exact numerical solution due to calculation errors is impossible, a special approximation is used to find

with accuracy unattainable in said patent.

Thirdly, the identification of incoming modes using not only the beam, but also the energy and fluctuation characteristics of the propagating signals using the maximum likelihood criterion.

Fourth, the adoption of special measures to ensure the stability of the solution of the problem of determining the location of the IRI when correcting the parameters of the ionosphere model in the process of solving incorrect inverse problems of the ionosphere EO and NS.

Fifth, the measurement of angles of arrival with an estimate of the number of effective propagation modes.

Sixth, the application of a single target approach to the construction of the ionosphere model, the solution of direct and inverse problems arising in the process of determining and correcting the ionosphere model.

The invention is illustrated by drawings, which depict:

in FIG. 1 - An example of the modal structure of HF signals at a frequency of 17.1 MHz on the path of 2233 km;

in FIG. 2 - Block diagram of a single-position location of coordinates of the IRI;

in FIG. 3 - The geometry of the propagation of radio waves in the spherical ionosphere.

The invention is illustrated in the structural diagram (Fig. 2) of the proposed method for solving the problem of single-position determination of IRI.

The device operates as follows:

The receiving antenna array includes at least 16 antenna elements (AE), which is determined by the possible resolution of up to 4 modes of the received field. Each mode is characterized by amplitude, phase, elevation angle and azimuth, i.e., for a unique solution of the problem in a single-mode field, at least 4 AEs are needed. The issue of polarization reception is solved using the AE design providing separate reception of both field components. AE fabrication technology ensures the unevenness of their transmission coefficient of not more than 1 dB in amplitude and 3 degrees in phase.

A multichannel analog-digital RPU with the number of channels equal to the number of AEs is used as a radio receiving device (RPU). The use of the analog-to-digital circuit is determined by the dynamic interference range in the HF range of radio waves, which reaches 120 dB / W, which is not provided by the analog-to-digital converters currently existing. The presence of the analog part requires calibration of the receiving channels to ensure their identity. The calibration carried out with the subsequent equalization of the complex transmission coefficients of the receiving channels ensures unevenness in amplitude of less than 1 dB and 1 degree in phase.

The high identity of the receiving channels (including AE) allows the use of superresolution methods for measuring the angles of arrival with a simultaneous estimate of the number of received modes. Evaluation of the energy of mods with fluctuation characteristics simplifies the task of identifying them when locating.

Magnetic data allow corrections for magnetic disturbances in the ionosphere model. Levels of geomagnetic activity are expressed using the index - Ak, showing the magnitude of the magnetic and ionospheric disturbances. The index is calculated on the basis of magnetic field measurements carried out daily with a three-hour interval, starting from zero hours on world (Greenwich) time. The maximum values of the magnetic disturbance are compared with the values of the magnetic field of a calm day for a particular observatory, and the largest value of the noted deviations is taken into account. Observations from 13 geomagnetic observatories located at geomagnetic latitudes from 44 to 60 degrees in both hemispheres of the planet allow us to determine the average planetary A _p- index. Index A _p is expressed in integers from 0 to 400.

The only generally accepted model used in IRI-2012, as a function of the response to a magnetic storm, is based on three-hour Ap indices for the 36 hour period preceding the subject. The analysis is based on data from 75 ionosondes for 43 storms. The model is empirical. It includes 1000 coefficients C _ij depending on the day of the year and magnetic latitude, based on which, depending on the integral level of magnetic activity, power factors are used to determine the storm factor equal to the ratio of the critical frequency of the F2 layer under disturbed conditions to the critical frequency of the layer in a calm ionosphere.

The algorithm used to account for Ar indices used in the IRI model is as follows. From the initial three-hour array {Ap _i : i = 1 ... 13}, an array {Ae _j : j = 1 ... 39} is formed that imitates the hourly values of the Ap indices. Each 3-hour value of Ae coincides with the corresponding value of Ap, and the intermediate values corresponding to the hourly values are determined by the method of linear interpolation between 3-hour nodes.

The sum corresponding to the time integral over 36 hour intervals is calculated starting from the 2nd, 3rd or 4th value of the element of the array Ae (value k = 1, 2 or 3):

where fap _i are the coefficients.

If Rp <200, no correction is performed, otherwise the storm factor is calculated.

The main problem that arises when using the 1st magnetometer when evaluating the Ap-index is the lack of a planetary representation, which is ensured by averaging measurements at 13 magnetic stations, data from which is practically impossible to obtain in the on-line mode.

To obtain the integral value of Rp determined by formula (3), the following procedure is used. On the magnetometer, which is part of the location complex, not three-hour indices Ak are determined, but hourly Ae _i , obtained in the model of perturbations by linear interpolation of three-hour values. Moreover, the assessment of these indices is carried out not by the random maximum emission of magnetic measurements per hour interval, but by estimating the quantile of the distribution of the values of A for this interval. This provides a more reliable estimate by replacing space averaging with time averaging, which greatly improves the reliability of the estimates. Further according to the formula

estimated Rp, which is used to calculate the storm factor.

The ionosphere model used in the method, unlike, for example, the IRI-2001 used in Patent RU No. 2285934, has been modernized. IRI-2001 and its latest version of IRI-2012 are a set of models, the number of combinations of which is measured in hundreds. The authors of the patent do not specify the installation options for the model, therefore, use standard settings. The disadvantages of this approach are as follows. Firstly, in calculating the critical frequencies of the F2 layer, the ursi decomposition coefficients are used, rather than the ccir recommended by ITU-R, which, according to the results of comparison with the data of modern continental ionosondes, gives less accurate representation of the critical frequencies of the F2 layer (f0F2). Secondly, the probability characteristics of the appearance of the F1 layer do not correspond to those observed for the region of the Russian Federation, which leads to a distortion of the shape of the electron concentration profile (N (h) profile) and, subsequently, to an incorrect assessment of multimode mode and propagation paths of radio waves. A significant drawback of IRI models is the lack of an adequate representation of the heights of the maximum of the F2 (hmF2) layer, which casts doubt on the possibility of accurately determining the location when the shape of the N (h) profile is fully taken into account in the calculations. In IRI models, hmF2 is determined from the coefficient M3000F2, which was calculated on the basis of a parabolic approximation of the profile of the electron concentration of the F2 region, which in most times of the daily-seasonal cycle leads to a systematic overestimation of altitude estimates and, therefore, range in radiation calculations.

These reasons required the synthesis of a model of the ionosphere that meets the requirements of location. The ionosphere model provides the calculation of the parameters of the model profile of the electron concentration of the ionosphere and other necessary parameters for given points in space of the required zone, time of day, season and level of solar activity. The IRI-2012 model is used as the basic ionosphere model. According to the H.3.2.1 report, the typical accuracy of the description of the electron concentration profile by the IRI model is

- 5-15% for altitudes of 100-200 km in the daytime,

- 15-30% for altitudes of 100-200 km at night,

- 15-25% for altitudes of more than 200 km in low and middle latitudes.

This implies the need to correct model parameters for real measurements. Since the IRI model includes a large set of private models, the specification of the option used is given below.

1) Model for calculating the parameters of the region F2

The model includes CCIR coefficients, which allow predicting the critical frequencies of the F2 region. The model includes 24 maps for the months of the year of two levels of solar activity 10 and 100. To predict f0F2, the current 12-month average value of the ionospheric index IG ₁₂ and linear interpolation for time and solar activity are used.

The CCIR coefficient arrays include the M3000F2 coefficients, which determine the height of the maximum F2 (hmF2). The height of the maximum is in close anticorrelation with the critical frequency and is determined by the formulas:

CF = ƒ1 / (ƒoF2 / ƒoE-ƒ2) + ƒ3.

Here hmF2 in km. Factors ƒ1, ƒ2 and ƒ3 are constants, depending on the current 12 month average of the number of sunspots Rz ₁₂ and magnetic latitude.

2) Model for calculating the parameters of regions E and F1

The electron density of regions E and F1 is determined to a greater extent by the balance of natural photochemical processes, and the maximum of plasma frequencies strictly depends on the zenith angle of the Sun χ. The IRI model on average shows the difference between real data from 5 to 15%.

For the height of the maximum of layer E, a constant value of 110 km is assumed. The value of the half-thickness of the layer is 20 km.

The foF1 model is based on magnetic latitudes. In this case, a calculation option is used from a set of IRI functions - by the zenith angle of the Sun with L-conditions. The height of the maximum electron concentration of the F1 (hmF1) region is determined by the shape of the N (h) profile.

3) The form of the N (h) profile corresponds to that recommended in the IRI-2007 model.

Differences from the models presented in the IRI are as follows.

1) The hmF2 calculated by formula (5) is adjusted using a special function

where d is the day of the year

h - time (hour, tenths of an hour in local time),

Rz12 is the number of sunspots.

Function D is based on the empirical coefficients obtained as a result of processing the data of ionosondes determining hmF2 by the N (h) profile of the ionosphere. The new value of HmF2 obtained in this way by formula (6) is used in further calculations.

2) The model for the probability of the appearance of the F1 layer is adjusted by introducing the seasonal factor fs = 1.0 + cos ((d-173.5) * 27π / 365), which when multiplied by the probability of the appearance of the F1 layer (f1pb) is used to predict the presence of the layer. If f1pb * fs exceeds the threshold determined by the data of the OT, then the layer is considered to be present.

3) A model of the sporadic layer Es has been introduced. The model allows estimating the limiting frequency of the Es layer by the day of the year, local time, the number of sunspots, and geographical coordinates. It is based on the EsKGU model. This is a predictive probabilistic model for calculating the median values of the limiting frequencies and heights of the Es layer, in which the daily variations of these parameters are described by a trigonometric polynomial in the form of a Fourier series expansion of the form

where a ₀ , a _k b _k are the coefficients of the Fourier series for frequencies,

k is the harmonic number,

t is the local time in hours.

Checks carried out by the authors of this model showed that the correspondence between the calculated and experimental distributions took place: in the winter - in 71% of cases, at the equinox - in 70%, in the summer - in 77%. Those. the probabilistic characteristics of the prediction of this model are not high. Therefore, when using the ionosphere as part of the model, these representations are used if the sporadic layer Es is observed according to the data of the ionosphere and (or) the ionosphere, with corresponding adjustment according to the measurement results.

4) The implementation of the IRI ionosphere model is performed in C ++, includes only the necessary components and is optimized for the structure of the language.

The radiophysical model implements the calculation of the trajectories of the propagation of radio waves along the sounding paths of the ionosphere and reception of IRI signals. The calculation of the propagation paths of radio waves is carried out in the frequency range 1.0 ... 30 MHz in the azimuth zone of 360 ° and ranges up to 4500 km relative to the center. The problem is solved for a three-dimensionally inhomogeneous ionosphere in approximations of geometric optics. The law of refraction of radio waves is used in the following form:

where n is the refractive index along the path of propagation of radio waves;

dS is an element of the trajectory whose points are determined by the coordinates of the spherical projection on mutually perpendicular planes: the plane of the arc of a large circle passing through the center of the earth transmission and reception points, and perpendicular to it. In the first plane, the position of the current point is determined by the coordinates R and θ, in the perpendicular - R and χ;

χ - lateral angular deviation of the trajectory from the plane of the arc of a large circle;

θ is the angular distance in the plane of the arc of a large circle;

ϕ and ψ are the angles between the projections of the wave vector and the radius R in the planes Rθ and Rχ.

The solution of equations (8) is carried out taking into account the results obtained in:

1) changes in the jump distance and angles of arrival in the vertical plane are mainly due to the gradients of the ionosphere in the plane of the arc of a large circle,

2) lateral deviations of the angles of arrival in the azimuthal plane are determined by gradients in the transverse plane.

This allows you to search for a solution first in the plane of a large circle with subsequent adjustment for lateral gradients. The solution in the plane of the large circle is sought in the form

for the range of the jump,

for the group path.

The notation used is illustrated in FIG. 3.

Here r is the distance from the center of the Earth;

r _e is the radius of the Earth;

r _t is the height of the trajectory at the point of rotation of the beam,

r ₀₁ is the height of the beam entry into the ionosphere,

r ₀₂ is the height of the beam exit from the ionosphere,

q (r) = r ² μ ² -ρ ² ,

ρ = r _e cosΔ,

Δ is the angle of the beam,

,μ is the phase refractive index associated with the electron concentration by the ratio

,

e, m is the charge and mass of the electron,

ε ₀ - dielectric constant of free space,

f is the wave frequency,

ε is a small quantity that depends on the accuracy of the calculations.

The pivot point r _t is determined from the condition

Это определяет разбитие ионосферной части траектории на 3 части.The division of integration along the trajectory S into five integrals is due to the following reasons. In free space μ = 1, the corresponding expressions for D and P _{g are} integrated by analytical formulas, and the initial integrals are divided into two parts - the off-ionosphere (the first and fifth integrals in formula (9) and formula (10)) and the ionosphere. The presence of gradients of electron concentration in the general case leads to a mismatch between the entry and exit angles of the ionosphere, which determines the breaking of the off-ionospheric zone into two integration regions. The integral in the ionospheric part is improper, having a gap at the turning point, where the denominator

This determines the breakdown of the ionospheric part of the trajectory into 3 parts.

With an arbitrary shape of the electron concentration profile, analytical integration of the ionospheric part is impossible and calculations are carried out by numerical methods.

For this, the electron concentration N (r _i ) is interpolated, formed by the geophysical model at heights r _i , by a second-order spline. The segment [r ₀ , r _m ] from the base to the height of the maximum electron concentration r _{m is} divided into M segments: r _i = r ₀ + Δri, where Δr = (r _m - r ₀ ) / M. On each segment [r _i , r _{i + 1} ] the distribution profile of the electron concentration is represented by a square trinomial:

N (r) = S _i (r) = a _i r ² + b _i r + c _i for r∈ [r _i , r _{i + 1} ]

with smoothness conditions at the ends:

N (r _i ) = S _i (r _i ) = S _{i + 1} (r _i ), i = 1, ..., M-1; N (r ₀ ) = S (r ₀ ), N (r _M ) = S _M-1 (r _M );

.

.

In the vicinity of the turning point, when the computational error does not allow the use of numerical methods, the profile description is replaced by a quasi-parabolic dependence, which allows us to take the third integral analytically.

ƒ _N ² (r) = Q ₁ (r) = (A ₁ r ² + B ₁ r + C ₁ ) / r ² for r ∈ [r _t-ε , r _{t + ε} ];

Q ₁ (r _t-ε ) = ƒ _N ² (r _t-ε ), Q ₁ (r _{t + ε} ) = ƒ _N ² (r _{t + ε} );

Q ₁ '(r _t-ε ) = (ƒ _N ² (r _t-ε ))'.

и в третьих интегралах выражений (8) и (9) функция F(r) - r²/μ² -ρ² заменяется на функцию

где μ₁ ²=1 - Q₁(r)/ƒ². Высота поворота r_t1 определяется из уравнения F₁(r_t)=0.As r _t + _e , the first integration point after r _t-ε is chosen, for which the root function

and in the third integrals of expressions (8) and (9), the function F (r) - r ² / μ ² -ρ ² is replaced by the function

where μ ₁ ² = 1 - Q ₁ (r) / ƒ ² . The turning height r _t1 is determined from the equation F ₁ (r _t ) = 0.

The second and fourth integrals are calculated numerically.

The assessment of the accuracy of determining the range with this representation gave a total calculation error of less than 0.2 km at ε = 0.05.

Azimuthal deviation (deviation of the beam from the plane of the big circle) is determined by the formula:

where iχ is the angle of inclination of the line of equal electron concentration (isolines).

The angle of the isolines in radians is estimated by the formula:

iχ = a rctg {(h2-h1) / (2 × r _e + h1 + h2) × ctg (χ / 2)},

substituting in (11) we obtain the expression for calculating the azimuthal deviation:

Δβ = a rctg {tg (Δ) × (h2-h1) / (2 × r _e + h1 + h2) × ctg (χ / 2)},

where h1, h2 are heights of equal electron concentration relative to the Earth’s surface at two adjacent contour points at the turning point range, provided that the electron concentration at these points is less than the height of the maximum electron concentration. The height ho = r _t -r _{e of} the turning point and the value of the plasma frequency fo at this point are determined. At azimuthally adjacent grid points of the same range, there are heights corresponding to the frequency fo;

χ is the central angle corresponding to the distance between points 1 and 2.

ctg (χ / 2) = Const / Ro,

where Ro is the distance to the turning point;

Const = r _e / tg ( a / 2);

a - azimuthal distance between the grid lines of the calculation of electron concentration.

True azimuth is determined by the formula:

β = β _MOD + Δβ,

where β _ism is the estimate of the azimuth of the arrival of IRI signals.

Due to the dynamics and unsteadiness of the ionosphere, model representations alone are not enough to determine the position of Iran. An adequate representation of ionization in the ionosphere is ensured by its diagnostics by radiophysical methods with subsequent correction by the parameter of the model of the medium according to its results. Correction is carried out at two levels, global and regional.

A mathematical apparatus was used that takes into account not only the correlation properties of the ionosphere, but also various accuracy and possibilities of determining the characteristics of the ionospheric plasma by various sounding methods, taking into account fluctuation characteristics.

The main weight in the adaptation and stabilization of solutions is made by the VZ method, which allows you to adjust the parameters of the lower (up to F2) ionosphere regions, extending these results to the entire region with a radius of up to 3000 km from the installation site of the single-position location complex. Region F2 is corrected in the center taking into account fluctuations in its parameters and, through correlation dependences, extends to the entire region. The data of space radiotomography, taking into account the accuracy of their obtaining, are used for further spatial correction of the parameters of the F2 region using the data of the airspace for calibration, and the results of the spacecraft characterizing the entire distribution area are taken into account through the correction of the storm factor.

To reduce fluctuation errors, temporary smoothing with effective memory of the obtained parameters of the ionosphere model using the results of a continuous series of measurements is used.

Implementation of the VZ method does not require special hardware and is implemented on the antenna array and the receiver of the direction finder with radiation power amplifiers distributed over the antenna elements. The sounding is carried out at specially allocated intervals, their total duration does not exceed 1.5% of the operating time of the direction finder. Obtaining and processing with obtaining a profile of the electronic concentration of the results of the airspace are performed automatically. The incorrectness of the solution of the inverse VZ problem is eliminated by the search for a solution in the class of N (h) profiles used in the synthesized ionosphere model given above. When constructing the profile, the hypothesis of the presence of a sporadic layer Es is checked. If the hypothesis is confirmed, then the type of layer (high / low) and its parameters with the correction of the shape of the N (h) profile are determined.

The obtained parameters of the electron concentration profile are: the critical frequency of the layer F2 (f0F2), the height of the maximum electron concentration of the layer F2 (hmF2), the critical frequency of the layer F1 (f0F1), the height of the maximum electron concentration of the layer F1 (hmF1), the critical frequency of the layer E (f0E), the height of the maximum electron concentration of the layer E (hmE), the critical frequency of the layer Es (f0Es), the height of the maximum electron concentration of the layer Es (hmEs), type Es serve as the basis for the correction of the ionosphere model, the result of which is to obtain the values of the electron concentration in the node At the points of the coordinate system, azimuth (β), range (R), height (h). When calculating the propagation paths of radio waves, these nodal values describing the adjusted model of the ionosphere are used to construct the distribution of electrons along the propagation path of radio waves.

The correction of the ionosphere model is divided into global, regional and fluctuation. The global ionosphere model based on IRI-2012 uses the average monthly ionospheric index IG ₁₂ and the number of sunspots Rz ₁₂ as input parameters. The determination of specific IG and Rz values for the required day and time of the day is carried out by linear interpolation of the neighboring monthly average IG ₁₂ and Rz ₁₂ values, the smoothed values of which are predicted at least a year in advance. Global correction allows you to get these indices for the required observation period.

The critical frequency of the F2 region is linearly related to the ionospheric index IG, which is calculated by averaging f0F2 obtained as a result of the VZ on 13 ionosonde scattered around the globe. In our case, there is one ionosonde, which received f0F2 values at one point. The global IG value is adjusted as follows. The value of IG _i corresponding to the measured value of the critical frequency f0F2 _i at the i-th moment of time is calculated by the formula

where IG is the index determined at the previous correction step or according to the forecast;

f0F2 is the critical frequency value determined by the IG index.

A new global index is being formed

where 0 <η <1 is a coefficient depending on the sensing coordinates.

In IRI, the number of sunspots Rz is involved in determining f0E, f0F1, and hmF2. However, as can be seen from (5), the connection is nonlinear. The accuracy of the estimates of f0E, f0F1, and hmF2 based on measurements at VZ and their relation to Rz are different. Therefore, the value of Rz _i is sought by minimizing the weighted average

where a _k , k = 1 ... 3 are weighting coefficients, the parameters f0E, f0F1 and hmF2 with index i correspond to those calculated by the model according to the value of Rz _i , and without the index determined from the N (h) profile calculated from the measurement data. The coefficients a _k are reset if the corresponding measurement is not obtained.

The value of Rz _i obtained in this way is smoothed with the previous

подобранный коэффициент и используется далее в качестве глобального.Where

selected coefficient and is used further as global.

If a sporadic layer Es is detected, the ratio of the measured critical frequency f0Es to the predicted one determined by formula (7) is calculated, and critical frequencies Es corrected by this value are formed from (7). The height of the maximum electron concentration of the Es layer in the zone is assumed to be equal to the measured one.

The final stage of the correction according to the OT data is the correction according to the measurements of hmE and YmE, which are global for the IRI model. The operation is performed according to formulas similar to (13) and (14) with the replacement of the index IG _i by the measured parameters hmE _i and ymE _i

The correction of the parameters of the ionosphere model according to space tomography is based on the use of two-frequency signals from the GLONASS and GPS navigation satellites received at the point of location of the VZ ionosonde. The method allows you to cover a zone with a radius of up to 1000 km. The difference in the signal arrival range at two frequencies in the approximation of a local spherically uniform ionosphere is associated with the electron concentration by the radio transmission equation

where h ₀ and h _m are the lower and upper heights of the boundaries of the ionosphere,

Y is the zenith angle of observation of the satellite from the observation point,

h is the current height from the surface of the Earth,

δ - fatal error of measurements, depending on the frequency.

This is an integral equation of the first kind of Fredholm type; its solution belongs to the class of incorrectly posed problems. The resulting N (h) profiles mainly characterize the F2 region and do not reflect sporadic formations. However, during the day, more than 20,000 electron concentration profiles can be obtained from one observation point, which makes it possible to bring the ionosphere model closer to reality.

Calibration of measurements according to the airborne data makes it possible to obtain a data array in a zone with a radius of up to 1000 km containing f0F2 and hmF2 for the geographical points above which navigation satellites are currently located. These data are used to determine regional indices IGr and Rzr.

A zone with a radius of 1000 km is divided into M sections {θ _m , m = 1 ... M} with a width of 15-30 ° in azimuth and ~ 250 km in range. In the time interval of the quasistationary state of the ionosphere (≤15 minutes), formula (12) determines the arrays of indices {IGr _im } from satellite profiles corresponding to sections θ _m . The regional index is calculated for each site in which information is received.

where Im is the number of measurements in the mth section.

и рассчитывается среднее за интервалAt the same time, Rzr _{im is} defined as

and the average for the interval is calculated

Then, using formulas (13) and (14), values smoothed relative to global indices are calculated, which are taken as regional for the next time interval. For an arbitrary point with azimuth-range coordinates (a, r) within a radius of 3000 km from the center, regional indices are determined by the formulas

Where

F (x _{a r} - x _m ) = F '(φ) ⋅ F' (λ) - correlation function for the point with coordinates (a, r) with the point x _m ;

ϕ is the difference between the latitudes of the point ( a , r) and the center of the segment θ _m (point x _m );

λ is the difference in the longitudes of the point ( a , r) and the center of the segment θ _m ;

Δ _λ , Δ _φ - parameters determined by correlation in longitude and latitude

depending on date, time and geographic coordinates.

The complexity of using the results of the NS of the ionosphere is due to the fact that the entire propagation medium along the sounding path is involved in the formation of the signals of the NS and it is difficult to apply these results (in contrast to the HE and satellite tomography characterizing one point). Storm factor cƒ is determined using the "STORM" function of the IRI model according to the Rp value calculated by formula (8). In the presence of disturbances (Rp> 200), the critical frequency F2 at the considered geographical point is adjusted by the magnitude of the storm factor: f0F2 = cf × f0F2. The value at neighboring points of the trajectory at a fixed point in time depends only on geomagnetic coordinates. For the considered routes, taking into account the accuracy of determining the results of NS, the value of s is considered constant.

Automatic processing and interpretation of the time-frequency characteristics (HFC) of the NS is carried out using the calculation of the trajectories and the adjusted model of the ionosphere described above. Processing involves finding the most plausible hypothesis about the estimated GFCFs that coincide in the sense of the maximum likelihood criterion with experimental measurements. The search involves finding the strain coefficient of the ionosphere model. That is, if a hypothesis satisfying the experimental data was found as a result of the search, then an additional factor cf 'is determined, which is fixed in the direction of the NS path and extends to the azimuthal sector of ± 15 ° relative to this direction.

The problem of one-position location is solved as follows. We have at the input a sequence of measurements of the angles of arrival of signals at a frequency f. Each measurement i is described by the vector X _i = {α _i , β _i , Q _i }, i = 1 ... I, where I is the number of measured angles of arrival of the modes, consisting of the components:

- азимутальный угол;

- azimuth angle;

β _i - elevation angle;

Q _i - signal-to-noise ratio.

And an i-ro measurement correlation matrix

σ _αi - standard deviation of azimuth estimation;

σ _βi - standard deviation of elevation angle estimation;

σ _Qi is the _standard deviation of the signal-to-noise ratio.

с матрицами ошибок

возможным m=0…M_i модам распространения под i-ми углами.On the other hand, for a given measurement sequence using the aforementioned method, the values of ranges and signal-to-noise ratios for all possible propagation modes arriving at angles (α _i , β _i ) are calculated using the adjusted ionosphere model. Those. calculated vectors are defined

with error matrices

possible m = 0 ... M _i propagation modes at i-th angles.

The task is to determine the most probable range with which these signals came. It is solved for two possible situations. The 1st occurs for i = 1, when it is not possible to determine the number of jumps from geometric representations, the 2nd for i> 1 narrows the uncertainty, but requires additional conditions.

In the first situation, taking into account a priori information about the product of the gain of the IRI antenna and the radiation power in the direction to the direction finder, the problem is solved: the adopted propagation mode has a 1-nd or 2-x jump. The limit on the number of jumps is associated with the maximum range of the solution of the problem (up to 3500 km). The criterion of the maximum of posterior probability is used, which in the case of normal distributions is converted to

where, C is a constant depending on a priori data and loss functions, the index m = 1 corresponds to the hypothesis of one jump, 2 to two jumps. If inequality (15) is satisfied, a decision is made on the arrival of the IRI signal from a range corresponding to one jump, otherwise, from a range of 2 jumps.

When deciding on two jump modes, the range of the second jump is specified by finding the trajectory of the second jump that meets the condition

where a ₂ is the angle of incidence of the second jump on the surface of the Earth.

In the second situation, for each i-ro measurement, the criterion (15) determines the conformity of the measurement — the situation of a one-hop mode. If all measurements correspond to single-hop modes, then the average weighted range of the IRI is calculated

where D _i - the range corresponding to the model calculations of the i-th dimension,

σ _Di - standard deviation of the i-th range assessment.

If among the measurements there are both single-hop and double-hop modes, then for single-hop modes, the weighted average range is calculated by formula (16), and for double-hop modes, the variant of hitting the second jump on the range D is searched. If this option is found, then this D is used in as an estimate of the coordinates of Iran. Otherwise, the range of the two-hop mode D 'is determined that is closest to D and, using formula (16), taking into account overdetermined dispersions, the range to IRI is refined.

, где D_v - дальность, рассчитанная по (16) для v-ой допускаемой комбинации скачков. Дальность D_v соответствующая этому минимуму принимается за дальность ИРИ.If all measurements correspond to multi-hop modes, the combination corresponding

, where D _v is the range calculated by (16) for the v-th permissible combination of jumps. The range D _v corresponding to this minimum is taken as the IRI range.

Improving the accuracy of single-position location of radio emission sources is achieved for the first time by implementing a unified target approach, which consists in combining the functions of measuring the spatial (azimuth and elevation angle) and energy parameters of the multipath field of the received signal of each beam, adjusting the ionospheric plasma model based on current data of vertical, inclined, and radiotomographic sounding and magnetometers, after correction of which geophysical and radiophysical are calculated clothed, allowing to restore the path of each beam in the ionosphere in the measured directions of arrival.

Salient features of the proposed technical solution compared to the prototype, providing a number of technical and economic advantages, are:

- improving the accuracy of measuring spatial parameters (azimuth and elevation angle) of the multipath signal field of each beam by introducing corrections according to the adjusted model of ionospheric plasma based on current ionograms of vertical and inclined sounding, as well as satellite tomography and magnetometers;

- increasing the reliability of the parameters of the ionosphere beyond the limits adopted in the prototype, which can significantly expand the conditions of use, actually bring them to year-round and round-the-clock use, regardless of the likelihood of the appearance of the F1 layer and / or the manifestation of the sporadic layer Es, not taken into account in any forecast models, or from the passage of moving ionospheric disturbances and other intense inhomogeneities of various scales;

- improving the accuracy of calculating the ray paths of propagation of radio waves, especially near the point of rotation of the beam with an arbitrary shape of the electron concentration profile, through the use of a special approximation that allows you to find the reflection height with accuracy unattainable for the prototype;

- elimination of anomalous positioning errors caused by the deviation of the ray path due to the identification of incoming modes using not only the beam, but also the energy and fluctuation characteristics of the propagating signals using the maximum likelihood criterion;

- unambiguous determination of the sources of radio emission due to special measures ensuring the stability of the solution of the problem of determining the location when correcting the parameters of the ionosphere model in the process of solving incorrect inverse problems of vertical and inclined sounding of the ionosphere.

Claims (1)

A one-way method for determining the coordinates of short-wavelength sources of radio waves during ionospheric propagation, including receiving a multipath signal by a phased array, converting a plurality of analog signals from each antenna element into digital signals, coherently processing them with measuring the spatial arrival angles (azimuth, elevation angle) of each ray of the received signal, characterized in that the energy parameters of each beam, formed by The ionosphere delta is adjusted based on current vertical and oblique sounding data using satellite tomography and magnetometers, and geophysical and radiophysical models are formed that allow you to restore the path of each ray in the ionosphere in the measured arrival directions, based on which primary estimates of the coordinates of the serifs of the alleged sources of radio emissions are determined find the coincidence of the estimated coordinates for different variants of single-hop and double-hop modes, coinciding s serifs are combined using a maximum a posteriori probability criterion allowing to increase the reliability of emitters estimates and unambiguously determine the location of radiation source.

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