RU2643521C1 - Method of active direction finding of targets - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: direction finding method consists in sequentially probing adjacent angular directions in a given sector with a step of varying the angle providing the required angular resolution of the targets and constructing a direction-finding characteristic on the basis of which a decision is made about the presence or absence of targets. According to the invention, the sector of the direction-finding characteristic is subsequently probed at different frequencies, the range of variation of which is chosen such that, due to the existing difference in range to the targets, it is possible to ensure a change in the phase difference of the coherent signals reflected from them at the largest and smallest sounding frequencies by an amount of multiples of 2π, and the step of changing the frequency is selected so as to provide a form of direction-finding characteristic with detail, allowing to decide on the number of targets.

EFFECT: increasing the angular resolution of the direction finder.

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Description

The invention relates to radio engineering and can be used in systems for determining the direction to the target, including in radar, radio navigation, communications.

The closest analogue of the proposed method is the classical method of active amplitude direction finding. It consists in sequentially sensing adjacent angular directions in a given sector (radiation of the probing signal, receiving and processing the signal reflected from the target) and constructing a direction-finding characteristic (depending on the output power of the receiving device of the direction finder from the angle), based on which they decide on the presence or absence of targets [ Belotserkovsky G.B. Basics of radar and radar devices. - M .: Owls. Radio, 1975 .-- p. 87-88; Theoretical Foundations of Radar: Textbook. manual for universities / A.A. Korostylev, N.F. Klyuev, Yu.A. Melnik et al. / Ed. V.E. Dulevich. - M .: Owls. Radio, 1978. - p. 260-262]. The step of changing the angle is chosen in accordance with the width of the radiation pattern of the direction finder antenna, which is usually equal to half the width of the radiation pattern, which ensures reliable detection of targets and their angular resolution.

In the case of single target DF DF characteristic finder P _sang (ν) the classical method DF same (to within a constant factor) from the direction finder antenna radiation pattern in power:

P _sang (ν) = F ² (ν), ν = sin (α),

where F (ν) is the antenna radiation pattern;

α is the angle of direction finding.

If there are several targets in the direction finding sector, the width of the radiation pattern determines the capabilities of the direction finder according to their angular resolution. The direction-finding characteristic of the direction finder is determined by the sum of radiation patterns for power for individual purposes:

where n is the number of goals;

a _i - the amplitude of the signal of the i-th target;

F _i (ν) is the antenna radiation pattern for voltage for the i-th target.

The angular resolution of the targets is maximized with a uniform amplitude-phase distribution of the field along the aperture of the antenna. In this case, the radiation pattern is described by the function Sinc (x) = sin (x) / x:

F _i (ν) = Sinc [k _p (ν _i -ν)], V _i = sin (α _i ), k _p = πL / λ,

where α _i - direction to the i-th target;

λ is the wavelength;

L is the magnitude of the aperture of the antenna.

In this case, the resolution of the classical direction finding method is characterized by the Rayleigh limit λ / L: two equal targets i and j located in the directions α _i and α _j , respectively, are solvable if the angular distance between them is not less than λ / L:

| Δν _{i, j} | = | ν _i -ν _j | ≥λ / L.

The disadvantage of the classical method of direction finding is not a sufficiently high angular resolution limited by the Rayleigh limit λ / L.

The technical result of using the proposed method is to increase the angular resolution of the targets: the angular resolution of the targets when using the proposed method is provided at any angular distances between them, including less than the Rayleigh limit.

Achievement of the claimed technical result is based on using the possibility of super-Rayleigh resolution of goals shown in article [1] in the presence of inter-angle coherence of signals received from them.

By the inter-angle coherence of signals received from a pair of targets i and j, we mean the constancy of the difference in the initial phases Δϕ _{i, j of} signals in the time interval for the formation of the direction-finding characteristic T _Px .

The difference in the initial phases of the signals Δϕ _{i, j} with an active location is determined by the difference in the distances from the direction finder to the targets:

where ϕ _i , ϕ _j are the initial phases of the signals of the i-th and j-th targets;

R _i , R _j - range of the i-th and j-th targets.

In the classical method of direction finding, the inter-angle coherence of signals is not used.

In the article [1] it was shown that in the presence of inter-angle coherence of the received signals, the direction-finding characteristic of the direction finder during direction finding of n targets is the sum of radiation patterns in power and pairwise (for all sets of pairs of n targets) interference terms:

In the absence of inter-angle coherence of the signals, the quantity Δϕ _{i, j} for each subsequent angular direction of direction finding takes a random value uniformly distributed in the range [0, 2π], as a result of which the direction-finding characteristic is a random value, and its mathematical expectation M _sang (ν) is determined by the expression (one). That is, the classical method of direction finding is a special case of the proposed method of direction finding in the absence of inter-angle coherence of signals.

For the case of direction finding of two targets, the equation for direction-finding characteristics taking into account the inter-angle coherence of the signals has the form:

and the mathematical expectation of the direction-finding characteristic is

From the analysis of the direction-finding characteristic (3) performed in [1], it follows that interference of coherent signals from targets received in adjacent directions of direction-finding leads to the fundamental possibility of resolving targets at any angular distance between them, including smaller Rayleigh limit λ / L. At the same time, the inter-angle coherence of the signals provides, but does not guarantee, super-resolution of the targets: for small angular distances between the targets, a dip in the direction-finding characteristic between two humps corresponding to the directions to the targets i and j exists only in a limited zone of phase differences, the width of which ΔФ _{i, j} , with small angular distances between targets, less than 2π. So, for the case of identical signal amplitudes a _i = a _j , the guaranteed resolution of targets, in the presence of inter-angle coherence of signals, is bounded from below by the angular distance | Δν _{i, j} | ≈1.325λ / L. At smaller angular distances, resolution is possible only if Δϕ _{i, j} falls into the phase zone whose width is less than 2π and is equal to

,Where

,

and the position of its center is determined by the equation

For example, for the angular distance between targets | Δν _{i, j} | = 0.5λ / L (half the Rayleigh resolution limit), we have:

ΔФ _{i, j} ≈0.586π, Δϕ _{qi, j} = 0.5π.

Dependence (6) is almost linear in the range of angular distances between targets | Δν _1,2 | ≤λ / L, corresponding to superresolution, and can be approximated by the function

Based on the essence of the inter-angle coherence of the signals underlying the achievable super-Rayleigh resolution of the targets and the described properties of the direction-finding characteristic, the proposed method consists in organizing direction finding within the direction-finding characteristic formation sector so as to achieve that the phase difference of the pair of received signals Δϕ _{i, j} gets into the phase resolution zone ΔФ _{i, j} and bring the value Δϕ _{i, j} as close as possible to the center of this zone Δϕ _{qi, j} .

In this case, if during the formation of the direction-finding characteristic (during the performance of sounding operations at adjacent direction-finding angles), the phase difference does not significantly disappear due to the dynamic properties of the targets and random fluctuations of the phase difference Δϕ _{i, j} , then the targets will be allowed.

According to (2), the value of the phase difference Δϕ _{i, j} at different sensing frequencies (for different λ) has a different value. Proceeding from this, in order to ensure that the quantity Δϕ _{i, j} falls into the phase zone ΔΦ _{i, j} and the maximum proximity of Δϕ _{i, j} to Δϕ _{qi, j,} it is necessary to sequentially probe the sector of the formation of the direction-finding characteristic at different frequencies, the range of which is chosen so that due to the available difference in the ranges to the targets, to ensure a change in the phase difference of the coherent signals reflected from them at the highest and lowest sensing frequencies by 2π, and select the frequency change step so as to ensure that We DF characteristics with detail, allowing to make a decision on the number of goals in the DF sector characteristics.

Formally, the organization of direction finding consists in sequential testing of the phase range [0, 2π] on a set of wavelengths λ _k = λ ₀ -k⋅Δλ in order to construct a number of direction-finding characteristics that allow resolving targets with the best quality. Moreover, k = 1, ..., n _λ -1, Δλ is the step of changing the wavelength, n _λ is the number of tests (the number of direction-finding characteristics obtained at different values of wavelengths λ _k ).

The value of the phase difference of the signals Δϕ _{i, j} during the construction of the direction-finding characteristic can vary from sounding to sounding due to mutual movement of targets (changes in the value of ΔR _{i, j} ) or due to random fluctuations in the phases of the signals, which leads to a decrease or disappearance of inter-angle coherence received signals (the value Δϕ _{i, j} goes beyond ΔФ _{i, j} ). To reduce the negative impact of moving targets and signal phase fluctuations on the inter-angle coherence of signals, the time taken to construct the direction-finding characteristic must be minimized. For this purpose, the width of the direction-finding characteristic and the period of sounding of the angular directions during the formation of the direction-finding characteristic are minimized.

The width of the sector of the formation of the direction-finding characteristic and the step of angular scanning are determined respectively by a priori information about the presence of targets and the desired value of the angular resolution. In [1], it was shown that the width of the direction-finding characteristic for two equally large targets with an angular distance between them less than the Rayleigh resolution limit does not exceed 3λ / L; therefore, for the superresolution of two goals it is advisable to form a direction-finding characteristic with an angular size of no more than 3λ / L with the required pitch.

Minimizing the time for constructing a direction-finding characteristic is desirable, but it is not an essential sign of the proposed method, since it does not guarantee, but improves the conditions for over-resolution of targets.

The choice of a set of wavelengths for testing the phase range [0.2π] (determination of the wavelength range and the step of their change) within the framework of the proposed method can be carried out both by sequential selection and, if the ranges to the targets are known, by the calculation method.

Consider the procedure for calculating sounding wavelengths in the event that the ranges to the targets are known.

The boundaries of the test range of wavelength changes (upper λ _in and lower λ _{n of the} boundary) relative to the initial value of λ ₀ , providing a change in the phase shift Δϕ _{i, j} (respectively increase and decrease) by 2π, can be determined from the equation:

,

,

where from

The step of changing the wavelength Δλ can be either a positive value, if the phase difference of the signals varies due to a decrease in wavelength, or negative, in the case of an increase in wavelength. It is found according to the formulas

Test constructions of direction-finding characteristics at different wavelengths can be performed not only on the basis of the need to test the phase range [0, 2π], but also a wider range [0, k _t 2π], where the coefficient k _t = 2, 3, ... This is advisable , for example, for tactical and technical reasons for choosing wavelengths. In this case, the upper and lower boundaries of the wavelengths are calculated according to formulas (9) with the replacement in the numerator of λ by k _t λ, and the step of changing the wavelength can be found, respectively, by the formulas:

Δλ _n = (λ ₀ -λ _n) k _m / n _λ, Δλ _a = (λ ₀ -λ _in) k _m / n _λ,

moreover, it is necessary to use multiple values of the quantities k _t and t _λ , which will exclude the repetition of tests with the same phase shifts Δϕ.

It is necessary to take into account that when expanding the phase range of testing, a change in the wavelength begins to affect not only the phase difference of the signals, but, due to relations (7), (8), and the width of the signal resolution zone and the position of its center. This effect is characterized by inverse proportionality to the wavelength, and therefore the long-wavelength range of location is preferable for the implementation of the proposed method.

Further, the invention is disclosed by the example of the technical implementation of the proposed method of direction finding.

Example 1. The direction finder of the long-wave range of the radar type "Sunflower-E". Let the aperture size be L = 300 m, the wavelength λ = 30 m. In the plane of the radar scan along the angle α, parallel courses toward the direction finder with constant (at a small time interval for constructing the direction-finding characteristic Т _пх ) speeds of V ₁ , V ₂ move two identical goals unsolvable in the angle in the classical way. The distance between the targets in depth is D _1.2 = 1 km, the front distance is L _1.2 = 4 km. The distance to the nearest target at the time of the beginning of the construction of the direction-finding characteristic D _nach = 60 km. A diagram explaining the conditions of direction finding and the coordinate system are shown in FIG. 1. The task is to assess the resolution of goals.

Intermediate variables for calculations are determined by the formulas:

,

, ΔR_1,2=R₁-R₂;- range to targets:

,

, ΔR _1,2 = R ₁ -R ₂ ;

,

, ν₁=sin(α₁), ν₂=sin(α₂), ν_1,2=ν₁-ν₂;- function angles of targets:

,

, ν ₁ = sin (α ₁ ), ν ₂ = sin (α ₂ ), ν _1,2 = ν ₁ -ν ₂ ;

.- phase difference of the signals:

.

Given the small relative distance between the targets (ΔR _1,2 / R ₁ = 0.017), we take the amplitude of the signals from the targets the same: a ₁ = a ₂ = 1.

Calculations using the above formulas show that the angular distance between targets for a given initial data is significantly less than the Rayleigh resolution limit:

ν ₁ = 0.0333, ν ₂ = - 0.0328, | Δν _1,2 | = 0.066 <λ / L = 0.1.

With such an angular distance, with direction finding without taking into account the inter-angle coherence of the signals, angular resolution of the targets is impossible. DF characteristic two considered goals (, V ₂ = 0 V ₁ = 0) calculated excluding mezhuglovoy signals coherency (i.e., with a random phase difference change at each bearing of the range [0, 2π]) in the absence of targets movement is shown in FIG. 2. The calculations were performed according to formula (4) with a step of 0.02 in the variable v at a wavelength of λ ₀ = 30 m. The obtained values of the direction-finding characteristic are indicated by crosses on the dashed line. Here, the bold dashed line shows the function M _sang (ν), corresponding to the direction-finding characteristic of the classical method. It is calculated by the formula (5).

We carry out the construction of direction-finding characteristics taking into account the inter-angle coherence of the signals.

For definiteness, we assume that testing the phase resolution zone is performed by reducing the wavelength. We take the number of tests equal to n _λ = 5. Then from formula (9) we get: λ _n = 29.556 m, and from (10) the step of changing the wavelength: Δλ _n = 0.089 m. Test wavelengths decreasing with the calculated step from the initial value λ ₀ = 30 m are equal to: λ ₁ = 29.911 λ ₂ = 29.823 m, λ ₃ = 29.734 m, λ ₄ = 29.645 m.

First, we consider the case of complete inter-angle coherence of signals: the targets are motionless (V ₁ = 0, V ₂ = 0), there are no random changes in the phase difference of the signals Δϕ _1,2 .

The results of evaluation of the functions P _sang (ν) at wavelengths λ _k, where k = 0, 1, ..., 4, of the formula (4) and the function M _sang (ν) from the formula (5) at a wavelength λ ₀ are shown in Figure . 3.

Construction of a number of direction-finding characteristics at different wavelengths yielded DF characteristic (wavelength λ _1), provide the best resolution of the two targets in an angular distance therebetween substantially smaller Rayleigh limit. An analysis of the phase relationships of signals (7), (8) shows that at a wavelength of λ _1, the phase difference of the signals has a value of Δϕ _1.2 = 1.081 rad and is close to the center of the phase resolution zone of signals Δϕ _c1.2 = 1.059 rad, whose width is ΔF _1.2 ≈ 2.5 rad. At other wavelengths, the width and center of the phase resolution zone differ slightly (in the third decimal place), while the phase difference of the signals Δϕ _1,2 on the set of wavelengths λ _k in accordance with (10) varies with a step of 2π / 5 glad.

шаг изменения переменных привязан к очередному моменту зондирования, выполняемого с периодом Т_п. Значения D₁, D₂ на

шаге моделирования соответственно равныConsider the case of moving targets. The movement is modeled by a step-wise change in the variables D ₁ , D ₂ from the initial value of D _beg . Everyone

the step of changing the variables is tied to the next moment of sounding performed with a period T _p . Values of D ₁ , D ₂ on

simulation steps are respectively equal

,

,

,

,

,

,

,

,

where T _p is the period of sensing angular directions (period of direction finding), trunc [x] is the operation of extracting the integer part of the number x.

Accordingly, the values of D ₁ , D ₂ change the variables R ₁ , R ₂ , α ₁ , α ₂ , Δϕ _1,2 depending on them, and the values of the functions P _sang (ν), M _sang (ν).

In FIG. Figure 4 shows the results of the calculation of direction-finding characteristics taking into account the inter-angle coherence of the signals for the cases: V ₁ = 300 m / s, V ₂ = 350 m / s (left figure) and V ₁ = 300 m / s, V ₂ = 400 m / s ( right figure). The direction finding period is taken equal to T _p = 0.002 s. The time of formation of the direction-finding characteristic for the selected step of changing the variable v was T _Px = 0.03 s.

From the drawings it follows that for given initial data, super-Rayleigh resolution of two targets is provided with a difference of their speeds of up to 100 m / s. Moreover, as the calculations show, the phase difference of the signals at a wavelength of λ ₁ due to the movement of targets during the construction of the direction-finding characteristic varies from the initial value of 1.081 rad to 2.34 rad and reaches the edge of the resolution phase zone.

Further, we additionally take into account the random component of the phase difference of the signals in adjacent directions of direction finding. During the sensing period, the phase difference of the signals Δϕ _1,2 may randomly change due to the action of random factors, for example, the propagation medium and changes in the position of the target surface. As a result, a certain degree of decorrelation of the reflected signal will occur and the inter-angle coherence of the signals may be partially or completely broken. It is known that the correlation time of the reflected signal τ _cor can be tens of milliseconds (see [2], p. 60).

The correlation and coherence parameters of the signals can be related as follows.

пеленге приобретает случайную добавку:With a small inter-angle time interval between bearings T _p (in the case of a short range to the target and a short duration of the probing signal), the magnitude of the random addition to the phase of the signal is small, since the action of random factors is short-lived. With an increase in the interval T _{p, the} random nature of the phase manifests itself to a greater extent. When T _n ≥τ _armature quantity φ _slab may randomly assume any value in the interval [0, 2π], will dekorellyatsiya signal mezhuglovaya offline coherence signals. For the direction finding period T _p <τ _{cor, the} upper boundary of the range of possible random values decreases proportionally to the ratio T _p / τ _cor . As a result, the phase difference of the two signals in

Bearing acquires a random additive:

,

,

- случайная составляющая разности фаз.Where

- random component of the phase difference.

представляет собой реализацию в

пеленге случайной равномерно распределенной в диапазоне [0, 2πk_сл] величины. Коэффициент k_сл задает верхнюю границу диапазона случайной величины:When modeling

represents an implementation in

bearing of a random evenly distributed in the range [0, 2πk _cl] value. The coefficient k _SL sets the upper boundary of the range of a random variable:

k _sl = T _p / τ _cor for T _p <τ _cor and k _sl = 1 for T _p ≥ τ _cor .

As applied to the considered practical example, we consider the cases when the correlation time of the reflected signal τ _cor is 0.02 s and 0.01 s. Using the above-described model of the relationship between the random phase and the correlation time, we obtain, respectively, _ksl = 0.1 and _ksl = 0.2. The results of the calculation of direction-finding characteristics, taking into account the decrease in inter-angle coherence of signals at target speeds V ₁ = 300 m / s, V ₂ = 350 m / s, are shown in FIG. 5. The direction-finding characteristic constructed at a wavelength λ ₁ for which the initial phase difference is closest to the center of the phase resolution zone is least affected by the random change in the phase difference of the signals.

Calculations show that for given initial data on target speeds and taking into account a random change in the phase difference of the signals, the application of the proposed direction finding method provides super-Rayleigh resolution of two targets.

Thus, the use of the proposed method of direction finding provides an increase in the angular resolution of targets.

Literature

1. Gorevich B.N. Investigation of the angular resolution of signals by a direction finder taking into account their inter-angle coherence // Antennas. 2016. No. 12.

2. Radar devices (theory and construction principles) / V.V. Vasin, O.V. Vlasov, V.V. Grigorin-Ryabov, P.I. Dudnik, B.M. Stepanov / Ed. V.V. Grigorina-Ryabova. - M .: Owls. radio, 1970.

Claims (1)

The method of active direction finding of targets, which consists in sequentially sensing adjacent angular directions in a given sector with a step of changing the angle that provides the required angular resolution of the targets, and constructing a direction-finding characteristic, based on which a decision is made about the presence or absence of targets, characterized in that the direction-finding characteristic building sector they are sequentially probed at different frequencies, the variation range of which is chosen so that, due to the available difference in the ranges to to take into account the change in the phase difference of the coherent signals reflected from them at the highest and lowest sensing frequencies by a multiple of 2π, and the frequency change step is chosen so as to provide a form of direction-finding characteristic with detail that allows you to decide on the number of targets.

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