RU2642846C2 - Method for determining coordinates of radio emission source - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: invention can be used for high-precision determination of the coordinates of radio emission sources (RES) with the aid of aircrafts, emitting continuous or quasicontinuous signals. The method of determination of the RES coordinates is RES signal receiving on three aircrafts, their relaying to the central point of processing and computing RES coordinates using radial velocity differentials, while additionally Doppler frequency shifts are there as a maximizing argument of amplitude spectrum of the product of a signal from one repeater by a signal from another repeater, subjected to complex pairing and shift for a time delay, which is defined as a maximizing argument of the function module of the mutual correlation of converted signals, obtained by multiplying the original signals by the same signals, subjected to complex pairing and temporary shift by the interval T, exceeding the value, which is inversely proportional to twice the spectrum bandwidth.

EFFECT: reduced hardware costs when implementing a method based on the products of functional electronics, and when implementing a method, based on digital signal processing hardware, improving the response time by reducing the amount of arithmetic operations.

1 cl

Description

The invention relates to radio engineering, and in particular to passive radio monitoring systems, and, in particular, can be used for high-precision determination of coordinates of radio emission sources (IRI) using aircraft, emitting continuous or quasicontinuous signals.

Of the known methods according to the technical essence, the closest analogue (prototype) of the proposed method is a method for determining the coordinates of the IRI [1], which consists in receiving signals of the IRI on three aircraft, relaying signals to a central processing point, calculating the differences of the radial speeds of the aircraft, with subsequent calculation Iran coordinates according to radial velocity differences, while the signals relayed from aircraft are mutually correlated, and the differences are rad The real speeds of aircraft are calculated based on the compression coefficients of the signals, determined by searching for the maximum cross-correlation function of the signals relayed from the aircraft.

In the prototype method, the radial velocity differences are calculated through a compression coefficient determined on the basis of maximizing the cross-correlation function of the signals. To this end, in [1], it is proposed, before calculating the cross-correlation function, to relay the transmitted signals to processing in acoustoelectronic devices (AUE), for example, in a dispersion delay line (DLS) on surface acoustic waves (SAW) having a slope of the frequency response of the group delay time (GW) , inverse to the slope of the compression (or stretching) function in time of the signal due to the Doppler effect [2, p. 257-258; from. 283-284].

The disadvantage of this embodiment of the prototype method is the large hardware redundancy, since in this case it is necessary to use a wide range of DLZ on SAWs with a different slope of the frequency characteristics of the GWZ, covering the entire range of possible changes in the compression coefficients (Doppler frequency shift) of the signals received and relayed by aircraft.

Another embodiment of the prototype method is the use of hardware digital signal processing (DSP) [3, p. 23]. Typically, in DSP equipment, when calculating the cross-correlation function, at the beginning, both signals are supplemented with zeros to double the number of samples in order to eliminate the effect of overlapping side periods during discrete convolution. Then, both doubled in volume samples of the signal are subjected to fast Fourier transform (FFT). Next, the complex conjugate spectrum of one of the signals is shifted in frequency by a resolution element in the range of possible values of Doppler shift. And finally, both spectra are multiplied and the inverse fast Fourier transform (IFFT) is performed from the resulting product, which, in accordance with the Wiener-Khinchin theorem, is the cross-correlation function of the relayed signals.

Based on the foregoing, it is clear that in order to search for a resolution element corresponding to the Doppler shift of relayed signals in the DSP equipment, it will be necessary to calculate M times (M is the number of resolution elements for Doppler shift) the cross-correlation function by performing two FFT and one IFFT. Since the FFT algorithm (FFT) contains 2⋅N⋅log ₂ [2⋅N] arithmetic operations [3, p. 14-15], then in the general case, the search for the Doppler shift of relayed signals based on the use of DSP methods will require 3⋅M⋅2⋅N⋅ (1 + log ₂ N) arithmetic operations, where N is the initial sample size of the signal.

Thus, both possible options for implementing the prototype method have drawbacks: when implementing functional electronics on the basis of products, there is a large hardware redundancy, and when using DSP hardware, a significant number of arithmetic operations.

The purpose of the invention is to reduce hardware costs when implementing the method on the basis of functional electronics products, and when implementing the method on the basis of DSP hardware, improving performance by reducing the number of arithmetic operations.

находятся как аргумент максимизации амплитудного спектра произведения сигнала с одного ретранслятора x_k(t) на сигнал x_i(t) с другого ретранслятора, подвергнутый комплексному сопряжению и сдвигу на временную задержку τ_ki: x_k(t)⋅x_i(t-τ_ki)^* (i≠k; i, k=1, 2, 3), при этом задержка τ_ki определяется как аргумент максимизации модуля функции взаимной корреляции преобразованных сигналов Y_k(t) и Y_t(t), полученных путем перемножения исходных сигналов на эти же сигналы, подвергнутые комплексному сопряжению и временному сдвигу на интервал Т: Y_m(t)=x_m(t)⋅x_m(t-Т)^*, где m=i,k; T≥1/(2⋅F); F - ширина спектра сигнала;

- знак комплексного сопряжения.This goal is achieved by the fact that in the known method, which consists in receiving the IRI signals x _i (t) (t is time) on three aircraft (i = 1, 2, 3), relaying them to the central processing point and calculating the coordinates of the IRI differences of radial velocities directly proportional to the values of the Doppler frequency shift corresponding to the global maximum of the cross-correlation function of the relayed signals, according to the invention, Doppler frequency shifts

are found as an argument for maximizing the amplitude spectrum of the product of a signal from one repeater x _k (t) to a signal x _i (t) from another repeater subjected to complex conjugation and a time delay shift τ _ki : x _k (t) ⋅ x _i (t-τ _ki ) ^* (i ≠ k; i, k = 1, 2, 3), and the delay τ _ki is defined as the argument for maximizing the modulus of the cross-correlation function of the converted signals Y _k (t) and Y _t (t) obtained by multiplying the original signals at these same signals subjected to complex conjugation and time shifted by an interval _{t: Y m (t) = x} m (t) ⋅x m (t- t) ^* rA m = i, k; T≥1 / (2⋅F); F is the signal spectrum width;

- a sign of complex pairing.

Comparative analysis with the prototype shows that the claimed method differs by the introduction of new operations - measuring the delay difference of the relayed signals after their preliminary conversion and calculating the difference of the Doppler frequency offset by determining the maximum spectral component in the spectrum of the product of the relayed signals when one of the signals is shifted by the calculated delay. Thus, the claimed method meets the criteria of the invention of "novelty."

Let us explain in more detail the essence of the proposed method.

Imagine the radiated IRI signal in a complex form:

where A (t) and ϕ (t) are the real amplitude and phase of the IRI signal, respectively; ω is the carrier frequency of the signal; j is the imaginary unit; t is time.

After the signal is relayed by the i-th (k-th) aircraft at the input of the receiver of the central processing point, this signal undergoes a Doppler shift ω _di (ω _dk ), a time delay of τ _i (τ _k ) and attenuation by μ _i (μ _k ) times :

If the i-th relay signal is delayed for the time τ _ki = τ _k -τ _i , i ≠ k, we obtain a signal in which the amplitude and phase repeat in time the amplitude and phase of the signal relayed by the k-th aircraft:

From the expressions (2) and (3) it can be seen that the product of the k-th signal on the delayed complex conjugate i-th signal:

- знак комплексного сопряжения позволяет сформировать гармонический сигнал с амплитудной модуляцией μ_i⋅μ_k⋅A(t-τ_k)² и фиксированной начальной фазой (ω_дi-ω_дk)-τ_k, несущая частота которого постоянна и равна разности доплеровских частот сигналов при ретрансляции i-м и k-м летательным аппаратом:

.Where

- the sign of complex conjugation allows you to generate a harmonic signal with amplitude modulation μ _i ⋅μ _k ⋅ A (t-τ _k ) ² and a fixed initial phase (ω _{di -ω dk} ) -τ _k , the carrier frequency of which is constant and equal to the difference of the Doppler frequencies of the signals when relaying the i-th and k-th aircraft:

.

We represent the converted signal x _k (t) ⋅ x _i (t-τ _ki ) ^* in the form:

;

; A_max=max{μ_i⋅μ_k⋅A(t-τ_k)²}; A_min=min{μ_i⋅μ_k⋅A(t-τ_k)²};where S _o is the mathematical expectation of the envelope μ _i ⋅μ _k ⋅A (t-τ _k ) ² ;

;

; A _max = max {μ _i ⋅ μ _k ⋅ A (t-τ _k ) ² }; A _min = min {μ _i ⋅ μ _k ⋅ A (t-τ _k ) ² };

, составляет более 2/3 мощности преобразованного сигнала (4).Formula (5) coincides with the traditional form of recording an amplitude-modulated signal with a modulation index m _AM , 0≤m _AM ≤1 [5, p. 67-69]. It is known [5, p. 69] that the power contained in the sidebands of the amplitude-modulated signal depends on the modulation index m _AM and increases with increasing modulation depth. However, even in the extreme case, when m _AM = 1, only 1/3 of the total oscillation power falls on two side bands. Therefore, the power per oscillation of the carrier frequency

is more than 2/3 of the power of the converted signal (4).

Thus, the Doppler shift can be found by determining the maximum spectral component in the amplitude spectrum of the product of the relayed signals (4), when one of the signals is shifted in time by the quantity τ _ki = τ _k −τ _i , i ≠ k.

To find the time shift τ _{ki, we} use the method proposed in [4]. It was shown in [4] that the conversion of relayed signals of the form: Y _m (t) = x _m (t) ⋅x _m (t-T) ^* , (where m = i, k) is invariant to the Doppler frequency shift and allows, in difference from the direct search method for the global maximum of the time-frequency uncertainty function, to determine the delay by a single calculation of the cross-correlation function of such converted signals without searching for the frequency of the Doppler shift. The essence of this method is that before calculating the cross-correlation function, the relayed IRI signals are subjected to additional processing:

- знак комплексного сопряжения.where T is a fixed time shift: T≥1 / (2⋅F); F is the signal spectrum width;

- a sign of complex pairing.

Next, the delay τ _ki is defined as the argument for maximizing the module of the inter-correlation function of the signals Y _k (t) and Y _i (t):

We use the Cauchy-Bunyakovsky-Schwartz inequality [6]:

и g(r) равны с точностью до постоянного множителя.Moreover, equality in (7) is achieved when

and g (r) are equal up to a constant factor.

In relation to signals (5), inequality (7) can be represented as follows:

Taking into account the previously adopted notation in (5), we obtain the formulas of the expressions included in the numerator and denominator (8):

where E _k {t} = A (t-τ _k ) ⋅ A (t-τ _k + T); E _l {t} = A (t-τ _i + τ) ⋅A (t-τ _i + T + τ);

Θ _k {t} = ϕ (t-τ _k ) -ϕ (t-τ _k + T); _{Θ i {t} = φ (} t-τ i + τ) -φ (t-τ i + T + τ);

. Следовательно, можно утверждать, что модуль взаимокорреляционной функции (6) не зависит от величины доплеровского сдвига

.When deriving formula (9), it was taken into account that

. Therefore, it can be argued that the modulus of the cross-correlation function (6) is independent of the magnitude of the Doppler shift

.

Substituting (9) - (11) into (8) we obtain the equivalent inequality:

Based on the properties of the Cauchy-Bunyakovsky-Schwartz inequality [6], it can be argued that if Θ _k {t} -Θ _i {t} ≠ 0, that is, when τ _ki ≠ τ _k -τ _i , the module of the correlation function of signals Y _k (t) and Y _i (t) (the left side of inequality (12)), will be less than unity. If τ _ki = τ _k -τ _i then inequality (12) is transformed into the equality:

It can be seen from (13) that the argument for maximizing the module of the inter-correlation function of the signals Y _k (t) and Y _i (t) (6) is equal to the difference in the propagation times of the IRI signals during relaying by the kth and ith aircraft: τ _ki = τ _k -τ _i . Moreover, when calculating the differences in the propagation times of the signals, it is not necessary to repeatedly calculate the inter-correlation functions for all possible values of the Doppler shifts.

We estimate the gain from the proposed technical solution. Since this solution differs from the prototype in the way of measuring the Doppler frequency shift of the signals during relaying, the comparison will be applied to devices that perform this operation.

When implementing the inventive method on the basis of functional products electronics for measuring delay τ _ki = τ _k -τ _i require two delay lines at a time T and two mixers forming the signals Y _k (t) and Y _{t (t),} and the SAW correlator convolver [2, p. 299-300], on which the indicated delay is measured as the maximum of the correlation integral (6). Doppler shift measurement will require the use of a multi-tap delay line with a switched output [2, p. 290-291, fig. 10.6], a mixer - for generating the product of signals x _k (t) ⋅x _i (t-τ _ki ) ^* and an analog Fourier processor for a SAW [2, p. 274-276]. Therefore, in the proposed method, the implementation of measuring Doppler shift on functional electronics products will require the use of two delay lines for a fixed time T, three mixers, a correlator on a SAW convolver, a multi-tap delay line with a switched output, and an analog Fourier processor.

In the prototype method, the measurement of the Doppler shift for a comparable time interval will require the use of M dispersion delay lines (DLS) on surface acoustic waves (SAWs) having different slopes of the frequency response of the group delay time (GW), compensating for Doppler shifts (M is the number of resolution elements by Doppler shift), and M correlators.

Thus, when using products of functional electronics, the gain will be approximately M times.

, где М - число элементов разрешения по доплеровскому сдвигу.When implemented according to the claimed method of measuring Doppler shift on DSP hardware, it will be necessary to perform 2⋅N multiplications (for generating signals Y _k (t) and Y _i (t) (5)), where N is the signal sample size. To calculate the cross-correlation function of the signals Y _k (t) and Y _i (t) by calculating two FFTs and one IFFT, 3⋅2⋅N⋅log ₂ [2⋅N] arithmetic operations are required [3, p. 14-15]. And finally, when calculating the Doppler shift, N multiplications will be required to generate the signal x _k (t) ⋅x _i (t-τ _ki ) ^* and N⋅log ₂ [N] arithmetic operations to calculate the signal spectrum x _k (t) ⋅ x _i (t-τ _ki ). Thus, when implementing the proposed method on DSP hardware, the total number of arithmetic operations will be N⋅ (9 + 7⋅log ₂ [N]). It follows that in this case, the gain compared to the prototype will be

where M is the number of Doppler shift resolution elements.

Information sources

1. Patent RU: No. 2278395, publ. 06/20/2006

2. Morgan D. Devices for processing signals on surface acoustic waves: Per. from English - M.: Radio and Communications, 1990. - 416 p.: Ill.

3. Digital signal processing: Reference / L.М. Goldenberg, B.D. Matyushkin, M.N. Pole. - M .: Radio and communications, 1985 .-- 312 p., Ill.

4. Patent RU: No. 2568104, publ. November 20, 2015

5. Theory of electrical communication: a training manual / K.K. Vasiliev, V.A. Glushkov, A.V. Dormidontov, A.G. Nesterenko; Under the total. ed. K.K. Vasilieva. - Ulyanovsk: UlSTU, 2008 .-- 452 p.

6. The Cauchy-Bunyakovsky inequality: [Electronic resource] // Wikipedia. URL: http://en.wikipedia.org/wiki/Hepa_Koshi_-_Bunyakovsky_domain (Date of access: 07.12.2015).

Claims (1)

A method for determining the coordinates of a radio emission source (IRI), which consists in receiving IRI signals x _i (t) (t - time) on three aircraft (i = 1, 2, 3), relaying them to the central processing point and calculating the coordinates of the IRI by differences radial velocity directly proportional to the value of the Doppler shift frequency corresponding to a global maximum of the cross correlation function relayed signals, characterized in that the Doppler frequency shifts (Δƒ _ik) as an argument are maximizing the amplitude spectrum mfr Denia signal from one transponder x _k (t) to a signal x _i (t) from another repeater subjected to complex conjugation and to shift the time delay _{τ ki: x k (t)} ⋅x i (t-τ ki) * (i ≠ k; i, k = 1, 2, 3), with a delay τ _ki is determined as an argument maximization module crosscorrelation function converted signals Y _k (t) and Y _i (t), obtained by multiplying the original signals on the same signal, subjected to complex conjugation and a time shift by the interval T: Y _m (t) = x _m (t) ⋅x _m (t-T) ^* , where m = i, k; T≥1 / (2⋅F); F is the signal spectrum width; (o) ^* is the sign of complex conjugation.