RU2293997C1 - Method for correlation processing of signals, reflected from fast-moving targets - Google Patents

Abstract

FIELD: special radio engineering, possible use in systems for detecting and tracking moving objects.

SUBSTANCE: it is known, that movement of object causes Doppler dispersion, making it harder to detect, due to decrease of signal/noise ratio at system output. In accordance to invention, emitted signals are supposed to be transformed in accordance to rule s(t)→s(arctg(t)} in time span. It is determined, that such signals are invariant relatively to acceleration of target, while speed causes only frequency shift of signal without distortion thereof. For correlation processing of received signal, echo signal is returned into original linear scale, realizing operation of interpolation of counts of received signal in accordance to rule s(arctg(t))→s(t)) in real time scale.

EFFECT: response of system, realizing described processing method, is stable during detection and tracking of targets moving at high speeds.

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Description

The present invention relates to the field of special radio engineering and can be used in radio and sonar systems when determining the coordinates and parameters of the target’s movement (KPDTs). As a rule, in radar and sonar systems, correlation processing takes into account the range and radial velocity of the target. In practice, the resolution of a location system is analyzed based on the uncertainty function (FN) of Woodward. The basis of this analysis is the assumption that the speed of the target is constant within the signal duration and negligible distortion of the modulating function. In the proposed technical solution, the radial acceleration of the target is used as an informative additional parameter. The possibility of measuring the radial component of acceleration was considered in [1]. It was also shown [1, p. 46] that for many practical problems in the expression for the velocity estimation error, the term depending on the acceleration can be neglected. Note that when acceleration is taken into account, the form of the FS is complicated [2]. In well-known technical solutions designed to resolve the target in speed in one element of range, acceleration is usually not taken into account [3, 4, 5, 6, 7, 8]. If necessary, the acceleration of the target is estimated indirectly by calculating the time derivative of the target’s speed [9]. The possibility of using one or another model is determined mainly by the signal base. So in [10] the permissible Doppler detuning in a sonar is given, which is

where T is the signal duration, W is its band.

In [11, p. 39] the need to take into account the nth derivative is determined by the order of magnitude

λ / T ⁿ ,

where λ is the wavelength. It is roughly believed that the approximation of the Doppler effect can be used by a simple shift of the spectrum when the condition

With an increase in signal duration, frequency band, target speed, and antenna device size, such approximations are unacceptable [12]. So, for example, when working with low-frequency, long-term and wideband signals in sonar, a small change in the radial velocity during the existence of the signal leads to decorrelation and significantly affects the characteristics of the system [10].

A similar effect is observed in radar tracking systems for such fast targets as satellites and guided missiles [13].

In such cases, it becomes necessary to match the received acceleration signal. In [11], a method for determining the range and radial velocity is disclosed. On Wednesday, a signal is emitted from a hyperbolic FM, shifted to the region of the carrier frequency, of the form:

where f ₁ is the carrier frequency, F, k are constants.

When receiving, a multi-channel Doppler filtering of the echo signal is carried out, the signal is heterodyne to the low-frequency region, it is temporarily delayed to compensate for errors in measuring the target range, a consistent filtering is performed, and the response is compared with a threshold.

From the time interval between the moments when the threshold is exceeded and the radiation from the probe pulse, the target range is determined, the radial speed of the target is found by the number of the Doppler channel where the threshold was exceeded. The time interval for error correction is determined by the ratio:

where ν _p is the radial velocity, c is the wave propagation velocity. The considered method allows for independent resolution in range and speed in one package. However, Doppler filtering is retained.

Close in technical essence to the proposed invention is the CAVORT system (a system for processing echo signals from targets with significant radial acceleration) [14]. This system works as follows: received pulses are passed through a delay line (LZ) at an intermediate frequency with a total number of taps, where N is the number of processed pulses. These taps are connected to two rows of mixers. The top row of mixers produces frequency shifts fv, 2fv, 3fv, ..., (N-1) fv. The resulting shifts at any given time are given at some given target speed. The adjustment of this coordination for targets experiencing acceleration of movement is achieved by a further shift provided by the second row of mixers. This nonlinear set of frequencies Fa, 3fa, 6fa, 10fa, ..., N (N + 1) fa / 2 at any moment in time is in phase with the signal for a certain value of radial acceleration. When fv≫fa, a search is made for speed and acceleration so that the speed and acceleration characteristics of the target are matched at some point in time on an interval of 1 / fa.

Thus, the considered method for estimating the radial acceleration of a target is as follows. A packet of probe pulses is emitted, received, amplified, matched filtering is carried out according to all possible values of radial velocities and accelerations, echo signals are combined in time and coherently summed, the resulting signal is compared with a threshold voltage and the target acceleration is determined by the value of the signal phase corresponding to the moment the threshold is exceeded. This method allows you to fully determine all the parameters of the movement of the target (speed and acceleration).

The disadvantage of this method is the complexity of its technical implementation. Since the optimal filter must be consistent with both radial velocity and radial acceleration, a set of such two-dimensional filters is required to process signals with different pairs of velocity and acceleration values. The required number of filters is very large and amounts to several hundred. In addition, for the operation of the device requires a sequence (at least two) of probe pulses.

, где ^* - представляет собой символ комплексного сопряжения. К результату перемножения применяется преобразование Фурье, в результате которого получают спектральную взаимно корреляционную функцию (ВКФ) вида:

Closest to the proposed invention is a method of consistent filtering of the received signal [15] (PROTOTYPE). The considered method makes it possible to isolate the signal against the background of interference in the conditions of the Doppler effect. The essence of the method is as follows. A probe pulse is emitted into the medium. The received echo and reference signal are multiplied

where ^* - is a symbol of complex conjugation. The Fourier transform is applied to the result of multiplication, as a result of which a spectral cross-correlation function (CCF) of the form is obtained:

where ν is the frequency shift of the echo due to the Doppler effect. If the signals in the time domain are real, then the corresponding correlation operations in the frequency domain are identical to the convolution operation. The resulting response of the correlation function is compared with a threshold voltage. Processing is carried out in real time, i.e. samples of the input implementation are updated in accordance with the Kotelnikov theorem. Exceeding the threshold value occurs at the time of delay compensation τ = 0. In this case, a decision is made to detect the target, and the moment itself will correspond to the distance to the target. The considered method is optimal in terms of signal-to-noise ratio for a deterministic signal. However, it does not allow avoiding losses in the signal-to-noise ratio under conditions of a variable Doppler effect. The aim of the invention is to increase noise immunity by reducing losses in relation to signal / noise associated with variable Doppler dispersion due to a change in the Doppler parameter within the signal duration.

, выполняемой в пределах временного интервала между двумя соседними отсчетами.This goal is achieved by the fact that the method of correlation processing of signals reflected from fast moving targets, based on the radiation of the probe signal, correlation processing of the received process in real time, which consists in multiplying the received echo signal with a copy of the emitted signal, calculating the Fourier transform from the result of multiplication, finding the square module, comparing the received response of the square of the module with a threshold voltage, further comprises probing operations a signal s (arctg (t)) before radiation according to the law, where t - current time interpolation of samples of the received signal according to the law

performed within the time interval between two adjacent samples.

таким образом, в среду излучается сигнал с эллиптической ЧМ от верхних частот к нижним вида:The essence of the method is as follows. The initial signal, which is a segment of the tonal pulse S (t) = cos (2 · π · f ₀ · t), is subjected to temporary transformation according to the law

Thus, an elliptical FM signal is emitted from the upper frequencies to the lower ones:

where t ₀ is the moment corresponding to the beginning of the signal,

f ₀ is the initial frequency,

β is a scale factor,

After a temporary conversion of the echo signal reflected from the moving target, the samples of the received signal are interpolated and mutually correlated (VKF) with the reference signal in real time.

The time interval between the moments of reception and emission of the signal τ corresponds to the range to the target. The echo signal as a result of the Doppler conversion has the form

- доплеровский параметр,Where

- Doppler parameter,

where α is the radial velocity of the target and β is the radial acceleration of the target.

The hypothesis is accepted that the radial acceleration is constant, and the radial velocity changes over the duration of the pulse. In other words, the range r (t) is approximated by the Taylor series up to the second term of the expansion. Such a Doppler effect will be called a variable. The variable Doppler parameter can be written as:

where r ⁽¹⁾ (t) = ν (t) is the relative speed of the source and receiver.

The variable Doppler parameter acts for a time according to the rule:

The time conversion in the current Doppler transformation is functional in nature.

Another characteristic of the Doppler effect is the conversion speed of the time carrier:

Note that the values of the current Doppler parameter do not coincide with the conversion rate of the time carrier, but these functions are locally close. Indeed, expanding (0.2) into a Taylor series and restricting ourselves to two terms of the expansion, we have

в (0.4) перепишемAssuming

in (0.4) we rewrite

A comparison of (0.3) with (0.5) proves the above.

Consider the representation of signals, taking into account the speed of conversion of the time carrier. The time transformation (up to a delay) can be found by integrating relation (0.3)

which coincides up to a delay with (0.3).

The time transformation taking into account the parameter β is called the variable Doppler effect [4, 5].

The variable Doppler effect can be approximately written as a single parameter φ

which corresponds to a matrix of the form:

Indeed, relation (0.7) is written as a composition of three matrices:

The first class of matrices is responsible for the shift of the signal in time, the second, of the hyperbolic type, is responsible for the Doppler transformations, and the third is for the variable Doppler effect [5].

т.е. преобразование, отвечающее за изменение доплеровского параметра во времени. В реальных условиях локации объектов параметр φ является малым. А коэффициенты матрицы второго класса имеют второй порядок малости. Действительно при малом параметре

Поскольку система по определению инвариантна относительно сдвига, то коэффициенты первой матрицы не оказывают влияние на преобразование сигнала. Так как сигнал в эллиптическом временном масштабе будет представлять собой отрезок гармонического сигнала, а в обычном временном масштабе он будет являться искаженным, то для его перехода к равномерному масштабу времени нам необходимо произвести интерполяцию отсчетов принятого эллиптического сигнала по тангенциальному закону.Thus, the group of transformations associated with matrices (0.9) includes shifts, Doppler transformations, and a variable Doppler effect. From the analysis of (0.9) it follows that for a small parameter φ the main contribution will be made by the transformation

those. transformation responsible for the change in the Doppler parameter in time. Under real conditions of location of objects, the parameter φ is small. And the coefficients of the matrix of the second class are of the second order of smallness. Valid for a small parameter

Since the system, by definition, is invariant with respect to the shift, the coefficients of the first matrix do not affect the signal transformation. Since the signal in the elliptical time scale will be a segment of the harmonic signal, and in the usual time scale it will be distorted, to transfer it to a uniform time scale, we need to interpolate the samples of the received elliptical signal according to the tangential law.

The next step is the selection of a signal approaching with great accuracy to a signal that is invariant with respect to the elliptical transformation. This signal is a signal of the form:

where f ₀ is the elliptical frequency,

T is the signal duration (0.10), where

Relation (0.10) defines the operation of generating a radiated signal from a tone segment.

After discretization of the received signal, interpolation is carried out according to its samples. This signal is a signal of the form (0.9). The use of this signal is due to the fact that in its scale it is a segment of an exponential tone signal. To implement a signal on its scale, it is necessary to interpolate it according to the law:

A numerical experiment showed that the signal (0.10) is invariant with respect to the elliptic transformation. We also note that the signal standard for the correlator must be complex

A device that implements the proposed method for detecting and filtering echoes from fast moving targets, is presented in figure 1.

It contains:

The master generator (ZG) - 1

Switch - 2

Elliptical Signal Transformation Block - 3

Digital to Analog Converter (DAC) - 4

Emitter - 5

The first synchronization block is 6

The second block synchronization - 7

Receiver - 8

Analog-to-Digital Converter (ADC) - 9

Delay Element (ES) - 10

Interpolation block - 11

Multiplication Block - 12

Fast Fourier Transform Unit (FFT) - 13

Unit square calculator - 14

Threshold block - 15

Analysis and Decision Making Unit - 16

ZG 1 is a probe pulse generator and can be implemented in digital form [16].

The first synchronization unit 6 generates spiky pulses that determine the repetition rate of the probing signals. These pulses are used to start the emitter and as reference range signals, i.e. to measure the delay time of the echo signal in the block analysis and decision 16 [17].

The signal conversion unit according to elliptic law 3 is made in digital implementation and performs the conversion in accordance with expression (0.1). The signal on an elliptical scale is presented in Appendix 1 (Fig. 2). The second synchronization unit 7 generates clock pulses that synchronize the operation of the DAC, ADC, EZ.

EZ 10 provides processing of the input implementation in real time. As an EZ, digital delay lines with recirculation (RLS) can be used [18].

где fν - верхняя частота среза спектра сигнала. Допустим, что сигнал имеет fν=5 кГц и содержит N=1024 отсчета. Длительность его при этом составит

Если шкала гидролокатора составляет D_max=30 км, а максимальный интервал корреляции

в этом случае между с моментом излучения и приема сигнала на вход устройства (без учета мертвой зоны) поступит

отсчетов.Let us explain the essence of the operation of the delay element based on radar. Compensation of the delay τ of the echo signal relative to the probe pulse is as follows. The radar receives samples of the input signal with a sampling interval

where fν is the upper cut-off frequency of the signal spectrum. Suppose that the signal has fν = 5 kHz and contains N = 1024 samples. In this case, its duration will be

If the sonar scale is D _max = 30 km, and the maximum correlation interval

in this case, between the moment of emission and reception of the signal at the input of the device (excluding the dead zone)

counts.

In this sequence, it is necessary to identify the samples corresponding to the useful echo signal. The total radar delay time is (N-1) · ΔT, where ΔT is the delay time between adjacent taps.

The sampling interval of the input signal is equal to the total delay time of the radar.

In our case

The second radar continuously recycles the reference signal. The obtained next implementation count is shifted along the entire first radar and is recycled in such a way that it is at the output of the second radar tap by the time the next count is taken. After that, the process is repeated and thus the last N-1 implementation counts will be located on the radar branches.

The Fast Fourier Transform Unit (FFT) 14 is designed to find the spectral density of a signal and is widely used in digital signal processing [19]. The response at the output of block 19 is a VKF given in Appendix 1 (Fig. 6).

The interpolation unit 11 is designed to interpolate the samples of the received signal and the standard according to the tangential law (0.11). Timing diagrams of the received and interpolated signals are given in Appendix 1 (Fig. 4).

In the analysis and decision block 16, when the threshold value is exceeded, a decision is made to detect the target, and the distance to the target is determined from the measured time interval between the moments of radiation of the probe pulse and the threshold is exceeded.

To verify the reliability of the proposed method and the device that implements it, modeling was carried out on a PC in the MathCad environment. The simulation results are given in Appendix 1.

The device as a whole operates as follows. The signal from the output of the probe pulse generator 1 enters the conversion unit according to the elliptic law (0.1). The received signal on an elliptical scale of the form (0.1) after digital-to-analog conversion in block 4 through a switch 2 is transmitted from the synchronization block 6 to the emitter 5 for emission into the medium from the synchronization block 6. The reflected echo signal from the output of the ADC 9 with the sampling frequency determined by Kotelnikov’s theorem fd≥2 · fw is fed to the input of the EZ 10, where a sample of the input implementation with the length of N-1 samples is generated and updated with each new sample.

In the block of interpolation 11, the input implementation is transformed according to the law (0.11), after which the signal becomes a tone. The generated current discrete sample of the converted signal is multiplied with a discrete sample of a copy of the reference signal, the result of the multiplication is fed to the input of the fast Fourier transform unit 13. From the output we obtain a spectral cross-correlation function

где с - скорость распространения колебаний.calculated at each moment of time taken with ADC discreteness at the receiver input, where ν is the frequency shift of the echo signal due to the Doppler effect (the timing diagram is shown in Appendix 1). After calculating the square of the module in block 14, the result is compared with the threshold in threshold block 15. If the threshold is exceeded in BA and PR 16, a decision is made about the presence of a useful signal. Since the input implementation is constantly updated, i.e. the processing is carried out in real time, measured in BA and PR 16 the time interval τ between the moments of radiation of the probe signal and exceeding the threshold in block 16 will correspond to the distance to the target

where c is the velocity of oscillation propagation.

Literature

1. Kelly. Radar measurement of range, speed and acceleration. Foreign Radio Electronics (ЗР), No. 2, 1962, p. 35-46.

2. Reference radar. Ed. Skolnik M., Sov. Radio, Volume 3, 1976, p. 122.

3. A.S. No. 537315 (USSR) dated 11.30.76. A method for determining the speed of a vessel relative to the bottom.

4. US patent No. 4282589, 1981. The correlation method of measuring range.

5. US patent No. 3938147, 1976. FM Doppler range measuring system.

6. Application No. 1482816 United Kingdom. Method and device for measuring Doppler frequency shift.

7. Application No. 2605933 Germany. A method of measuring distance and speed based on the use of a pulsed Doppler radar.

8. Application No. 56-41953 Japan 1981. A method and apparatus for measuring distance using a continuous-wave radar with FM.

9. A.S. No. 687427 (USSR). Device for digital signal analysis.

10. Cramer. Permissible detuning of speed and acceleration in highly sensitive broadband correlation sonars with linear FM, TIIER vol. 55 No. 5, 1967, p.3.

11. Rikhachek. Signals that are acceptable in terms of the Doppler effect. TIIER vol. 54 No. 6, 1966, p. 39-41.

12. Rikhachek. Resolution of moving targets in radar. ЗР №1, 1968, p.3.

13. Kelly, Wischner. Theory of consistent filtering of targets moving accelerated at high speeds. ZR No. 10, 1965, p. 38.

14. Kibler. KEVORT - device for optimal processing of a burst radar signal taking into account acceleration of targets, 1968, p. 27-33.

15. Burdick B.C. Analysis of sonar systems. L., Shipbuilding. 1988, p. 194 (PROTOTYPE).

16. Knight W. Digital signal processing in sonar systems. TIIER vol. 69 No. 11, 1981, p. 127.

17. Belotserkovsky G. Fundamentals of radar and radar devices. M., Sov. Radio, 1975, p. 25-26.

18. The use of digital signal processing, ed. Oppenheim E.M. World, 1980, p. 417-418.

19. Korneev V., Kisilev A. Modern microprocessors. M., ed. Nolidzh, 1998, p.136-138.

Annex 1

The program for the formation of a correlation receiver with elliptical modulation of signals.

Set the weighted rectangular window:

Set the number of elliptical waves:

Nw: = 128

Set the elliptical signal duration:

T0: = π

Determine the elliptical frequency of the signal:

f0=40.744

f0 = 40.744

Band expansion coefficient: β: = 1

Set the source signal:

s (t): = exp (-i · 2 · π · f0 · t) · rect (t)

We carry out the modulation of the signal according to the elliptic law:

Sample the received signal:

H: = 10 n: = 0 ... 2 ^H -1 N: = 2 ^H γ: = 1

t _n : = n

s2 _n : = s1 (t _n )

D _n : = n

Performing signal interpolation according to the tangential law:

Ssum: = cfft (sumsig)

Claims (1)

A method for detecting fast moving targets, which consists in emitting a probe signal s (t), where t is the current time, receiving the signal reflected from the target in real time in the form of samples, multiplying the received signal with a copy of the emitted signal, and performing the Fourier transform of the multiplication result forming a cross-correlation function, find the square of the module of the converted signal, compare the received signal with a threshold, upon exceeding which they decide to detect the target, characterized in that q the radiation generates a probe signal according to the law s (arctan (t), when receiving the signal reflected from the target, interpolation of the samples of the received signal according to the law

performed within the time interval between two adjacent samples.

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