RU2757197C1 - Method for determining the coordinates of a radio emitting object in the working area of a multipositional passive radio engineering complex and apparatus for implementation thereof - Google Patents

Abstract

FIELD: radio engineering.

SUBSTANCE: group of inventions relates to the field of radio engineering surveillance and can be used to determine the location coordinates of a scattered radio emission source (radio emitting object (REO)) by radio location stations using receiving posts with radio emission frequency scanning of a multipositional passive radio engineering complex (MPREC). In the claimed method, pairs of receiving posts of the MPREC, synchronised with each other in time and spaced on the territory receive the radio REO emission data through sensors with sequential frequency scanning, including the difference in the time of radio emission reception, the carrier frequency of the onboard radio electronic tool of the REO, and the time of receiving the bearing measurement. The measurement data of the receiving posts is transmitted to the central receiving post. The received data is converted in the central post into a single central Cartesian coordinate system with the origin in the central receiving post, and the coordinates of the air radio emitting object are determined by solving a range-difference problem by the criterion of the maximum of the likelihood function. In order to specify the coordinates of the object in the sectors of failure of the working area of the complex, the functional of the quadratic approximation of the differentiable likelihood function is minimised using the Newton iteration method according to the obtained initial approximation of the REO coordinates.

EFFECT: provided possibility of an all-round view and accurate determination of the coordinates of the REO in the sectors of failure of the working area of the MPREC.

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Description

The invention relates to the field of electronic intelligence and can be used to determine the coordinates of the location of the source of scattered radio emission (radio-emitting object (RIO)) by radar stations using receiving posts with scanning of radio emissions at the frequency of a multi-position passive radio engineering complex (MPRTK).

There are known methods for determining the coordinates of the RIO, based on a frequency survey of the airspace by a network of receivers with frequency scanning of a passive multi-position radio technical complex, radio direction finding of the RIO, measuring the difference in the time delay of signals from the RIO of the same frequency to spaced-apart receivers and calculating the spatial coordinates of the RIO by the method of triangulation, spherical interpolation, spherical intersection , quadratic and linear correction, hyperbolic and / or parabolic correction of the measured data [Buzuverov GV, Gerasimov OI. Algorithms for passive location in a distributed network of sensors using the difference-ranging method. Information-measuring and control systems, No. 5, v.6, 2008., from 12-24; Smirnov Yu.A. "Radio-technical intelligence" - Moscow, 1997. - from 164, 165, 190-193, 203-205, 211; Chernyak B.C., Zaslavsky L.P., Osipov L.V. Multi-position radar stations and systems "Foreign Radioelectronics" №1 - 1987 - p. 11, 15-17, 29-33, 42-54].

The disadvantage of the known methods of obtaining radio technical information on the MPRTK is: incompleteness of information about moving air objects received by the receiving posts and processed by the central receiving post; incomplete composition of coordinate information is not identified and combined with observation vectors; redundant information is irrationally used in trajectory tracking algorithms.

There is a delay in the detection of the track, the break of the track from the tracking. The indicator of continuous target tracking decreases. The root-mean-square ratio of errors in determining the coordinates and parameters of movement of the trajectories of tracked air objects increases, which significantly reduces the quality of tracking in existing multi-position complexes of passive location. At the stage of tracking an airborne object using radio technical information, it is not advisable to recalculate the observed parameters into radio technical marks with subsequent filtering of the results of solving the difference-ranging problem.

The existing algorithms for processing radio technical information are performed in two stages, followed by the stage of its integration. At the primary stage, signals are detected, the parameters of signals and the observed coordinates are measured. At the secondary stage of processing, the marks received from one target are linked in time, and the parameters of the target trajectory are calculated. In the process of secondary processing, the task of detecting and tracking target traces is solved. This division does not take into account the peculiarities of constructing a multi-position complex of passive location. The radiation of radio electronic stations is not detected by all receiving posts, in this case an incomplete vector of the observed information is observed, in the absence of which it is impossible to determine all the spatial coordinates of the target. The incompleteness of the processed information leads to a delay in the detection of the track, the breakdown of the track from the tracking, which leads to a decrease in the indicator of continuous tracking, as well as to an increase in the standard deviation of errors in determining the coordinates and parameters of the tracked target's trajectory.

Coordinates are determined only by the minimum required number of primary radio engineering measurements, other measurements are not taken into account when forming a mark and in filtering algorithms.

For the existing filtering algorithms, it is necessary to determine the moment of radiation of an air object at least by 4 receiving posts in one survey in order to determine the coordinates of an air object with subsequent assessment.

There are no methods of using the redundancy of primary radio engineering measurements from the receiving post in the trajectory tracking algorithms. Due to the lack of prioritization of radio technical information when determining the coordinates (calculating the center of gravity of the figure), as well as with the subsequent filtering of the account of the entire vector of the observed information, the parameters of the movement of the tracked target are deteriorating.

The above factors lead to the need to create a bearing information filter in multi-position passive location complexes, taking into account the difference in timing and incompleteness of the observed parameters.

, где x,y,z - координаты воздушного объекта, x^э,y^э,z^э - экстраполированные координаты, вычисляют начальные параметры траектории и их подтверждение по решению (v/m-l) об обнаружении при появлении ν отметок в m смежных обзорах при отсутствии отметок в 1 смежных обзорах, устанавливают вектор S(t) состояния траектории, составляют модель движения как S(t+Δt)=F_Δt⋅S(t), где Δt=t_k+1-t_k - период обзора, F_Δt - матрица перехода траектории воздушного объекта при маневрировании, получают матрицу H_n(S) производной функции наблюдения

, для каждой пары информационный датчиков вычисляют экстраполированные значения вектора состояния S_k+1=F_Δt⋅S(t) и алгоритмической ковариационной матрицы Q_k+1=F_Δt⋅Q_k⋅(F_Δt)^T,

- вектор экстраполяции разностей дальности, а также матрицу производной функции наблюдения в виде

, рассчитывают дисперсионную ошибку экстраполяции в пространстве наблюдаемых параметров

, вычисляют отклонение ΔRⁱ, на t_k+1 шаге наблюдения, от ожидаемого наблюдения при произведенной экстраполяции

, определяют коэффициент усиления

, где σ₀ - среднеквадратическая ошибка измерения времени прихода сигнала, уточняют значение вектора состояния

и алгоритмическую ковариационную матрицу

, где Ε - диагональная единичная матрица, и производят оценку работы фильтра при сглаживании разности времен прихода сигнала на станции радиотехнической разведки по частному показателю среднеквадратического отклонения ошибки измерения плоскостных координат

, где

- расстояние от цели до оценки координат в момент времени t, N_реал - количество реализаций (N_реал≥1000), отличающейся тем, что при сопровождении воздушного объекта по первичной радиотехнической информации на приемных постах производят одновременную первичную фильтрацию отдельных разностей времени прихода сигналов по времени их поступления, при этом движение принимают прямолинейным и равномерным, а в противном случае - принимают за маневр, формирование начальной оценки приближенного вектора параметров траектории и ковариационной матрицы ошибок на приемных постах производят по первой фиксации разности времен прихода сигнала от цели, поступившей от одной пары информационных датчиков по новому воздушному объекту, далее производят окончательную фильтрацию информации с получением уточненного вектора параметров траектории и алгоритмической ковариационной матрицы ошибок параметров наблюдения приемных постов, выдают точную оценку параметров траектории для четкого отслеживания характера и параметров его полета, при этом на приемных постах фильтрацию разностно-дальномерной информации по воздушному объекту по времени ее поступления производят следующим образом: задают вектор состояния траектории в виде S(t)=(x,y,z,V_x,V_y,V_z), где V_x,V_y,V_z - проекции вектора скорости координат x,y,z, фильтрацию координатной информации производят по зависимостиThe closest in technical essence to the claimed invention is the method for determining the coordinates of the RIO ["Method Bondarenko A.V. receiving radio technical information and a radio technical complex for its implementation. " Patent 2599259. Russia. Bondarenko A.V. Appl. 05.11.2015 Publ. 10.10.2016 Bul. No. 28], which consists in the fact that pairs of receiving posts of radio-technical reconnaissance stations synchronized with each other in time and spaced apart on the ground through sensors with sequential frequency scanning receive data of passive radio emission - the difference in the time of receiving radio emission, the carrier frequency of the onboard radio-electronic device and the time of receipt bearing measurements, the data is sent to the central receiving station, converted into a single central Cartesian coordinate system with the origin at the central receiving station and tied to the radio technical trajectories available on the tracking, on the set of isolated radio technical marks formed during scanning, the operation of filtering the results of solving the differential-range finding the tasks of detecting a radio technical trajectory in the following sequence: determine the size of the auto-lock gates

, where x, y, z are the coordinates of the airborne object, x ^e , y ^e , z ^e are extrapolated coordinates, the initial parameters of the trajectory are calculated and their confirmation by the decision (v / ml) about detection when ν marks appear in m adjacent surveys in the absence of marks in 1 adjacent surveys, set the vector S (t) of the trajectory state, make up the motion model as S (t + Δt) = F _Δt ⋅S (t), where Δt = t _{k + 1} -t _k is the survey period, F _Δt - the matrix of the transition of the trajectory of an airborne object during maneuvering, the matrix H _n (S) of the derivative of the observation function is obtained

, for each pair of information sensors, the extrapolated values of the state vector S _{k + 1} = F _Δt ⋅S (t) and the algorithmic covariance matrix Q _{k + 1} = F _Δt ⋅Q _k ⋅ (F _Δt ) ^{T are} calculated,

is the vector of extrapolation of the range differences, as well as the matrix of the derivative of the observation function in the form

, calculate the dispersion error of extrapolation in the space of observed parameters

, calculate the deviation ΔR ⁱ , at t _{k + 1} observation step, from the expected observation with the extrapolation performed

, determine the gain

, where σ ₀ is the root-mean-square error in measuring the signal arrival time, the value of the state vector is specified

and the algorithmic covariance matrix

, where Ε is the diagonal unit matrix, and the filter operation is assessed when smoothing the difference in the signal arrival times at the electronic intelligence station according to the particular indicator of the standard deviation of the measurement error of the plane coordinates

, where

- the distance from the target to the coordinates assessment at the time t, N _real - the number of realizations (N _real ≥1000), which differs in that when the air object is accompanied by the primary radio technical information at the receiving posts, a simultaneous primary filtering of individual time differences of the arrival of signals in time is performed their arrival, while the motion is taken as rectilinear and uniform, and otherwise it is taken as a maneuver, the formation of the initial estimate of the approximate vector of the trajectory parameters and the covariance matrix of errors at the receiving posts is carried out according to the first fixation of the difference in the arrival times of the signal from the target received from one pair of information sensors for a new air object, then the final filtering of the information is carried out to obtain an updated vector of trajectory parameters and an algorithmic covariance matrix of errors of observation parameters of receiving posts, give an accurate estimate of the trajectory parameters for clear tracking of the character and pairs meters of its flight, while at the receiving posts, the difference-ranging information on an airborne object by the time of its arrival is filtered as follows: the state vector of the trajectory is set in the form S (t) = (x, y, z, V _x , V _y , V _z ), where V _x , V _y , V _z are the projections of the velocity vector of the coordinates x, y, z, the coordinate information is filtered according to the dependence

, где R_n={R_1,2,R_1,3,R_1,4} - разность дальностей прихода сигналов; τ_n - разности времени прихода сигналов;

порядковый номер групп пары i-ых приемных постов от источника радиолокационной информации в эти приемные посты R_n=(с_*⋅τ₁;c_*⋅τ₂;с_*⋅τ₃)^T, с_* - скорость света (с_*≈3⋅10⁸ м/с); далее с учетом влияния ошибок экстраполяции производят сглаживание ошибок разности времен прихода сигнала, при этом матрицу производной функции наблюдения выражают в виде

, где

, where R _n = {R _1,2 , R _1,3 , R _1,4 } is the difference between the signal arrival distances; τ _n is the difference in the time of arrival of signals;

the sequence number of the groups of a pair of i-th receiving posts from the source of radar information to these receiving posts R _n = (s _* ⋅τ ₁ ; c _* ⋅τ ₂ ; s _* ⋅τ ₃ ) ^T , s _* is the speed of light (s _* ≈ 3⋅10 ⁸ m / s); then, taking into account the influence of extrapolation errors, the errors of the difference in the time of arrival of the signal are smoothed, while the matrix of the derivative of the observation function is expressed in the form

, where

Moreover, the reception of information from a radio-emitting object and its subsequent processing are carried out at the receiving posts and at the central post through blocks connected in series with each other, which are connected by communication channels to the antenna control device with sensors of the receiving posts and the device for spatio-temporal synchronization of the information received by them, which is then filtered ...

The disadvantage of the known method for determining the coordinates of the RIO is that the pairs of receiving posts (PP) of the MPRTK synchronized with each other in time and spaced apart on the ground through radio receivers with frequency scanning of the airspace and the central receiving post do not allow measuring the coordinates of the RIO at the line connecting two PP, in sector of the failure of the MPRTK working area, and their absence is compensated by filtering the scanned data.

, которые по каналам связи направляют в блок вычисления функции правдоподобия для оценки координат РИО, которые формируют по правилуThe set goal of the possibility of a circular view and accurate determination of the coordinates of the RIO in the sectors of the failure of the working area of the MPRTK in the outer corners α, β, γ, composed by straight lines connecting in pairs each PP in the triangle of their location, in the proposed method for determining the coordinates of a radio-emitting object in the working area of the MPRTK, consisting in the fact that synchronized with each other in time and spaced apart on the ground pairs of receiving posts of the MPRTK through radio receivers with frequency scanning of the airspace receive data of passive detection of the RIO, including the difference Δt of the time of receiving radio emission from the PP, the carrier frequency f of the onboard radio electronic means of the RIO and the moment t of time their direction finding, the received data is sent to the central receiving station of the MPRTK, where the received data is tied to the central Cartesian coordinate system with the origin at the central receiving station and to the radio technical trajectories supported by the MPRTK on a set of isolated radio technical marks formed when scanning the airspace, then on the formed set of radio technical marks, the coordinates of the detected RIO are determined by solving the differential-rangefinder problem according to the criterion of the maximum likelihood function, and the reception of information from the RIO and its subsequent processing are carried out at the receiving posts and at the central post by sequentially connected together blocks that communication channels connected to the antenna control unit with sensors receiving posts and device spatiotemporal synchronization they adopted the information that is then filtered, is achieved in that in the computing unit RIO initial coordinates produce measurement time difference Δt _2u, Δt _3C ward signal and calculating the initial approximation of coordinates

, which are sent through communication channels to the unit for calculating the likelihood function to estimate the coordinates of the RIO, which are formed according to the rule

, x_i,y_i - координаты местонахождения ПП, х,у - координаты РИО, Δt_2ц - разность времени прихода сигнала от РИО на 2-й и центральный ПП, Δt_3ц - разность времени прихода сигнала от РИО на 3-й и центральный ПП, R_ц2 - разность расстояний ПП _ц - РИО и ПП₂ - РИО, R_ц3 - разность расстояний ПП _ц - РИО и ПП₃ - РИО,

- вектор измерений разностей времен прихода сигнала от РИО на ПП, Q_R - ковариационную матрицу ошибок определения времени прихода сигнала от цели i-м ПП определяют какwhere

, x _i , y _i are the coordinates of the location of the PP, x, y are the coordinates of the RIO, Δt _2ts is the difference in the time of arrival of the signal from the RIO to the 2nd and central PP, Δt _3ts is the difference in the time of arrival of the signal from the RIO to the 3rd and central PP, R _c2 - the difference between the distances PP _c - RIO and PP ₂ - RIO, R _c3 - the difference between the distances PP _c - RIO and PP ₃ - RIO,

is the vector of measurements of the differences in the times of arrival of the signal from the RIO to the PP, Q _R is the covariance matrix of errors in determining the time of arrival of the signal from the target of the i-th PP is determined as

, где

,

- СКО определения времени прихода сигнала от цели i-м ПП, с_* - скорость света; далее данные вычислений направляют в блок решения задачи минимизации функционала:

; а затем в блок квадратичной аппроксимацию функции φ(х,у) методом Ньютона в каждой точке (x^k,y^k)^T

, where

,

- RMSD of determining the time of arrival of the signal from the target of the i-th PP, s _* - the speed of light; then the computation data is sent to the block for solving the problem of minimizing the functional:

; and then in a block quadratic approximation of the function φ (x, y) by Newton's method at each point (x ^k , y ^k ) ^T

- матрица первых частных производных функции,

- матрица вторых частных производных функции φ(х,у), (x^k,y^k)^T - начальное приближение плоскостных координат х,у, при k=1 приравнивают

, на последующих итерациях их уточняют,

- номер итерации, Τ - математический символ транспонирования; откуда данные вычислений направляют в блок определения координат РИО, где для квадратичного функционала φ(х,у) точку (x^k,y^k)^T принимаю за точку минимума, а минимум такой функции из любой начальной точки достигают за один шаг метода Ньютона; в случае линейной аппроксимации матрицу F(x^k,y^k) принимают единичной, и поиск выражают в градиентный; для нелинейной унимодальной функции, отличной от квадратичной, точки последовательности при

асимптотически приближают к минимуму; условие окончания поиска принимают градиентным методомwhere

- the matrix of the first partial derivatives of the function,

is the matrix of the second partial derivatives of the function φ (x, y), (x ^k , y ^k ) ^T is the initial approximation of the plane coordinates x, y, for k = 1 they are equated

, at subsequent iterations they are refined,

- iteration number, Τ - mathematical symbol of transposition; from where the computation data is sent to the unit for determining the coordinates of the RIO, where for the quadratic functional φ (x, y) I take the point (x ^k , y ^k ) ^T as a minimum point, and the minimum of such a function from any starting point is reached in one step of Newton's method; in the case of a linear approximation, the matrix F (x ^k , y ^k ) is taken to be one, and the search is expressed in a gradient; for a nonlinear unimodal function other than quadratic, the point of the sequence at

asymptotically approach the minimum; the search termination condition is accepted by the gradient method

where ε is the specified required calculation accuracy, and the functional φ (x, y) is transformed as follows

where С, Ν, K are constants calculated according to the rules:

and then the partial derivatives are determined by the formulas:

where l is a parameter that is selected taking into account the required accuracy of calculating the derivative, provided that the more accurately it is necessary to calculate the derivative, the less l should be and the commensurability of the difference between the values of the function φ (x, y) or l with the absolute calculation error is inadmissible.

на поиск минимума дифференцируемого функционала φ(х,у) в секторах провала рабочей зоны приемных постов многопозиционного радиотехнического комплекса пассивной локации.The proposed invention makes it possible to replace the search for the numerical values of the RIO coordinates by the maximum likelihood function

on the search for the minimum of the differentiable functional φ (x, y) in the sectors of the failure of the working zone of the receiving posts of the multi-position radio-technical complex of passive location.

The use of the differentiable functional φ (x, y), in turn, makes it possible to apply a quadratic approximation of the differentiable function φ (x, y) at each point (x ^k , y ^k ) of the central database of PP measurements, as well as to apply Newton's method to ensure the required slope of the differentiable function φ (x, y) and increasing the accuracy of measurements of the coordinates of the RIO. Registration of the numerical values (x, y) of the RIO coordinates, corresponding to the minimum point of the functional φ (x, y), in the form of the true values (x, y) of the RIO coordinates allows solving the problem of measuring the RIO coordinates in the sectors of the failure of the working zone of the receiving posts of the multi-position radio engineering complex. In general, the indicated technical advantages make it possible to solve the problem of measuring the coordinates of the RIO in the sector of the dip of the working zone of the MPRTK and, as a result, to ensure the required measurement accuracy in the specified zone.

2. There is a known device for a radio-technical complex of passive location with sequential scanning of radio emissions from air objects, consisting of receiving posts with information sensors of an electronic intelligence station, capable of measuring in the azimuthal plane the direction of movement of air objects with emitting radio-electronic means and fixing the moment of transition of pulses from emitting means when changing direction the movement of an airborne object, scan in frequency and determine the location of an airborne object by solving a differential-rangefinder problem and equipped with electronic auto-capture units in a strobe of size

, где x,y,z - координаты воздушного объекта, x^э,y^э,z^э - экстраполированные координаты воздушного объекта, а также блока трассового сопровождения воздушных объектов с фильтром Калмана динамики воздушных объектов, достигается тем, что фильтр динамики воздушных объектов на каждом из приемных постов составлен из электронного блока установки вектора состояния воздушного объекта S(t)=(x,y,z,V_x,V_y,V_z), где V_x,V_y,V_z - проекции вектора скорости координат x, y, z производящего фильтрацию координатной информации по зависимостям

, where x, y, z are the coordinates of the air object, x ^e , y ^e , z ^e are the extrapolated coordinates of the air object, as well as the block of route tracking of air objects with the Kalman filter of the dynamics of air objects, is achieved by the fact that the filter of the dynamics of air objects on each from receiving posts is composed of an electronic unit for setting the state vector of an air object S (t) = (x, y, z, V _x , V _y , V _z ), where V _x , V _y , V _z are the projections of the velocity vector of coordinates x, y, z filtering coordinate information by dependencies

порядковый номер групп пары i-x приемных постов от источника радиолока-ционной информации в эти приемные посты R_n=(с_*⋅τ₁,с_*⋅τ₂,с_*⋅τ₃)^T, с_* - скорость света (с_*≈3⋅10⁸ м/с); далее с учетом влияния ошибок экстраполяции производят сглаживание ошибок разности времен прихода сигнала, при этом матрицу производной функции наблюдения выражают в виде

, гдеwhere R _n = (R _1,2 , R _1,3 , R _1,4 ) is the difference between the arrival distances of the signals τ _n ;

the sequence number of the groups of a pair of ix receiving posts from the source of radar information to these receiving posts R _n = (s _* ⋅τ ₁ , s _* ⋅τ ₂ , s _* ⋅τ ₃ ) ^T , s _* - the speed of light (s _* ≈ 3⋅10 ⁸ m / s); then, taking into account the influence of extrapolation errors, the errors of the difference in the time of arrival of the signal are smoothed, while the matrix of the derivative of the observation function is expressed in the form

, where

a unit for calculating the extrapolated value of the state vector S _{k + 1} = F _Δt S (t), a unit for determining the gain k, a unit for refining the state vector and an algorithmic covariance matrix, and a unit for evaluating the filter operation when smoothing the difference in signal arrival times at an electronic intelligence station. [Patent No. 2599259 “Method Bondarenko A.V. receiving radio technical information and a radio technical complex for its implementation "from 05.11.2015, Bul. No. 28 of 10/10/2016].

The known device of the radio engineering complex of passive location with sequential scanning of radio emissions from air objects with a triangular arrangement of receiving posts (PP) on the ground does not allow continuous circular scanning of radio emissions from air objects due to the presence of open windows without scanning in the three outer corners formed by the connection lines of three PP ...

The essence of the invention is illustrated by graphic materials: Fig. 1 is a block diagram of the operation of the antenna control device for determining the coordinates of a radio-emitting object in the working area of the MPRTK; figure 2 shows a figure explaining the principle of measuring the coordinates of the RIO in the sector of the failure of the working area of the three-position MPRTK; figure 3 - refinement of the initial approximation of the coordinates of the RIO; figure 4 - the dependence of the root-mean-square errors (RMS) of measurements of in-plane coordinates σ _x, RIO from errors in measuring the time of arrival of the signal σ _τ ; Fig. 5 shows a block diagram of an algorithm for solving the difference-ranging problem.

РИО, соединенного каналами связи с блоком 8 вычисления функции правдоподобияAn apparatus for determining the coordinates of radio-emitting object in the work area multipoint passive radio complex consists of two receiving stations PP _i, PP _2, and PP ₃ (2) with information sensors 1 (1) ELINT station capable of measuring in azimuth direction the movement of an airborne radio-emitting object (RIO) 13 with emitting radio electronic means, scan in frequency and determine the location of an airborne object 13, equipped with antennas 3 (Fig. 1), arranged in a triangle (Fig. 2) on the ground and synchronized with each other in space and in time by applying the user terminal device 4 and GLONASS 5 spatio-temporal synchronization, and PP _i, with the filters 6, the filter 6 are connected to the unit 7 calculating initial coordinates of the measurement time differences Δt and Δt _{2u 3C} and calculating an initial approximation coordinates

RIO connected by communication channels with block 8 for calculating the likelihood function

according to the determination of the vector for measuring the differences in the arrival times of the signal

- разность времени прихода сигнала от РИО на 2-ой и центральный ПП;

- разность времени прихода сигнала от РИО на 3-ий и центральный ПП; R_ц2 - разность расстояний ПП _ц - РИО и ПП₂ - РИО; - разность расстояний ПП _ц - РИО и ПП₃ - РИО; с_* - скорость света, и данным ковариационной матрицы ошибок определения времени прихода сигнала от цели i-м ППwhere x _i , y _i - PP coordinates; x, y - coordinates of RIO;

- the difference in the time of arrival of the signal from the RIO to the 2nd and central PP;

- the difference in the time of arrival of the signal from the RIO to the 3rd and central PP; R _c2 - the difference between the distances PP _c - RIO and PP ₂ - RIO; - the difference between the distances PP _c - RIO and PP ₃ - RIO; c _* is the speed of light, and the data of the covariance matrix of errors in determining the time of arrival of the signal from the target by the i-th PP

, где R_n - разности дальностей от источника радиолокационного излучения РИО 13 до приемного поста (ПП);

- среднеквадратическая ошибка (СКО) определения времени прихода сигнала от РИО i-м ПП; τ_i - разность прихода сигналов, измеряемая парой ПП, и

; последовательно соединенного через блок 9, решения задачи минимизации дифференцируемого функционала

, where R _n - the difference between the ranges from the source of radar radiation RIO 13 to the receiving post (PP);

- root-mean-square error (RMS) of determining the time of arrival of the signal from the RIO of the i-th PP; τ _i is the difference in the arrival of signals measured by a pair of PPs, and

; connected in series through block 9, solving the problem of minimizing the differentiable functional

with block 10 of the quadratic approximation of the function φ (x, y) at the point (x ^k , y ^k ) by Newton's method in the form

- матрица первых частных производных функции, а

- матрица вторых частных производных функции φ(х,у); (x^k,y^k)^T - начальное приближение плоскостных координат х,у, (при k=1 приравнивается

, а на последующих итерациях (x^k,y^k)^T уточняется); k=1,5 - номер итерации; Τ - математический символ транспонирования, и окончательно с блоком 11 определения координат РИО по условиюwhere

is the matrix of the first partial derivatives of the function, and

- the matrix of the second partial derivatives of the function φ (x, y); (x ^k , y ^k ) ^T is the initial approximation of the plane coordinates x, y, (for k = 1 it is equated

, and at subsequent iterations (x ^k , y ^k ) ^{T is} refined); k = 1.5 - iteration number; Τ - the mathematical symbol of transposition, and finally with the block 11 for determining the coordinates of the RIO by the condition

where ε is the specified required accuracy of the calculation, after the transformation of the functional φ (x, y) in the following form

где

where

and the partial derivatives

where l is a parameter that is selected taking into account the required accuracy of calculating the derivative, provided that the more accurately it is necessary to calculate the derivative, the less l should be and the commensurability of the difference between the values of the function φ (x, y) or l with the absolute calculation error is inadmissible.

The essence of the proposed method for determining the coordinates of a radio-emitting object in the working area of a multi-position passive radio engineering complex is as follows.

On the ground, at a certain distance from each other, there are three receiving posts PP _c , PP ₂ , PP ₃ (Fig. 2), included in the working area 12 of the three-position (multi-position) radio-technical detection complex RIO 13, carrying radio-emitting on-board equipment, and also including the central receiving post 1 PP _c , the function of which is performed by PP ₁ to find the coordinates (x, y) of a radio-emitting object 13 (Fig. 2), moving along a trajectory 14. By the difference in ranges - the intersection of lines (hyperbolas) of constant difference in distances 15, 16 from the RIO 13 to PP _c , PP ₂ , PP ₃ solve the system of equations

- время прихода на i-й ПП сигнала от РИО 13, D_i,

- наклонные дальности от ПП до РИО 13, r=D₁, с_* - скорость света. Тогдаwhere t is the time instant of signal emission, t _i ,

is the time of arrival at the i-th PP of the signal from RIO 13, D _i ,

- slant ranges from PP to RIO 13, r = D ₁ , s _* - speed of light. Then

The system of equations (1) is represented as

To solve the system of equations (2), the squares of the left and right sides of each of the equations of this system are equated in the form of coordinates

Equation (3) is transformed and represented in matrix form

In dependence (4), the unknowns х, у are linearly expressed in terms of r. To solve the equation, two variables are introduced - vectors

After substitution of the introduced variables, equation (4) is obtained in the following form

- квадраты векторов

и

соответственно,

скалярное произведение векторов

и

, а r_1,2 - два вещественных корняwhere

- squares of vectors

and

respectively,

dot product of vectors

and

, and r _1,2 are two real roots

where

(фиг.3) производят одним из следующих методов: сначала в уравнении (6) принимают значение q=0 [Гольдштейн А.Л. Теория принятия решений. Задачи и методы исследования операций и принятия решений. ПГТУ - Санкт-Петербург: «Учебное пособие», 2002; Моисеев Η.Н. Математические задачи системного анализа. - М: «Наука», 1981], а далее находят комплексные корни уравнения (6)After substitution of the found values of r in equation (4), the unknown (x, y) coordinates of the RIO 13 are found. For q> 0, equation (4) corresponds to two solutions. When q <0, RIO 13 is found on line 17 connecting PP _c and PP ₂ , and the error ellipse 18 of measuring coordinates of RIO 13 becomes infinite along line 17, and equation (5) has no real roots. In this case, the calculation of the initial approximation of the plane coordinates 20

(figure 3) produced by one of the following methods: first, in equation (6) take the value q = 0 [Goldstein A.L. Decision making theory. Tasks and methods of operations research and decision making. PSTU - St. Petersburg: "Textbook", 2002; Moiseev Η.N. Mathematical problems of system analysis. - M: "Science", 1981], and then find the complex roots of the equation (6)

where α is the real part of the complex root of equation (7), ib is the imaginary part.

. Так как полученные корни

лежат на линии 17, соединяющей пары постов ПП _ц и ПП₂ МПРТК, симметрично от местоположения РИО 13, то

20 вычисляют по следующему уравнению

From equation (7), the real part of the complex roots is distinguished -

... Since the roots obtained

lie on line 17, connecting the pairs of posts PP _c and PP ₂ MPRTK, symmetrically from the location of RIO 13, then

20 is calculated by the following equation

Further, the solution is refined and a likelihood function is made to estimate the coordinates by the difference-ranging method. For this, the vector of measurements of the differences in the signal arrival times is found:

- время прихода сигналов от РИО 13 на ПП _ц , ПП₂ и ПП₃;

,

- разность времени прихода сигналов измеряют парой ПП₂, ПП _ц и парой ПП₃, ПП _ц ;

- разности расстояний ПП _ц - РИО и ПП₂ - РИО, ПП _ц - РИО и ПП₃ - РИО соответственно.where

- the time of arrival of signals from RIO 13 to PP _c , PP ₂ and PP ₃ ;

,

- the difference in the time of arrival of signals is measured by a pair of PP ₂ , PP _c and a pair of PP ₃ , PP _c ;

- the difference between the distances PP _c - RIO and PP ₂ - RIO, PP _c - RIO and PP ₃ - RIO, respectively.

The covariance matrix of errors in determining the time of arrival of the signal from the target of the i-th PP is written in the form

- СКО определения времени прихода сигнала от РИО 13 i-м ПП; τ_n - разность времени прихода сигналов, измеряемая парой ПП, где

.where R _n - the difference between the ranges from the source of radar information to the PP;

- RMS for determining the time of arrival of the signal from the RIO 13 of the i-th PP; τ _n is the difference in the time of arrival of signals, measured by a pair of PPs, where

...

Then, the likelihood function method is implemented to estimate the coordinates of the RIO 13

; x_i,y_i - координаты ПП_i; х,у - координаты РИО 13; Δt_2ц - разность времени прихода сигнала от РИО 13 на ПП₂ и ПП _ц ; Δt_3ц - разность времени прихода сигнала от РИО 13 на ПП₃ и ПП _ц ; R_ц2 - разность расстояний ПП _ц - РИО и ПП₂ - РИО; R_ц3 - разность расстояний ПП _ц - РИО и ПП₃ - РИО;

- вектор измерений разностей времен прихода сигнала от РИО 13 на ПП; a Q_R - ковариационную матрицу ошибок определения времени прихода сигнала от цели i-м ПП определяют какwhere

; x _i , y _i - coordinates of PP _i ; x, y - coordinates RIO 13; Δt _2ts - the difference in the time of arrival of the signal from the RIO 13 to the PP ₂ and PP _c ; Δt _3ts - the difference in the time of arrival of the signal from RIO 13 to PP ₃ and PP _c ; R _c2 - the difference between the distances PP _c - RIO and PP ₂ - RIO; R _c3 - the difference between the distances PP _c - RIO and PP ₃ - RIO;

- vector of measurements of the time differences of arrival of the signal from RIO 13 to the PP; a Q _R - the covariance matrix of errors in determining the time of arrival of the signal from the target of the i-th PP is determined as

, где

;

- СКО определения времени прихода сигнала от цели i-м ПП.

, where

;

- RMS deviation of the time of arrival of the signal from the target of the i-th PP.

Further, the estimate of the coordinates of the difference-ranging problem by the criterion of the maximum likelihood function (8) is replaced by the solution of the problem of minimizing the differentiable functional of the form

When φ (x, y) is differentiable at the point (x ^k , y ^k ) 19 (Fig. 3), Newton's method is used for the quadratic approximation of the functional, while the problem of finding coordinates (x ^k , y ^k ) 19 RIO 13 is written in the form

- матрица первых частных производных функции, а

- матрица вторых частных производных функции φ(х,у); (x^k,y^k)^T - начальное приближение плоскостных координат х,у; при k=1 приравнивают

20, на последующих итерациях их уточняют;

- номер итерации; Τ - математический символ транспонирования.where

is the matrix of the first partial derivatives of the function, and

- the matrix of the second partial derivatives of the function φ (x, y); (x ^k , y ^k ) ^T is the initial approximation of the plane coordinates x, y; for k = 1 equate

20, they are refined at subsequent iterations;

- iteration number; Τ is the mathematical symbol for transposition.

19 считают точкой минимума, следовательно, минимум такой функции из любой начальной точки достигают за один шаг метода Ньютона. В случае линейной аппроксимации матрицу F(x^k,y^k) принимают единичной, и поиск вырождают в градиентный. Для нелинейной унимодальной функции, отличной от квадратичной, точки последовательности при

асимптотически приближают к минимуму.For a quadratic functional φ (x, y) the point

19 is considered a minimum point, therefore, the minimum of such a function from any starting point is reached in one step of Newton's method. In the case of linear approximation, the matrix F (x ^k , y ^k ) is taken to be one, and the search degenerates into a gradient one. For a nonlinear unimodal function other than quadratic, the points of the sequence at

asymptotically approach the minimum.

Next, the functional φ (x, y) is transformed as follows

where С, Ν, K are constants calculated according to the rules

and then find the partial derivatives

where l is a parameter selected taking into account the required accuracy of calculating the derivative.

The more accurately the derivative is calculated, the less l should be. It is unacceptable that the difference between the values of the function φ (x, y) or l is commensurate with the absolute calculation error.

The search for the numerical values (x, y) of the coordinates RIO 13 ends according to the rule

where ε is the specified required calculation accuracy; and the results of the numerical values (x, y) of the coordinates of the RIO 13, corresponding to the minimum point of the functional φ (x, y), are recorded in the form of the true values (x, y) of the coordinates of the RIO 13 in the failure sectors - the error ellipses 18 (Fig. 2) of the working zones of receiving posts of a multi-position radio engineering complex.

In the proposed method, when conducting successive iterations, successive approximations x, y are found. The number of iterations is limited by the maximum value of the error ellipse 18 for measuring the coordinates of the RIO 13, which is the most optimal value for a sufficiently rough initial approximation.

The numerical values (x, y) of the RIO 13 coordinates that satisfy rule (9) are memorized and given to the consumer of radio technical information, for example, to the air traffic control (ATC) and radio technical intelligence (RTR) dispatch service. Below is an algorithm for solving the difference-ranging problem.

For the first time, a method has been developed for determining the location of the RIO in the sectors of the failure of the working zone of a multi-position radio engineering complex and for determining the convergence of the results of measurements of the coordinates of the RIO, depending on the errors in measuring the time of arrival of the signal σ _τ from the RIO at the receiving posts of the MPRTK.

асимптотически приближают к минимуму.For a quadratic functional φ (x, y), the point (x ^{k + 1} , y ^{k + 1} ) ^T is a minimum point. Consequently, the minimum of such a function from any starting point is achieved in one step of Newton's method. In the case of linear approximation, the matrix F (x ^k , y ^k ) becomes unit, and the search degenerates into a gradient one. For a nonlinear unimodal function other than quadratic, the points of the sequence at

asymptotically approach the minimum.

The method set following the most difficult conditions to measure coordinates RIO 1) RIO is located on a line connecting two of PP _i and PP ₃ (2) radio complex; 2) measurement error of the signal arrival time σ = 0 ... 60 (ns) with a step of 1 (ns); the number of realizations of the random process for each σ _τ - 1000; 3) the number of steps to find the coordinates of the RIO by Newton's method - no more than 5.

The results of modeling and estimation of the root-mean-square errors in determining the in-plane coordinates σ _{x, y} RIO from errors in measuring the time of arrival of the signal σ _τ , are presented in Fig. 4.

The analysis of the dependencies shown in Fig. 4 shows that in the absence of measurement errors of the difference in the arrival of signals to the PP MPRTK, the errors in determining the coordinates of the RIO in the place of the failure of the working zone of the radio engineering complex are minimal. However, in case of errors in measuring the difference in the arrival of the SP signals, which takes place in practice, the RMS of determining the plane coordinates of the RIO by the existing method 21 (Fig. 4) is 5 ... 10 times higher than the RMS for the proposed method 22 (Fig. 4).

), меньше соответствующей величины для существующих способов определения координат РИО, что позволяет устранить ситуацию провала рабочей зоны МПРТК.The magnitude of the error in determining the location of the object when it is in the sector ± 5 ° relative to the line connecting the pair of PPs, when using the developed method, is 1.5 ... 10 times (depending on

) is less than the corresponding value for the existing methods for determining the coordinates of the RIO, which makes it possible to eliminate the situation of the failure of the working area of the MPRTK.

Claims (46)

1. A method for determining the coordinates of a radio-emitting object in the working area of a multi-position passive radio technical complex (MPRTK), which consists in the fact that synchronized with each other in time and spaced apart on the ground pairs of receiving posts (PP) MPRTK through radio receivers with frequency scanning of the airspace receive passive detection data radio-emitting objects (RIO), including the difference Δt of the time of reception of radio emission from the PP, the carrier frequency ƒ of the on-board radio electronic means of the RIO and the time t of their direction finding, the received data is sent to the central receiving post of the MPRTK, where the received data is tied to the central Cartesian coordinate system with the origin in the central the receiving post and to the radio technical trajectories supported by the MPRTK on the set of isolated radio technical marks formed during scanning the airspace, then on the formed set of radio technical marks the coordinates of the detected RIO by solving the differential-range-finding problem according to the criterion of the maximum likelihood function, and the reception of information from the RIO and its subsequent processing are carried out at the receiving posts and at the central post through blocks connected in series with each other, which are connected by communication channels t to the antenna control device with sensors of the receiving posts and the apparatus space-time synchronization of the received information, which was then filtered, characterized in that in the computing unit RIO produce initial coordinate measuring time differences Δt _2u, Δt _3C, the arrival of the signal and calculating an initial approximation coordinates

, which are sent through communication channels to the unit for calculating the likelihood function to estimate the coordinates of the RIO, which are formed according to the rule

where

, where x _i , y _i are the coordinates of the PP _i , x, y are the coordinates of the RIO, Δt _2ts is the difference in the time of arrival of the signal from the RIO to the 2nd and central PP, Δt _3ts is the difference in the time of arrival of the signal from the RIO to the 3rd and central PP, R _c2 - the difference between the distances PP _c - RIO and PP ₂ - RIO, R _c3 - the difference between the distances PP _c - RIO and PP ₃ - RIO,

is the vector of measurements of the differences in the time of arrival of the signal from the RIO to the PP, Q _R is the covariance matrix of errors in determining the time of arrival of the signal from the target of the i-th PP - is determined as

, where

,

- RMSD for determining the time of arrival of the signal from the RIO of the i-th PP, s _* - the speed of light; then the computation data is sent to the block for solving the problem of minimizing the functional

and then into the block of quadratic approximation of the function φ (x, y) by Newton's method at each point (x ^k , y ^k ) ^T

where

- the matrix of the first partial derivatives of the function;

is the matrix of the second partial derivatives of the function φ (x, y), (x ^k , y ^k ) ^T is the initial approximation of the plane coordinates x, y, for k = 1 they are equated

, at subsequent iterations they are refined,

- iteration number, Τ - mathematical symbol of transposition; from where the computational data is sent to the unit for determining the coordinates of the RIO, where for the quadratic functional φ (x, y) the point (x ^k , y ^k ) ^{T is} taken as a minimum point, and the minimum of such a function from any starting point is reached in one step of Newton's method; in the case of linear approximation, the matrix F (x ^k , y ^k ) is taken to be one, and the search degenerates into a gradient one; for a nonlinear unimodal function other than quadratic, the point of the sequence at

asymptotically approach the minimum; the search termination condition is accepted by the gradient method

where ε is the specified required calculation accuracy; and the functional φ (x, y) is transformed as follows

where C, N, K are constants calculated according to the rules

and then the partial derivatives are determined by the formulas

where l is a parameter, selected taking into account the required accuracy of calculating the derivative, provided that the more accurately it is necessary to calculate the derivative, the less l should be and the commensurability of the difference between the values of the function φ (x, y) or l with the absolute calculation error is inadmissible. 2. A device for determining the coordinates of a radio-emitting object in the working area of a multi-position passive radio-technical complex, consisting of receiving posts with information sensors of a radio-technical reconnaissance station, capable of measuring in the azimuthal plane the direction of movement of an air object with emitting radio-electronic means, equipped with antennas arranged in a triangle on the ground and synchronized with each other in space and time by applying GLONASS subscriber terminal device and the space-time synchronization with the filters, wherein the filters associated with blocks calculating initial coordinates of the measurement time difference Δt and Δt _{2u 3C} and calculating an initial approximation coordinates

radio-emitting object (RIO), connected by communication channels with the unit for calculating the likelihood function

according to the determination of the vector of measurement of the difference in the arrival times of the signal

x _i , y _i - coordinates of the _{RIO i} , x, y - coordinates of the RIO, Δt _2ts - the difference in the time of arrival of the signal from the RIO to the 2nd and central PP, Δt _3ts - the difference in the time of arrival of the signal from the RIO to the 3rd and central PP , R _c2 is the difference between the distances PP _c - RIO and PP ₂ - RIO, R _c3 is the difference between the distances PP _c - RIO and PP ₃ - RIO, s _* is the speed of light, and the data of the covariance matrix of errors in determining the time of arrival of the signal of the i-th PP

, where R _n is the difference between the distances from the source of the radio-emitting object to the receiving post (PP);

- root-mean-square error (RMS) of determining the time of arrival of the signal from the RIO of the i-th PP; τ _i is the difference in the arrival of signals measured by a pair of PPs, and

; connected in series through a block for solving the problem of minimizing a differentiable functional

with a block of quadratic approximation of the function φ (x, y) at the point (x ^k , y ^k ) by Newton's method in the form

where

is the matrix of the first partial derivatives of the function, and

- the matrix of the second partial derivatives of the function φ (x, y); (x ^k , y ^k ) ^T is the initial approximation of the plane coordinates x, y, (for k = 1 it is equated

, and at subsequent iterations (x ^k , y ^k ) ^{T is} refined);

- iteration number; Τ - a mathematical symbol of transposition, and finally with a block for determining the coordinates of the RIO by the condition

where ε is the specified required accuracy of the calculation, after the transformation of the functional φ (x, y) in the following form

where

and the partial derivatives

where l is the parameter of the required accuracy for calculating the derivative.

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