RU2699552C9 - Method for passive single-position angular-doppler location of radio-emitting objects moving in space - Google Patents

Abstract

FIELD: radio equipment.

SUBSTANCE: invention relates to radio engineering and can be used in passive radar and radio surveillance systems for single-position determination of velocities, coordinates and trajectories of radio-emitting objects (REO) moving in space. Estimating values of spatial heading angles γ_k of REO on inclined planes 0A_lA_k, passing through sections A₁A_k trajectories, where A₁, A₂, … A_k, … A_K – points on movement trajectory REO, in which it is at equidistant moments in time, and the observation point lying outside the trajectory, calculating the ratio of Doppler frequency shifts to obtain an equation for the inclined course angle γ₁, solving which determine current values of heading angles, magnitude of velocity module REO, length of path passed by object between points of trajectory A₁ and A_k, and the value of the inclined range in case the object is in points A_k trajectory, as well as modulus of speed of radio-emitting object when it is in points A_k. Then trajectories of objects are constructed using measured and calculated values of their angular coordinates, inclined distances, heading angles and speeds of movement.

EFFECT: one-position measurement of directions and speeds of movement REO, moving in space uniformly and rectilinearly with variable altitude of flight, as well as trajectories of set construction REO, moving with arbitrary course angles and diving angles (pitching).

1 cl, 1 tbl, 6 dwg

Description

The invention relates to the field of radio engineering and can be used in passive radar and radio surveillance systems for on-off determination of coordinates, speeds and trajectories of radio-emitting objects (RIO) moving in space - artificial Earth satellites, ships, planes, unmanned aerial vehicles.

Passive radar systems (radar) are used to measure the parameters of the movement of RIO from the radiations of their airborne transmitting devices. These radars have less complexity and lower cost than active radars, due to the lack of a radio transmitting part. They have high secrecy, which significantly complicates the determination of their dislocation and characteristics. To determine the location and trajectories of RIO by passive methods [1 - Passive radar: methods for detecting objects / Ed. prof. R.P. Bystrov and prof. A.V. Sokolova. M: Radio engineering. 2008. 320 pp.] Usually use several diversity stations, combined using data relays in a multi-position system. But such a system, in comparison with a single-position system, has a larger volume of equipment, increased complexity and cost.

Until recently, a single-position location did not provide the determination of inclined ranges, velocities, and trajectories of RIOs moving in space by measuring their angular coordinates (UK) and parameters of emitted signals. Therefore, the search for methods and the creation of devices for an overview of passive one-position locations that ensure the determination of these parameters with sufficient accuracy for practice are relevant.

Single-position passive radars must determine the CC of the located objects with high accuracy and in a relatively short time, since these objects can move at high (including hypersonic) speeds and move along complex unpredictable trajectories, and their law of motion can contain alternating derivatives of high orders. The monopulse method widely used in radar and direction finding is considered the best basis for achieving high accuracy in determining the UK of located objects [2 - Leonov A.I., Fomichev K.I. Monopulse radar. - M: Radio and communications, 1984. 312 p., P. 6]. UK RIO are determined by measuring the direction of arrival of the received signals relative to the known equal signal direction (RSN).

Ways to achieve high accuracy in determining the criminal code and sufficient speed of the survey amplitude monopulse direction finder are justified in [3 - Patent 2583849, Russian Federation. A method of digital signal processing in a survey monopulse amplitude total-difference direction finding using an antenna array (options) and a survey monopulse amplitude total-difference direction finder using an antenna array and digital signal processing / Dzhioev A.L., Omelchuk I.S., Fominchenko G. .L., Fominchenko G.G., Yakovlenko V.V. Declared April 13, 2015, published May 10, 2016]. In this work, the choice of the type of weight function at the aperture of the antenna and the separation angle of the radiation patterns (LH) provided the direction-finding characteristic (HR), which is almost linear over the entire width of the monopulse group of rays (MGL). After receiving the RIO signals and their analog-to-digital conversion (ADC), the direct-counting method is used, which allows using a quick direct and easily implemented (solving the linear equation) calculation of the criminal code with an error of no more than 1/100 of the beam width at half power level with a low level of side lobes ( below minus 40 dB) and acceptable use of the antenna surface. The high linearity of the HRP over the entire width of the MGL, which provides a quick and accurate determination of the object's CC without using an iterative algorithm, significantly reduces the time for viewing the space and increases the number of objects controlled without RSN movements and repeated soundings. However, this does not select the located objects according to their speed and their paths in space are not determined.

временных моментах, отстоящих друг от друга на равные интервалы Т, затем из множества возможных (условных) параллельных траекторий движения, соответствующих измеренным УК, выбирают одну условную, на которой точки А, В и С равноудалены по времени на равные интервалы 0,5 NT, определяют проекции координат точек А, В, С в зависимости (функциональной) от соответствующих проекций линейной скорости, и наконец, задавшись значениями координат точки С, определяют значения проекций V_x, V_y, V_z текущей линейной скорости объекта, а также саму условную линейную скорость и экстраполированные значения УК. Однако в [4] не определяются истинные координаты, скорости и траектории движения РИО в пространстве.A known method of measuring from one position the angular velocity of an object [4 - Alpatov B.A., Balashov O.E. Measurement of the speed of an object in systems of automatic tracking of objects // Vestnik RGRTU. Ryazan. 2014. No4 (issue 50). S. 5-10]. In it, on the basis of angular measurements, the conditional speed of the object is determined, proportional, with a constant coefficient, to its real speed, under the assumption that the object moves in space uniformly and rectilinearly. In this case, the asset's asset is measured in

time moments spaced from each other by equal intervals T, then from the set of possible (conditional) parallel trajectories of motion corresponding to the measured CC, one conditional is chosen at which points A, B and C are equally distant in time at equal intervals of 0.5 NT, determine the projections of the coordinates of points A, B, C depending (functional) on the corresponding projections of the linear velocity, and finally, having given the values of the coordinates of the point C, determine the projection values V _x , V _y , V _{z of the} current linear velocity of the object, as well as the conditional linear speed and extrapolated values of the Criminal Code. However, in [4] the true coordinates, velocities, and trajectories of the RIO in space are not determined.

An analogue of the proposed method is [5 - Patent 2617830, RF. The method of a passive one-position goniometric-difference-Doppler location of a radio-emitting object moving in space and a radar system for implementing this method / Dzhioev A.L., Omelchuk I.S., Tyurin D.A., Fominchenko G.L., Fominchenko G.G. ., Yakovlenko V.V. Declared April 11, 2016, published April 28, 2017]. During reception, it detects the detection of the RIO signal and determines its parameters - the width of the spectrum, the average frequency of the signal spectrum and the type of modulation. Carry out the auto-tracking of the selected object in angular coordinates, measure and remember the values of the samples of the angular coordinates (azimuth β and elevation angle ε), as well as the current time corresponding to these samples. Then restore, knowing the type of modulation, the carrier frequency ƒ _{H of the} received signal, form at time t _i and remember the values of its samples. Next, the increments of the CC and Doppler frequency shifts of the received signals are calculated at the intervals Δt _{k, n} , which are sufficiently small for the assumption of uniformity and straightforwardness of the RIO motion with the speed V at a constant height N. Then the horizontal components of the increments of the Doppler frequency shifts are determined, these increments and calculate their ratio

в виде

и определяют координаты РИО в моменты времени t₀ и t₄ как точки пересечения окружности с центром О' и лучей длиной d₀ и d₄, проведенных из начала координат под углами β₀ и β₄.to find the angle α between the velocity vector and the horizontal range. Next, determine the current value of the heading angle q _k = β _k + α and the horizontal velocity modulus V _g = V, and then the distance S ₄ , ₀ traveled by the object for the time interval Δt ₄ , ₀ . Then find the radius R of the circle passing through the origin, the chord of which is the distance S _4.0 , find the center O 'of this circle, fixing a point at the end of the ray of length R drawn from the origin 0 at an angle β _C = β ₀ + q ₄ -90 °, calculate the range d ₀ and d ₄ using the ratio

as

and determine the coordinates of the RIO at time t ₀ and t ₄ as the point of intersection of the circle with the center O 'and rays of length d ₀ and d ₄ drawn from the origin at angles β ₀ and β ₄ .

However, the analogue [5] is not without drawbacks, which include:

1. The impossibility of measuring ranges, directions and velocities of movement in space, as well as RIO trajectories in cases of their movement with a variable flight height, that is, with arbitrary diving angles (cabrio).

2. The need to use two functioning algorithms with a limited scope of applicability of each of them:

- the first, applicable in case of changes in the azimuth and elevation angle of the RIO at its approach (removal) relative to the radar,

- the second, applicable only with a constant azimuth of the object.

3. The use of the radar tracking mode, which, compared with the survey mode, reduces its performance and the number of monitored objects.

Производят два последовательных измерения частот ƒ₁ и ƒ₂ принятых сигналов в моменты времени t₁ и t₂ соответственно, и на основании этих измерений определяют величину

далее на основании измеренных углов азимута β₁ и β₂ определяют Δβ₂₁=β₂-β₁. После этого вычисляют дальность до цели по формулеThe closest in technical essence to the claimed method is [6 - Patent 2557808, RF. A method for determining the slant range to a moving target with a passive monostatic direction finder / Borisov E.G., Martemyanov I.S. Declared April 9, 2014, published July 27, 2015], adopted as a prototype. It jointly processes two successive measurements of bearings (azimuth angles β ₁ and β ₂ ) and powers P _C1 and P _{C2 of} signals for measurement times t ₁ and t ₂ . Considering that the base measurement point corresponds to the geometric center of the goniometric system, and the line C ₁ C _N (the trajectory of the target) corresponds to the points C ₁ and C _{2 of the} measurement of the bearing of the target at time t ₁ and t ₂ , assuming that the target moves in a straight line, based on the obtained values of P _C1 and P _C2 calculate the value

Two consecutive measurements of the frequencies ƒ ₁ and ƒ _{2 of the} received signals at time t ₁ and t _{2 are} performed, respectively, and based on these measurements, determine the value

then, based on the measured azimuth angles β ₁ and β ₂ determine Δβ ₂₁ = β ₂ -β ₁ . After that, calculate the distance to the target by the formula

where c is the propagation velocity of electromagnetic waves;

T = Δt ₁₂ .

The accuracy characteristics of the prototype [6] are determined by errors in measuring the angular coordinates of the RIO, the carrier frequencies and powers of the signals emitted by it. At the maximum possible accuracy of measuring angles and frequencies, the error in determining the slant range depends on its value and is in the range of 5-35%, which is not always acceptable. In addition, under real conditions, objects of observation usually emit modulated signals with a suppressed carrier, which does not allow the method to be applied [6]. Finally, when using the method [6], the power of the received signals is measured, and it is subject to fluctuations, which are caused by interference of vibrations reflected by the structural elements of the object, changes in propagation conditions, and reflections from local objects. The magnitude of these fluctuations can reach 10-15 dB; the error in measuring the range according to the method [6] with a fluctuation coefficient of 6 dB is 5%, and with a fluctuation coefficient of 12 dB, it reaches 250%, that is, the method becomes inoperative.

Thus, the disadvantages of the prototype [6] are:

1. A large error in measuring the range at the maximum possible accuracy of measurements of the primary parameters.

2. The impossibility of measuring range when complex modulated emissions are used as signals.

3. The need to measure the power of the received signals, which is subject to fluctuations, the value of which can reach 10-15 dB; in this case, the error in measuring the range with a fluctuation coefficient of 6 dB is 5%, and with a fluctuation coefficient of 12 dB, it reaches 250%, that is, the method becomes inoperative.

Inventions that solve the aforementioned problems by the methods of a passive one-position location moving in space along arbitrary trajectories of RIOs, the authors of the proposed method were not found in the technical literature.

The technical problem that the proposed method seeks to solve is the determination of coordinates, directions and speeds, as well as the construction of trajectories of the entire set of RIOs moving in space in arbitrary directions uniformly and rectilinearly with all possible directional angles and diving angles (cabrio).

To solve this technical problem, a method is proposed for a passive one-position goniometric-Doppler location (UDL) of radio-emitting objects moving in space, in which:

a digital antenna array (CAR) or an antenna array with digital signal processing is used for receiving radio signals,

form in space using the Hamming weight function, a monopulse group of beams with a common phase center and direction-finding characteristics with working areas Δβ _PX in azimuth and Δε _PX in elevation, linear over the entire MGL width due to specially selected beam displacement angles β _cm and ε _cm

divide the given area of the space review into sections of size Δβ _PX in azimuth and Δε _PX in elevation and, sequentially setting the equal-signal direction of the MGL to the centers of these sections, review the said area,

объектов в упомянутой области обзора и определяют параметры их сигналов - ширину и среднюю частоту спектра, а также вид модуляции,receive signals of radio-emitting objects during the observation interval at each section of the partition in a given frequency range, when these signals appear, they detect the entire population

objects in the mentioned field of view and determine the parameters of their signals - the width and average frequency of the spectrum, as well as the type of modulation,

describe the spatial position of RIO moving uniformly and rectilinearly along trajectories with arbitrary diving angles (cabriages), current values of the angular coordinates (azimuth β _T and elevation angle ε _T ), slant distance vectors D _T , absolute values of velocity vectors V and course values angles γ _k between the velocity vectors and slant ranges,

measure and store for each of the detected objects the values of the samples β _m , ε _{m of the} angular coordinates of the m-th object, calculated relative to the equal-signal directions, as

β _m = β _PCH + Δβ _m , ε _m = ε _PCH + Δε _m ,

Where

и

- сигналы угловых рассогласований с выходов угловых дискриминаторов длят m-го объекта;

and

- signals of angular mismatches from the outputs of the angular discriminators for the m-th object;

и

- значения коэффициентов линейных членов разложений пеленгационных характеристик в ряды Маклорена по координатам

and

- the values of the coefficients of the linear terms of the expansion of direction-finding characteristics in the Maclaurin series in coordinates

β, ε at the selected values of the displacements β _cm and ε _{cm of} rays from equal-signal directions,

select, using data on the measured parameters of the signals and the angular coordinates, N objects (from the set M) selected for auto tracking,

где

- номер наблюдаемого объекта,smooth, to reduce noise, the values of the measured angular coordinates of each object using auto tracking filters, presenting them as averaged dependencies

Where

- number of the observed object,

form for receiving signals of selected objects N single beams, whose guidance in angular coordinates is carried out by control signals generated on the basis of data on the angular coordinates of the accompanying radio-emitting objects,

simultaneously take N rays and process the signals of radio-emitting objects, restore, knowing the type of modulation, the carrier frequencies ущие _{Hn of the} received signals, measure and store the values of their samples, smooth and present the results in the form of averaged dependencies

а также усредненную зависимость

получая непрерывные функции β(t), ε(t) и ƒ_H (t), причем здесь и далее индекс n наблюдаемого объекта не указывается - расчет проводят для каждого из N объектов.interpolate averaged angular dependencies

as well as the average dependence

receiving continuous functions β (t), ε (t) and ƒ _H (t), and hereinafter, the index n of the observed object is not indicated - the calculation is carried out for each of N objects.

According to the invention, in the claimed method:

used to estimate the parameters of the movement of objects in space inclined planes 0A ₁ A _k formed by the rays OA _k , sections A ₁ A _{k of the} trajectories, where A ₁ , A ₂ , ... A _k , ... A _K are the points on the trajectory of the RIO, in which it is located at equally spaced times t ₁ , t ₂ , ... t _K , and an observation point lying outside the trajectory located at the origin 0 of the coordinate system Oxyz, while the moduli of the vectors of the inclined ranges D _T coincide with the length of the rays OA _k , the velocity vectors V directed along sections A ₁ A _{k of} paths, angles between rays OA _k and segments A ₁ A _k are directional angles γ _k , and angles c _{k, 1} between vectors of oblique ranges 0A ₁ and current values of oblique ranges 0A _k are used as analogues of the UK objects, angles c _{k, 1} , each of which is a hypotenuse of a spherical right-angled triangle with legs Δβ _{k, 1} , Δε _{k, 1} and is equal to the angular size of the projection onto the celestial sphere of the path of the object during the time Δt _{k, 1} = t _k -t _l , in accordance with the formula

- номера точек А₁, А₂, … A_k на траектории объекта в моменты времени t=t₂, t₃, … t_k;Where

- the numbers of points A ₁ , A ₂ , ... A _k on the trajectory of the object at time t = t ₂ , t ₃ , ... t _k ;

Δβ _{k, i} = (β _k -β ₁ ) ⋅cos [min (ε _k , ε ₁ )];

Δε _{k, 1} = ε _k -ε ₁ ;

β _k = β (t _k )

ε _k = ε (t _k ),

the values of ƒ _Hk are extracted from the dependence моменты _H (t) at time t ₁ , t ₂ , ... t _k , due to the Doppler effect

where ƒ _H0 is the value of the carrier frequency of the signal of the observed object at rest;

ƒ _Dk - Doppler shift of the carrier frequency;

λ is the wavelength of the signal of the object,

and determine their increments in the intervals Δt _2,1 and Δt _3,1 equal

calculate the magnitude of the ratio of the increments of the carrier, getting the equation relative to the heading angle γ ₁ , deciding which determine its preliminary value

Where

and preliminary value of the module of the velocity vector of the object

where c = 299792458 m / s is the propagation velocity of electromagnetic waves,

calculate on the basis of the estimates obtained, the preliminary value of the carrier frequency of the signal of the object, conditionally at rest, as

calculate the adjusted value ƒ _{H0 of the} carrier frequency of the RIO signal at rest, as the oscillation frequency of a digital generator controlled by a self-tuning signal generated by comparing the frequency increments Δƒ _{k, k-1} = ƒ _k -ƒ _k-1 and

determined at time t _k and stored together with the values of angles c _{k + 1, k the} Doppler frequency shifts of the signals ƒ _Дk = ƒ _k -ƒ _{H0 of the} object, the values of the Doppler frequency shifts ƒ _D1 and ƒ _D2 , as well as the angle from _{2 , 1} ,

calculate the ratio of Doppler shifts

and get the equation for the inclined heading angle γ ₁ , solving which determine the value

repeat the calculation of the values of ctg γ ₁ for P times t _k and determine

where k = 2, 3, ... P, ..., K,

calculate the average value

as well as the average value of the spatial heading angle

and current heading angle values

, величину модуля скорости радиоизлучающего объекта какdetermined using the found average value of the heading angle

, the magnitude of the velocity module of the radiating object as

and the length of the path traveled by the object between the points of the trajectory A ₁ and A _k

where k = 2, 3, ..., K,

хордами которых являются отрезки пути S_k,1, а радиусы равныdetermine the spatial location of the object by the intersection points on the inclined planes 0A ₁ A _{k of the} rays emanating from the origin at angles c _{k, 1} relative to the beam 0A ₁ , and circles with centers

whose chords are segments of the path S _{k, 1} , and the radii are equal

упомянутых окружностей как точки на концах лучей длиной R_k, проведенных из начала координат под углами ψ_k относительно луча 0А₁ и равныхfix the centers

these circles as points at the ends of rays of length R _k drawn from the origin at angles ψ _k relative to the beam 0A ₁ and equal

calculate the value of the slant range in the case of finding the object at point A ₁

values of inclined ranges when the object is located at points A _{k of the} trajectory

and also the values of the velocity modulus of the radio-emitting object when it is located at points A _{k of the} trajectory

carry out the construction of the trajectories of objects using the measured and calculated values of their angular coordinates, inclined ranges, heading angles and speeds of movement,

determine the difference | V | _k - | V | ₁ = Δ | V | _{k, 1} and compare the obtained value with a threshold value

in the case when Δ | V | _{k, 1} > | V | _n , note the beginning of the maneuver of the object, and to further construct its trajectory in the next section of its piecewise linear approximation, the course angles, velocities and ranges are repeated using the above formulas.

The technical result achieved as a result of the creation of the present invention is the possibility of a single-position measurement of the directions, speeds and trajectories of the RIO moving in space uniformly rectilinearly within the controlled sector with arbitrary directional angles and diving angles (cabrio).

The present invention is not known in modern radio engineering, and information sources containing information about similar technical solutions having features similar to those distinguishing the claimed solution from the prototype, as well as having properties that match the properties of the proposed solution, are therefore not known, therefore, that it has significant differences follows from them in an unobvious way and, therefore, meets the criteria of “novelty” and “inventive step”.

The invention is illustrated by the following figures:

figure 1 - the geometry of the problem in space using a spherical coordinate system;

figure 2 - the geometry of the problem on the auxiliary inclined plane;

figure 3 is a diagram of an electrical structural system that implements the proposed method;

figure 4 - graphs of the dependencies of the error in determining the spatial course angle from the magnitude of this angle;

figure 5 - graphs of the dependencies of the error in determining the speed of the RIO from the magnitude of the spatial course angle;

на наклонных плоскостях 0A₁A_k.figure 6 - graphs of the dependencies of the error in determining the slant range from the angle

on inclined planes 0A ₁ A _k .

When implementing the proposed method, the following sequence of operations is performed.

1. Apply to receive radio signals the CAR or antenna array with digital signal processing.

2. Generate a space using an antenna array in the aperture weighting function W (x, y) is the Hamming group monopulse beams with a common phase center and working areas with HRP _HRP Δβ Δε in azimuth and elevation _HRP linear throughout the width of the band monopulse rays due to specially selected in accordance with the method described in [3], the angles of displacement of the rays β _cm and ε _cm

3. The given space survey area (solid angle) is divided into sections of size Δβ _PX in azimuth and Δε _PX in elevation and, sequentially installing the PCN of a single-pulse group of beams in the centers of these sections, they review this area.

объектов в упомянутой области обзора и определяют параметры их сигналов - ширину и среднюю частоту спектра, а также вид модуляции.4. Receive RIO signals during the observation interval at each section of the partition in a given frequency range, when these signals appear, they detect the entire population

objects in the mentioned field of view and determine the parameters of their signals - the width and average frequency of the spectrum, as well as the type of modulation.

5. Describe the spatial position of the RIO moving uniformly and rectilinearly along the trajectories with arbitrary diving angles (cabling), the current values of the angular coordinates (azimuth β _T and elevation angle ε _T ), the vectors of the inclined ranges D _T , the absolute values of the velocity vectors V and the values of the course angles γ _k between the velocity vectors and the vectors of inclined ranges (Fig. 1).

6. Measure and store for each of the detected objects the values of the samples β _m , ε _{m of the} angular coordinates of the m-th object, calculated relative to the equal-signal directions, as

Where

- сигналы угловых рассогласований с выходов угловых дискриминаторов для m-го объекта;

- signals of angular mismatches from the outputs of the angular discriminators for the m-th object;

- значения коэффициентов линейных членов разложений пеленгационных характеристик в ряды Маклорена по координатам β, ε при выбранных значениях смещений β_см и ε_см лучей от равносигнальных направлений.

- the values of the coefficients of the linear terms of the expansion of direction-finding characteristics in the Maclaurin series in the coordinates β, ε for the selected values of the displacements β _cm and ε _{cm of the} rays from the equal signal directions.

7. Select, using data on the measured signal parameters and angular coordinates, N objects (from the set M) selected for auto tracking.

где

- номер наблюдаемого объекта.8. Smooth the values of the measured CM of each object using auto tracking filters, presenting them as averaged dependencies

Where

- number of the observed object.

9. To receive the signals of the selected objects, an additional N single beams are formed in space, the guidance of which in angular coordinates is carried out by control signals generated on the basis of data on the criminal code followed by the RIO.

10. At the same time, they receive N rays and process RIO signals, reconstruct, knowing the type of modulation, the carrier frequencies ƒ _{Hn of the} received signals, measure and store the values of their samples, smooth and present the results in the form of averaged dependencies

а также усредненную зависимость

получая непрерывные функции β(t), ε(t) и ƒ_H(t) причем здесь и далее индекс n наблюдаемого объекта не указывается - расчет проводят для каждого из N объектов.11. Interpolate the average angular dependencies

as well as the average dependence

receiving continuous functions β (t), ε (t) and ƒ _H (t), and hereinafter, the index n of the observed object is not indicated - the calculation is carried out for each of N objects.

12. Use for estimating the parameters of the movement of objects in space inclined planes 0A ₁ A _k formed by the rays OA _k , sections A ₁ A _{k of the} trajectories, where A ₁ , A ₂ , ... A _k , ... A _K are the points on the trajectory of the RIO, in which it is located at equally spaced instants of time t ₁ , t ₂ , ... t _K , and an observation point lying outside the trajectory located at the origin 0 of the coordinate system 0xyz, while the moduli of the vectors of the inclined ranges D _T coincide with the length of the rays OA _k , vectors velocities V are directed along sections A ₁ A _{k of} trajectories, the angles between the rays OA _k and segments A ₁ A _k are directional angles γ _k , and angles c _{k, 1} between the vectors of inclined ranges 0A ₁ and the current values of inclined ranges 0A _k are used as analogues of the criminal objects objects (Fig. 2).

13. The values of the angles c _{k, 1} , each of which is the hypotenuse of a spherical right-angled triangle with legs Δβ _{k, 1} , Δε _{k, 1, are} calculated and equal to the angular size of the projection onto the celestial sphere of the object’s path for the time Δt _{k, 1} = t _k -t ₁ , in accordance with the formula

- номера точек А₁, А₂, … A_k на траектории объекта в моменты времени t=t₂, t₃, … t_k,Where

- the numbers of points A ₁ , A ₂ , ... A _k on the trajectory of the object at time t = t ₂ , t ₃ , ... t _k ,

Δβ _{k, 1} = (β _k -β ₁ ) ⋅cos [min (ε _k , ε ₁ )];

Δε _{k, 1} = ε _k -ε ₁ ;

β _k = β (t _k );

ε _k = ε (t _k ).

14. The values of ƒ _{Hk are} extracted from the dependence ƒ _H (t) at time instants t1, t ₂ , ... t _k , due to the Doppler effect

where ƒ _H0 is the value of the carrier frequency of the signal of the observed object at rest;

ƒ _Dk - Doppler shift of the carrier frequency;

λ is the wavelength of the signal of the object,

and determine their increments in the intervals Δt _2,1 and Δt _3,1 equal

15. Calculate the ratio of the increments of the carrier, getting the equation relative to the heading angle γ ₁ , deciding which determine its preliminary value

Where

and preliminary value of the module of the velocity vector of the object

where c = 299792458 m / s is the propagation velocity of electromagnetic waves.

16. Based on the obtained estimates, the preliminary value of the carrier frequency of the signal of an object conditionally at rest is calculated, as

17. The updated value ƒ _{H0 of the} carrier frequency of the RIO signal, which is at rest, is calculated as the oscillation frequency of a digital generator controlled by a self-tuning signal generated by comparing the frequency increments Δƒ _k , _k-1 = ƒ _k -ƒ _k-1 and

18. Determine at times t _k and remember together with the values of angles c _{k + 1, k the} Doppler frequency shifts of the signals ƒ _Дк = ƒ _k -ƒ _{H0 of the} radio-emitting object, the values of the Doppler frequency shifts ƒ _D1 and ƒ _D2 are extracted from the memory, and angle from _2.1 .

19. Calculate the ratio of Doppler shifts

and get the equation for the inclined heading angle γ ₁ , solving which determine the value

20. Repeat the calculations ctg γ ₁ for P times t _k and determine

where k = 2, 3, ... P, ... K,

calculate the average value

as well as the average value of the spatial heading angle

and current heading angle values

величину модуля скорости РИО как21. Determine using the found average value of the heading angle

the magnitude of the RIO velocity modulus as

and the length of the path traveled by the object between the points of the trajectory A ₁ and A _k

where k = 2, 3, ... K.

хордами которых являются отрезки пути S_k,1, а радиусы равны22. The spatial location of the object is determined by the intersection points on the inclined planes 0A ₁ A _{k of the} rays emanating from the origin at angles c _{k, 1} relative to the beam 0A ₁ , and circles with centers

whose chords are segments of the path S _{k, 1} , and the radii are equal

упомянутых окружностей как точки на концах лучей длиной R_k, проведенных из начала координат под углами ψ_k относительно луча 0А₁ (фиг. 2), равных

and fix the centers

the said circles as points at the ends of the rays of length R _k drawn from the origin at angles ψ _k relative to the beam 0A ₁ (Fig. 2) equal to

23. The value of the slant range is calculated if the object is at point A ₁

values of inclined ranges when the object is located at points A _{k of the} trajectory

as well as the values of the RIO velocity modulus when it is located at points A _{k of the} trajectory

24. Carry out the construction of the trajectories of objects using the measured and calculated values of their angular coordinates, inclined ranges, heading angles and speed.

25. Determine the magnitude of the difference | V | _k - | V | ₁ = Δ | V | _{k, 1} and compare the obtained value with a threshold value

26. In the case when Δ | V | _{k, 1} > | V | _n , note the beginning of the maneuver of the object, and to further construct its trajectory in the next section of its piecewise linear approximation, the course angles, velocities and ranges are repeated using the above formulas.

After that, the RIO trajectory is constructed in space over the entire observation interval, using the measured and calculated values of CC, range, speed and heading angles, if necessary, recalculating the coordinates into a cylindrical or Cartesian system.

- линиями положения.Since the above operations of the goniometric-Doppler method of location are realized in the process of moving the RIO relative to the stationary passive meter, this method is inverse kinematic, the path value S _{k, 1} is a pseudo-base, and the rays 0A _k and circles with centers

- lines of position.

An example of the implementation of the proposed method is a passive one-position goniometer-Doppler radar, the structural diagram of which is shown in FIG. 3, where the following notation is accepted:

1 - antenna fabric of a digital antenna array (AP CAR), the channels of which contain antenna elements, low noise amplifiers (LNA) and ADC;

2 - a block of multipliers and a data stream router (BUMPD);

3 - chart-forming device direction finder (DOU Pl);

4 - block detection and measurement of signal parameters (BOIPS);

5 - control device (UE);

6 - a device for storing samples of the weight function (UZVF);

7 - calculator direction finding characteristics (VPH);

8 - calculator of the optimal angle of displacement of the maxima of the ND from the RSN and the decomposition coefficients of the function that describes the HR (VUSKR);

9 ₁ , ..., 9 _N - auto tracking blocks in angular coordinates (BASUK);

10 ₁ , ..., 10 _N - beam-forming devices of signal reception channels (DOU Pr);

11 ₁ , ..., 11 _N - device reception and restoration of carrier frequencies (UPVN);

12 ₁ , ..., 12 _N - calculators of increments of the carrier frequencies (HPLC);

13 ₁ , ..., 13 _N - angle calculators on inclined planes (VUNP);

14 - synchronization device (CSS);

15 ₁ , ... 15 _N - calculators of estimated values of heading angles, speeds and bearing frequencies (VOKUSNCH);

16 ₁ , ..., 16 _N - calculators of the adjusted values of the carrier frequencies (VUZNCH);

17 ₁ , ..., 17 _N - calculators of Doppler shifts of carrier frequencies (VDSF);

18 ₁ , ..., 18 _N - calculators of averaged course angle values (VUZKU);

19 ₁ , ... 19 _N - speed and inclined range calculators (VVD);

20 - trajectory builder (PT).

The abbreviations used here are: VM - type of modulation, ID - source data, KU - control command, PD - data stream, SU - control signal, Tr - trajectories, UK - angular coordinates.

The passive one-position goniometric-Doppler radar contains (Fig. 2) AP CAR 1, which includes antenna elements, LNA and ADC, and connected to it by transmission lines 1 ... G BUMPD 2. The first output of the BUMPD 2 is connected to the DOW PL 3 (PD input ), the first (total) output of which is connected to the input of BOIPS 4, the output of which is connected to the first input of UU 5. The sixth input of UU 5 is connected to the first output of UZVF 6, which is also connected to the first input of VHF 7. The eleventh output of UU 5 is connected to the input of UZVF 6, and the twelfth output - with the third input of the water supply complex 7. The second output of UZVF 6 is connected to the second input of the VPH 7, the output of which is connected to the input VUSKR 8, and the output VUSKR 8 is connected to the seventh input of the SU 5.

The second output of DOU Pl 3 (differential) is connected to the second input of UU 5, the sixth and seventh outputs of which are connected to the inputs of BASUK 9 _N and BASUK 9 _1, respectively. The first output of UU 5 is connected to a separate control input of BUMPD 2, and the second and third outputs of UU 5 are connected to the first and second separate inputs of DOU Pl 3, respectively. The fourth output of UU 5 is connected to a separate input of DOU Pr 10 _N , and the tenth output of UU 5 to a separate entrance of the preschool educational institution Pr 10 ₁ . The inputs of the PD devices from the DOU Pr 10 ₁ to the DOU Pr 10 _{N are} connected respectively with the outputs from the second to the N-th BUMPD 2, and the outputs of the DOU Pr 10 ₁ and the DOU Pr 10 _N are connected to the first inputs of the UPVN 11 ₁ and UPVN 11 _N , respectively to the second inputs of which the fifth output of UU 5 is connected.

The output of BASUK 9 _{1 is} connected to the first input of VUNP 13 ₁ and the third input of UU 5, and the output of BASUK 9 _N is connected to the first input of VUNP 13 _N and the fourth input of UU 5. The eighth output of UU 5 is connected to the input of US 14, the ninth output of UU 5 is with the third input of the PT 20, and the fifth input of UU 5 - with the output of the PT 20.

VOKUSNCH 15 ₁ ... VOKUSNCH 15 _N , HIGH SCHOOL 16 ₁ ... HIGH SCHELD 16 _N , VDSHCH 17 ₁ ... VDSHCH 17 _N , HIGH SCHOOL 18 ₁ ... HIGH SCHOOL 18 _N and VSD 19 ₁ ... VSD 19 _N.

The output of the UPVN 11 _{1 is} connected to the first input of the HPLF 12 ₁ and the third input of the HPLF 17 ₁ , and the output of the UPVN 11 _N to the first input of the HPLF 12 _N and the third input of the HPLF 17 _N. The output of the HPLC 12 _{1 is} connected to the first input of the VOKUSNCh 15 ₁ , and the output of the HPLC 12 _N is connected to the first input of the VOKUSCh 15 _N. The output of VUNP 13 _{1 is} connected to the third input of VOKUSNCh 15 ₁ , and the output of VUNP 13 _N is connected to the third input of VOKUSNCh 15 _N. Yield FF 14 is connected to second inputs VPNCH 12 _1, ... VPNCH 12 _N, VUNP 13 ₁ ... VUNP 13 _N, VOKUSNCH 15 ₁ ... VOKUSNCH 15 _N, VUZNCH 16 ₁ ... VUZNCH 16 _N, VDSNCH 17 ₁ ... VDSNCH 17 _N, VUZKU 18 ₁ ... HIGH SCHOOL 18 _N , VSD 19 ₁ ... VSD 19 _N and FET 20. Moreover, the output VOKUSNCh 15 ₁ ... VOKUSNCh 15 _{N is} connected to the first input, respectively HIGH SCHOOL 16 ₁ ... HIGH SCHOOL 16 _N , and the output HIGH SCHOOL 16 ₁ ... HIGH SCHOOL 16 _N - to the first entrance of the VDSF 17 ₁ ... VDSF 17 _N and the third input of the VVD 19 ₁ ... VVD 19 _N.

The output of VDSKh 17 ₁ ... VDSKh 17 _{N is} connected to the first input, respectively, HIGH SCHOOL 18 ₁ ... HIGH SCHOOL 18 _N , and the output of HIGH SCHOOL 18 ₁ ... HIGH SCHOOL 18 _N is connected to the first input of the VSD 19 ₁ ... VSD 19 _N and ПТ20 (inputs 1-1 ... 1 -N). The output of the VSD 19 ₁ ... VSD 19 _{N is} also connected to the PT 20 (inputs 1 ... N).

The system output is the thirteenth output of UU 5.

The radar operates as follows. After turning on the power, the antenna elements of the digital antenna array from the AP CAR 1 receive RIO radio signals coming from a given field of view of the space (solid angle), which are further amplified, converted to an intermediate frequency and subjected to analog-to-digital conversion. From the outputs of the AP CAR 1, the samples of the mixture of RIO signals and noise are fed to the inputs of the multiplier unit and the BUMPD 2 data stream router, where they are weighted by multiplying by the samples of the W (x, y) Hamming function, which are received in the BUMPD 2 from the first output of the device control UU 5. These samples are extracted from UZVF 6 (output 1) by the command received in UZOF 6 from UU 5 (output 11).

линейных частей разложений ПХ в ряды Маклорена.From the outputs of the BUMPD 2 bus, the data flows to the beam-forming device of the DOW Pl 3 direction finder and to the beam-forming devices of signal reception channels DOW Pr 10 ₁ ... DOW Pr 10 _N. In DOU Pl 3 a monopulse group of rays with a common phase center is formed, consisting of two pairs of partial rays shifted by β _cm and ε _cm angles in the azimuthal and elevation planes and the total beam. The angles β _cm and ε _{cm are} determined by preliminary modeling the process of receiving and processing the signals of the amplitude total-difference direction finder, using the CAR parameters, in VPH 7 and VUSKR 8, from where they arrive at the seventh input of VU 5. After that, in VPH 7 and VUSKR 8, the calculation of the working areas Δβ _HR in azimuth and Δε _HR in elevation, within which linearity of direction-finding characteristics is provided with an error not exceeding 0.01 of the beam width at half power level, and the coefficients

linear parts of decompositions of HRP in Maclaurin series.

In the control unit of control unit 5, control signals of the control system and sets of phase distributions W are generated, the use of which allows using the DOU Pl 3 to review a given area of space due to the sequential installation of RSL MGL in the centers of the working areas Δβ _PX and Δε _PX . In the process of the survey, RIO signals are received over the total channel, and spectroscopic analysis of a given frequency range is carried out in BOIPS 4, detection of the entire set of M RIO signals and measurement during the observation interval at each section of the partition of their parameters: average frequencies of the spectrum, spectral widths and types of modulation signals. In DOU Pl 3 for each of the detected signals, the values of the samples relative to the RSN of the angular coordinates Δβ _m and Δε _{m are} determined by solving linear equations

and

- сигналы угловых рассогласований с выходов угловых дискриминаторов.Where

- signals of angular mismatches from the outputs of angular discriminators.

The obtained data is transferred to UU 5, where N objects (from the set M) selected for auto tracking are selected on their basis, and their UK values are calculated in the form of sums

β _{tech n} (t _i ) = β _{PCH n} + Δβ _n

ε _{tech n} (t _i ) = ε _{PCH n} + Δε _n ,

- номер наблюдаемого объекта.Where

- number of the observed object.

формируются наборы фазовых распределений полей в раскрыве ЦАР, которые используются в диаграммообразующих устройствах каналов приема сигналов ДОУ Пр 10₁ … ДОУ Пр 10_N для формирования N одиночных ДН приема сигналов выбранных объектов. Отсчеты смеси сигналов РИО и шумов с выходов ДОУ Пр 10₁ … ДОУ Пр 10_N поступают в устройства приема и восстановления несущих частот УПВН 11₁ … УПВН 11_N, в которых осуществляют их согласованную с видом спектра фильтрацию и восстанавливают на основе известного вида модуляции, а затем фильтруют с помощью систем фазовой автоподстройки частоты их несущие частоты, образуя усредненные зависимости

The obtained values of the angular coordinates are smoothed out in the automatic tracking blocks along the angular coordinates BASUK 9 ₁ ... BASUK 9 _N , and then again go to UU 5, where according to their average values

sets of phase distributions of fields in the CAR opening are formed, which are used in diagram-forming devices of signal reception channels DOW Pr 10 ₁ ... DOW Pr 10 _N to form N single signal reception paths of selected objects. The samples of the mixture of RIO signals and noise from the outputs of the DOU Pr 10 ₁ ... DOU Pr 10 _N are received in the receiving and recovery carrier frequencies of the UPVN 11 ₁ ... UPVN 11 _N , in which they are filtered and reconstructed based on the known type of spectrum, and then their carrier frequencies are filtered using phase-locked loop systems, forming averaged dependencies

Further, considering the movement of the accompanied objects on the time interval Δt _{k, 1} = t _k -t ₁ uniformly rectilinear with all possible directional angles and diving angles (cabrio), for each RIO in angle calculators on inclined planes VUNP 13 ₁ ... VUNP 13 _N determined, under the control of the synchronization device US 14, using formula (3), the angles c _{k, 1} , each of which is the hypotenuse of a spherical right triangle with legs Δβ _{k, 1} and Δε _{k, 1} is equal to the angular size of the projection onto the celestial sphere of the path of the object during the time Δt _{k, l} = t _k -t ₁ and in calculators of increments of the carrier frequencies of the HPLF 12 ₁ ... HPLF 12 _N are the values at the same time intervals of the increments of the carriers Δƒ _{Hk, 1} according to formulas (5.6), due to the Doppler effect.

модулей векторов скоростей |V|^П объектов и предварительных значений несущих частот

сигналов РИО, находящихся в покое. С использованием значений

в ВУЗНЧ 16₁ … ВУЗНЧ 16_N рассчитываются уточненные значения ƒ_H0 несущих частот сигналов РИО, находящихся в покое. В ВДСНЧ 17₁ … ВДСНЧ 17_N и ВУЗКУ 18₁ … ВУЗКУ 18_N определяются, в соответствии с формулами (10-15), величины усредненных значений пространственных курсовых углов

и значения текущих курсовых углов γ_k. Далее в ВСД 19₁ … ВСД 19_N с использованием значений Δƒ_Д,

определяются значения модулей скоростей |V|_k и наклонных дальностей D_k при нахождении объектов в точках A_k их траекторий, определяют величины разности |V|_k-|V|₁=Δ|V|_k,1, производят их сравнение с пороговыми значениями Δ|V|_n и в случае, когда Δ|V|_k,1>|V|_n, констатируют начало маневра объекта.The calculation results of the angles c _{k, 1} and the increments of the carriers Δƒ _{Hk, 1} are received in VOKUSNCH 15 ₁ ... VOKUSNCH 15 _N , in which, in accordance with formulas (7-9), the preliminary values of the course angles are calculated

velocity vector modules | V | ^P objects and preliminary values of carrier frequencies

RIO signals at rest. Using values

at VUZCh 16 ₁ ... VUZCh 16 _{N, the} updated values ƒ _{H0 of the} carrier frequencies of the RIO signals at rest are calculated. In VDSHC 17 ₁ ... VDSHC 17 _N and HIGH SCHOOL 18 ₁ ... HIGH SCHOOL 18 _{N are} determined, in accordance with formulas (10-15), the values of the averaged values of the spatial course angles

and values of current heading angles γ _k . Further, in the VSD 19 ₁ ... VSD 19 _N using the values Δƒ _D ,

the velocity moduli | V | _k and inclined ranges D _k when finding objects at points A _{k of} their trajectories, determine the difference | V | _k - | V | ₁ = Δ | V | _{k, 1} , they are compared with threshold values Δ | V | _n and in the case when Δ | V | _{k, 1} > | V | _n , state the beginning of the maneuver of the object.

After that, at PT 20, RIO trajectories are built over the entire observation time using the measured and calculated values of CC, velocities and heading angles, and if an object maneuver is detected, repeated calculations are performed according to the above formulas. The results are issued to consumers through UU 5.

Implementation of the proposed radar based on the existing backlogs on the creation of the Central African Republic and digital signal processing devices will not meet significant difficulties.

We estimate the accuracy of measuring the parameters of the RIO motion by the proposed UDL method depending on the measurement errors of the primary parameters — the angular coordinates of the objects and the Doppler frequency shifts of the signals emitted by them — based on the linearization theorem of the function of several random arguments, assuming that these errors obey the normal distribution law and are uncorrelated.

Digital signal processing methods allow measuring their frequency and time parameters with a relative error of no worse than 10 ^-5 ... 10 ^-7 , while the relative measurement errors of the AC even when using antenna systems with a large aperture are in the range 10 ^-2 ... 10 ^{- 4} . Therefore, the main contribution to the measurement errors of the parameters of the RIO motion is made by the errors of measuring their UK. Since the recalculations of the RIO CC into angles c _{k, 1} on the inclined plane 0А ₁ А _К do not introduce errors, we will look for error estimates for measuring the parameters of the RIO motion according to the proposed UDL in the functional dependence on the angles c _{k, 1} on the inclined plane, which is equivalent real calculation of the motion parameters of the object in space.

In the proposed method of DDL, the average value of the spatial heading angle when the object is located at point A ₁ (see Fig. 1) is determined by expression (14) and is

in which the Kth value of the cotangent of the angle γ ₁ is associated with the values of the angles c _{k + 1,1} on the inclined plane and Doppler frequency shifts by formula (12), and the index K determines the number of measurements of the parameters of the angle c _{k + 1,1} on the inclined plane and frequencies ƒ _{DK + 1} .

определяется какIn accordance with the above provisions, the standard deviation of the angle γ ₁ from the average value

defined as

- среднеквадратическая погрешность измерения угла с_К+1,1.Where

- standard error of the angle measurement with _{K + 1.1} .

Performing the operations of differentiation and transformation, we obtain

or

For cos c _{K + l, 1} ≈ 1.0, formula (24) is transformed to

- к видуand with the number of members of the series p≤10 and

- to view

находим результирующее аналитическое выражение для определения среднеквадратического отклонения (СКО) усредненного значения курсового угла

Calculating the partial sums S _{P of the} members of the series

we find the resulting analytical expression for determining the standard deviation (RMS) of the average value of the heading angle

(их величины приведены в табл. 1).where S _P are the partial sums of the terms of the series for

(their values are given in table. 1).

от его величины при

=0,1 град., sin с_2,1=0,1, S₁=1 и S₁₀=0,3 представлены на фиг. 4.Dependence graphs of the relative standard deviation for measuring the course angle of the RIO

from its value at

= 0.1 deg., Sin with _2.1 = 0.1, S ₁ = 1 and S ₁₀ = 0.3 are shown in FIG. four.

In the proposed method, the value of the modulus of the velocity vector based on (16) is defined as

Using the above methodology, we obtain the standard deviation of the error value for calculating the velocity module in the form

and its relative value

Formula (28) is obtained by substituting relations (17) and (26) into expression (27).

от величины его курсового угла

при

=0,1 град., sin с_2,1=0,1, S₁=1 и S₁₀=0,3 представлены на фиг. 5.RMS dependency graphs for RIO velocity measurement

on the value of its heading angle

at

= 0.1 deg., Sin with _2.1 = 0.1, S ₁ = 1 and S ₁₀ = 0.3 are shown in FIG. 5.

In the proposed method, the current and extrapolated values of the slant ranges between the passive radar and the RIO located at points A _K , is determined by the ratio

In accordance with the above method, the root mean square value of the measurement error of inclined ranges is

and its relative value can be determined by the formula

в функции от величины угла c_k,1 при

, равных 2 и 6 угловым минутам соответственно, представлены на фиг. 6.Dependence graphs of the relative standard deviation of the range measurement

as a function of the value of the angle c _{k, 1} for

equal to 2 and 6 arc minutes, respectively, are shown in FIG. 6.

а величины относительных СКО измерения наклонных дальностей РИО - РЛС определяются величиной используемого угла c_k,1 и при его изменении в пределах (5-25) градусов не превосходят величин (0,3-1,9)×10^-2 при ошибке измерения УК менее 6 угловых минут и (1,0-6,2)×10^-3 при ошибке измерения УК менее 2 угловых минут.As a result of the above operations, analytical expressions are obtained that allow us to evaluate the accuracy characteristics of the proposed method of a passive one-position goniometric-Doppler location. An analysis of these analytical expressions showed that in the case of high-precision measurements of the Doppler frequency shifts of the emitted RIO signals, the values of the relative standard deviations of the calculation of the spatial directional angles and the velocities of the RIO motion are determined by the accuracy of measuring their angular coordinates, depend on the direction of the RIO motion and in the working sector of the inclined course angles (3 -85) angular degrees, with errors in measuring angular coordinates σ _{k, 1} <2 angular minutes, do not exceed relative values

and the values of the relative standard deviations of measuring the inclined ranges of the RIO - radar are determined by the value of the used angle c _{k, 1} and when it changes within (5-25) degrees, they do not exceed the values of (0.3-1.9) × 10 ^-2 with the measurement error of UK less than 6 arc minutes and (1.0-6.2) × 10 ^-3 with a measurement error of CC less than 2 arc minutes.

The proposed location method and the one-position passive radar that implements it reliably function under the conditions of receiving fluctuating signals with a sufficient signal-to-noise ratio (about 12-15 dB), since fluctuations affect only the detection characteristics and the accuracy of measuring energy parameters.

The implementation of the method and device based on it does not meet difficulties at the current level of development of radio engineering and devices for digital signal processing. The possibility of implementing the proposed method provides him with the criterion of "industrial applicability".

Using the proposed method, in comparison with the prototype, provides the following technical effects:

- the ability to measure according to a single algorithm the directions of motion, velocities and trajectories of RIO moving in space in arbitrary directions with a variable flight height;

- the efficiency of the method and device when receiving complex frequency-phase-modulated signals;

- the ability to measure spatial directional angles and RIO velocities with relative errors not exceeding 5.2 × 10 ^-3 , and, as a result of this, the ability to select objects according to the set of parameters “angular coordinates - speed”;

- the ability to measure the inclined ranges of the RIO - radar with relative errors of not more than (0.3-1.9) × l0 ^-2 , which is 17 times better than the prototype, in which they are (5-35) × 10 ^{- 2} .

Claims (60)

A method of passive one-position angular-Doppler location of radio-emitting objects moving in space, in which a digital antenna array or antenna array with digital signal processing is used to receive radio signals, is formed in space using the Hamming weight function, a monopulse group of beams with a common phase center at the aperture of the antenna array and direction-finding characteristics with operating areas Δβ _HR in azimuth and Δε _HR in elevation, linear over the entire width of the monopulse group of rays due to t of specially selected ray displacement angles β _cm and ε _cm , divide a given viewing region of space into sections of size Δβ _PX in azimuth and Δε _PX in elevation and, sequentially setting the mono-pulse direction of the monopulse group of rays to the centers of these sections, review the said region, take the signals of radio-emitting objects during the observation interval at each section of the partition in a given frequency range, when these signals appear, they detect the entire population

objects in the aforementioned field of view and determine the parameters of their signals - the width and average frequency of the spectrum, as well as the type of modulation, describe the spatial position of radio-emitting objects moving in space uniformly and rectilinearly along trajectories with arbitrary diving (cabling) angles, current angular coordinates (azimuth β _T and elevation angle ε _Т ), inclined range vectors D _T , absolute values of velocity vectors V and directional angle values γ _k between the velocity and inclined range vectors, For each of the detected objects, the values of the samples β _m , ε _{m of the} angular coordinates of the m-th object are calculated and stored, calculated relative to the equal-signal directions, as β _m = β _PCH + Δβ _m , ε _m = ε _RSN + Δε _m , Where

and

- signals of angular mismatches from the outputs of the angular discriminators for the m-th object;

and

- the values of the coefficients of the linear terms of the expansion of direction-finding characteristics in Maclaurin series with respect to the coordinates β, ε for the selected values of the displacements β _cm and ε _{cm of the} rays from the equal signal directions, are selected using data on the measured signal parameters and angular coordinates, N objects (from the set M), selected for auto tracking, smooth the values of the measured angular coordinates of each object using auto tracking filters, presenting them as averaged dependencies

Where

- the number of the observed object, form for receiving signals of selected objects N single beams, the guidance of which in angular coordinates is carried out by control signals generated on the basis of data on the angular coordinates of the accompanying radio-emitting objects, in parallel take on N beams and process the signals of the radio-emitting objects, restore, knowing the form modulations carrying frequencies ƒ _{Hn of} received signals measure and store the values of their samples, smooth and present the results in the form of averaged over dependencies

interpolate averaged angular dependencies

and

as well as the average dependence

getting continuous functions β (t), ε (t) and ƒ _H (t), and hereinafter the index n of the observed object is not indicated - the calculation is carried out for each of N objects, characterized in that the inclined planes 0A ₁ A _k are used to estimate the parameters of the movement of objects in space, formed by the rays OA _k , sections A ₁ A _{k of the} paths, where A ₁ , A ₂ , ... A _k , ... A _K , points on the motion path of a radio-emitting object in which it is located at equally spaced times t ₁ , t ₂ , ... t _K , and an observation point lying outside the trajectory located at the origin of the coordinate system 0xyz, while the magnitudes of the angular range vectors D _T coincide with the ray length OA _k , velocity vectors V are directed along sections A ₁ A _k Cobria, the angles between the rays OA _k and the segments A ₁ A _k are the directional angles γ _k , and angles c _{k, 1} between the vectors of the inclined ranges 0A ₁ and the current values of the inclined ranges 0A _k are used as analogues of the angular coordinates of the objects, and the angles c _{k, 1} , each of which is the hypotenuse of a spherical right-angled triangle with legs Δβ _{k, 1} , Δε _{k, 1} and is equal to the angular size of the projection onto the celestial sphere of the object’s path for the time Δt _{k, l} = t _k -t ₁ , in accordance with the formula

Where

- the numbers of points A ₁ , A ₂ , ... A _k on the trajectory of the object at time t = t ₂ , t ₃ , ... t _k ; Δβ _{k, 1} = (β _k -β ₁ ) ⋅cos [min (ε _k , ε ₁ )]; Δε _{k, 1} = ε _k -ε ₁ ; β _k = β (t _k ); ε _k = ε (t _k ) the values of ƒ _Hk are extracted from the dependence моменты _H (t) at time t ₁ , t ₂ , ... t _k , due to the Doppler effect

where ƒ _H0 is the value of the carrier frequency of the signal of the observed object at rest; ƒ _Dk - Doppler shift of the carrier frequency; λ is the wavelength of the signal of the object, and determine their increments in the intervals Δt _2,1 and Δt _3,1 equal

calculate the magnitude of the ratio of the increments of the carrier, getting the equation relative to the heading angle γ ₁ , deciding which determine its preliminary value

Where

and preliminary value of the module of the velocity vector of the object

where c = 299792458 m / s is the propagation velocity of electromagnetic waves, calculate on the basis of the estimates obtained, the preliminary value of the carrier frequency of the signal of the object, conditionally at rest, as

calculate the adjusted value ƒ _{H0 of the} carrier frequency of the signal of the radio-emitting object that is at rest, as the oscillation frequency of a digital generator controlled by a self-tuning signal generated by comparing the frequency increments Δƒ _{k, k-1} = ƒ _k -ƒ _k-1 and Δƒ _{Dk, k -1} = (ƒ _k- ƒ ₀ ^P ) - (ƒ _k-1- ƒ ₀ ^P ), determined at time t _k and stored together with the values of angles c _{k + 1, k} Doppler shifts of signal frequencies ƒ _Дk = ƒ _k - ƒ _{H0 of the} radio-emitting object, the values of Doppler frequency shifts ƒ _D1 and ƒ _D2 , as well as the angle from _2.1 , are extracted from the memory; Doppler shift

and get the equation for the inclined heading angle γ ₁ , solving which, determine the value

repeat the calculations of the values of ctg γ ₁ for P times t _k and determine the values

where k = 2, 3, ..., P, ..., K, calculate the average value

as well as the average value of the spatial heading angle

and current heading angle values

determined using the found average value of the heading angle

the magnitude of the velocity modulus of the radiating object as

and the length of the path traveled by the object between the points of the trajectory A ₁ and A _k

where k = 2, 3, ..., K, determine the spatial location of the object by the intersection points on the inclined planes 0A ₁ A _{k of the} rays emanating from the origin at angles c _{k, 1} relative to the beam 0A ₁ , and circles with centers

whose chords are segments of the path S _{k, 1} , and the radii are equal

fix the centers

the said circles as points at the ends of rays of length R _k drawn from the origin at angles ψ _k relative to the ray 0A ₁ and equal

calculate the value of the slant range in the case of finding the object at point A ₁

values of inclined ranges when the object is located at points A _{k of the} trajectory

and also the values of the velocity modulus of the radio-emitting object when it is located at points A _{k of the} trajectory

they construct the trajectories of objects using the measured and calculated values of their angular coordinates, inclined ranges, heading angles and speeds, determine the difference | V | _k - | V | ₁ = Δ | V | _{k, 1} and compare the obtained value with a threshold value

in the case when Δ | V | _{k, 1} > | V | _n , note the beginning of the maneuver of the object, and to further construct its trajectory in the next section of its piecewise linear approximation, the course angles, velocities and ranges are repeated using the above formulas.

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