CN110988821B - Radar target simulator and control method thereof - Google Patents

Radar target simulator and control method thereof Download PDF

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Publication number
CN110988821B
CN110988821B CN201911099456.7A CN201911099456A CN110988821B CN 110988821 B CN110988821 B CN 110988821B CN 201911099456 A CN201911099456 A CN 201911099456A CN 110988821 B CN110988821 B CN 110988821B
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pitch
attenuator
distance
output
power splitter
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CN110988821A (en
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黄超
董柳青
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Xi'an Tianhe Defense Technology Co ltd
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Xi'an Tianhe Defense Technology Co ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/40—Means for monitoring or calibrating
    • G01S7/4052—Means for monitoring or calibrating by simulation of echoes
    • G01S7/4056—Means for monitoring or calibrating by simulation of echoes specially adapted to FMCW
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/40—Means for monitoring or calibrating
    • G01S7/4052—Means for monitoring or calibrating by simulation of echoes
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/40—Means for monitoring or calibrating
    • G01S7/4052—Means for monitoring or calibrating by simulation of echoes
    • G01S7/4082—Means for monitoring or calibrating by simulation of echoes using externally generated reference signals, e.g. via remote reflector or transponder

Abstract

The invention relates to a radar target simulator and a control method thereof. The radar target simulator comprises an input control means, a first frequency synthesiser, a power divider P1 and a first pitch attenuation means. The input control device can directly acquire the spatial data of the target to be simulated, which is input by the user, and generate a control signal according to the spatial data. The first frequency synthesizer may acquire the control signal and generate a first analog signal based on the control signal. The first analog signal passes through the power divider P1 and the first pitch attenuation device, and then forms an electromagnetic wave simulating a radar target. The radar target simulator can directly release electromagnetic waves according to the space data of the target to be simulated, which is input by a user, and a target waveform which is calculated in advance does not need to be stored by a digital memory, so that the radar target simulator gets rid of the storage capacity limitation of the digital memory, and the use performance of the radar target simulator is improved.

Description

Radar target simulator and control method thereof
Technical Field
The invention relates to the technical field of radar testing, in particular to a radar target simulator and a control method thereof.
Background
A radar is an electronic device that finds a target by electromagnetic waves and determines its spatial position. When the radar works, electromagnetic waves can be transmitted to irradiate a target and receive echoes from the target, so that information such as the radial distance, the radial speed, the azimuth angle difference and the pitch angle of the target can be obtained.
The object simulated by the radar target simulator is the target and the environment of the radar, and the simulation result is the reproduction of a radar echo signal containing the information of the radar target and the target environment. Conventionally, a radar target simulator generally includes a digital memory and a digital-to-analog converter. The digital memory is used for storing a pre-calculated target waveform, and the digital-to-analog converter is used for performing digital-to-analog conversion on the target waveform stored in the digital memory, so that electromagnetic waves are released.
The applicant found in the course of implementing the conventional technique that: the time period in which a conventional radar target simulator can be used is limited by the storage capacity of the digital memory.
Disclosure of Invention
Based on this, it is necessary to provide a radar target simulator and a control method thereof, aiming at the problem that the use time of the radar target simulator is limited by the storage capacity of the digital memory in the conventional technology.
A radar target simulator, comprising:
the input control device is used for acquiring spatial data of a target to be simulated and generating a control signal according to the spatial data of the target to be simulated;
the first frequency synthesizer is in communication connection with the input control device and is used for acquiring the control signal and generating a first analog signal according to the control signal;
a power splitter P1, an input of the power splitter P1 communicatively connected to the first frequency synthesizer to obtain the first analog signal, the power splitter P1 configured to power split the first analog signal;
and the first pitch attenuation device is connected with the output end of the power divider P1 and the input control device in a communication mode, so that the first analog signal after the power division is attenuated according to the control signal.
The radar target simulator comprises an input control device, a first frequency synthesizer, a power divider P1 and a first pitch attenuation device. The input control device can directly acquire the spatial data of the target to be simulated, which is input by the user, and generate a control signal according to the spatial data. The first frequency synthesizer may acquire the control signal and generate a first analog signal based on the control signal. The first analog signal passes through a power divider P1 and a first pitching attenuation device, and then electromagnetic waves simulating a radar target can be formed. The radar target simulator can directly release electromagnetic waves according to the space data of the target to be simulated, which is input by a user, and a target waveform which is calculated in advance does not need to be stored by a digital memory, so that the radar target simulator gets rid of the storage capacity limitation of the digital memory, and the use performance of the radar target simulator is improved.
A method of controlling a radar target simulator, comprising:
acquiring spatial data of a target to be simulated, wherein the spatial data comprises a radial distance R and a radial velocity v of the target to be simulatedeAzimuth angle difference delta theta and pitch angle
Figure BDA0002269392460000021
Calculating the radial distance based on the radial distance RR amplitude modulation k (R) of the output signal and said radial distance R frequency f of the output signalRModulation;
based on said radial velocity veCalculating said radial velocity veCorresponding Doppler frequency modulation fd；
Calculating azimuth beam amplitude modulation f (delta theta) corresponding to the azimuth angle difference delta theta based on the azimuth angle difference delta theta;
based on the pitch angle
Figure BDA0002269392460000031
Calculating the pitch angle
Figure BDA0002269392460000032
Corresponding three-dimensional amplitude modulation
Figure BDA0002269392460000033
And
Figure BDA0002269392460000034
based on the amplitude modulation k (R), frequency modulation fRDoppler frequency modulation fdAzimuth beam amplitude modulation f (delta theta) and three-dimensional amplitude modulation
Figure BDA0002269392460000035
A control signal is generated.
The control method of the radar target simulator is applied to the radar target simulator in the embodiment. The control method can acquire the spatial data of the target to be simulated and generate a control signal according to the spatial data of the target to be simulated, so that the radar target simulator releases the electromagnetic waves simulating the radar target. The control method ensures that the radar target simulator does not need to store the pre-calculated target waveform through the digital memory, thereby ensuring that the radar target simulator gets rid of the storage capacity limitation of the digital memory and improving the service performance of the radar target simulator.
Drawings
Fig. 1 is a schematic structural block diagram of a radar target simulator in an embodiment of the present application.
Fig. 2 is a schematic structural block diagram of a radar target simulator in another embodiment of the present application.
Fig. 3 is a flowchart illustrating a control method of a radar target simulator according to an embodiment of the present application.
Wherein, the meanings represented by the reference numerals of the figures are respectively as follows:
10. a radar target simulator;
100. an input control device;
110. an input device;
120. a control device;
210. a first frequency synthesizer;
220. a second frequency synthesizer;
230. a clutter generation chip;
310. a first pitch attenuation device;
320. a second pitch attenuation device;
330. a third pitch attenuation device;
410. a first distance attenuation device;
420. a second distance attenuation device;
510. a first combiner;
520. a second combiner;
530. a third combiner;
610. a first radio frequency connector;
620. a second radio frequency connector;
630. a third radio frequency connector.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein.
The present application provides a radar target simulator 10 and a control method suitable for the same. As shown in fig. 1, a radar target simulator 10 includes an input control device 100, a first frequency synthesizer 210, a power divider P1, and a first pitch attenuation device 310.
Specifically, the input control device 100 is configured to acquire spatial data of an object to be simulated, and generate a control signal according to the spatial data of the object to be simulated. In other words, the input control device 100 includes two parts, the input device 110 and the control device 120. The input device 110 may be a human input device such as a keyboard or a touch screen, so that a user may input spatial data of an object to be simulated through the input device 110; the control means 120 may be an (ARM, Advanced RISC Machines) processor for generating control signals according to spatial data input by a user. The spatial data here typically includes radial distance, radial velocity, azimuth difference and pitch angle of the tape simulation target. The input control means 100 may control the first frequency synthesizer 210 and the first attenuating means by means of control signals. Generally, the input control device 100 may be a notebook computer, so as to obtain the spatial data of the object to be simulated, and process the spatial data of the object to be simulated and generate the control signal.
The first frequency Synthesizer 210 may be a Direct Digital Synthesizer (DDS). The first frequency synthesizer 210 is communicatively coupled to the input control device 100 for generating a usable analog signal based on the control signal output by the input control device 100, and the analog signal generated by the first frequency synthesizer 210 is named a first analog signal.
The power divider P1 is used to divide a single input signal into two or more output signals, and thus the power divider P1 may have one input and multiple outputs. An input of the power splitter P1 is communicatively coupled to the first frequency synthesizer 210 for obtaining a first analog signal. The power divider P1 is used to divide the first analog signal into two or more energy output signals. In other words, the power divider P1 is used to perform power division on the first analog signal.
The first pitch attenuation device 310 is used to attenuate the output signal of the power splitter P1. As is known from the above description, the power divider P1 has a plurality of output terminals for outputting two or more energy output signals. Thus, the first pitch attenuation device 310 is an attenuation device made up of a plurality of pitch attenuators, corresponding to the plurality of outputs of the power splitter P1, such that each pitch attenuator in the first pitch attenuation device 310 corresponds to one output of the power splitter P1. The pitch is used here to limit the type of attenuator so that the effect of the pitch attenuator on the output signal of the power splitter P1 is only affected by the pitch angle in the spatial data. The first pitch attenuation device 310 is also communicatively coupled to the input control device 100 to obtain a control signal and attenuate the output signal of the power splitter P1 in response to the control signal. In other words, each of the first pitch attenuators 310 is communicatively coupled to the input control device 100 to obtain a control signal and attenuate the first analog signal after power splitting based on the control signal.
More specifically, in the radar target simulator 10 of the present application, a user inputs spatial data of a target to be simulated through the input control device 100. The input control device 100 acquires the spatial data and generates a control signal based on the spatial data. The control signal controls the first frequency synthesizer 210 to generate the first analog signal. The first analog signal may be low pass filtered and amplified before being passed to the power splitter P1. The first analog signal is distributed by the power divider P1 and then outputted from a plurality of different output terminals of the power divider P1. Each output of the power splitter P1 is connected to a pitch attenuator. The pitch attenuator is connected to the input control device 100 for attenuating the output signal of the power divider P1 according to the control signal transmitted by the input control device 100, so as to simulate the electromagnetic wave emitted by the radar target, i.e. simulate the radar target echo signal. The radar target simulator 10 can directly release electromagnetic waves according to the space data of the target to be simulated, which is input by a user, and a target waveform which is calculated in advance does not need to be stored by a digital memory, so that the radar target simulator 10 gets rid of the storage capacity limitation of the digital memory, and the service performance of the radar target simulator 10 is improved.
Further, as shown in fig. 2, the radar target simulator 10 further includes a first distance attenuation device 410.
Specifically, the first distance attenuation device 410 is connected between the first frequency synthesizer 210 and the power divider P1, and is configured to attenuate the first analog signal output by the first frequency synthesizer 210. The first distance attenuation device 410 is also communicatively connected to the input control device 100 to obtain the control signal output by the input control device 100 and to be controlled by the control signal.
More specifically, in general, the first frequency synthesizer 210 may be a direct digital frequency synthesizer, which itself has a certain dynamic range of attenuation. However, when the range of the object to be simulated varies widely, the first frequency synthesizer 210 may not provide sufficient attenuation dynamic range. Based on this, the first distance attenuation means 410 may be communicatively connected between the first frequency synthesizer 210 and the power divider P1. The first distance attenuation device 410 may comprise a plurality of distance attenuators in series. The distance faders here differ from the pitch faders described above in that the effect of the distance faders on the first analogue signal is only affected by the radial distance in the spatial data.
Further, as shown in FIG. 2, first distance attenuation device 410 includes a distance attenuator A1, a distance attenuator B1, and a distance attenuator C1 in series.
In particular, the distance attenuator A1 may be a 31dB distance attenuator. The input of the distance attenuator a1 is connected to the first frequency synthesizer 210 for obtaining the first analog signal.
The distance attenuator B1 may be a 0 to 20dB distance attenuator. The input of distance attenuator B1 is connected to the output of distance attenuator A1.
The distance attenuator C1 may be a 0 to 20dB distance attenuator. The input of distance attenuator C1 is connected to the output of distance attenuator B1, and the output of distance attenuator C1 is connected to the input of power splitter P1.
The first distance attenuation device 410 may be used to simulate the radial distance of the object to be simulated, thereby providing a depth distance control capability and increasing the applicability of the radar target simulator 10.
In one embodiment, as shown in FIG. 2, the power divider P1 of the radar target simulator 10 has three outputs. At this point, the first pitch attenuation device 310 includes three pitch attenuators, pitch attenuator A1, pitch attenuator B1, and pitch attenuator C1. The pitch attenuator A1 is connected to the first output terminal of the power divider P1, and is connected to the input control device 100, for attenuating the output signal of the first output terminal of the power divider P1 according to the control signal. The pitch attenuator B1 is connected to the second output of the power divider P1 and to the input control means 100 for attenuating the output signal at the second output of the power divider P1 in dependence on the control signal. The pitch attenuator C1 is connected to the third output of the power divider P1 and to the input control means 100 for attenuating the output signal at the third output of the power divider P1 in dependence on the control signal.
Further, as shown in fig. 2, the radar target simulator 10 may further include a first radio frequency connector 610, a second radio frequency connector 620, and a third radio frequency connector 630 for transmitting electromagnetic waves.
Specifically, the first rf connector 610 is connected to the pitch attenuator a1 for converting the output signal of the pitch attenuator a1 into an electromagnetic wave. In other words, the pitch attenuator A1 is communicatively connected between the first output of the power splitter P1 and the first RF connector 610.
The second radio frequency connector 620 is connected with the pitch attenuator B1 and is used for converting the output signal of the pitch attenuator B1 into an electromagnetic wave. In other words, pitch attenuator B1 is communicatively coupled between the second output of power splitter P1 and second RF connector 620.
The third rf connector 630 is connected to the pitch attenuator C1 for converting the output signal of the pitch attenuator C1 into an electromagnetic wave. In other words, the pitch attenuator C1 is communicatively connected between the third output of the power splitter P1 and the third RF connector 630.
The other ends of the first, second and third rf connectors 610, 620 and 630, remote from the pitch faders a1, B1 and C1, may be provided with coaxial cables.
The first pitch attenuation device 310 of the radar target simulator 10 comprises the pitch attenuator A1, the pitch attenuator B1 and the pitch attenuator C1, which can be used for simulating the echo power when a single target is simultaneously irradiated by A, B and C three beams and controlling the pitch angle of the target to be simulated, thereby achieving the purpose of simulating the three-dimensional information of the target to be simulated and increasing the application range of the radar target simulator 10.
In one embodiment, as shown in fig. 2, the radar target simulator 10 further includes a clutter generation chip 230, a power splitter P2 and a second pitch attenuation device 320.
Specifically, the clutter generating chip 230 is communicatively connected to the input control device 100, and is configured to generate clutter according to a control signal output by the input control device 100, so as to simulate clutter generated when a target to be simulated operates. The clutter generation chip 230 is operative to generate the desired clutter type and intensity based on the control signal. The clutter can be formed by collecting real clutter and playing the real clutter; or the method can be formed by adopting theoretical clutter and a playing mode. Before the clutter generating chip 230 works, clutter loading is generally required, at least one piece of clutter data of CPI adjacent coherent accumulation time is loaded, and then the clutter data is played circularly.
The power divider P2 is used to divide a single input signal into two or more output signals, and thus the power divider P2 may have one input and multiple outputs. The input end of the power divider P2 is communicatively connected to the noise generation chip 230, and is used for obtaining the noise output by the noise generation chip 230. The power divider P2 is used to divide the noise into two or more energy output signals. In other words, the power divider P2 is used to perform power division on the spurs. In this embodiment, the power divider P2 has one input and three outputs.
The second pitch attenuation device 320 is used to attenuate the output signal of the power splitter P2. As is known from the above description, the power divider P2 has three output terminals, and can output three output signals. Thus, the second pitch attenuation device 320 includes three pitch attenuators, pitch attenuator A2, pitch attenuator B2 and pitch attenuator C2, corresponding to the three outputs of power splitter P2. The pitch is used here to limit the type of attenuator so that the effect of the pitch attenuator on the output signal of the power splitter P2 is only affected by the pitch angle in the spatial data.
The pitch attenuator A2 is connected to the first output terminal of the power divider P2, and is connected to the input control device 100, for attenuating the output signal of the first output terminal of the power divider P2 according to the control signal. The pitch attenuator B2 is connected to the second output of the power divider P2 and to the input control means 100 for attenuating the output signal at the second output of the power divider P2 in dependence on the control signal. The pitch attenuator C2 is connected to the third output of the power divider P2 and to the input control means 100 for attenuating the output signal at the third output of the power divider P2 in dependence on the control signal. Meanwhile, the output end of the pitch attenuator A2 is also communicatively connected with the first radio frequency connector 610, that is, the pitch attenuator A2 is communicatively connected between the first output end of the power divider P2 and the first radio frequency connector 610; the output of pitch attenuator B2 is also communicatively connected to the second RF connector 620, i.e., pitch attenuator B2 is communicatively connected between the second output of power splitter P2 and the second RF connector 620; the output of the pitch attenuator C2 is also communicatively connected to the third radio frequency connector 630, i.e., the pitch attenuator C2 is communicatively connected between the third output of the power splitter P2 and the third radio frequency connector 630.
In one embodiment, as shown in fig. 2, the radar target simulator 10 further includes a second frequency synthesizer 220, a power divider P3, and a third pitch attenuation device 330.
In particular, the second frequency Synthesizer 220 may be a Direct Digital Synthesizer (DDS). The second frequency synthesizer 220 is communicatively coupled to the input control device 100 for generating a usable analog signal based on the control signal output by the input control device 100. For ease of distinction, the analog signal generated by the second frequency synthesizer 220 is designated as the second analog signal.
The power divider P3 is used to divide a single input signal into two or more output signals, and thus, the power divider P3 may have one input terminal and a plurality of output terminals. The input of the power divider P3 is communicatively connected to the second frequency synthesizer 220 for obtaining a second analog signal. The power divider P3 is used to divide the second analog signal into two or more energy output signals. In other words, the power divider P3 is used to perform power division on the second analog signal. In this embodiment, the power divider P3 has one input and three outputs.
The third pitch attenuation device 330 is used to attenuate the output signal of the power splitter P3. As is known from the above description, the power divider P3 has three output terminals, and can output three output signals. Thus, the third pitch attenuation device 330 includes three pitch attenuators, pitch attenuator A3, pitch attenuator B3 and pitch attenuator C3, corresponding to the three outputs of power splitter P3. Pitch is used here to limit the type of fader so that the effect of the pitch fader on the output signal of power splitter P3 is only affected by the pitch angle in the spatial data.
The pitch attenuator A3 is connected to the first output terminal of the power divider P3, and is connected to the input control device 100, for attenuating the output signal of the first output terminal of the power divider P3 according to the control signal. The pitch attenuator B3 is connected to the second output of the power divider P3 and to the input control means 100 for attenuating the output signal at the second output of the power divider P3 in dependence on the control signal. The pitch attenuator C3 is connected to the third output of the power divider P3 and to the input control means 100 for attenuating the output signal at the third output of the power divider P3 in dependence on the control signal. Meanwhile, the output end of the pitch attenuator A3 is also communicatively connected with the first radio frequency connector 610, that is, the pitch attenuator A3 is communicatively connected between the first output end of the power divider P3 and the first radio frequency connector 610; the output of pitch attenuator B3 is also communicatively connected to the second RF connector 620, i.e., pitch attenuator B3 is communicatively connected between the second output of power splitter P3 and the second RF connector 620; the output of pitch attenuator C3 is also communicatively connected to a third radio frequency connector 630, i.e., pitch attenuator C3 is communicatively connected between the third output of power splitter P2 and third radio frequency connector 630.
Further, as shown in fig. 2, a second distance attenuation device 420 is connected between the second frequency synthesizer 220 and the power divider P3.
Specifically, the second distance attenuation device 420 is connected between the second frequency synthesizer 220 and the power divider P3, and is configured to attenuate the second analog signal output by the second frequency synthesizer 220. The second distance attenuation device 420 is also communicatively coupled to the input control device 100 to obtain and be controlled by the control signal output by the input control device 100.
More specifically, in general, the second frequency synthesizer 220 may be a direct digital frequency synthesizer, which itself has a certain dynamic range of attenuation. However, when the range of the object to be simulated varies widely, the second frequency synthesizer 220 may not provide sufficient attenuation dynamic range. Based on this, a second distance attenuation device 420 may be communicatively connected between the second frequency synthesizer 220 and the power splitter P3. The second distance attenuation means 420 may comprise a plurality of distance attenuators in series. The distance fader here differs from the pitch fader described above in that the effect of the distance fader on the second analogue signal is only affected by the radial distance in the spatial data.
Further, as shown in FIG. 2, the second distance attenuation device 420 includes a distance attenuator A2, a distance attenuator B2, and a distance attenuator C2 in series.
In particular, the distance attenuator A2 may be a 31dB distance attenuator. The input of the distance attenuator a2 is connected to the second frequency synthesizer 220 for obtaining the second analog signal.
The distance attenuator B2 may be a 0 to 20dB distance attenuator. The input of distance attenuator B2 is connected to the output of distance attenuator A2.
The distance attenuator C2 may be a 0 to 20dB distance attenuator. The input of distance attenuator C2 is connected to the output of distance attenuator B1, and the output of distance attenuator C2 is connected to the input of power splitter P3.
In one embodiment, the radar target simulator 10 further includes a first combiner 510, a second combiner 520, and a third combiner 530.
Specifically, the first combiner 510 is communicatively connected between the first rf connector 610 and the pitch fader a1, the pitch fader a2 and the pitch fader A3, so as to combine the signals of different frequency bands output by the pitch fader a1, the pitch fader a2 and the pitch fader A3 together and input the combined signals to the first rf connector 610.
The second combiner 520 is communicatively connected between the second radio frequency connector 620 and the pitch fader B1, the pitch fader B2 and the pitch fader B3, so that the signals of different frequency bands output by the pitch fader B1, the pitch fader B2 and the pitch fader B3 are combined together and input to the second radio frequency connector 620.
And a third combiner 530 communicatively connected between the third radio frequency connector 630 and the pitch fader C1, pitch fader C2 and pitch fader C3, so as to combine the signals of different frequency bands output by the pitch fader C1, pitch fader C2 and pitch fader C3 together and input the combined signals to the third radio frequency connector 630.
The present application also provides a control method of a radar target simulator, which is applied to the radar target simulator 10 in any one of the above embodiments, as shown in fig. 3, and includes the following steps:
and S100, acquiring spatial data of the target to be simulated, wherein the spatial data comprises the radial distance, the radial speed, the azimuth angle difference and the pitch angle of the target to be simulated.
The control device 120 in the input control device 100 may acquire spatial data of an object to be simulated through the input device 110. In this applicationIn various embodiments, the spatial data of the target to be simulated may include a radial distance R and a radial velocity v of the target to be simulatedeAzimuth angle difference Δ θ and pitch angle
Figure BDA0002269392460000131
The azimuth angle difference Δ θ here refers to the difference in azimuth angle between the antenna and the object to be simulated. Specifically, the azimuth angle difference Δ θ may be: Δ θ ═ θant-θtar(ii) a Wherein, thetaantIs the azimuth angle of the antenna, thetatarThe azimuth angle of the target to be simulated is Δ θ, which is the difference between the azimuth angles of the antenna and the target to be simulated.
S200, calculating amplitude modulation and frequency modulation of the radial distance to the output signal based on the spatial data; calculating Doppler frequency modulation corresponding to the radial velocity; calculating azimuth beam amplitude modulation corresponding to the azimuth angle difference; and calculating three-dimensional amplitude modulation corresponding to the pitch angle.
Obtaining the radial distance R and the radial velocity v of the target to be simulatedeAzimuth angle difference delta theta and pitch angle
Figure BDA0002269392460000132
The target to be simulated can be calculated according to the spatial data of the target to be simulated. The calculation process comprises the following steps:
calculating the amplitude modulation k (R) of the radial distance R on the output signal based on the radial distance R of the target to be simulated;
calculating the frequency modulation f of the radial distance R on the output signal based on the radial distance R of the target to be simulatedR；
Based on radial velocity veCalculating the radial velocity veCorresponding Doppler frequency modulation fd；
Calculating azimuth beam amplitude modulation f (delta theta) corresponding to the azimuth angle difference delta theta based on the azimuth angle difference delta theta;
based on pitch angle
Figure BDA0002269392460000133
Calculating pitch angle
Figure BDA0002269392460000134
Corresponding three-dimensional amplitude modulation
Figure BDA0002269392460000135
And
Figure BDA0002269392460000136
and S300, generating a control signal based on the amplitude modulation and frequency modulation, Doppler frequency modulation, azimuth beam amplitude modulation and three-dimensional amplitude modulation of the radial distance pair output signal.
In step S200, the amplitude modulation k (R) and the frequency modulation f of the radial distance to the output signal are calculatedRRadial velocity veCorresponding Doppler frequency modulation fdAzimuth beam amplitude modulation f (delta theta) and pitch angle corresponding to azimuth angle difference delta theta
Figure BDA0002269392460000143
Corresponding three-dimensional amplitude modulation
Figure BDA0002269392460000144
And
Figure BDA0002269392460000145
then, a control signal is generated according to the calculation result. The control method of the radar target simulator is applied to the radar target simulator 10 in the above embodiment. The control method may acquire spatial data of the target to be simulated and generate a control signal according to the spatial data of the target to be simulated, thereby causing the radar target simulator 10 to release electromagnetic waves simulating the radar target. The control method enables the radar target simulator 10 to store the pre-calculated target waveform without a digital memory, thereby enabling the radar target simulator 10 to get rid of the storage capacity limitation of the digital memory and improving the use performance of the radar target simulator 10.
In an embodiment, after the step S300, the method for controlling a radar target simulator further includes:
s400, generating an analog signal according to the control signal, wherein the generated analog signal is as follows:
Figure BDA0002269392460000141
the analog signal here may be any one of the first analog signal and the second analog signal described above. Wherein, A (t), B (t) and C (t) are respectively A-path analog signals, B-path analog signals and C-path analog signals. f. ofIFThe radar target simulator 10 corresponds to the center frequency of the radar.
Further, in the above control signal:
the formula for the amplitude modulation k (r) is:
Figure BDA0002269392460000142
wherein k is a polynomial fitting coefficient.
Frequency modulation fRThe calculation formula of (2) is as follows:
Figure BDA0002269392460000151
wherein, B is the frequency modulation signal bandwidth, and c is the speed of light; t is a unit ofrIs the pulse repetition period of the radar.
Doppler frequency modulation fdThe calculation formula of (2) is as follows:
Figure BDA0002269392460000152
wherein λ is the radar operating wavelength.
The polynomial fit formula for the azimuth beam amplitude modulation f (Δ θ) is:
f(Δθ)＝k0+k1Δθ+k2Δθ2+k3Δθ3(ii) a Wherein k is0、k1、k2And k3Fitting coefficients for the polynomial.
Three-dimensional amplitude modulation
Figure BDA0002269392460000153
And
Figure BDA0002269392460000154
the polynomial fitting formula of (a) is:
Figure BDA0002269392460000155
wherein, a0、a1、a2、a3、b0、b1、b2、b3、c0、c1、c2And c3Fitting coefficients for the polynomial.
The radar target simulator 10 and the control method thereof according to the present application will be described in detail with reference to fig. 2 and 3, which are specific embodiments.
As shown in fig. 2, a radar target simulator 10 includes an input control device 100, a first frequency synthesizer 210, a first distance attenuation device 410, a power divider P1, a first pitch attenuation device 310, a clutter generation chip 230, a power divider P2, a second pitch attenuation device 320, a second frequency synthesizer 220, a second distance attenuation device 420, a power divider P3, a third pitch attenuation device 330, a first combiner 510, a second combiner 520, a third combiner 530, a first rf connector 610, a second rf connector 620, and a third rf connector 630.
Wherein, the input control device 100 is a notebook computer with an ARM processor for obtaining the radial distance R and the radial velocity v input by the usereAzimuth angle difference delta theta and pitch angle
Figure BDA0002269392460000156
And according to the radial distance R and the radial speed veAzimuth angle difference Δ θ and pitch angle
Figure BDA0002269392460000157
A control signal is generated. The ARM processor may be a Samsung type S3C2440AL processor.
The first frequency synthesizer 210 and the second frequency synthesizer 220 are respectively connected to the input control device 100 for obtaining the control signal. The input control device 100 programs the first frequency synthesizer 210 and the second frequency synthesizer 220 with control signals. The first frequency synthesizer 210 and the second frequency synthesizer 220 may employ direct digital frequency synthesizers of model AD 9957. The first frequency synthesizer 210 and the second frequency synthesizer 220 are responsible for frequency modulation and amplitude modulation of the signal. In this embodiment, the radar target simulator 10 has both the first frequency synthesizer 210 and the second frequency synthesizer 220, and can simulate the spatial trajectories or positions of two targets at the same time.
The first distance attenuation means 410 is connected between the first frequency synthesizer 210 and the input of the power divider P1. The second distance attenuation means 420 is connected between the second frequency synthesizer 220 and the input of the power divider P3. First distance attenuation device 410 includes, in series, distance attenuator A1, distance attenuator B1, and distance attenuator C1; the second distance attenuation device 420 comprises in series a distance attenuator A2, a distance attenuator B2, and a distance attenuator C2. Wherein the distance attenuator A1 and the distance attenuator B1 are 31dB attenuators with the model number of HMC 542; distance attenuator B1, distance attenuator C1, distance attenuator B2, and distance attenuator C2 are 0 to 20dB attenuators model HMC802LP 3.
The clutter generating chip 230 is connected to the input control device 100, and is used to obtain a control signal. The input control device 100 controls the operation of the noise generation chip 230 through the control signal. When the noise generation chip 230 operates, noise is released to the power divider P2.
The power divider P1, the power divider P2 and the power divider P3 are power dividers model AD4PS-1 +.
The first pitch attenuation device 310 includes a pitch attenuator A1, a pitch attenuator B1, and a pitch attenuator C1. Pitch fader a1, pitch fader B1 and pitch fader C1 are communicatively connected to three outputs of power splitter P1, respectively. At the same time, pitch fader A1, pitch fader B1 and pitch fader C1 are also communicatively connected to input control device 100 so as to acquire and be controlled by the control signals. The second pitch attenuation device 320 includes a pitch attenuator A2, a pitch attenuator B2, and a pitch attenuator C2. Pitch fader a2, pitch fader B2 and pitch fader C2 are communicatively connected to three outputs of power splitter P2, respectively. At the same time, pitch fader A2, pitch fader B2 and pitch fader C2 are also communicatively connected to input control device 100 so as to acquire and be controlled by the control signals. The third pitch attenuation device 330 includes a pitch attenuator A3, a pitch attenuator B3, and a pitch attenuator C3. Pitch fader a3, pitch fader B3 and pitch fader C3 are communicatively connected to three outputs of power splitter P3, respectively. At the same time, pitch fader A3, pitch fader B3, and pitch fader C3 are also communicatively connected to input control apparatus 100 so as to acquire and be controlled by control signals. Pitch attenuators a1, B1, C1, a2, B2, C2, A3, B3, and C3 may all be 31dB attenuators of model HMC 542.
The input end of the first combiner 510 is connected with the pitch fader a1, the pitch fader a2 and the pitch fader A3 in communication, and the output end of the first combiner 510 is connected with the first rf connector 610. The output end of the first rf connector 610 is connected to a coaxial cable, thereby releasing a-path electromagnetic waves. The input end of the second combiner 520 is connected with the pitch fader B1, the pitch fader B2 and the pitch fader B3 in communication, and the output end of the second combiner 520 is connected with the second radio frequency connector 620. The output end of the second rf connector 620 is connected to a coaxial cable, thereby releasing B-path electromagnetic waves. The input of the third combiner 530 is communicatively connected to the pitch attenuator C1, the pitch attenuator C2 and the pitch attenuator C3, and the output of the third combiner 530 is connected to the third radio frequency connector 630. The output end of the third rf connector 630 is connected to a coaxial cable, thereby releasing the C-path electromagnetic wave.
By controlling the first frequency synthesizer or the second frequency synthesizer, the first pitch damping device or the second pitch damping device, etc. according to the control signal, the radar target simulator can output a simulated signal, i.e. a simulated target echo signal. The output analog signals are:
Figure BDA0002269392460000171
the analog signals comprise an A-path analog signal, a B-path analog signal and a C-path analog signal.
The radar target simulator 10 may provide amplitude modulation, phase modulation and frequency modulation functions when generating control signals, and thus may be used to simulate any target characteristic of any radar. Take FMCW (Frequency Modulated Continuous Wave) radar as an example: the amplitude modulation can be used for simulating the distance between a target and the ground, the pitch angle and the direction of an antenna; the phase modulation can simulate the speed of a target; the frequency modulation may simulate the range of the target.
The simulation of the radar target simulator 10 may be classified into static simulation and dynamic simulation. Wherein the static simulation is directed to fixed target spatial data, including the azimuth, elevation, and distance of the target to be simulated. The input control device 100 converts the azimuth, elevation angle and distance of the target to be simulated into corresponding modulation parameters, and controls other devices, so as to generate corresponding target echo signals. For example:
when the user inputs the radial distance R and the radial velocity v of the target to be simulated through the input control device 100eAzimuth angle difference delta theta and pitch angle
Figure BDA0002269392460000184
Then, the input control device 100 calculates this to obtain:
(1) radial distance R amplitude modulation k (R) of the output signal:
Figure BDA0002269392460000181
wherein k is a polynomial fitting coefficient.
(2) Radial distance R versus frequency modulation f of the output signalR：
Figure BDA0002269392460000182
Wherein, B is the frequency modulation signal bandwidth, and c is the speed of light; t isrIs the pulse repetition period of the radar;
(3) radial velocity veCorresponding Doppler frequency modulation fd：
Figure BDA0002269392460000183
Wherein, lambda is the radar working wavelength;
(4) azimuth beam amplitude modulation f (Δ θ) corresponding to the azimuth angle difference Δ θ: f (Δ θ) ═ k0+k1Δθ+k2Δθ2+k3Δθ3(ii) a Wherein k is0、k1、k2And k3Fitting coefficients for the polynomial;
(5) pitch angle
Figure BDA0002269392460000185
Corresponding three-dimensional amplitude modulation
Figure BDA0002269392460000186
And
Figure BDA0002269392460000187
Figure BDA0002269392460000191
wherein, a0、a1、a2、a3、b0、b1、b2、b3、c0、c1、c2And c3Fitting coefficients for the polynomial.
After obtaining the above modulation functions, the modulation functions can be obtained according to the amplitude modulation k (R) in (1) and the frequency modulation f in (2)RProgramming the first distance attenuation device 410 or/and the second distance attenuation device 420, and the first frequency synthesizer 210 or/and the second frequency; modulating f according to the Doppler frequency in (3)dProgramming the first frequency synthesizer 210 or/and the second frequency; programming the first frequency synthesizer 210 or/and the second frequency according to the azimuth beam amplitude modulation f (Δ θ) in (4); according to the three-dimensional amplitude modulation in (5)
Figure BDA0002269392460000193
And
Figure BDA0002269392460000194
for the first pitch attenuation device 310 or/and the third pitch attenuation deviceAnd 330, performing programming control.
The resulting analog signals were:
Figure BDA0002269392460000192
the analog signals here include a-path analog signals, B-path analog signals, and C-path analog signals. Wherein, the A path of analog signals correspond to a pitch attenuator A1 and a pitch attenuator A3; the B path of analog signals correspond to a pitch attenuator B1 and a pitch attenuator B3; the C-path analog signals correspond to pitch fader C1 and pitch fader C3. And after the clutter is combined, an electromagnetic wave echo signal of the target to be simulated can be obtained.
In a further specific embodiment, the radar target simulator 10 further comprises a power supply module, a clock divider and a crystal oscillator (not shown), wherein the power supply module is used for supplying power to other power utilization modules of the radar target simulator 10, such as the input control device 100, the first frequency synthesizer 210, the second frequency synthesizer 220, the clutter generation chip 230, the first distance reduction device 410 and the second distance reduction device 420. The power supply module may have a plurality of voltage conversion circuits to convert the mains voltage to the rated voltage of the device to be powered. The power supply module can also comprise a constant voltage direct current power supply, a direct current voltage conversion module and a linear voltage stabilizer, so as to provide voltage for the device to be powered. This is a routine skill in the art and will not be described further.
The crystal oscillator is used to provide a clock. In this application, a 40MHz crystal oscillator of type SOXO18-A100M may be used to provide the clock. The clock distributor is used for distributing the clock provided by the crystal oscillator, and a clock distribution chip with the model number AD9953 can be adopted. The clock distributor may distribute the clock to the ARM processor and spur generation chip 230, the first frequency synthesizer 210, and the second frequency synthesizer 220 via power division and amplification. The working clocks of the first frequency synthesizer 210 and the second frequency synthesizer 220 are 1GHz, are obtained by frequency multiplication of input 40MHz through an internal PLL phase-locked loop module, and are assisted by an inverse SINC filter to realize arbitrary intermediate frequency output of 0-400 MHz.
In a particular embodimentIn an embodiment, the radar target simulator 10 of the present application may also be used for simulation of dynamic targets. Taking a straight line route with equal height and constant speed as an example, designing a route hook path G to be 1000 meters; the initial entry angle is 20 deg. north, corresponding to the azimuth angle theta020 degrees, wherein the azimuth angle specifies true north as 0 degrees, increasing clockwise; moving away in the northwest direction. Farthest entry distance R of dynamic targetin31000 m; maximum distance Rout31000 m; the flying speed v of the target is 300 m/s; the flying height H was 3000 meters. Therefore, the radial distance, the radial speed, the azimuth angle and the pitch angle of the target to be simulated at different time points on the route can be calculated according to the given route. The calculation process is as follows:
firstly, determining the initial position of a three-dimensional space of a target to be simulated:
Figure BDA0002269392460000201
then, the velocity is subjected to vector decomposition, and a velocity vector decomposition formula can be obtained as follows:
Figure BDA0002269392460000211
according to the velocity vector decomposition formula and the three-dimensional space initial position, a three-dimensional space track formula of the target to be simulated can be obtained:
Figure BDA0002269392460000212
further, according to the three-dimensional space track formula, the formula of the radial distance, the radial speed, the azimuth angle and the pitch angle of the target to be simulated, which change along with time, can be obtained:
Figure BDA0002269392460000213
after the formulas of the radial distance, the radial speed, the azimuth angle and the pitch angle of the target to be simulated changing along with time are obtained, the radial distance, the radial speed, the azimuth angle and the pitch angle of the target to be simulated at different time points can be obtained. And then the radial distance, the radial speed, the azimuth angle and the pitch angle of the target to be simulated at different time points are sequentially input into the input control device 100 of the radar target simulator 10, so that the track of the dynamic target can be simulated.
According to the radar target simulator 10 and the control method thereof, amplitude modulation, phase modulation and frequency modulation coefficients of output signals are calculated according to spatial data of a target to be simulated, which is input by a user, so that target electromagnetic waves are simulated. The radar target simulator 10 can be applied to electromagnetic waves with any frequency in the range of 0-250MHz, and is wide in application range. Meanwhile, the radar target simulator 10 can be used for searching radars and tracking radars; the method can be used for both continuous wave radar and pulse radar, and has a wide application range. The radar target simulator 10 outputs A, B and the three paths of intermediate frequencies of the C circuit at the same time, and can realize measurement of key indexes such as radar angle measurement precision and resolution. The radar target simulator 10 can simulate a point target in a three-dimensional space, can set a track of a dynamic target by itself, and is wider in application range. As can be seen from the above description, the radar target simulator 10 adopts full digital phase modulation, so that the problem of mirror frequency caused by analog phase modulation and the problem of isolation caused by analog switches do not exist, and the frequency precision is higher. The radar target simulator 10 also has a clutter simulation function, so that the output signal-to-noise ratio of the radar target simulator is controllable, and the simulation precision of the radar target simulator 10 is improved.
The radar target simulator 10 further has the advantages of being simple in structure, small in weight and size, and capable of saving manufacturing cost.
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (10)

1. A radar target simulator, comprising:
the input control device (100) is used for acquiring spatial data of a target to be simulated and generating a control signal according to the spatial data of the target to be simulated;
a first frequency synthesizer (210) communicatively coupled to the input control device (100) for obtaining the control signal and generating a first analog signal based on the control signal;
a power splitter P1, an input of the power splitter P1 communicatively coupled to the first frequency synthesizer (210) to obtain the first analog signal, the power splitter P1 configured to power split the distance attenuated first analog signal;
a first pitch attenuation device (310) communicatively coupled to the output of the power splitter P1 and the input control device (100) for pitch attenuating the power-split first analog signal in accordance with the control signal;
-first distance attenuating means (410) communicatively connected between said first frequency synthesizer (210) and said power divider P1 and communicatively connected to said input control means (100) for distance attenuating said first analog signal in accordance with said control signal.
2. The radar target simulator of claim 1, characterized in that said first distance attenuating means (410) comprises a distance attenuator a1, a distance attenuator B1 and a distance attenuator C1 in series; the input end of the distance attenuator A1 is connected to the first frequency synthesizer (210) for obtaining the first analog signal, the input end of the distance attenuator B1 is connected to the output end of the distance attenuator A1, the input end of the distance attenuator C1 is connected to the output end of the distance attenuator B1, and the output end of the distance attenuator C1 is connected to the input end of the power divider P1.
3. The radar target simulator of claim 1, further comprising: a first radio frequency connector (610), a second radio frequency connector (620), and a third radio frequency connector (630);
the first pitch attenuation device (310) includes a pitch attenuator A1, a pitch attenuator B1, and a pitch attenuator C1;
the pitch attenuator A1 is communicatively connected between the first output of the power splitter P1 and the first radio frequency connector (610);
the pitch attenuator B1 is communicatively connected between the second output of the power splitter P1 and the second radio frequency connector (620);
the pitch attenuator C1 is communicatively connected between the third output of the power splitter P1 and the third radio frequency connector (630).
4. The radar target simulator of claim 3, further comprising:
the clutter generating chip (230) is in communication connection with the input control device (100) and is used for acquiring the control signal and generating clutter according to the control signal;
a power splitter P2, an input of the power splitter P2 communicatively connected to the spur generation chip (230) to obtain the spur, the power splitter P2 to power split the spur;
a second pitch attenuation device (320) comprising a pitch attenuator A2, a pitch attenuator B2, and a pitch attenuator C2, said pitch attenuator A2 being connected between a first output of said power splitter P2 and said first radio frequency connector (610); the pitch attenuator B2 is connected between the second output of the power splitter P2 and the second radio frequency connector (620); the pitch attenuator C2 is connected between the third output of the power splitter P2 and the third radio frequency connector (630).
5. The radar target simulator of claim 4, further comprising:
a second frequency synthesizer (220) communicatively coupled to the input control device (100) for obtaining the control signal and generating a second analog signal according to the control signal;
a power splitter P3, an input of the power splitter P3 communicatively coupled to the second frequency synthesizer (220) to obtain the second analog signal, the power splitter P3 configured to power split the second analog signal;
-third pitch attenuation means (330) communicatively connected to the output of said power splitter P3 and to said input control means (100) for attenuating said power split second analog signal in accordance with said control signal; said third pitch attenuation means (330) including a pitch attenuator A3, a pitch attenuator B3 and a pitch attenuator C3, said pitch attenuator A3 being connected between a first output of said power splitter P3 and said first radio frequency connector (610); the pitch attenuator B3 is connected between the second output of the power splitter P3 and the second radio frequency connector (620); the pitch attenuator C3 is connected between the third output of the power splitter P3 and the third radio frequency connector (630).
6. The radar target simulator of claim 5, further comprising:
a first combiner (510) communicatively connected between the first radio frequency connector (610) and the pitch fader A1, the pitch fader A2, and the pitch fader A3;
a second combiner (520) communicatively connected between the second radio frequency connector (620) and the pitch fader B1, the pitch fader B2, and the pitch fader B3;
a third combiner (530) communicatively connected between the third radio frequency connector (630) and the pitch fader C1, the pitch fader C2, and the pitch fader C3.
7. The radar target simulator of claim 5, further comprising:
-second distance attenuating means (420) communicatively connected between said second frequency synthesizer (220) and said power splitter P3 and communicatively connected to said input control means (100) for attenuating said second frequency synthesizer (220) in response to said control signal.
8. A control method of a radar target simulator applied to the radar target simulator according to any one of claims 1 to 7, characterized by comprising:
obtaining space data of a target to be simulated, wherein the space data comprises a radial distance R and a radial speed v of the target to be simulatedeAzimuth angle difference delta theta and pitch angle
Figure FDA0003513700820000031
Calculating the amplitude modulation k (R) of the output signal by the radial distance R and the frequency modulation f of the output signal by the radial distance R based on the radial distance RR；
Based on said radial velocity veCalculating said radial velocity veCorresponding Doppler frequency modulation fd；
Calculating azimuth beam amplitude modulation f (delta theta) corresponding to the azimuth angle difference delta theta based on the azimuth angle difference delta theta;
based on the pitch angle
Figure FDA0003513700820000041
Calculating the pitch angle
Figure FDA0003513700820000042
Corresponding three-dimensional webDegree modulation
Figure FDA0003513700820000043
And
Figure FDA0003513700820000044
based on the amplitude modulation k (R), frequency modulation fRDoppler frequency modulation fdAzimuth beam amplitude modulation f (delta theta) and three-dimensional amplitude modulation
Figure FDA0003513700820000045
Generating a control signal;
generating an analog signal according to the control signal;
and performing distance attenuation on the analog signal.
9. The method of controlling a radar target simulator of claim 8, wherein the analog signal is:
Figure FDA0003513700820000046
wherein f isIFAnd the radar target simulator corresponds to the center frequency of the radar.
10. The control method of a radar target simulator according to claim 8 or 9,
the calculation formula of the amplitude modulation k (R) is as follows:
Figure FDA0003513700820000047
wherein k is a polynomial fitting coefficient;
said frequency modulation fRThe calculation formula of (2) is as follows:
Figure FDA0003513700820000048
wherein, B is the frequency modulation signal bandwidth, and c is the speed of light; t isrIs the pulse repetition period of the radar;
the Doppler frequency modulation fdThe calculation formula of (c) is:
Figure FDA0003513700820000049
wherein λ is the radar operating wavelength;
the polynomial fitting formula of the azimuth beam amplitude modulation f (Δ θ) is:
f(Δθ)＝k0+k1Δθ+k2Δθ2+k3Δθ3(ii) a Wherein k is0、k1、k2And k3Fitting coefficients for the polynomial;
the three-dimensional amplitude modulation
Figure FDA0003513700820000051
And
Figure FDA0003513700820000052
the polynomial fitting formula of (a) is:
Figure FDA0003513700820000053
wherein, a0、a1、a2、a3、b0、b1、b2、b3、c0、c1、c2And c3Fitting coefficients for the polynomial.
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