RU2515580C1 - Method to measure external ballistic characteristics of projectile and device for its realisation - Google Patents

Abstract

FIELD: measurement equipment.SUBSTANCE: method is based on radiation of electromagnetic energy in direction of projectile movement, reception of electromagnetic energy reflected from the projectile, conversion of an analogue signal into digital form, recording of signals into a memory unit, generation of a sequence of discrete values of its current speed by realisations of a Doppler echo-signal of the projectile, calculation of the initial speed of the projectile using the current speed with account of the established delay in the start of its observation relative to the moment of flight from the weapon barrel, definition of the frequency of harmonics of secondary modulation of the echo-signal in the spectrum of the Doppler echo-signal, caused by asymmetry of distribution of the mass of the projectile relative to its longitudinal axis, calculation of the angular speed of projectile rotation around the longitudinal axis using frequencies that correspond to maxima of the first paired harmonics of the secondary modulation of the Doppler echo-signal. The device that realises the method comprises a Doppler radar, a key, a delay line, an analogue-to-digital converter, a memory block, a data processing block, an indicator of projectile motion speed, an indicator of spectrum width, an indicator of angular speed of projectile rotation, which are in a certain manner made and connected to each other.EFFECT: higher information value of measurements.6 cl, 6 dwg

Description

The invention relates to measuring systems, and in particular to means of radar observation of the trajectories of ballistic objects, and can be used to measure external ballistic characteristics of shells.

A known method of measuring the initial velocity of the projectile [1], according to which the implementation of the Doppler echo signal of the projectile form a sequence of discrete values of its current speed and calculate the initial velocity of the projectile based on the set delay of the start of its observation relative to the time of departure from the gun’s barrel, for each position in the obtained sequence of discrete values of the current velocity of the projectile, the reliability of the data contained in them is evaluated and, taking into account the results obtained, is isolated in this after ovatelnosti portion mainly containing valid data, which determine the initial velocity of the projectile, the data in the evaluation of the current projectile velocity validity criteria used, considering the accuracy requirements asked measuring muzzle velocity; when forming a section of the mentioned sequence for calculating the initial velocity of the projectile, the beginning of this section is determined by the presence of at least three consecutive positions with reliable data, and its end - by the presence of two or more positions with false data; used to calculate the initial velocity of the projectile, the delay time of the start of the observation is the sum of the set delay and the total duration of the implementation of the Doppler echo signal preceding the first position in the data area formed to calculate the initial velocity of the projectile; if there are single positions with inaccurate data in a selected section of the sequence of discrete values of the current projectile velocity, the data contained in such single positions is replaced by the average value of reliable data from two directly adjacent positions of this section, the reliability of the data on the current velocity of the projectile is checked by exceeding the actual ratio signal / noise of its value, which is necessary to ensure a given accuracy of determining the initial velocity of the projectile, reliability yes data on the current velocity of the projectile is estimated from changes in the values of the current velocity of the projectile presented at adjacent positions in the obtained sequence, while first, by the magnitude of these changes, zones containing inaccurate data are detected, and then by reliable data obtained from positions directly adjacent to these zones , determine for each position in the detected zone the expected speed values and localize each position with inaccurate data, and those positions for which the changes made in the values of the current velocity of the projectile do not exceed the value of the specified error in measuring the initial velocity of the projectile, determine the spectrum width of the Doppler echo signal, determine the area of the maximum section of the projectile by a plane perpendicular to the line of sight of the projectile, judging by the change in this area at each position, the nutation value is shell.

A device for measuring the initial velocity of the projectile [1], containing a computer, a series-connected Doppler radar, a shaper implementation of the Doppler echo signal and a shaper of discrete values of the current velocity of the projectile, as well as a series-connected pulse shaper photo-start and timer, the output of which is connected to the second input of the shaper the implementation of the Doppler echo, the second timer input is connected to the initial delay time sensor, and the third timer input is connected to the second output of the Doppler radar, an implementation counter, a buffer memory, a data reliability analyzer, a data generator for calculating the initial velocity, a meter for the total duration of the initial implementation and an adder, while one output of the discrete value generator of the current projectile speed and the output of the implementation counter are connected to data input inputs a buffer memory device, the recording control input of which, together with the counting input of the implementation counter, is connected to the second the output of the shaper of discrete values of the current velocity of the projectile, and the data output of the buffer storage device is connected to the input of the data reliability analyzer, which is connected through the shaper to calculate the initial speed to the first input of the calculator, the second input of which is connected to the adder, the first input of which is connected to the initial time sensor delays, and the second input through the meter of the total duration of the initial implementations is connected to the second output of the data shaper to calculate the initial speed, as well as series-connected fast Fourier transform calculation unit, spectrum width estimator and indicator, while the input of the fast Fourier transform calculation unit is connected to the output of the Doppler radar.

A disadvantage of the known method and device is the low information content due to the fact that during the test only two external ballistic characteristics of the projectile are measured - its initial velocity and angle of nutation, and the angular velocity of rotation of the projectile relative to the longitudinal axis is not determined.

An object of the invention is to expand the information content of the method and device by additionally determining the angular velocity of rotation of the projectile relative to the longitudinal axis.

угловую скорость вращения снаряда вокруг продольной оси, где f_вр=(f₁-f₂)/2, f₁ и f₂ - частоты, соответствующие максимумам первых парных гармоник вторичной модуляции доплеровского эхо-сигнала.The essence of the invention lies in the fact that in the method of measuring the external ballistic characteristics of the projectile, which consists in emitting electromagnetic energy in the direction of movement of the projectile, receiving electromagnetic energy reflected from the projectile, converting the analog signal to a digital form, recording signals in a memory unit, forming a sequence of discrete values of it the current speed for the implementation of the Doppler echo of the projectile, the calculation of the current speed of the initial velocity of the projectile taking into account the delayed start of its observation relative to the moment of departure from the gun’s barrel, evaluating the reliability of discrete values of the current velocity of the projectile for each position in the obtained sequence of data contained in them, selecting, taking into account the results obtained in this sequence, a section containing mainly reliable data by which the initial velocity is determined projectile, while evaluating the reliability of data on the current velocity of the projectile using criteria that take into account the specified requirements Measurement accuracy muzzle velocity, the formation portion of said sequence for calculating the muzzle velocity of the top portion is determined by the presence of at least three consecutive positions with valid data, and its end - by the presence of two or more positions with invalid data; used to calculate the initial velocity of the projectile, the delay time of the start of the observation is the sum of the set delay and the total duration of the implementation of the Doppler echo signal preceding the first position in the data area formed to calculate the initial velocity of the projectile; if there are single positions with inaccurate data in a selected section of the sequence of discrete values of the current projectile velocity, the data contained in such single positions is replaced by the average value of reliable data from two directly adjacent positions of this section, the reliability of the data on the current velocity of the projectile is checked by exceeding the actual ratio signal / noise of its value, which is necessary to ensure a given accuracy of determining the initial velocity of the projectile, reliability yes data on the current velocity of the projectile is estimated from changes in the values of the current velocity of the projectile presented at adjacent positions in the obtained sequence, while first, by the magnitude of these changes, zones containing inaccurate data are detected, and then by reliable data obtained from positions directly adjacent to these zones , determine for each position in the detected zone the expected speed values and localize each position with inaccurate data, and those positions for which the changes made in the values of the current velocity of the projectile do not exceed the value of the specified error in measuring the initial velocity of the projectile, determine the spectrum width of the Doppler echo of the signal, determine the area of the maximum section of the projectile by a plane perpendicular to the line of sight of the projectile, judging by the change in this area at each position, the value of the nutation of the projectile , additionally, in the spectrum of the Doppler echo signal, the harmonics frequencies of the secondary modulation of the echo signal caused by the asymmetry of the distribution The mass of the projectile relative to its longitudinal axis is calculated by the formula $$\dot{\gamma }=2\pi f_{\mathrm{at}R}$$

the angular velocity of rotation of the projectile around the longitudinal axis, where f _BP = (f ₁ -f ₂ ) / 2, f ₁ and f ₂ are the frequencies corresponding to the maxima of the first pair harmonics of the secondary modulation of the Doppler echo signal.

The inventive method is implemented in a device for measuring the extrinsic ballistic characteristics of a projectile containing a Doppler radar, a spectral width indicator, in which a key, a delay line, an analog-to-digital converter, a memory unit, a data processing unit, an indicator of the initial velocity of the projectile and an indicator of the angular velocity of rotation of the projectile are entered moreover, the output of the Doppler radar is connected to the first input of the key, the second input of which is connected to the output of the delay line, the input of which is connected to the output ind a sensor located on the barrel bore of a missile body, and an output with an input of an analog-to-digital converter, the output of which is connected to the input of the memory unit, the output of which is connected to the input of the signal processing unit, the first, second, and third outputs of which are connected respectively to the inputs of the indicator of the initial velocity of the projectile , an indicator of the width of the spectrum and an indicator of the angular velocity of rotation of the projectile.

In addition, the data processing unit consists of a data reliability analyzer, a spectrum width determination unit, a projectile angular velocity determination unit, wherein the input of the signal processing unit is an input of a data reliability analyzer, the output of which is connected to the input of a spectrum width determination unit and an angular velocity determination unit the rotation of the projectile, the outputs of the data reliability analyzer, the unit for determining the width of the spectrum and the unit for determining the angular velocity of rotation of the projectile are respectively the first, in the second and third outputs of the signal processing unit.

In addition, the algorithm of the data reliability analyzer consists in evaluating the accuracy of the discrete values of the current projectile velocity for each position in the obtained sequence of contained data, selecting, taking into account the results obtained in this sequence, a section containing mainly reliable data by which the initial velocity of the projectile is determined, while when assessing the reliability of data on the current velocity of the projectile using criteria that take into account the specified requirements for accuracy measurement the initial velocity of the projectile; when forming a section of the mentioned sequence for calculating the initial velocity of the projectile, the beginning of this section is determined by the presence of at least three consecutive positions with reliable data, and its end - by the presence of two or more positions with false data; used to calculate the initial velocity of the projectile, the delay time of the start of the observation is the sum of the set delay and the total duration of the implementation of the Doppler echo signal preceding the first position in the data area formed to calculate the initial velocity of the projectile; if there are single positions with inaccurate data in a selected section of the sequence of discrete values of the current projectile velocity, the data contained in such single positions is replaced by the average value of reliable data from two directly adjacent positions of this section, the reliability of the data on the current velocity of the projectile is checked by exceeding the actual ratio signal / noise of its value, which is necessary to ensure a given accuracy of determining the initial velocity of the projectile, reliability yes data on the current velocity of the projectile is estimated from changes in the values of the current velocity of the projectile presented at adjacent positions in the obtained sequence, while first, by the magnitude of these changes, zones containing inaccurate data are detected, and then by reliable data obtained from positions directly adjacent to these zones , determine for each position in the detected zone the expected speed values and localize each position with inaccurate data, and those positions for which iziruemye change the current projectile velocity values do not exceed the value given by the measurement error of the initial velocity of the projectile, the projectile speed is determined in accordance with the expression

, $$V=\frac{\Delta f\lambda }{2_{\cos }\Delta \varphi }$$

,

where Δf is the Doppler frequency, λ is the wavelength, Δφ is the observation angle.

In addition, the unit for determining the width of the spectrum operates in accordance with the algorithm, the essence of which is to calculate the module of the fast Fourier transform

$$S_n=|\; |\; |{\displaystyle \sum _{k=0}^{N-\mathrm{one}}{y}_k\exp \left(-j\frac{2\pi nk}{N}\right)}|\; |\; |,n=0...N-\mathrm{one,}$$

определение величины порога:where y _k = y (k / F _d ) is the input signal y (t) digitized by an analog-to-digital converter, F _d is the sampling frequency of the original signal, N is the number of DFT samples, S _n is the actual amplitude of the nth spectral harmonic, frequency which can be defined as: $$f_n=\frac{n}{N}{F}_d,$$

threshold value determination:

$$S_{P\mathrm{about}R}=\sqrt{-2\cdot {\sigma }_w^2\cdot \ln \left(P_{lt}\right)},$$

where P _lt is the probability of false alarm, which in practice is usually

- дисперсия шума, значение которой можно вычислить, проанализировав БПФ выходного сигнал радиолокатора при отсутствии движущихся объектов в его зоне видимости на соответствие закону распределения Релея, обнуление гармоник, не превысивших значение порога S_пор и находящихся в области ожидаемых частот Доплера:taken equal to 10 ^-5 , $${\sigma }_w^2$$

- noise dispersion, the value of which can be calculated by analyzing the FFT of the radar output signal in the absence of moving objects in its field of view for compliance with the Rayleigh distribution law, zeroing harmonics that do not exceed the threshold value S _then and are in the range of the expected Doppler frequencies:

$$S_n^{\text{'}\text{'}}=\{\begin{array}{l}{S}_n,PR\mathrm{and}\left(S_n>S_{P\mathrm{about}R}\right)\wedge \left(f_{\mathrm{about}\mathrm{well}.\min }<f_n<f_{\mathrm{about}\mathrm{well}.\max }\right)\\ 0PR\mathrm{and}\left(S_n<S_{P\mathrm{about}R}\right)\vee \left(f_{\mathrm{about}\mathrm{well}.\min }>f_n\right)\wedge \left(f_n>f_{\mathrm{about}\mathrm{well}.\max }\right)\end{array},$$

where f _ozh.min , f _ozh.max. - the lower and upper boundaries of the region of the expected Doppler frequencies, respectively, the determination of the width of the spectrum of the signal:

, $$f_{c.\min }=\underset{S_n^{*}\ne 0}{\min \left(f_n\right)}$$

,

, $$f_{c.\max }=\underset{S_n^{*}\ne 0}{\max \left(f_n\right)}$$

,

Δf = f _c.max -f _c.min ,

where f _c.min is the lower limit of the signal spectrum, f _c.max is the upper limit of the signal spectrum, Δf is the width of the signal spectrum, determined by the width of the spectrum of the area of the maximum projectile cross section by a plane perpendicular to the line of sight of the projectile, determining the value of the nutation of the projectile by changing this area at each position.

In addition, the unit for determining the angular velocity of rotation of the projectile operates in accordance with the algorithm, the essence of which is to calculate the frequencies of the harmonics of the secondary modulation in the amplitude-frequency spectrum of the selected measurement section, while upon receipt of the amplitude-frequency spectrum, an algorithm for compensating the influence of phase modulation of the reflected radar signal is used :

- determination of the complex spectral amplitude at the output of the FFT algorithm:

$${\dot{S}}_n={\displaystyle \sum _{k=0}^{K-\mathrm{one}}{\dot{s}}_k}\exp \left(-j\frac{2\pi nk}{K}\right),n=0...N-\mathrm{one}\left(N=K\right),$$

- выбранный участок отраженного эхо-сигнала, K - число отсчетов выбранного участка сигнала,Where $${\dot{s}}_k$$

- the selected portion of the reflected echo, K is the number of samples of the selected portion of the signal,

- determination of the spectrum boundary of the dominant harmonic:

N _e.min = (n _pl -Δn _pl / 2);

N _e.max = (n _pl + Δn _pl / 2),

where [N _e.min , N _e.max ] is the interval of spectral samples containing the frequencies of the dominant harmonic, n _pl is the frequency position of the maximum spectral amplitude, Δn _pl is the a priori specified width of the search interval of the energy center of the spectrum of the dominant harmonic,

- determination of the energy center of the spectrum of the dominant harmonic, by the squares of the spectral amplitudes:

$$N_{\mathrm{uh}.c}=\underset{k\in \left[N_{\mathrm{uh}.\min },N_{\mathrm{uh}.\max }\right]}{\arg \max \left(E_k\right)},$$

n_c - априорно известная ширина спектра доминирующей гармоники, выделение спектра сигнала, отраженного от снаряда, и осуществление дополнения его нулями:Where $$E_k={\displaystyle \sum _{i=-n_c/2}^{n_c/2}{|\; |\; |{\dot{S}}_{k+i}|\; |\; |}^2;}$$

n _c is the a priori known spectrum width of the dominant harmonic, the allocation of the spectrum of the signal reflected from the projectile, and the implementation of its complement by zeros:

$$\{\begin{array}{l}{\dot{S}}_{Pl.n}={\dot{S}}_{n}PR\mathrm{and}N{}_{\mathrm{uh}.c.}-n_f/2\le n\le N_{\mathrm{uh}.c.}+n_f/2\\ {\dot{S}}_{Pl.n}=0PR\mathrm{and}n<N_{\mathrm{uh}.c.}-n_f/2;n>N_{\mathrm{uh}.c.}+n_f/2\end{array}$$

,where n _f is the width of the spectrum of the signal reflected from the projectile, including the harmonics of the secondary modulation, conducting a cyclic shift of the spectrum so that the energy center of the spectrum is in the zero position in accordance with the expression: $${\dot{S}}_{\mathrm{to}\mathrm{about}R.n}={\dot{S}}_{Pl.n+N}{}_{\mathrm{uh}.c.}$$

,

и получение корректирующего сигнала:- the implementation of the operation of the inverse FFT spectrum $${\dot{S}}_{\mathrm{to}\mathrm{about}R.n}$$

and receiving a correction signal:

, $${\dot{s}}_{\mathrm{to}\mathrm{about}R.k}=\frac{\mathrm{one}}{K}{\displaystyle \sum _{n=0}^{K-\mathrm{one}}{\dot{S}}_{\mathrm{to}\mathrm{about}R.n}\exp \left(j\frac{2\pi nk}{K}\right)}$$

,

на комплексно-сопряженный корректирующий сигнал $${\dot{s}}_{кор.k}^{\ast }$$

и выполнение операции БПФ:- implementation of the multiplication of the original signal $${\dot{s}}_k$$

to complex conjugate correction signal $${\dot{s}}_{\mathrm{to}\mathrm{about}R.k}^{\ast }$$

and FFT operation:

, $$Z_n=|\; |\; |{\displaystyle \sum _{k=0}^{K-\mathrm{one}}{\dot{s}}_k{\dot{s}}_{\mathrm{to}\mathrm{about}R.k}^{\ast }}\exp \left(-j\frac{2\pi nk}{K}\right)|\; |\; |$$

,

- selection from the spectrum of the echo signal Z _{n of} two pairs of harmonics of the secondary modulation, located closest to the dominant harmonic, and determining the values of the frequencies f ₁ and f ₂ at which they reach a maximum,

- calculation of the angular velocity of rotation of the projectile around the longitudinal axis according to the formula

$$\dot{\gamma }=2\pi f_{\mathrm{at}R}$$

where f _BP = f ₁ -f ₂ ) / 2, f ₁ and f ₂ are the frequencies corresponding to the maxima of the first pair harmonics of the secondary modulation of the Doppler echo signal.

New features that have significant differences in the method is the following set of actions:

1. In the spectrum of the Doppler echo signal, the harmonics frequencies of the secondary modulation of the echo signal caused by the asymmetry of the mass distribution of the projectile relative to its longitudinal axis are determined;

угловую скорость вращения снаряда вокруг продольной оси, где f_вр=(f₁-f₂)/2, f₁ и f₂ - частоты, соответствующие максимумам первых парных гармоник вторичной модуляции доплеровского эхо-сигнала.2. For given positions, the measurements are calculated by the formula $$\dot{\gamma }=2\pi f_{\mathrm{at}R}$$

the angular velocity of rotation of the projectile around the longitudinal axis, where f _BP = (f ₁ -f ₂ ) / 2, f ₁ and f ₂ are the frequencies corresponding to the maxima of the first pair harmonics of the secondary modulation of the Doppler echo signal.

New elements that have significant differences in the device are a key, a delay line, an analog-to-digital converter, a memory unit, a signal processing unit, an indicator of the initial projectile speed and an indicator of the angular velocity of the projectile and the connection between known and new elements of the device.

The inventive method and device are the result of research and experimental work.

Figure 1 shows the diagram of the experiments, where 1 is a device for measuring the external ballistic characteristics of the projectile, 2 is a propelling device, 3 is an induction sensor, 4 is a missile body, figure 2 is a structural diagram of the proposed device for measuring the external ballistic characteristics of the projectile, where 5 - Doppler radar, 6 - key, 7 - delay line, 8 - analog-to-digital converter, 9 - memory unit, 10 - data processing unit, 11 - projectile speed indicator, 12 - spectrum width indicator, 13 - rotation angular speed indicator projectile, in Fig. 3 is a structural diagram of a data processing unit, where 14 is a data reliability analyzer, 15 is a spectrum width determination unit, 16 is a unit for determining the angular velocity of the projectile rotation, in Fig. 4 is a data reliability analyzer operation algorithm, in Fig. .5 shows the law of motion of the projectile, Fig.6 shows the amplitude-frequency characteristic of the signal reflected from the projectile.

A device for measuring the external ballistic characteristics of a projectile operates as follows.

When you press the combat button, the device 1 for measuring external ballistic characteristics is simultaneously launched and the throwing device 2 is triggered, while at the moment the projectile leaves the barrel channel, the induction sensor 3 is activated (Fig. 1).

The Doppler radar 5 emits electromagnetic energy in the direction of projectile movement, the signal reflected from the projectile is fed to the first input of the key 6, the second input of which receives a signal from the output of the delay line 7, the input of which receives the signal from the output of the induction sensor 3 (Fig. 2) .

The choice of the delay time is due to the need to measure the initial velocity of the projectile, since it is at the moment of the shot that the moment is observed when the velocity of the projectile reaches its maximum value (Fig. 5).

The signal from the output of the key 6 through an analog-to-digital converter 8 is fed to the input of the memory unit 9, where it is recorded.

The processing of the obtained data is carried out in the data processing unit 10, while the data reliability analysis is performed in the data reliability analyzer 14.

The data reliability analyzer 14 selects a site containing increased reliable data, with the beginning of the site being determined by the presence of at least three consecutive positions with reliable data, and its end by the presence of two or more positions with inaccurate data, which determine the initial velocity of the projectile .

The algorithm for determining the area of increased reliable data is shown in Fig.4.

The reliability of the data on the current velocity of the projectile is evaluated based on:

- set requirements for the accuracy of measuring the initial velocity of the projectile;

- the actual excess of the signal-to-noise ratio of its value, which is necessary to ensure the specified accuracy of determining the initial velocity of the projectile,

- by changes in the values of the current velocity of the projectile, presented at adjacent positions in the resulting sequence (figure 4).

Then, zones containing inaccurate data are found in case of exceeding changes in the values of the current velocity of the projectile relative to the specified one, and then, based on reliable data obtained from positions directly adjacent to these zones, the expected velocity values are determined for each position in the detected zone and localize each position with inaccurate data, moreover, those positions for which the analyzed changes in the values of the current velocity of the projectile do not exceed the value of the specified error are measured are considered reliable I muzzle velocity.

Calculation of the initial velocity of the projectile is carried out at time t ₀ = t _ass + t _Σ , where t _ass is the set delay, t _Σ is the total duration of the implementation of the Doppler echo signal preceding the first position in the data section formed to calculate the initial velocity of the projectile (Fig. .5).

If there are single positions with inaccurate data in a selected section of the sequence of discrete values of the current projectile velocity, the data contained in such single positions is replaced by the average value of reliable data from two directly adjacent positions of this section.

Thus, the analyzer 10 data reliability provides a sample of the plot of increased data reliability and provides a check of the reliability of the current speed, while the speed is determined in accordance with the expression

, $$V=\frac{\Delta f\lambda }{2\cos \Delta \varphi }$$

,

where Δf is the Doppler frequency, λ is the wavelength, Δφ is the observation angle.

From the output of the analyzer 14 data reliability signals are fed to the inputs of the block 15 determine the width of the spectrum and block 16 determine the angular velocity of rotation of the projectile.

In addition, the signal from the output of the analyzer 14 data reliability is fed to the input of the indicator 11 of the velocity of the projectile.

Block 15 determining the width of the spectrum provides:

- calculation of the module of the fast Fourier transform (FFT):

, $$S_n=|\; |\; |{\displaystyle \sum _{k=0}^{N-\mathrm{one}}{y}_k\exp \left(-j\frac{2\pi nk}{N}\right)}|\; |\; |,n=0...N-\mathrm{one}$$

,

.where y _k = y (k / F _d ) is the input signal y (t) digitized by an analog-to-digital converter, F _d is the sampling frequency of the original signal, N is the number of FFT samples, S _n is the real amplitude of the nth spectral harmonic, whose frequency can be defined as: $$f_n=\frac{n}{N}{F}_d\mathrm{..}$$

.

- determination of the threshold value:

$$S_{P\mathrm{about}R}=\sqrt{-2\cdot {\sigma }_w^2\cdot \mathrm{one}t(P_{lt}),}$$

- дисперсия шума, значение которой можно вычислить, проанализировав БПФ выходного сигнал радиолокатора при отсутствии движущихся объектов в его зоне видимости на соответствие закону распределения Релея;where P _lt is the probability of false alarm, which in practice is usually taken equal to 10 ^-5 , $${\sigma }_w^2$$

- noise dispersion, the value of which can be calculated by analyzing the FFT of the radar output signal in the absence of moving objects in its visibility range for compliance with the Rayleigh distribution law;

- zeroing harmonics that do not exceed the value of the threshold S _then and are in the region of the expected Doppler frequencies:

, $$S_n^{\text{'}\text{'}}=\{\begin{array}{l}{S}_n,PR\mathrm{and}\left(S_n>S_{P\mathrm{about}R}\right)\wedge \left(f_{\mathrm{about}\mathrm{well}.\min }<f_n<f_{\mathrm{about}\mathrm{well}.\max }\right)\\ 0PR\mathrm{and}\left(S_n<S_{P\mathrm{about}R}\right)\vee \left(f_{\mathrm{about}\mathrm{well}.mi}{}_n>f_n\right)\vee \left(f_n>f_{\mathrm{about}\mathrm{well}.\max }\right)\end{array}$$

,

where f _ozh.min , f _ozh.max - the lower and upper boundaries of the region of the expected Doppler frequencies, respectively,

- determination of the signal spectrum width:

, $$f_{c.\min }=\underset{S_n^{\ast }\ne 0}{\min (f_n)}$$

,

, $$f_{c.\max }=\underset{S_n^{*}\ne 0}{\max (f_n)}$$

,

Δf = f _c.max -f _c.min,

where f _c.min is the lower boundary of the spectrum of the signal, f _c.max is the upper boundary of the spectrum of the signal, Δf is the width of the spectrum of the signal (Fig.6);

- determination of the width of the spectrum of the area of the maximum cross section of the projectile by a plane perpendicular to the line of sight of the projectile,

- determination of the value of the nutation of the projectile by changing this area at each position.

The signal from the output of the block 15 determining the width of the spectrum is fed to the input of the indicator 12 of the spectrum width.

Block 16 determines the angular velocity of rotation of the projectile determines the angular velocity of rotation of the projectile relative to the longitudinal axis for the selected measurement site.

For the obtained complex spectrum, an algorithm for compensating the influence of phase modulation of the reflected radar signal is used, since it takes a long time to coherently accumulate the signal to detect harmonics of the secondary modulation, and due to the nutational motion of the projectile, the condition of coherent accumulation is violated.

The compensation algorithm for the effect of phase modulation of the reflected radar signal is implemented as follows:

1. The complex spectral amplitude at the output of the FFT algorithm is determined:

$${\dot{S}}_n={\displaystyle \sum _{k=0}^{K-\mathrm{one}}{\dot{s}}_k\exp \left(-j\frac{2\pi nk}{K}\right),n=0...N-\mathrm{one}\left(N=K\right),}$$

- выбранный участок отраженного эхо-сигнала, K - число отсчетов выбранного участка сигнала;Where $${\dot{s}}_k$$

- the selected portion of the reflected echo, K is the number of samples of the selected portion of the signal;

2. The boundaries of the spectrum of the dominant harmonic are determined:

N _e.min = (n _pl -Δn _pl / 2);

N _e.max = (n _pl + Δn _pl / 2),

where [N _e.min, N _e.max] - spectral interval samples containing dominant harmonic frequency, n _pl - frequency position of the maximum spectral amplitude, Δn _mp - priori predetermined width of the search interval energy center dominant harmonic spectrum;

3. The energy center of the dominant harmonic spectrum is determined from the squares of spectral amplitudes

, $$N_{\mathrm{uh}.c.}=\underset{k\in \left[N_{\mathrm{uh}.\min },N_{\mathrm{uh}.\max }\right]}{\arg \max \left(E_k\right)}$$

,

n_c - априорно известная ширина спектра доминирующей гармоники;Where $$E_k={\displaystyle \sum _{i=-n_c/2}^{n_c/2}{|\; |\; |{\dot{S}}_{k+i}|\; |\; |}^2;}$$

n _c is the a priori known spectrum width of the dominant harmonic;

4. The spectrum of the signal reflected from the projectile is highlighted, and its zeros are added:

$$\{\begin{array}{l}{\dot{S}}_{Pl.n}={\dot{S}}_{n}PR\mathrm{and}{N}_{\mathrm{uh}.c.}-n_f/2\le N_{\mathrm{uh}.c.}+n_f/2\\ {\dot{S}}_{Pl.n}=0PR\mathrm{and}n<N_{\mathrm{uh}.c.}-n_f/2;>N_{\mathrm{uh}.c.}+n_f/2\end{array}$$

where n _f is the width of the spectrum of the signal reflected from the projectile, including the harmonics of the secondary modulation;

5. The spectrum is cycled in such a way that the energy center of the spectrum is in the zero position $${\dot{S}}_{\mathrm{to}\mathrm{about}R.k}={\dot{S}}_{Pl.n+N\mathrm{uh}.c.}$$

, получение корректирующего сигнала6. The operation of the inverse FFT spectrum is performed. $${\dot{S}}_{\mathrm{to}\mathrm{about}R.n}$$

receiving correction signal

$${\dot{S}}_{\mathrm{to}\mathrm{about}R.k}=\frac{\mathrm{one}}{K}{\displaystyle \sum _{n=0}^{K-\mathrm{one}}{\dot{S}}_{\mathrm{to}\mathrm{about}R.n}\exp \left(j\frac{2\pi nk}{K}\right)}$$

на комплексно-сопряженный корректирующий сигнал $${\dot{s}}_{кор.k}^{\ast }$$

и выполнение операции БПФ:7. The source signal is multiplied. $${\dot{s}}_k$$

to complex conjugate correction signal $${\dot{s}}_{\mathrm{to}\mathrm{about}R.k}^{\ast }$$

and FFT operation:

$$Z_n=|\; |\; |{\displaystyle \sum _{k=0}^{K-\mathrm{one}}{\dot{s}}_k}{\dot{s}}_{\mathrm{to}\mathrm{about}R.k}\exp \left(-j\frac{2\pi nk}{K}\right)|\; |\; |.$$

As a result of the operations of the above algorithm, after compensating for the effect of phase modulation of the reflected radar signal, an echo signal spectrum Z _n with clearly defined harmonics of the secondary modulation is obtained. For a pair of harmonics of the secondary modulation, located closest to the dominant harmonic in the spectrum of the echo signal, the frequencies f ₁ and f _{2 are} determined at which they reach a maximum.

Next, the angular velocity of rotation of the projectile around the longitudinal axis is determined by the formula

$$\dot{\gamma }=2\pi f_{\mathrm{at}R},$$

where f _BP = (f ₁ -f ₂ ) / 2, f ₁ and f ₂ are the frequencies corresponding to the maxima of the first pair harmonics of the secondary modulation.

The signal from the output of the block 16 for determining the angular velocity of rotation of the projectile is input to the indicator 16 of the angular velocity of rotation of the projectile.

Thus, the use of the invention allows to expand the information content by additionally determining the angular velocity of rotation of the projectile relative to the longitudinal axis.

Claims (6)

1. A method of measuring the extrinsic ballistic characteristics of a projectile, which consists in emitting electromagnetic energy in the direction of projectile motion, receiving electromagnetic energy reflected from the projectile, converting the analog signal to a digital form, writing signals to a memory unit, forming a sequence of discrete values of its current speed according to Doppler echo implementations -the signal of the projectile, calculated from the current speed of the initial velocity of the projectile, taking into account the set delay of the start of its observation relative to m the moment of departure from the gun’s barrel, evaluating the reliability of discrete values of the current projectile velocity for each position in the obtained sequence of data contained in them, highlighting, taking into account the results obtained in this sequence, a section containing mainly reliable data by which the initial velocity of the projectile is determined, while assessing the reliability of the data on the current velocity of the projectile use criteria that take into account the specified requirements for the accuracy of measuring the initial velocity of the projectile; when forming a section of the mentioned sequence for calculating the initial velocity of the projectile, the beginning of this section is determined by the presence of at least three consecutive positions with reliable data, and its end - by the presence of two or more positions with false data; used to calculate the initial velocity of the projectile, the delay time of the start of the observation is the sum of the set delay and the total duration of the implementation of the Doppler echo signal preceding the first position in the data area formed to calculate the initial velocity of the projectile; if there are single positions with inaccurate data in a selected section of the sequence of discrete values of the current projectile velocity, the data contained in such single positions is replaced by the average value of reliable data from two directly adjacent positions of this section, the reliability of the data on the current velocity of the projectile is checked by exceeding the actual ratio signal / noise of its value, which is necessary to ensure a given accuracy of determining the initial velocity of the projectile, reliability yes data on the current velocity of the projectile is estimated from changes in the values of the current velocity of the projectile presented at adjacent positions in the obtained sequence, while first, by the magnitude of these changes, zones containing inaccurate data are detected, and then by reliable data obtained from positions directly adjacent to these zones , determine for each position in the detected zone the expected speed values and localize each position with inaccurate data, and those positions for which the changes made in the values of the current velocity of the projectile do not exceed the value of the specified error in measuring the initial velocity of the projectile, determine the spectrum width of the Doppler echo signal, determine the area of the maximum section of the projectile by a plane perpendicular to the line of sight of the projectile, judging by the change in this area at each position, the nutation value is projectile, characterized in that in the spectrum of the Doppler echo signal determine the frequency of the harmonics of the secondary modulation of the echo signal caused by asymmetry aspredeleniya projectile mass relative to its longitudinal axis, is calculated by the formula $$\dot{\gamma }=2\pi f_{\mathrm{at}R}$$

the angular velocity of rotation of the projectile around the longitudinal axis, where f _BP = (f ₁ -f ₂ ) / 2, f ₁ and f ₂ are the frequencies corresponding to the maxima of the first pair harmonics of the secondary modulation of the Doppler echo signal. 2. A device for measuring the extrinsic ballistic characteristics of a projectile, comprising a Doppler radar, a computer, a spectral width indicator, characterized in that a key, a delay line, an analog-to-digital converter, a memory unit, a signal processing unit, an initial projectile velocity indicator and an angular velocity indicator are additionally introduced rotation of the projectile, the output of the Doppler radar connected to the first input of the key, the second input of which is connected to the output of the delay line, the input of which is connected to the output of the inductor sensor, and the output is connected to the input of an analog-to-digital converter, the output of which is connected to the input of the memory block, the output of which is connected to the input of the signal processing unit, the first, second, and third outputs of which are connected respectively to the inputs of the indicator of the initial velocity of the projectile, the indicator of the spectral width and indicator of the angular velocity of rotation of the projectile. 3. The device according to claim 2, characterized in that the signal processing unit consists of a data reliability analyzer, a spectral width determination unit, an angular projectile rotation speed determination unit, wherein the input of the signal processing unit is an input of a data reliability analyzer, the output of which is connected to the inputs the unit for determining the width of the spectrum and the unit for determining the angular velocity of rotation of the projectile, the outputs of the analyzer for data reliability, the unit for determining the width of the spectrum and the unit for determining the angular velocity of rotation of the projectile lyayutsya respectively first, second and third outputs of the signal processing unit. 4. The device according to claim 3, characterized in that the algorithm of the signal accuracy analyzer consists in evaluating the accuracy of the discrete values of the current projectile velocity for each position in the obtained sequence of contained data, selecting, taking into account the results obtained, in this sequence of the section containing mainly reliable data, by which they determine the initial velocity of the projectile, while in assessing the reliability of data on the current velocity of the projectile, criteria are used that take into account the given requirements for the accuracy of measuring the initial velocity of the projectile; when forming a section of the mentioned sequence for calculating the initial velocity of the projectile, the beginning of this section is determined by the presence of at least three consecutive positions with reliable data, and its end - by the presence of two or more positions with false data; used to calculate the initial velocity of the projectile, the delay time of the start of the observation is the sum of the set delay and the total duration of the implementation of the Doppler echo signal preceding the first position in the data area formed to calculate the initial velocity of the projectile; if there are single positions with inaccurate data in a selected section of the sequence of discrete values of the current projectile velocity, the data contained in such single positions is replaced by the average value of reliable data from two directly adjacent positions of this section, the reliability of the data on the current velocity of the projectile is checked by exceeding the actual ratio signal / noise of its value, which is necessary to ensure a given accuracy of determining the initial velocity of the projectile, reliability yes data on the current velocity of the projectile is estimated from changes in the values of the current velocity of the projectile presented at adjacent positions in the obtained sequence, while first, by the magnitude of these changes, zones containing inaccurate data are detected, and then by reliable data obtained from positions directly adjacent to these zones , determine for each position in the detected zone the expected speed values and localize each position with inaccurate data, and those positions for which iziruemye change the current projectile velocity values do not exceed the value given by the measurement error of the initial velocity of the projectile, determination of the spectrum of the Doppler frequency of the echo signal modulation secondary harmonic echo signal caused by the asymmetry of the distribution of the mass of the projectile about its longitudinal axis. 5. The device according to claim 3, characterized in that the algorithm for determining the spectrum width is to calculate the FFT module:
$$S_n=|\; |\; |{\displaystyle \sum _{k=0}^{N-\mathrm{one}}{y}_k\exp \left(-j\frac{2\pi nk}{N}\right)}|\; |\; |,n=0...N-\mathrm{one}$$

,
where y _k = y (k / F _d ) is the digitized ADC input signal y (t), F _d is the sampling frequency of the original signal, N is the number of DFT samples, S _n is the real amplitude of the nth spectral harmonic, the frequency of which can be determined as: $$f_n=\frac{n}{N}{F}_d$$

, determination of the threshold value:
$$S_{P\mathrm{about}R}=\sqrt{-2\cdot {\sigma }_w^2\cdot \ln (P_l{}_t)}$$

,
where P _lt is the probability of false alarm, which in practice is usually taken equal to 10 ^-5 , $${\sigma }_w^2$$

- noise dispersion, the value of which can be calculated by analyzing the FFT of the radar output signal in the absence of moving objects in its field of view for compliance with the Rayleigh distribution law, zeroing harmonics that do not exceed the threshold value S _then and are in the range of the expected Doppler frequencies:
$$S_n^{\text{'}\text{'}}=\{\begin{array}{l}Sn,PR\mathrm{and}\left(S_n>S_{P\mathrm{about}R}\right)\wedge \left(f_{\mathrm{about}\mathrm{well}.\min }<f_n<f_{\mathrm{about}\mathrm{well}.\max }\right)\\ 0PR\mathrm{and}\left(S_n<S_{P\mathrm{about}R}\right)\vee \left(f_{\mathrm{about}\mathrm{well}.\min }>f_n\right)\vee \left(f_n>f_{\mathrm{about}\mathrm{well}.\max }\right)\end{array}$$

,
where f _ozh.min , f _ozh.max - the lower and upper boundaries of the region of the expected Doppler frequencies, respectively, the definition of the width of the signal spectrum:
$$f_{c.\min }=\underset{S_n^{*}\ne 0}{\min (f_n)}$$

,
$$f_{c.\max }=\underset{S_n^{*}\ne 0}{\max (f_n)}$$

,
Δf = f _c.max -f _c.min ,
where f _c.min is the lower limit of the signal spectrum, f _c.max is the upper limit of the signal spectrum, Δf is the width of the signal spectrum, determined by the width of the spectrum of the area of the maximum projectile cross section by a plane perpendicular to the line of sight of the projectile, determining the value of the nutation of the projectile by changing this area at each position. 6. The device according to claim 3, characterized in that the algorithm of the unit for determining the angular velocity of rotation of the projectile consists in calculating the frequencies of the harmonics of the secondary modulation in the amplitude-frequency spectrum of the selected measurement section, while upon receipt of the amplitude-frequency spectrum, an algorithm for compensating the influence of phase modulation is used reflected radar signal:
- determination of the complex spectral amplitude at the output of the FFT algorithm:
$${\dot{S}}_n={\displaystyle \sum _{k=0}^{K-\mathrm{one}}{\dot{s}}_k\exp \left(-j\frac{2\pi nk}{K}\right),n=0...N-\mathrm{one}\left(N=K\right)}$$

,
Where $${\dot{s}}_k$$

- the selected portion of the reflected echo, K is the number of samples of the selected portion of the signal,
- determination of the spectrum boundary of the dominant harmonic:
N _e.min = (n _pl -Δn _pl / 2);
N _e.max = (n _pl + Δn _pl / 2),
where [N _e.min , N _e.max ] is the interval of spectral samples containing the frequencies of the dominant harmonic, n _pl is the frequency position of the maximum spectral amplitude, Δn _pl is the a priori specified width of the search interval of the energy center of the spectrum of the dominant harmonic,
- determination of the energy center of the spectrum of the dominant harmonic, by the squares of the spectral amplitudes:
$$N_{\mathrm{uh}.c.}=\underset{k\in \left[N_{\mathrm{uh}.\min },N_{\mathrm{uh}.\max }\right]}{\arg \max (E_k)}$$

,
Where $$E_k={\displaystyle \sum _{i=-n_c/2}^{n_c/2}{|\; |\; |{\dot{S}}_k{}_{+i}|\; |\; |}^2}$$

; n _c is the a priori known spectrum width of the dominant harmonic, the allocation of the spectrum of the signal reflected from the projectile, and the implementation of its complement by zeros:
$$\{\begin{array}{l}{\dot{S}}_{Pl.n}={\dot{S}}_{n}PR\mathrm{and}{N}_{\mathrm{uh}.c.}-n_f/2\le n\le N_{\mathrm{uh}.c.}+n_f/2\\ {\dot{S}}_{Pl.n}=0PR\mathrm{and}n<N_{\mathrm{uh}.c.}-n_f/2;n>N_{\mathrm{uh}.c.}+n_f/2\end{array}$$

where n _f is the width of the spectrum of the signal reflected from the projectile, including the harmonics of the secondary modulation, conducting a cyclic shift of the spectrum so that the energy center of the spectrum is in the zero position in accordance with the expression: $${\dot{S}}_{\mathrm{to}\mathrm{about}R.n}={\dot{S}}_{Pl.n}{}_{+N_{\mathrm{uh}.c.}}$$

,
- the implementation of the operation of the inverse FFT spectrum $${\dot{S}}_{\mathrm{to}\mathrm{about}R.n}$$

and receiving a correction signal:
$${\dot{s}}_{\mathrm{to}\mathrm{about}R.k}=\frac{\mathrm{one}}{K}{\displaystyle \sum _{n=0}^{K-\mathrm{one}}{\dot{S}}_{\mathrm{to}\mathrm{about}R.n}\exp \left(j\frac{2\pi nk}{K}\right)}$$

,
- the implementation of the multiplication of the original section of the signal $${\dot{s}}_k$$

to complex conjugate correction signal $${\dot{s}}_{\mathrm{to}\mathrm{about}R.k}^{\ast }$$

and FFT operation:
$$Z_n=|\; |\; |{\displaystyle \sum _{k=0}^{K-\mathrm{one}}{\dot{s}}_k{\dot{s}}_{\mathrm{to}\mathrm{about}R.k}^{\ast }}\exp \left(-j\frac{2\pi nk}{K}\right)|\; |\; |$$

,
- the selection of the spectrum of the echo signal Z _n two pairs of harmonics of secondary modulation, located closest to the dominant harmonic and the determination of the frequencies f ₁ and f ₂ at which they reach a maximum,
- calculation of the angular velocity of rotation of the projectile around the longitudinal axis according to the formula $$\dot{\gamma }=2\pi f_{\mathrm{at}R}$$

where f _bp = (f ₁ -f ₂ ) / 2, f ₁ and f ₂ are the frequencies corresponding to the maxima of the first pair harmonics of the secondary modulation of the Doppler echo signal.

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