RU2232402C2 - Method for determination of range to sources of radio emission and rate of closure to them in single-position radar systems - Google Patents

Abstract

FIELD: the method provides for determination of the range to the sources of radio emission and the rate of closure to them in radar systems by the measured values of angular co-ordinates of the sources of radio emission.

SUBSTANCE: the process of determination of the range and the rate of closure is divided into two stages. In the preliminary stage the approximate values of the range to the source of radio emission (

) and the rate of closure to the source of radio emission (

) are computer by the measured values of pitch, angle of jaw, altitude of the flight vehicle, lateral accelerations of the flight vehicle (

), bearings

and angular velocities of the sighting line of the source of radio emission

in the horizontal and vertical planes. Dispersions of measurement errors of

and

are memorized. According to the computer values of

and

, the values of variables

determining the degree of coupling of various co-ordinates and parameters of mutual movement of the flight vehicle and the source of radio emission are computed and memorized. The apriori and a posteriori dispersions of distribution of

and

are memorized. The values of

and

are measured in the main stage. The current values of dispersions of distribution of

and

; the gains of the errors of prediction of

and

are computer and memorized; the current values of variables

are estimated, and the current values of components

of fundamental matrix are computed and memorized according to them.

and

are computed according to the obtained values of components of the matrix. Prediction of the values of

and

for the next step of measurements is made. Then, the process described above, beginning from the second stage, is repeated.

EFFECT: enhanced accuracy of determination of co-ordinates.

4 dwg

Description

The invention relates to the field of radar, including passive radar. The use of the invention will allow to measure the distance to moving sources of radio emission (IRI), including the directors of interference, and the speed of approach with them using goniometric data in single-position radar systems (radar).

The main source of information about the air and ground conditions on aircraft (aircraft) are airborne radars, the effectiveness of aviation significantly depends on the quality of their operation. With the development of radar technology, there is simultaneously an improvement in electronic warfare and their capabilities to suppress radar [1]. In this connection, during the operation of the radar with a high degree of probability, a situation is possible when in it the channels for measuring range and speed will be suppressed by radio interference created by active jamming stations located at the located objects [2, 3]. In such a situation, the determination of the range to the positioned object, which in the case under consideration becomes an IRI, and the approach speed with it can be carried out according to its goniometric data - bearing and angular velocity of the line of sight, measured by radar from interfering signals using passive methods [4-11], since measurement of bearings and angular velocities of the IRI line of sight can be carried out by methods known in radio engineering and does not cause any particular difficulties.

Various methods are known to determine the distance to the IRI and the speed of approach with it, among which the most widely used are static methods, including azimuth-elevation, triangulation and kinematic, and position-velocity methods, including pseudotriangulation and dynamic-kinematic [12].

The azimuthal elevation method uses the results of simultaneous measurements of the azimuth and elevation angle of a fixed ground-based IRI [4], however, its scope is limited only to stationary IRI [12].

The triangulation method for determining the position of the IRI uses formula dependencies between the sides and angles of a triangle whose vertices are connected with the IRI and aircraft. However, the scope of its application is also limited only by motionless ground-based IRI [12].

Kinematic methods rely on knowledge of the equations describing the process of mutual movement of the aircraft and Iran, including the moving one. In the literature [12], it was shown that the main drawback of the known kinematic methods is the rather low accuracy of determining the distance to mobile IRI and the speed of approach with them, an increase which can only be achieved by increasing the tangential component of the speed of the IRI V _tang relative to the aircraft as a result of maneuvering the aircraft with a lapel from the IRI, which contradicts the need to maintain a certain flight path of the aircraft.

The pseudo-triangulation method for determining the range and speed of approach to a mobile IRI from the goniometric data of a radar operating in a passive mode has been developed as an alternative to the triangulation method, but is largely similar to it [13, 14]. The main advantage of this method is the relative simplicity of its implementation. In [13], it was shown that using this method, it is possible to accurately estimate the distance to the IRI and the speed of approach with it, however, high accuracy of the assessment can be achieved only when performing an aircraft lapel from the IRI at a sufficiently large angle. In addition, when determining the coordinates of moving IRI in this way, it is necessary to use derivatives of the measured coordinates up to and including 3rd order, which imposes significant limitations on this method.

Dynamic-kinematic methods are based on a mathematical description in the state space of the intrinsic or relative motion of the IRI and the aircraft - radar carrier. A rather detailed description of these methods is given in the literature [12] and it is shown that such an approach to solving the problem of determining the range and speed of convergence with non-maneuvering IRI allows using them in practice. However, in real conditions, with a fairly high degree of probability, the IRI will maneuver. In this case, the algorithms for estimating the phase coordinates, as well as the movement of the LA carrier of the radar, are complicated, which often leads to the formation of diverging estimates of the distance to the IRI and the speed of approach with it [12].

Of the known technical solutions, the closest is the method of determining the distance to the IRI and the speed of approach with it, described in the literature [12, p. 79-81] based on the materials described in [15]. The essence of the method lies in the fact that at the first preliminary stage at time k-1 on the aircraft displayed in Fig. 1 with the symbols “LA” and moving at a speed of V _la , x _la (k-1), z _la (k -1), y _la (k-1) - the coordinates of their own location in the fixed Earth coordinate system OXYZ and remember them.

At the same time on the aircraft receive signals from the emitter, 1 symbols mapped "IRI" and moving with velocity V _iri. The azimuth α (k-1) and elevation angle β (k-1) of the IRI are measured from these radio signals, the values of which are remembered.

и угла места

запоминают в виде значений сооответствующих компонент матрицыSince any meter makes measurements with errors, the dispersion of which is known for any meter, then in order to take into account further errors in measuring azimuth and elevation, the variance of errors in azimuth measurement

and elevation

stored in the form of values of the corresponding matrix components

called the matrix of variances of measurement noise.

Based on the mentioned stored values of the coordinates of the location of the aircraft, the azimuth and elevation angle of the IRI, the coordinates of the coordinates of the IRI in the same coordinate system are calculated (see figure 1) in accordance with the formulas

where x _iri (k-1), z _iri (k-1) are the coordinates of the IRI along the X and Z axes.

In addition, based on the range of possible speeds and accelerations of the given types of moving _IRIs , the values of V _xiri , V _ziri are the velocities and a _hiri , and _ziri are the accelerations of the IRI, along the corresponding axes of the mentioned coordinate system.

The calculated values of x _iri (k-1), z _iri (k-1) and the given values of V _hiri , V _ziri , and _hiri , and _{ziri are} stored in the form of the corresponding values of the components of the vector

R _iri (k-1) = [x _iri (k-1) a _hiri (k-1) z _iri (k-1) V _ziri (k-1) a _ziri (k-1)] ^T ,

called the state vector of IRI, where the symbol “t” defines the transpose operation.

по осям Х и Z соответственно запоминают в виде соответствующих значений компонент матрицыSince the calculation of the coordinates of the IRI is accompanied by random errors, the variances of which are known, and the speed and acceleration of the IRI are also set with large errors, then to take into account these errors in the future, the most significant of which are the errors in determining the accelerations of the IRI, the variance of the noise of the accelerations of the IRI

along the X and Z axes, respectively, the components of the matrix are stored in the form of corresponding values

called the state noise variance matrix. The dimension of the matrix is determined in accordance with the dimension n of the state vector: since six components are included in the state vector of the IRI, i.e. n = 6, then the dimension of the matrix is d _r n × n = 6 × 6.

The translation of all the coordinate values and motion parameters of the aircraft and IRI mentioned above into a vector-matrix form is due to the fact that modern calculators are capable of processing the data presented in such a form that is more convenient for programming and storing data.

The mentioned values of the coordinates of the location of the IRI and the parameters of their motion, stored in the form of the values of the components of the vector R _iri (k-1), are extrapolated to the next k-th moment of measurement according to the formula

R _airy (k) = Ф (k, k-1) R _iri (k-1),

Where

R _eiri (k) = [x _eiri (k) V _heiri (k) a _heiri (k) z _airi (k) V _ziriu (k) a _zairi (k)] ^T

is a vector whose components are x _eiri (k), V _xheiri (k), and _xiri (k), z _eiri (k), V _zeiiri (k),

and _zeiiri (k) are the extrapolated at the next measurement moment the coordinates of the location of the IRI x _iri (k), z _iri (k), speed V _hiri (k), V _ziri (k) and acceleration a _hiri (k) and _ziri (k ) its movement along the corresponding axes of the coordinate system mentioned above;

- a matrix called transitional or fundamental in the literature, in which λ _x and λ _z are known constants that determine the IRI maneuver time constants in the corresponding coordinate, depending on its nature and set based on a priori information about the type of IRI;

τ is the sampling interval.

The extrapolated values of the coordinates of the location of the IRI and the parameters of their motion are stored in the form of the corresponding values of the components of the state vector R _eiri (k).

In addition, for the next k-th time instant, the extrapolated values of the posterior variances and mutual variances of the filtering errors D _e (k) components of the state vector are calculated in accordance with the formula

D _e (k) = Ф (k, k-1) D (kl) Ф ^T (k, k-1) + D _R ,

Where

представляют собой экстраполированные апостериорные дисперсии и взаимные дисперсии ошибок фильтрации соответствующих значений компонент вектора состояния R_эири;- a matrix of extrapolated posterior values of variances and mutual variances of filtering errors, in which the values of its components are d _eij , where

represent extrapolated a posteriori variances and mutual variances of filtering errors of the corresponding values of the components of the state vector R _eiri ;

в начальный момент времени задают исходя из априорных сведений о корреляционной матрице распределения соответствующих значений плотности вероятности соответствующих компонент вектора состояния ИРИ R_ири, а в дальнейшем вычисляют.- a matrix of posterior variances and mutual variances of filtering errors, the component values of which d _ij , where

at the initial moment of time, they are set based on a priori information about the correlation matrix of the distribution of the corresponding probability density values of the corresponding components of the state vector of the IRI R _iri , and are further calculated.

The calculated extrapolated values of posterior dispersions and mutual dispersions of filtering errors d _{eij are} stored in the form of the corresponding values of the components of the matrix D _e (k).

In the second main stage, at time k, which is τ − sampling interval from time k-1, the sampling interval, the aircraft speed V _la (k), its location coordinates x _la (k), z _la (k) and y _la ( k) and receive radio signals from the IRI, which measure the azimuth α (k) and elevation angle β (k) of the IRI. The measured values of the azimuth α (k) and elevation angle β (k) IRI are stored in the form of the corresponding values of the components of the vector

z (k) = [α (k) ((k)] ^T ,

called the measurement vector.

From the measured values of the aircraft location x _la (k), z _la (k), yla (k), azimuth α (k), elevation angle β (k) IRI and stored extrapolated values of a posteriori dispersions and mutual dispersions of filtering errors d _eij calculate the values components of the matrix D (k) - posterior variances and mutual variances of filtering errors in accordance with the formula

- представляет собой матрицу производных, в которойWhere

- is a matrix of derivatives in which

- a vector whose components are the azimuth and elevation angle of the IRI, respectively.

In addition, according to the measured values of the location of the aircraft x _la (k), z _la (k), y _la (k), azimuth α (k), elevation angle β (k) IRI, stored extrapolated values of the coordinates of the location of the IRI, speed and acceleration its motion and the calculated values of the components of the matrix D (k) evaluate the values of the components of the state vector IRI R _iri (k) in accordance with the formula

Where

- a vector whose components are the estimated values of the corresponding components of the state vector; the symbol “^” means that the estimated values of the components of the corresponding component of the vector or matrix are used.

- координат ИРИ,

- скоростей и ускорений ИРИ по соответствующим осям земной системы координат вычисляют дальность до ИРИ Д_ири и скорости сближения с ним V_xcб, V_zcб по соответствующим осям по формуламAccording to estimated values

- coordinates of Iran,

- IRI velocities and accelerations of the respective axes terrestrial coordinate system calculated range to the D _iri IRI and closing velocity to it _xcb V, V _zcb along the corresponding axes according to the formulas

D (k) = y _la (k) / sinβ (k);

Further, the above process, starting from the second stage, is repeated.

The disadvantage of the prototype is the restriction in the use of only terrestrial inactive IRI [12]. In the case of using this method according to intensively maneuvering IRI, the procedure for estimating the distance to the IRI and the speed of approach with it is much more complicated, and the method becomes practically inoperative due to the low stability of the process of evaluating the components of the state vector of the IRI [12].

Thus, the objective of the invention is to develop a high-precision method for determining the range to maneuvering IRI and the speed of approach with them in single-position radar systems.

The principal difference from the prototype of the claimed invention lies in the fact that the unknown values of the prototype vector components R _iri state IRI, i.e. the coordinates of the location of the IRI, the speed and acceleration of its movement, are estimated taking into account the completely considered maneuver parameters of the IRI, specified by the constants λ _x and λ _z included in the corresponding components of the fundamental matrix Φ (k, k-1), and in the proposed method, the values are estimated unknown component of the fundamental matrix F (k, k-1) according to the computed values of the components of IRI state provided that the components are functions of the fundamental matrix E _iri - ranges up to the IRI and V _{~ Sat} - closing speed with no And then these components calculated range values to IRI and closing velocity to it.

Below, before the essence of the invention is described, to facilitate understanding of the subsequent material, we consider the solution of the problem in the mathematical aspect.

The inventive method for determining the distance to the IRI and the approximation speed with it was obtained on the basis of one of the simplest known identification methods [16, 17], called in the literature in honor of its developer the Maine method [16]. The algorithm for identifying the parameters of the state model, proposed by Maine, is essentially a linear filtering algorithm in which not the values of the components of the state vector are evaluated, but the values of the components of the vector of parameters of the state model.

Let the process of changing φ - the angle of sight of the IRI in one of the planes, ω - the angular velocity of the line of sight of the IRI and j _p- transverse acceleration of the aircraft, be written in vector form by changing the state vector

where R _iri (k), R _iri (k-1), R _iri (0) is the n-dimensional state vector at the kth, (k-1) th and initial time instants, the components of which in the general case can be IRI sight angles φ, angular velocities of the IRI sight line ω in different planes and lateral acceleration LA j _p (n - is determined by the total number of components included in its composition);

is the transition matrix of the state vector, the components f _ij (k, k-1) of which in the general case are functions that depend on the distance to the IRI _DIRI and the speed of approach to it V _sb , and there are inverse functions η _m (m = 1, 2 ), allowing them to calculate D _iri and V _cb according to the formulas

ξ _r is the n-dimensional vector of state noise with a known dispersion determined by the matrix of noise variances of the state vector d _r ;

the entry “k, k-1” means that with the help of the components of the transition matrix f _ij (k, k-1), which determine the degree of connection between the various location coordinates and the relative parameters of the mutual movement of the aircraft and the IRI, the relationship between the values of the components of the state vector is uniquely determined from time k-1 to time k.

All components f _ij (k, k-1) of the state transition matrix Φ (k, k-1) (2) are combined into a vector

called the state model parameter vector, the components a _l (k) of which are found from the components f _ij (k, k-1) by the formulas

where n is the total number of phase coordinates included in the state vector.

Let it be possible to measure the values of all or part of the parameters of the state vector R _iri (k) (1). The measurement process is recorded as a measurement vector

where H (k) is the transition matrix of the measurement vector by which the measured components of the state vector are determined; ξ _and is the vector of measurement noise with a known dispersion, determined by the dispersion matrix of the measurement noise D _and .

вектора параметров модели состояния a(k) (5) осуществляют, используя алгоритм Мейна [12]:Rating

the vector of parameters of the state model a (k) (5) is carried out using the Maine algorithm [12]:

In the expressions (8) - (10) is indicated:

and ₀ is the value of the vector of parameters of the state model at the initial instant of time, the components of which are determined by a priori data on the distance to the IRI and the speed of approach with it;

K (k) is the matrix gain;

- the transition matrix of the vector of parameters of the state model of size n × n ² ;

D (k) is the matrix of variances and mutual variances of errors in estimating the components of the vector of parameters of the state model, the values of the components of which at the initial moment of time are set based on a priori information about the correlation matrix of the distribution of values of the components of the state vector;

0 - n-dimensional zero vectors.

и дальностью до ИРИ Д_ири и скоростью сближения с ним V_cб, то по формулам (3) и (4) вычисляют дальность до ИРИ и скорость сближения с ним.Since there is an unambiguous correspondence between the obtained estimates of the state model parameters vector

and the range to IRI D _iri and the speed of approach with him V _sb , then using formulas (3) and (4) calculate the distance to IRI and the speed of approach with him.

Thus, the task is achieved in that at the first preliminary stage, the following is performed.

1. At time k-2 in an aircraft (AC) measured θ (k-2) - pitch, ψ (k-2) - and a yaw angle y _la (k-2) - the height of the aircraft. At the same time, the radio signals from the IRI are received on the aircraft, according to which, using any of the known methods [4-6], the values of φ _g (k-2) and φ _in (k-2) are measured for IR bearings in the horizontal and vertical planes, respectively. The measured values of ϑ (k-2), ψ (k-2), y _la (k-2), φ _g (k-2), φ _in (k-2) are remembered.

2. At the next instant of time k-1, which is τ-sampling interval, apart from the instant of time k-2, the values of the altitude y _la (k-1) of the aircraft, its pitch ϑ (k-1) and the yaw angle ψ (k- 1), as well as transverse accelerations j _g (k-1), j _in (k-1) aircraft in the horizontal and vertical planes, respectively. Receive radio signals from the IRI, which measure the values of bearings φ _g (k-1), φ _in (k-1) IRI and angular velocities of the line of sight ω _g (k-1), ω _in (k-1) IRI in horizontal and vertical planes respectively. The measured values of y _la (k-1), ϑ (k-1) and ψ (k-1) are stored. The measured values of φ _g (k-1), ω _g (k-1), j _g (k-1), φ _in (k-1), ω _in (k-1), j _in (k-1) are stored as the values of the corresponding components of the vector

called a state vector.

The claimed method does not impose restrictions on the state vector. If any of the components mentioned above is not available for measurement, or, conversely, it will be possible to measure other coordinates or parameters of the IRI movement, then the composition of the state vector can be changed.

3. Based on the values of the height y _la , the bearing angle φ _in and the pitch ϑ stored in the (k-2) th and (k-1) th time instants, the approximate values of the distance to the IRI D _{iri taking} place at the time instants k- 2 and k-1, according to the formulas

4. Using the calculated values of the distance to the IRI _DIRI and the stored values of φ _g , φ _in , ϑ and ψ calculate the approximate values of the projections of the speed of approach with the IRI V _ycb , V _zcb and V _xcb on the axis Y, Z and X, respectively, of a fixed rectangular earth system OYZX coordinates by formulas

which calculate the approximate values of the rate of approximation with IRI V _cb according to the formula

угловых скоростей линии визирования ИРИ

поперечных ускорений

в горизонтальной и вертикальной плоскостях соответственно запоминают в виде значений соответствующих компонент матрицы5. Since measurements of the angular coordinates of the IRI and parameters of their change are accompanied by random errors, the variances of which are known, then to take them into account in the future, the variance of the measurement errors of the bearings of the IRI

angular velocities of the IRI line of sight

lateral accelerations

in horizontal and vertical planes, respectively, are stored in the form of values of the corresponding matrix components

called the matrix of dispersions of measurement noise, the off-diagonal components of which are equal to zero. The claimed method does not impose restrictions on the dispersion matrix of measurement noise: if the composition of the meters is different, then the composition of its components can be changed.

6. According to the stored values of the components φ _g (k-1), ω _g (k-1), j _g (k-1), φ _in (k-1), ω _in (k-1), j _in (k -1) the state vector R _iri (k-1) (12) and the calculated values of the distance to the IRI D _iri (k-1) (14) and the speed of approach of the aircraft with the IRI V _s (k-1) (16) extrapolate to the k-th time instant of all the mentioned values of the components of the state vector according to the formula

Where

transition matrix of the state vector, which are well-known functions [18, p. 285, 291, 305, 332] component f _ij (k, k-1) by which the associated φ _r, ω _r, j _r, φ _a, ω _c , j _c with D _iri and V _sb . For example, for the state vector R _iri (k-1) (12), the transition matrix Φ (k, k-1) can have the following form:

wherein

f ₁₁ (k, k-1) = 1, f ₁₂ = (k, k-1) = τ,

f ₃₃ (k, k-1) = 1, f ₄₄ (k, k-1) = 1,

f₆₆(k,k-2)=1,

f ₆₆ (k, k-2) = 1,

and the rest of the functions are null; D _yrig , D _iriv , V _sbg , D _sbv - the values of the projections of the range to the IRI and the speed of convergence with it on the horizontal and vertical planes, respectively.

The method does not impose any restrictions on the specific form of the functions f _ij (k, k-1), which are determined during the development of specific devices for measuring the distance to the IRI and the approximation speeds with them in single-position radars.

The number of the mentioned functions also depends on the specific device: it is equal to the square of the number of components n that make up the state vector.

The extrapolated values of the components φ _ei (k), ω _ei (k), j _ei (k), φ _ev (k), ω _ev (k), j _ev (k) of the state vector R _eiri (k) (18) are remembered.

7. Based on the calculated values of the distance to the IRI D _iri (14) and the speed of approach with it V _sat (16), the values of the functions fij (k, k-1) (19) are calculated and by the formulas

вектораassign their values to the corresponding components

of vector

данного вектора, как и значение соответствующей ей функции f_ij(k,k-1), определяет степень связи между собой различных координат местоположения и параметров взаимного перемещения ЛА и ИРИ.called a vector of state model parameters that remember. The value of each component

of this vector, as well as the value of the function f _ij (k, k-1) corresponding to it, determines the degree of connection between each other of the location coordinates and the parameters of the mutual movement of the aircraft and IRI.

Since at the moment of time k-1, the calculation of the values of the components a _l (k-1) of the state model parameter vector was carried out using approximate values of the distance to the IRI and the approximation speed with it, their values have rather large errors. Therefore, in order to take into account these errors in the future, the initial values of the matrix components are set and stored

а диагональные значения компонент d_ij(k-1), при i=j, заданы исходя из априорных сведений о корреляционных функциях распределения значений плотности вероятности соответствующих компонент вектора состояния ИРИ R_ири.called the matrix of posterior variances and mutual variances of errors in estimating the vector of parameters of the state model, whose component values d _ij (k-1) = 0, for i ≠ j, where

and the diagonal values of the components d _ij (k-1), for i = j, are set based on a priori information about the correlation functions of the distribution of the probability density values of the corresponding components of the state vector of the IRI R _iri .

будут сопровождаться ошибками, поэтому для учета в дальнейшем и этих ошибок задают и запоминают значения компонент матрицыSince it is impossible to accurately describe the relationship between the components of the state vector at neighboring times, since the IRI can move arbitrarily, always calculate the values of the components f _ij (k, k-1) and the corresponding components

will be accompanied by errors, therefore, to take into account in the future these errors are also set and stored values of the matrix components

a d_ij при i=j, задают исходя из конкретной структуры вектора состояния R_ири и априорных сведений о корреляционных функциях распределения значений плотности вероятности его компонент.called the dispersion matrix of the state vector whose components d _ij = 0, for i ≠ j, where

ad _ij for i = j, they are set based on the specific structure of the state vector R _iri and a priori information about the correlation functions of the distribution of the probability density values of its components.

8. Based on the stored values of the components of the state vector R, _airy (k) form and store the corresponding values of the transition matrix of the vector of parameters of the state model M (k) according to the formula

where 0 are n-dimensional zero vectors.

In the second main stage, starting from time k, the following is performed.

1. Measure the values of j _g , j _in . Receive radio signals from the IRI, which measure the values of φ _g , φ _in , ω _g and ω _in . The measured values of φ _g , ω _g , j _g , φ _in , ω _in and j _{in are} stored in the form of values of the corresponding components of the vector

called the measurement vector, where φ _gi (k) = φ _g (k), ω _gi (k) = ω _g (k), j _gi (k) = j _g (k), φ _vi (k) = φ _in ( k), ω _ext (k) = ω _in (k), j _vi (k) = j _in (k).

The claimed method does not impose restrictions on the vector of measurements. If any of the components mentioned above are not available for measurement, then the composition of the state vector can be changed.

2. According to the stored values of the components of the matrices D (k-1) (24), DR (25) and M (k) (26) by the formula

calculate and store the current values of the components d _ij (k) of the matrix D (k).

3. According to the stored values of the components of the matrices D (k) (28), M (k) (26) and D _and (17) by the formula

матричного коэффициента усиления K(k).compute and store the values of the components to _ij (k), where

matrix gain K (k).

(23), z(k) (27) и матриц M(k) (26), K(k) (29) по формуле4. According to the stored values of the components of the vectors

(23), z (k) (27) and the matrices M (k) (26), K (k) (29) by the formula

вектора параметров модели состояния

evaluate current component values

state model parameter vectors

и значениями компонент f_ij(k+1,k) переходной матрицы вектора состояния, то по формулам5. Since there is a unique correspondence between the estimated values of the components

and the values of the components f _ij (k + 1, k) of the transition matrix of the state vector, then by the formulas

assign values to the corresponding components f _ij (k + 1, k) of the transition matrix of the state vector and store them in the form

6. Since there is a well-known unambiguous correspondence between the obtained values of f _ij (k + 1, k) and the distance to the IRI D _iri and the approach speed V _sb with it, then by the formulas

calculate the distance to IRI D _iri (k) and the speed of approach with him V _sb (k), which give various consumers of information, such as an indicator to the pilot.

On the specific form of the functions η ₁ {f _ij (k + 1, k)} and η ₂ {f _ij (k + 1, k)}, determined during the development of specific devices for measuring the distance to the IRI and the speed of approach with them in single-position radars on based on well-known kinematic equations, for example, given in the literature [18, p. 178, 184], the method does not impose any restrictions. For example, in the case of using the transition matrix Φ (k, k-1) of the form (20) with components f _ij (k + 1, k) of the form (21), the mentioned functions obtained from the functions f ₂₂ (k + 1, k), f ₂₃ (k + 1, k), f ₅₅ (k + 1, k) and f ₅₆ (k + 1, k) have the form:

7. According to the stored values of the components φ _g (k), ω _g (k), j _g (k), φ _in (k), ω _in (k), j _in (k) the state vector R _iri (k) and obtained values of matrix components

F (k + 1, k) no formula

extrapolated to the next k + 1st measurement step and store the values of the components of the state vector R _airy (k + 1).

8. According to the stored values of the components of the state vector R _airy (k + 1) by the formula

form and remember the values of the components of the transition matrix of the vector of parameters of the state model M (k + 1) for the next measurement step.

Next, the above process, starting from the second stage, is repeated.

Figure 1 shows the spatial position of the IRI and LA, where indicated:

OXYZ - motionless earth coordinate system;

x _la , z _la , y _la , V _la - the coordinates of the aircraft along the X and Z axes, the height of the aircraft and its airspeed, respectively;

r _prod , r _xprod , r _pop - orth of the longitudinal axis of the aircraft, its projection on the X axis and the unit of the transverse axis of the aircraft, respectively;

ϑ, ψ - pitch and yaw angle of the aircraft;

φ _g , φ _in , ω _g , ω _in - bearings of the IRI and the angular velocity of the line of sight of the IRI in the horizontal and vertical planes, respectively;

α, β - azimuth and elevation angle of the IRI;

x _iri , z _iri , V _iri - the coordinates of the IRI along the X and Z axes and its speed, respectively;

D _iri - range to IRI.

Figure 2 shows a simplified structural diagram of a range meter to IRI and the approximation speed with them in single-position radar systems, which implements the claimed method, where:

1 - stand-alone meters, which include pitch and yaw angle sensors, aircraft speeds, Doppler speed and drift angle meters, accelerometers, etc .;

2 - storage device (memory);

3 - the first calculator;

4 - second calculator;

5 - the third computer;

6 - radar system (radar);

7 - the fourth calculator;

8 - fifth calculator;

9 - the sixth calculator;

10 - a source of radio emission (IRI);

11 - seventh calculator;

12 - eighth calculator.

The numbers for meters 1, radar 6 and memory 2 are conventionally designated numbers of the corresponding inputs and outputs.

Figure 3 shows graphs of current errors in estimating the range to maneuvering IRI, where it is indicated: D _iriist - the true value of the range to IRI; D _iri - calculated in accordance with the claimed method, the value of the distance to the IRI.

Figure 4 shows graphs of current errors in estimating the speed of approach with maneuvering IRI, where it is indicated: U _sist - the true value of the speed of approach with IRI; V _SB - the value of the speed of approximation with the IRI, calculated in accordance with the claimed method.

As an example of the implementation of the method of measuring the distance to the IRI and the approach speed with them in single-position radar systems, we consider a meter, in the development of which it was assumed that:

1) the vertical and horizontal measurement channels do not affect each other, in connection with which the principle of operation of the meter for only one vertical plane is considered;

2) the kinematic equations relating the coordinates of the absolute and relative motion of the aircraft and the IRI, in a discrete form, obtained on the basis of known analogous relations [18, p. 178], are determined by the formulas

where ω _in, ω _e0 - angular velocity of the line of sight of IRI in the vertical plane and its value at the initial time, respectively; j _in , j in ₀ - the acceleration of the aircraft in the vertical plane and its value at the initial time, respectively; D _iri and V _sb - range to Iran and the speed of rapprochement with him, respectively; τ is the sampling interval; ξ _j is the acceleration noise of an aircraft with a known dispersion

3) the angular velocity of the IRI line of sight is measured by a radar goniometer

where ξ and _ω are the noise measurements of the angular velocity of the IRI line of sight with a known dispersion

4) aircraft acceleration j _in measured by an accelerometer

ξ and _j are the noise of acceleration measurements with a known dispersion

5) the state vector R _iri (k) (12), the measurement vector z (k) (27) and the corresponding noise variance matrix of the state vector D _R (25) and the measurement vector D _and (17), determined on the basis of formulas (37 ) - (40), have the following form

7) the components f _ij (k, k-1) of the state transition matrix Φ (k, k-1) (19) are determined based on equations (18), (37), (38):

8) based on the state vector R _iri (41), the vector of parameters of the state model a (5) for time k-1 will have the form:

whose components are found in accordance with expressions (22) and (43), (45)

9) in accordance with the vectors R _iri (k) (41) and R _airi (k) (18), the transition matrix of the vector of parameters of the state model M (k) (26) has the form:

10) having solved the system of equations (45) and (46) with respect to D _iri and V _sb , we obtain the inverse functions η _m {f _ij (k, k-1)} that appear in equations (33) and (34):

whence in accordance with formulas (33) (34) we have that

The considered distance meter to the IRI and the approach speed with them in single-position radar systems operates as follows.

At the first preliminary stage, the following is performed.

At time k-2 in the aircraft via mounted thereon autonomous measuring instruments 1 measure θ (k-2) - pitch, ψ (k-2) - yaw angle and _la (k-2) - the height of the aircraft, and they the first output of the stand-alone meters 1 is fed to the first input of the memory 2. At the same time using a radar 6 operating in the passive mode, receive radio signals from IRI 10 and using any of the known methods [4-6] measure the values of φ _g (k- 2), φ _in (k-2) - bearings of the IRI in the horizontal and vertical planes, which from the first output of the radar 6 are fed to the fourth input of the memory 2. In memory 2 all changes The aforementioned values of the mentioned coordinates of the aircraft and Iran are stored.

At the next time moment k-1, autonomous meters 1 measure the values of y _la (k-1), ϑ (k-1) and ψ (k-1), which from the first output of the autonomous meters 1 are fed to the first input of the memory 2. In addition measured at the same moment of time by autonomous meters 1, the aircraft acceleration in the vertical plane j _in (k-1) from the second output of autonomous meters 1 is fed to the second input of the memory 2. At the same time, using radar 6 receive radio signals from IRI 10 and These measured values of bearings IRI φ _r (k-1), φ _a (k-1) in the respective planes, and the angular velocity sight line Bani IRI _in ω (k-1) in a vertical plane. The measured values of φ _g (k-1), φ _in (k-1) from the first output of the radar 6 are fed to the fourth input of the memory 2. The measured value of ω _in (k-1) from the second output of the radar 6 is fed to the fifth input of the memory 2. In memory 2, the measured values of y _la (k-1), ϑ (k-1) and ψ (k-1) are stored. In addition, in memory 2, the measured values of φ _in (k-1) and j _in (k-1) are stored as the values of the corresponding components of the _iri vector (k-1) R (41).

From the eighth output stored in the memory 2 (k-2) th and (k-1) -th instants heights y _la, bearings φ _r, φ _V, pitch θ, and yaw angle ψ is fed to a first calculator 3, wherein they calculate the approximate values of the distance to the IRI D _iri , which took place at time moments k-2 and k-1, according to formulas (13) and (14) and the approximate value of the speed of approach to the IRI V _sat according to formulas (15) and (16) . The calculated values of D _iri and V _sb from the output of the first calculator 3 are fed to the fifteenth input of the memory 2, where they are stored.

и поперечного ускорения ЛА

с третьих выходов РЛС 6 и автономных измерителей 1 соответственно подают на шестой и третий входы ЗУ 2, где их запоминают в виде значений соответствующих компонент матрицы дисперсий шумов измерений D_и (42).Since both radar 6 and autonomous meters 1 measure, respectively, ω _in (k-1) and j _in (k-1), with errors, the variances of which are known, then to account for them, the variance of the measurement errors of the angular velocity of the IRI line of sight

and transverse acceleration of an aircraft

from the third outputs of the radar 6 and autonomous meters 1, respectively, are fed to the sixth and third inputs of the memory 2, where they are stored in the form of the values of the corresponding components of the matrix of dispersions of noise measurements D _and (42).

From the seventh output of the memory 2, the stored values of the components ω _in (k-1) and j _in (k-1) the state vector R _iri (k-1) and the calculated values of the distance to the IRI D _iri (k-1) and the approach speed V _sb (k-1) is fed to the second calculator 4, where they are used to forecast for the k-th instant of time all the values of the components of the state vector R _iri (k) according to formula (18), where the components f _ij (k, k-1) are transitional state vector matrices are determined by formula (43). The predicted values of the components ω _ev (k) and j _ev (k) of the state vector R _eiri (k) from the output of the second calculator 4 are fed to the fourteenth input of the memory 2, where they are stored.

(44).From the sixth output of the memory unit 2, the stored values of the distance to the IRI _DIRI and the approach speed with it V _sat are fed to the third calculator 5, where according to formulas (45) - (48) the values of the components a ₁ (k-1), a ₂ (k -1), and ₃ (k-1), a ₄ (k-1) of the state model parameter vector a (k-1) (44), which from the output of the third computer 5 are fed to the thirteenth input of the memory 2, where they are stored in in the form of estimated values of the components of the state model parameter vector

(44).

On the seventh input of memory 2, based on a priori information about the correlation functions of the distribution of probability density values ω _in (k) and j _in (k), the variances of the error estimates of the vector of state model parameters d ₁₁ (k-1) and d ₁₂ (k -1) according to which initial values are assigned and stored in memory 2 to the corresponding components of the matrix of posterior variances and mutual variances of errors in estimating the vector of parameters of the state model

the values of the components of which are d ₁₂ (k-1) = 0, d ₂₁ (k-1) = 0.

, по которому в ЗУ 2 формируют и запоминают значения компонент матрицы дисперсий шумов вектора состояния D_R (41).On the same seventh input of the memory device 2, based on a priori information about the correlation function of the distribution of the values of the probability density of lateral acceleration, enter the dispersion values of this distribution of acceleration of the aircraft

according to which in the memory 2 form and store the values of the components of the matrix of noise variances of the state vector D _R (41).

In the memory 2 according to the stored values of the components of the state vector R _airi (k) according to the formula (49) form and store the values of the transition matrix of the vector of parameters of the state model M (k).

In the second main stage, starting from time k, the following is performed.

Autonomous meters 1 measure the value of j _in , which from the second output of the meters 1 is fed to the second input of the memory 2.

Using radar 6 receive radio signals from the IRI, which measure the value of ω _in . The measured value of ω _in from the second output of the radar 6 is fed to the fifth input of the memory 2, where it and the value of j _are stored in the form of values of the corresponding components of the measurement vector z (k) (42).

From the fifth output of the memory 2, the stored values of the components of the matrices D (k-1) (51), M (k) (49) and D _R (41) are fed to the input of the fourth calculator 7, where the current values of the components d are calculated by formula (28) ₁₁ (k), d ₁₂ (k), d ₂₁ (k), d ₂₂ (k) of the matrix D (k), which from its output are fed to the twelfth input of the memory 2, where they are stored.

From the fourth output of the memory 2, the stored values of the components of the matrices D (k) (28), M (k) (49) and D _and (42) are fed to the input of the fifth calculator 8, where the values of the components to ₁₁ (k ), to ₁₂ (k), to ₂₁ (k), to ₂₂ (k) of the matrix gain K (k), which from its output are fed to the eleventh input of the memory 2, where they are stored.

(44), z(k) (42) и матриц M(k) (49), K(k) (29) подают на вход шестого вычислителя 9, где по формуле (30) оценивают текущие значения компонент

вектора параметров модели состояния

которые с его выхода подают на десятый вход ЗУ 2, где их запоминают.From the third output of memory 2, the stored values of the components of the vectors

(44), z (k) (42) and the matrices M (k) (49), K (k) (29) are input to the sixth calculator 9, where the current values of the components are estimated by formula (30)

state model parameter vectors

which from its output are fed to the tenth input of the memory 2, where they are remembered.

вектора параметров модели состояния по формулам (31) присваивают значения соответствующим компонентам f₁₁(k+1,k), f₁₂(k+1,k), f₂₁(k+1,k), f₂₂(k+1,k) переходной матрицы вектора состояния и запоминают их в виде значений компонент матрицы Ф(k+1,k) (32).In memory 2 according to the obtained estimated values of the components

the state model parameters vectors by formulas (31) assign values to the corresponding components f ₁₁ (k + 1, k), f ₁₂ (k + 1, k), f ₂₁ (k + 1, k), f ₂₂ (k + 1, k) the transition matrix of the state vector and store them in the form of the values of the components of the matrix Φ (k + 1, k) (32).

и

подают на вход седьмого вычислителя 11, где по формулам (50) вычисляют дальность до ИРИ Д_ири(k) и скорость сближения с ним V_сб(k), которые с его выхода подают на девятый вход ЗУ 2, где их запоминают. Кроме этого, Д_ири(k) и V_сб(k) выдают потребителям информации.From the second output of memory 2, the stored values of the components

and

fed to the input of the seventh calculator 11, where according to formulas (50) calculate the distance to the IRI D _iri (k) and the approximation speed V _sat (k) with it, which from its output is fed to the ninth input of the memory 2, where they are stored. In addition, D _iri (k) and V _sat (k) issue information to consumers.

From the first output of the memory 2, the stored values of ω _in (k) and j _in (k) are fed to the input of the eighth calculator 12, where, according to formula (35), the values of the components of the state vector R of the _airy (k + 1) are calculated, which are fed to the eighth input of memory 2, where they are remembered.

In the memory 2 according to the stored values of the components of the state vector R _airy (k) according to the formula (49), the values are assigned to the corresponding components of the matrix M (k + 1) for the next measurement step, which are stored.

Next, the above process, starting from the second stage, is repeated.

The proposed method for measuring the range has a difference from the known methods, consisting in the possibility of determining the range to the intensively maneuvering IRI and the speed of convergence with it. In addition, the inventive method has a sufficiently high accuracy in determining the specified coordinates of the aircraft and Iran. This conclusion is based on the simulation results, given as an example of the implementation of the meter. Graphs of current errors D _{iriist -} D _iri determine the distance to the maneuvering IRI and V _sist -V _sb approach speeds with it are shown in Figs. 3 and 4, respectively.

Thus, it is confirmed that the proposed method ensures the achievement of the goal: high-precision measurement of the distance to the maneuvering IRI and the speed of approach with it according to goniometric data in single-position radar systems.

The inventive method, when implemented, does not impose any restrictions on the elemental base and composition of the aircraft equipment and can be used on a modern aircraft equipped with any modern radar system.

References

1. Vikulov OV, Dobykin VD, Drogalin VV and other Current status and prospects for the development of aircraft electronic warfare // Foreign Radioelectronics, 1998, No. 12, p.3-16.

2. Fundamentals of the theory of electronic warfare / MP Bobnev, VD Kazakov, NF Nikolenko, ed. N.F. Nikolenko. - M .: Military Publishing House, 1987.

3. Tsvetnov V.V., Demin V.P., Kupriyanov A.I. Electronic warfare: radio intelligence and radio countermeasures. - M .: Publishing House of the Moscow Aviation Institute, 1998.

4. Yuzhakov V.V. Modern methods for determining the location of electromagnetic radiation sources // Foreign Radio Electronics, 1987, No. 8, p. 67-79.

5. Sokolova N.S. Opportunities for observing target maneuvers by measuring only the bearing or only the rate of change of the bearing // News of foreign science and technology. Ser. Aviation system. - Gos. Research Institute of Aviation Systems, 1993, No. 4, pp. 5-15.

6. Makukhina TP Estimation of the current coordinates of a moving object according to its direction finding // Questions of radio electronics. Ser. ASUPR, 1992, issue 4.

7. Patent RU 2128848, MKI 6 G 01 S 15/00. Published on 10.4.99.

8. Patent RU 2066458, MKI 6 G 01 S 5/16. Published 10.9.96.

9. US patent 5917449, MKI 6 G 01 S 3/02. Published on June 29, 1999.

10. US patent 5479360, MKI 6 G 01 S 7/00. Published 12/26/95.

11. US patent 5343212, MKI 5 G 01 S 5/02. Published 08/30/94.

12. Drogalin V.V., Dudnik P.I., Kanaschenkov A.I. et al. Determination of coordinates and motion parameters of sources of radio emissions from goniometric data in single-position onboard radar systems. // Foreign radio electronics. Advances in Modern Radio Electronics, 2002, No. 3, p. 64-94.

13. Bulychev Yu.G., Burlai I.V., Motorkin V.A. Estimation of motion parameters of objects based on high-precision goniometric systems // Radio Engineering and Electronics, 1992, v. 37, No. 4, p. 618-627.

14. Bulychev Yu.G., Burlai I.V., Motorkin V.A. Kalman filtration equations for pseudo-triangulation systems of location // Radio Engineering, 1992, No. 3, pp. 10-13.

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17. Ljung L. Identification of systems. Theory for users. - M.: Science, 1991.

18. Merkulov V.I., Lepin V.N. Aircraft radio control systems, part 1, part 2. - M .: Radio and communications, 1997.

Claims (1)

A method for determining the distance to sources of radio emissions (IRI) and the speed of approach with them in single-position radar systems, based on measuring the angular coordinates of the IRI, characterized in that at the first, preliminary, stage at time k-2 on an aircraft (LA) measure яют (k-2) - pitch, ψ (k-2) - yaw angle, for a _la (k-2) - aircraft altitude and receive radio signals from the IRI, which measure the values of φ _g (k-2), φ _in (k -2) - bearings of the IRI in the horizontal and vertical planes, respectively, the measured values of ϑ (k-2), ψ (k-2), for _la (k-2), φ _g (k- 2), φ _a (k-2) is stored in the next time k-1, spaced from time k-2 τ - sampling interval measured values of height y _la (k-1) aircraft, its pitch θ (k -1) and yaw angle ψ (k-1), lateral accelerations j _g (k-1), j _in (k-1) aircraft in the horizontal and vertical planes, respectively, receive radio signals from the IRI, which measure the values of bearings φ _g (k-1), φ _in (k-1) IRI and angular velocities of the line of sight ω _g (k-1), ω _in (k-1) IRI in the horizontal and vertical planes, respectively, the measured values of _la (k -1), ϑ (k-1) and ψ (k-1) are stored by changing The values of φ _g (k-1), ω _g (k-1), j _g (k-1), φ _in (k-1), ω _in (k-1) and j _in (k-1) are remembered as the values of the corresponding components of the vector

called a state vector, the values of the height y _la stored in the (k-2) th and (k-1) th instants of time, the bearing φ _in and the pitch ϑ calculate the approximate values of the distance to the IRI D _iri , which took place at times k-2 and k -1, according to the formulas D _iri (k-2) = y _la (k-2) / sin [φ _in (k-2) -ϑ (k-2)], D _iri (k-1) = y _la (k-1) / sin [φ _in (k-1) -ϑ (k-1)], from the calculated values of the distance to the IRI D _iri and the stored values of φ _g , φ _in , ϑ and ψ calculate the approximate values of the projections of the speed of approaching the IRI V _usb , V _zsb and V _hsb on the axis Y, Z and X, respectively, of a fixed rectangular earth system OYZX coordinates by formulas

which calculate the approximate values of the rate of approximation with IRI V _sat according to the formula

variance of measurement errors of bearings IRI

angular velocities of the IRI line of sight

transverse accelerations of an aircraft

in the horizontal and vertical planes, respectively, are stored in the form of values of the corresponding matrix components

called the matrix of dispersions of measurement noise, the off-diagonal components of which are equal to zero, according to the stored values of the components φ _g (k-1), ω _g (k-1), j _g (k-1), φ _in (k-1), ω _in (k-1), j _{in the} (k-1) state vector R _iri (k-1) (1) and the calculated values of the distance to the IRI D _iri (k-1) and the approach speed V _sb (k-1) of the aircraft with IRI extrapolates to the k-th instant of time all the values of the components of the state vector according to the formula

Where

is the transition matrix of the state vector, the components f _ij (k, k-1),

which represent functions by which the associated φ _r, ω _r, j _r, φ _a, ω _a, j _in a D _iri and V _sb, predicted values of the components φ _r (k), ω _r (k), j _g ( k), φ _in (k), ω _in (k), j _in (k) of the vector R _airy (k) (3) are remembered, according to the calculated values of the distance to the IRI D _iri and the speed of approach to it V _{sb, the} values of the above functions are calculated f _ij (k, k-1) and by the formulas

assign their values to the corresponding components a _l (k-1) of the vector

called a vector of state model parameters that remember, in the formula (6) the symbol

means that the values of the components are estimated, and the value of each of the components

of this vector, as well as the value of the function f _ij (k, k-1) corresponding to it, determines the degree of connection between the various location coordinates and the parameters of the mutual movement of the aircraft and IRI, to take into account the initial and subsequently current errors in estimating the values of the components of the vector

(6) remember the matrix

called the matrix of posterior variances and mutual variances of errors in estimating the vector of parameters of the state model, whose component values d _ij (k-1) = 0, for i ≠ j, where

n is the number of components of the state vector, and the diagonal components are set, based on a priori information about the correlation functions of the distribution of probability density values of the corresponding components of the vector R _iri (1), to take into account the lack of accurate data on the movement of IRI, the matrix is stored

called the error variance matrix of the state vector whose component values d _ij = 0, for i ≠ j, where

and the diagonal components are set, based on the specific structure of the vector R _iri (1) and a priori information about the correlation functions of the distribution of the probability density values of its components, from the stored values of the components, the vector R _airy (k) (3) form and store the corresponding values of the components of the transition matrix of the vector of parameters of the state model M (k) for the next k-th step of calculations by the formula

where 0 are n-dimensional zero vectors, at the second, basically, stage, starting from time k, measure the values of j _g , j _c , and also receive radio signals from the IRI, which measure the values of φ _g , φ _c , ω _g and ω _c , the measured values of φ _g , ω _g , j _g , φ _in , ω _in and j _{in are} stored in the form of values of the corresponding components of the vector

called the measurement vector, where φ _gi (k) = φ _g (k), ω _gi (k) = ω _g (k), j _gi (k) = j _g (k), φ _vi (k) = φ _in ( k), ω _wi (k) = ω _in (k), j _wi (k) = j _in (k), from the stored values of the components of the matrices d (k-1) (7), D _R (8) and M ( k) (9) by the formula

calculate and remember the current values of the components d _ij (k) of the matrix D (k) (7), from the stored values of the components of the matrices D _and (2), M (k) (9) and D (k) (11), according to the formula

calculate and store the values of the components to _ij (k-1), where

matrix gain K (k), from the stored values of the components of the vectors

(6), z (k) (10) and the matrices M (k) (9), K (k) (12) by the formula

evaluate current component values

of vector

(6), based on the obtained estimated values of the components

according to the formulas

assign values to the corresponding components f _ij (k + 1, k) of the matrix Φ (k + 1, k) (4), from the obtained values of the components f _ij (k + 1, k) of the matrix Φ (k + 1, k) calculate the range to IRI D _iri (k) and the speed of approach with him V _sat (k) according to the formulas D _iri = η ₁ {f _ij (k + 1, k)}, V _sat = η ₂ {f _ij (k + 1, k)}, where η ₁ {f _ij (k + 1, k)} and η ₂ {f _ij (k + 1, k)} are the functions by which φ _g , ω _g , j _g , φ _c , ω _c , j _in with D _iri and V _sat , the calculated values of the distance to the IRI D _iri (k) and the speed of approach with it V _sat (k) give information to consumers, according to the stored values of the components of the vector R _iri (k) (1) and the matrix Ф (k + 1, k) using formula (3), calculate and store the values of the components of the _airy vector R (k + 1) (3) to the next (k + 1) -th measurement step, according to the stored values of the components of the _airy vector R (k + 1) by the formula (9) form and store the values of the components of the matrix M (k + 1) for the next measurement step, further, the process described above, starting from the second step, is repeated.

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