Radar error measurement method and system under composite electromagnetic interference

Abstract

The invention provides a radar error measurement method and system under composite electromagnetic interference, and the method comprises the steps: generating random numbers which obey the normal distribution of specific parameters for all time points in a certain time period through employing a random number generator based on radar characteristic parameters and shipboard aircraft characteristic parameters; and forming a random number sequence to simulate Gaussian white noise and clutter interference signals in the time period according to random numbers of Rayleigh distribution obeying specific scale parameters, so as to obtain instantaneous amplitudes of the Gaussian white noise and clutter interference signals. Then, instantaneous amplitudes of noise amplitude modulation and frequency modulation interference signals are respectively calculated by adopting a specific calculation method, instantaneous power of a composite electromagnetic interference signal is further calculated, and a signal-to-noise ratio of the radar is calculated by adopting the specific calculation method; and respectively inputting the root mean square of the angle measurement error and the root mean square of the distance measurement error into a random number generator, and outputting the angle measurement error and the distance measurement error to realize accurate measurement of the radar error.

Description

Technical Field

[0001] The present invention relates to the technical field of radar signal processing, and in particular to a radar error measurement method and system under composite electromagnetic interference. Background Art

[0002] With the development of science and technology, carrier-based drones have become an important part of aircraft carrier operations. However, maritime operations are not easy. Every time an aircraft takes off and lands on an aircraft carrier, it is a "dance on the edge of a knife". First of all, the maritime environment is complex. If it is rainy, the rain will reflect the radar signal into clutter, affecting the measurement of the radar system; if there is lightning in the sky, a large number of narrow pulses with random amplitude and phase will be generated due to multiple discharges, so the radar system is very susceptible to the interference of the sky lightning; at the same time, due to the radar electronic system of the carrier-based aircraft, the radar avionics system on the aircraft carrier, and the interference signals generated by the enemy's jammer, the maritime space is also full of electromagnetic interference. In a complex electromagnetic environment, the airborne equipment of drones, such as radars and optoelectronic equipment, is very susceptible to the complex environment, causing measurement signal errors and affecting the landing safety of drones. Therefore, in the marine battlefield, the study of complex composite electromagnetic interference is very important, which will directly affect the landing of carrier-based aircraft, an important combat force on the aircraft carrier, so it is necessary to study the safety of radar-guided landing of carrier-based drones under electromagnetic interference conditions.

[0003] Radar-guided landing refers to the use of the radar's range and angle measurement functions to determine the relative position of the aircraft relative to the radar on the aircraft carrier, thereby locating the specific position of the aircraft's tail hook relative to the ideal glide path. The specific process is to transform the radar's measurement data, solve the data difference of the aircraft's tail hook relative to the ideal glide path, add deck motion compensation, and then transmit the guided data to the command computer to generate control command signals for the throttle and elevator, and then transmit the command signal to the aircraft's flight control system for corresponding operations, thereby controlling the size of the aircraft's throttle and the movement of the elevator, achieving corresponding changes in flight parameters, and finally realizing a complete fully automatic landing system. In this process, due to the measurement error of the radar, it is very likely to affect the final landing success. The main principle of radar is the propagation of electromagnetic waves. In a complex electromagnetic environment, when the original waveform returned by the radar is superimposed with the interference waveform, it will cause errors in the signal received by the radar receiver and the final processing result. Therefore, the radar is susceptible to electromagnetic interference. As for the influence of electromagnetic interference on radar, the current research on the influence of electromagnetic interference on radar mainly focuses on anti-interference research. Then the premise of studying anti-interference must be to study how the radar will be affected. In the large environment of ocean warfare, the sea space is also full of electromagnetic interference due to the interference signals generated by the radar electronic systems of carrier-based aircraft, the radar avionics systems on aircraft carriers, and the enemy's jammers. These interferences will cause the radar measurement errors to increase and seriously affect the landing safety of carrier-based drones; at the same time, the artificial interference signals emitted by enemy jammers will also affect the radar's measurement accuracy.

[0004] Although some technologies have been used to try to solve specific types of electromagnetic interference, most of the existing technologies focus on suppressing a single interference source, such as eliminating Gaussian white noise by designing special filtering algorithms, or using signal processing technology to reduce the impact of clutter. However, these methods are not very effective when facing complex electromagnetic interference, because they usually only focus on one or several forms of interference, and do not fully consider the interactive effects when multiple interference sources exist at the same time, and fail to fully cover the situation of complex electromagnetic interference. This means that when faced with actual scenarios where multiple interferences coexist, the effectiveness of these technologies will be greatly reduced, so it is impossible to accurately predict and quantify the radar performance in such a complex environment. Summary of the invention

[0005] The present invention aims at the problems that the current radar error measurement process only focuses on one or several interference forms, and does not fully consider the interaction effects when multiple interference sources exist at the same time. A radar error measurement method under composite electromagnetic interference is provided. Based on radar characteristic parameters and carrier-based aircraft characteristic parameters, a composite electromagnetic interference signal including Gaussian white noise, clutter, noise amplitude modulation and noise frequency modulation is generated by simulation means and mathematical modeling, and a radar signal-to-noise ratio, angle measurement error root mean square and distance measurement error root mean square are calculated by a specific calculation method, and then the angle measurement error and distance measurement error are generated by a random number generator, so that the radar error measurement has higher accuracy, and the working performance of the radar can be more accurately evaluated in a complex electromagnetic environment, which is helpful to improve the landing safety of carrier-based UAVs. The present invention also relates to a radar error measurement system under composite electromagnetic interference.

[0006] The technical solution of the present invention is as follows:

[0007] A radar error measurement method under composite electromagnetic interference, characterized in that it comprises the following steps:

[0008] Parameter acquisition step: acquiring radar characteristic parameters and carrier-based aircraft characteristic parameters, wherein the radar characteristic parameters include carrier voltage, wavelength, root mean square bandwidth, center frequency and amplitude of carrier signal, radar transmit power, radar transmit antenna gain, radar receive antenna gain and radar antenna aperture of electromagnetic waves transmitted by the radar; and the carrier-based aircraft characteristic parameters include scattering cross-sectional area of ​​the carrier-based aircraft and the distance between the carrier-based aircraft and the radar;

[0009] The instantaneous amplitude generation step of the Gaussian white noise interference signal is as follows: a random number generator is used to generate random numbers that obey a normal distribution with specific parameters for all time points within a certain time period, thereby forming a random number sequence to simulate the Gaussian white noise interference signal within the time period, and the random number at each time point in the random number sequence is used as the instantaneous amplitude of the Gaussian white noise interference signal at the corresponding time point; and each random number representing the Gaussian white noise interference signal in the random number sequence is subjected to band-limiting processing to obtain Gaussian band-limited white noise;

[0010] The instantaneous amplitude generation step of the clutter interference signal is as follows: a random number generator is used to generate random numbers that obey the Rayleigh distribution with a specific scale parameter for all time points within a certain time period, thereby forming a random number sequence to simulate the clutter interference signal within the time period, and the random number at each time point in the random number sequence is used as the instantaneous amplitude of the clutter interference signal at the corresponding time point;

[0011] The instantaneous amplitude calculation steps of the noise AM and FM interference signals are as follows: the instantaneous amplitude of the noise AM interference signal is calculated according to the carrier voltage, the Gaussian band-limited white noise and the center frequency of the carrier signal; and the instantaneous amplitude of the noise FM interference signal is calculated according to the amplitude of the carrier signal, the Gaussian band-limited white noise and the center frequency of the carrier signal;

[0012] Instantaneous power calculation step: the amplitude of the composite electromagnetic interference signal is calculated according to the instantaneous amplitude of the Gaussian white noise interference signal, the instantaneous amplitude of the clutter interference signal, the instantaneous amplitude of the noise amplitude modulation interference signal and the instantaneous amplitude of the noise frequency modulation interference signal, and then the instantaneous power of the composite electromagnetic interference signal is calculated according to the amplitude of the composite electromagnetic interference signal;

[0013] SNR calculation steps: Calculate the radar received echo power based on radar transmit power, radar transmit antenna gain, radar receive antenna gain, wavelength, scattering cross-section, and the distance between the carrier-based aircraft and the radar; Calculate the radar signal-to-noise ratio based on the received echo power and the instantaneous power of the composite electromagnetic interference signal;

[0014] Calculation steps of angle measurement and distance measurement error root mean square: Calculate the angle measurement error root mean square according to the signal-to-noise ratio, radar antenna aperture and wavelength, and calculate the distance measurement error root mean square according to the signal-to-noise ratio and root mean square bandwidth;

[0015] Angle measurement and ranging error generation steps: The angle measurement error root mean square and the ranging error root mean square are respectively input into the random number generator, and the angle measurement error and the ranging error are output to realize the measurement of radar error.

[0016] Preferably, in the signal-to-noise ratio calculation step, after calculating the received echo power of the radar, the received echo power is corrected using the loss factor to obtain the corrected received echo power to reflect the reduction in effective received power due to loss in actual situations.

[0017] Preferably, in the step of generating the instantaneous amplitude of the Gaussian white noise interference signal, using a random number generator to generate random numbers that obey a normal distribution with specific parameters for all time points within a certain time period specifically includes:

[0018] A random time seed with a normal distribution that obeys a first specific parameter is generated by a random number generator in MATLAB software, and the random time seed is input into a SIMULINK model in MATLAB software. The SIMULINK model generates random numbers with a normal distribution that obey a second specific parameter for all time points within a certain time period.

[0019] Preferably, in the parameter acquisition step, the radar characteristic parameters also include the effective receiving area of ​​the radar receiving antenna and the transmitting antenna, the electromagnetic wave propagation speed, and the time delay of receiving the signal echo after the radar transmits a signal; the radar receiving antenna gain is calculated based on the effective receiving area and wavelength of the radar receiving antenna; the radar transmitting antenna gain is calculated based on the effective receiving area and wavelength of the radar transmitting antenna.

[0020] Preferably, in the step of calculating the instantaneous amplitude of the noise amplitude modulation and frequency modulation interference signal, digital signal processing technology is also used to refine the instantaneous amplitude of the noise amplitude modulation and frequency modulation interference signal respectively to obtain the instantaneous amplitude with higher resolution; the digital signal processing technology includes wavelet transform or Fourier transform.

[0021] Preferably, the distance between the carrier-based aircraft and the radar is calculated based on the propagation speed of electromagnetic waves and the time delay of receiving the echo of a signal after the radar transmits the signal.

[0022] A radar error measurement system under composite electromagnetic interference, characterized by comprising a parameter acquisition module, a Gaussian white noise interference signal instantaneous amplitude generation module, a clutter interference signal instantaneous amplitude generation module, a noise amplitude modulation and frequency modulation interference signal instantaneous amplitude calculation module, an instantaneous power calculation module, a signal-to-noise ratio calculation module, an angle measurement and distance measurement error root mean square calculation module and an angle measurement and distance measurement error generation module, which are connected in sequence.

[0023] The parameter acquisition module acquires radar characteristic parameters and carrier-based aircraft characteristic parameters, wherein the radar characteristic parameters include the carrier voltage, wavelength, root mean square bandwidth, center frequency and amplitude of the carrier signal, radar transmission power, radar transmission antenna gain, radar receiving antenna gain and radar antenna aperture of the electromagnetic wave transmitted by the radar; and the carrier-based aircraft characteristic parameters include the scattering cross-sectional area of ​​the carrier-based aircraft and the distance between the carrier-based aircraft and the radar;

[0024] The Gaussian white noise interference signal instantaneous amplitude generation module uses a random number generator to generate random numbers that obey a normal distribution with specific parameters for all time points within a certain time period, thereby forming a random number sequence to simulate the Gaussian white noise interference signal within the time period, and uses the random number at each time point in the random number sequence as the instantaneous amplitude of the Gaussian white noise interference signal at the corresponding time point; and then performs band-limiting processing on each random number representing the Gaussian white noise interference signal in the random number sequence to obtain Gaussian band-limited white noise;

[0025] The clutter interference signal instantaneous amplitude generation module uses a random number generator to generate random numbers that obey Rayleigh distribution with specific scale parameters for all time points within a certain time period, thereby forming a random number sequence to simulate the clutter interference signal within the time period, and uses the random number at each time point in the random number sequence as the instantaneous amplitude of the clutter interference signal at the corresponding time point;

[0026] The noise AM and FM interference signal instantaneous amplitude calculation module calculates the instantaneous amplitude of the noise AM interference signal according to the carrier voltage, Gaussian band-limited white noise and the center frequency of the carrier signal; and calculates the instantaneous amplitude of the noise FM interference signal according to the amplitude of the carrier signal, Gaussian band-limited white noise and the center frequency of the carrier signal;

[0027] The instantaneous power calculation module calculates the amplitude of the composite electromagnetic interference signal according to the instantaneous amplitude of the Gaussian white noise interference signal, the instantaneous amplitude of the clutter interference signal, the instantaneous amplitude of the noise amplitude modulation interference signal, and the instantaneous amplitude of the noise frequency modulation interference signal, and then calculates the instantaneous power of the composite electromagnetic interference signal according to the amplitude of the composite electromagnetic interference signal;

[0028] The signal-to-noise ratio calculation module calculates the radar receiving echo power based on the radar transmitting power, the radar transmitting antenna gain, the radar receiving antenna gain, the wavelength, the scattering cross-sectional area and the distance between the carrier-based aircraft and the radar, and calculates the radar signal-to-noise ratio according to the receiving echo power and the instantaneous power of the composite electromagnetic interference signal;

[0029] The angle measurement and distance measurement error root mean square calculation module calculates the angle measurement error root mean square according to the signal-to-noise ratio, radar antenna aperture and wavelength, and calculates the distance measurement error root mean square according to the signal-to-noise ratio and root mean square bandwidth;

[0030] The angle measurement and ranging error generation module inputs the angle measurement error root mean square and the ranging error root mean square into a random number generator respectively, and outputs the angle measurement error and the ranging error to achieve radar error measurement.

[0031] Preferably, in the signal-to-noise ratio calculation module, after calculating the received echo power of the radar, the received echo power is corrected using the loss factor to obtain the corrected received echo power to reflect the reduction in effective received power due to loss in actual situations.

[0032] Preferably, in the Gaussian white noise interference signal instantaneous amplitude generation module, using a random number generator to generate random numbers that obey a normal distribution with specific parameters for all time points within a certain time period specifically includes:

[0033] A random time seed with a normal distribution that obeys a first specific parameter is generated by a random number generator in MATLAB software, and the random time seed is input into a SIMULINK model in MATLAB software. The SIMULINK model generates random numbers with a normal distribution that obey a second specific parameter for all time points within a certain time period.

[0034] Preferably, the radar characteristic parameters also include effective receiving areas of the radar receiving antenna and the transmitting antenna, electromagnetic wave propagation speed, and the time delay of receiving the signal echo after the radar transmits a certain signal; the radar receiving antenna gain is calculated according to the effective receiving area and wavelength of the radar receiving antenna; the radar transmitting antenna gain is calculated according to the effective receiving area and wavelength of the radar transmitting antenna; the distance between the carrier-based aircraft and the radar is calculated according to the electromagnetic wave propagation speed and the time delay of receiving the signal echo after the radar transmits a certain signal.

[0035] The beneficial effects of the present invention are:

[0036] The present invention provides a radar error measurement method under composite electromagnetic interference. The method is based on radar characteristic parameters and carrier-based aircraft characteristic parameters, and uses a random number generator to generate random numbers of normal distribution obeying specific parameters for all time points within a certain time period, and generates random numbers of Rayleigh distribution obeying specific scale parameters, so as to form a random number sequence to simulate Gaussian white noise interference signals and clutter interference signals that are more in line with the actual situation within the time period, and the random number at each time point in the random number sequence is used as the instantaneous amplitude of the Gaussian white noise interference signal and the clutter interference signal at the corresponding time point; then a specific calculation method is used to calculate the instantaneous amplitude of the noise amplitude modulation and frequency modulation interference signals respectively, and then the amplitude and instantaneous power of the composite electromagnetic interference signal are calculated. By comprehensively considering the influence of the complex electromagnetic interference environment composed of multiple interference signals on the radar, the working performance of the radar can be more accurately evaluated in the complex electromagnetic environment, with higher accuracy, which is helpful to improve the landing safety of the carrier-based unmanned aerial vehicle. Then, a specific calculation method is used to calculate the received echo power of the radar, and the signal-to-noise ratio of the radar is calculated according to the received echo power and the instantaneous power of the composite electromagnetic interference signal. By combining the physical characteristics of the radar and the influence of the composite electromagnetic interference, the error performance of the radar in different environments can be more accurately estimated, so that it can still maintain high performance in a complex electromagnetic environment; and then the root mean square of the angle measurement error and the root mean square of the ranging error are calculated according to the signal-to-noise ratio, and finally the root mean square of the angle measurement error and the root mean square of the ranging error are respectively input into the random number generator, and the angle measurement error and the ranging error are output to achieve accurate measurement of the radar error. Since the signal-to-noise ratio corresponding to different moments is different, the radar error generation that meets different conditions (i.e., mean and root mean square) is generated at each moment. By analyzing the radar error change trend under different signal-to-noise ratio conditions, the research and development personnel can identify which factors have a greater impact on the radar accuracy, and adjust the radar parameter settings accordingly, improve the overall performance, and better calibrate and compensate for the radar measurement error, thereby improving the accuracy of target tracking and positioning. The present invention helps to formulate effective anti-interference strategies and enhance the survivability and combat effectiveness of the radar system by understanding the response characteristics of the radar under different interference conditions.

[0037] The present invention also relates to a radar error measurement system under composite electromagnetic interference, which corresponds to the above-mentioned radar error measurement method under composite electromagnetic interference, and can be understood as a system for implementing the above-mentioned radar error measurement method under composite electromagnetic interference, comprising a parameter acquisition module, a Gaussian white noise interference signal instantaneous amplitude generation module, a clutter interference signal instantaneous amplitude generation module, a noise amplitude modulation and frequency modulation interference signal instantaneous amplitude calculation module, an instantaneous power calculation module, a signal-to-noise ratio calculation module, an angle measurement and ranging error root mean square calculation module, and an angle measurement and ranging error generation module, which are sequentially connected. The modules cooperate with each other, based on radar characteristic parameters and carrier-based aircraft characteristic parameters, a composite electromagnetic interference signal including Gaussian white noise, clutter, noise amplitude modulation and noise frequency modulation is generated by simulation means and mathematical modeling, and a specific calculation method is used to calculate the radar's signal-to-noise ratio, angle measurement error root mean square and ranging error root mean square, and then the angle measurement error and ranging error are generated by a random number generator, which has higher accuracy, can more accurately evaluate the working performance of the radar in a complex electromagnetic environment, and is helpful to improve the landing safety of carrier-based UAVs. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a flow chart of the radar error measurement method under composite electromagnetic interference of the present invention.

[0039] Figure 2 This is a flow chart of converting pseudo-random numbers into true random numbers in the present invention. DETAILED DESCRIPTION

[0040] The present invention will be described below in conjunction with the accompanying drawings.

[0041] The present invention relates to a radar error measurement method under composite electromagnetic interference. The flow chart of the method is as follows: Figure 1 As shown, the following steps are included in sequence:

[0042] Parameter acquisition step: Acquire radar characteristic parameters and carrier-based aircraft characteristic parameters. Radar characteristic parameters include the carrier voltage, wavelength, root mean square bandwidth, center frequency and amplitude of the carrier signal, radar transmission power, radar transmission antenna gain, radar receiving antenna gain and radar antenna aperture of the electromagnetic wave emitted by the radar; carrier-based aircraft characteristic parameters include the scattering cross-sectional area of ​​the carrier-based aircraft and the distance between the carrier-based aircraft and the radar. Preferably, the radar characteristic parameters also include the effective receiving area of ​​the radar receiving antenna, the effective receiving area of ​​the transmitting antenna, the electromagnetic wave propagation speed and the time delay of receiving the echo of the signal after the radar transmits a certain signal; according to the effective receiving area A of the radar receiving antenna r The radar receiving antenna gain is calculated by the following formula:

[0043]

[0044] Among them, A r is the effective receiving area of ​​the radar receiving antenna, and λ is the wavelength of the electromagnetic wave emitted by the radar.

[0045] And according to the effective receiving area A of the radar transmitting antenna t The radar transmitting antenna gain is calculated by the following formula:

[0046]

[0047] Among them, A t is the effective receiving area of ​​the radar transmitting antenna, and λ is the wavelength of the electromagnetic wave emitted by the radar.

[0048] In addition, when the radar is working, it transmits a series of periodic high-frequency pulses into space. Assume that the time delay of receiving the echo of the signal after transmitting is t r , the electromagnetic wave propagation speed is c, then the straight-line distance between the target and the antenna, that is, the distance R between the carrier-based aircraft and the radar is calculated according to the following formula:

[0049]

[0050] The instantaneous amplitude generation step of the Gaussian white noise interference signal is as follows: a random number generator is used to generate random numbers that obey a normal distribution with specific parameters for all time points within a certain time period, thereby forming a random number sequence to simulate the Gaussian white noise interference signal within the time period, and the random number at each time point in the random number sequence is used as the instantaneous amplitude of the Gaussian white noise interference signal at the corresponding time point; and each random number representing the Gaussian white noise interference signal in the random number sequence is band-limited to obtain Gaussian band-limited white noise.

[0051] Specifically, in a naval combat environment, due to the presence of various types of interference, the waveform, phase and power of electromagnetic signals are often highly random, forming a complex electromagnetic interference environment, which will directly affect the accuracy and stability of electronic equipment. This environment is particularly unfavorable for radars. This is because in a complex electromagnetic interference environment, the receiver will receive interference waves and generate measurement errors. Therefore, a full understanding of the complex electromagnetic interference environment will be of great significance for the safety analysis of the radar-guided landing mission of carrier-based aircraft in this environment. The types of interference are mainly divided into natural electromagnetic interference and man-made interference, among which natural electromagnetic interference includes noise interference (i.e., noise interference signal) and clutter interference (i.e., clutter interference signal).

[0052] Assuming that the aircraft carrier is far away from the land, the interference signals received by its radar detection are classified into the above three categories:

[0053] 1) Noise interference: electronic noise from equipment on board ships, such as radar receiver noise;

[0054] 2) Clutter interference: There is no need to detect the reflected echo generated by the object and the scattering effect of the medium on the electromagnetic wave, such as rain clutter and sea clutter;

[0055] 3) Human interference: interference signals emitted by enemy jammers, such as noise FM interference, noise AM interference, etc.

[0056] The noise interference signal is mainly composed of two aspects: the noise existing in the natural environment and the noise generated by the common frequency equipment of both the enemy and us. This noise signal is similar to white noise, so Gaussian white noise is selected as the simulation model, and its description formula is as follows:

[0057] J(t)=U n (t)cos[w j t+φ(t)]

[0058] Among them, U n (t) and φ(t) are both independent functions, functions of time t, and can be random variables. j is the carrier frequency constant.

[0059] However, due to the fact that pseudo-random numbers are mostly used in the simulation process of Gaussian white noise, pseudo-random numbers are random numbers generated for each time node in sequence starting from the initial time point within a certain time period, that is, there is a random sequence, but the time of appearance is progressive from the initial time to the end time, which is not random. Therefore, each simulation will generate the same random number sequence, resulting in repeatability of the simulation results, unable to truly reflect the random behavior of the aircraft landing process and unable to simulate the real random interference environment. At the same time, since the simulation cannot cover all possible interference situations, it will lead to deviations in the simulation results, and it is impossible to fully evaluate the performance of the system under different interference conditions. Therefore, Figure 2 As shown, a random time seed 'Seed' that obeys the normal distribution of the first specific parameter is first generated by the random number generator in the MATLAB software. The value of the random time seed parameter variable adopts the normal distribution that satisfies the first specific parameter N (mean is 0, variance is 10000), and the random time seed 'Seed' parameter is composed of random variables. Therefore, when generating the 'Seed' variable, a reset time seed statement is used to make the 'Seed' variable a true random number; then the random time seed is input into the SIMULINK model in the MATLAB software, and the SIMULINK model generates a random number that obeys the second specific parameter (i.e., the mean is 0, the variance is σ) for all time points within a certain time period. 2) is a normally distributed random number (i.e., a true random number), and then a random number sequence is formed to simulate the Gaussian white noise interference signal within the simulation time period. The initial time seed of the Gaussian white noise can maintain the random characteristics in each simulation, that is, the Gaussian white noise random number sequence in each simulation is different, which can ensure the diversity and authenticity of the simulation results, more accurately simulate the random interference environment, help to improve the accuracy of the simulation, make the simulation results closer to the actual situation, and more comprehensively evaluate the success rate of radar-guided landing of aircraft under different interference conditions.

[0060] Then, the random number at each time point in the random number sequence is used as the instantaneous amplitude U1 of the Gaussian white noise interference signal at the corresponding time point; and each random number representing the Gaussian white noise interference signal in the random number sequence is band-limited to obtain a mean of 0 and a variance of σ 2 Gaussian band-limited white noise u A (t). The probability density formula satisfied by the instantaneous amplitude of the Gaussian white noise interference signal is:

[0061]

[0062] Where, u is the instantaneous amplitude of the Gaussian white noise interference signal, σ 2 is the interference signal power.

[0063] The instantaneous amplitude generation step of the clutter interference signal is as follows: a random number generator is used to generate random numbers that obey the Rayleigh distribution with a specific scale parameter for all time points within a certain time period, thereby forming a random number sequence to simulate the clutter interference signal within the time period, and the random number at each time point in the random number sequence is used as the instantaneous amplitude of the clutter interference signal at the corresponding time point.

[0064] Specifically, clutter signals refer to the echo components in the received radar echo signals caused by surface scattering or volume scattering, which usually come from the ground and buildings, oceans, rainy and snowy weather, bird flocks and insects, etc. In essence, clutter signals are interference signals received by the radar in the working state. These signals are the same as the echo signals of the target objects, but have more complex characteristics. In essence, the clutter scattering phenomenon is a random distribution process based on the morphological characteristics of the ground and sea surface. The commonly used clutter amplitude statistical model and clutter correlation analysis model can fully describe the distribution structure of clutter. The clutter models recognized in the academic community include Rayleigh, Log Normal, Weibull, K distribution, etc. Therefore, the Rayleigh distribution model, which mainly describes meteorological clutter signals, radar clutter signals with low resolution, and foil interference signals, is used as the research object for simulation. Therefore, a random number generator is first used to generate random numbers that obey the Rayleigh distribution with a specific scale parameter (that is, the scale parameter is σ) for all time points within a certain time period, and then a random number sequence is formed to simulate the clutter interference signal within the time period. Then, the random number at each time point in the random number sequence is used as the instantaneous amplitude U2 of the clutter interference signal at the corresponding time point.

[0065] Among them, the probability distribution density function of the Rayleigh distribution model is:

[0066]

[0067] Here, the Rayleigh distribution clutter with a scale parameter of 5 is selected for simulation. The meaning of the scale parameter is the σ value in the function, which determines the overall size of the signal amplitude. When σ increases, although the signal amplitude can be large or small due to random distribution, the overall amplitude shows an increasing trend; vice versa. It should be noted that the scale parameter is not a unique limitation, and its value will change with time and random factors. Scale parameters of different sizes can be selected according to actual needs.

[0068] The instantaneous amplitude calculation step of the noise AM and FM interference signal is as follows: the instantaneous amplitude of the noise AM interference signal is calculated according to the carrier voltage, the Gaussian band-limited white noise and the center frequency of the carrier signal; and the instantaneous amplitude of the noise FM interference signal is calculated according to the amplitude of the carrier signal, the Gaussian band-limited white noise and the center frequency of the carrier signal. Preferably, after the instantaneous amplitude of the noise AM and FM interference signals are calculated, digital signal processing technology (such as wavelet transform or Fourier transform) is used to refine the instantaneous amplitude of the noise AM and FM interference signals respectively to obtain an instantaneous amplitude with higher resolution.

[0069] Specifically, artificial electromagnetic interference is mainly generated by interference signals emitted by enemy jammers, such as noise amplitude modulation interference and noise frequency modulation interference. Among them, the interference that uses noise to modulate the amplitude of the RF signal is called noise amplitude modulation interference, and the noise amplitude modulation interference signal is expressed as follows:

[0070] J(t)=[U0+u A (t)]cos(w j t)

[0071] In the above formula, U0 is the carrier voltage; u A (t) has zero mean and variance σ 2 Gaussian band-limited white noise is a random variable whose value will change with time and random factors. By taking the absolute value of J(t) (i.e. calculating |J(t)|), we can get the instantaneous amplitude U3 of the noise amplitude modulation interference signal at time t.

[0072] Noise frequency modulation interference refers to an interference signal formed by frequency modulating the carrier signal with a random baseband signal waveform. j , the center frequency is w j The carrier signal is frequency modulated to generate a noise frequency modulation interference signal J(t), as shown in the following formula:

[0073]

[0074] In the above formula, U j is the amplitude of the carrier signal, w j is the center frequency of the carrier signal, K FM is the frequency modulation slope, u(t) modulation noise is a zero-mean, wide-sense stable random process, which can be expressed as 2 The Gaussian band-limited white noise is used instead. By finding the absolute value of J(t) (i.e. calculating |J(t)|), the instantaneous amplitude U4 of the noise frequency modulation interference signal at time t can be obtained.

[0075] Instantaneous power calculation steps: The amplitude of the composite electromagnetic interference signal is calculated according to the instantaneous amplitude of the Gaussian white noise interference signal, the instantaneous amplitude of the clutter interference signal, the instantaneous amplitude of the noise amplitude modulation interference signal and the instantaneous amplitude of the noise frequency modulation interference signal, and then the instantaneous power of the composite electromagnetic interference signal is calculated according to the amplitude of the composite electromagnetic interference signal.

[0076] Specifically, firstly, the amplitude U of the composite electromagnetic interference signal is calculated according to the instantaneous amplitude U1 of the Gaussian white noise interference signal, the instantaneous amplitude U2 of the clutter interference signal, the instantaneous amplitude U3 of the noise amplitude modulation interference signal, and the instantaneous amplitude U4 of the noise frequency modulation interference signal, and the calculation is performed according to the following formula:

[0077] U=U1+U2+U3+U4

[0078] When noise interference, clutter interference and jammer interference act at the same time, the receiver will receive the composite electromagnetic interference, which is called composite electromagnetic interference. Therefore, the instantaneous power P of the composite electromagnetic interference signal is calculated based on the amplitude of the composite electromagnetic interference signal. n , calculated according to the following formula:

[0079] P n =U 2

[0080] The signal-to-noise ratio calculation step is as follows: the radar received echo power is calculated based on the radar transmit power, the radar transmit antenna gain, the radar receive antenna gain, the wavelength, the scattering cross-sectional area, and the distance between the carrier-based aircraft and the radar, and the radar signal-to-noise ratio is calculated according to the received echo power and the instantaneous power of the composite electromagnetic interference signal. Preferably, before calculating the signal-to-noise ratio, the radar received echo power and the instantaneous power of the composite electromagnetic interference signal are normalized to obtain the normalized received echo power and the instantaneous power of the composite electromagnetic interference signal, so as to ensure that the calculation result is not affected by the absolute power level.

[0081] Specifically, the radar receiving echo power is first calculated based on the radar transmitting power, radar transmitting antenna gain, radar receiving antenna gain, wavelength, scattering cross-section, and the distance between the carrier-based aircraft and the radar, and is calculated according to the following formula:

[0082]

[0083] In the above formula, P t is the radar transmission power, G t is the radar transmitting antenna gain, G r is the radar receiving antenna gain, λ is the wavelength of the electromagnetic wave emitted by the radar, σ is the scattering cross-sectional area of ​​the carrier-based aircraft, and R is the distance between the carrier-based aircraft and the radar.

[0084] The actual loss of the equipment and environmental factors are added, and the received echo power equation taking into account the two influencing factors is given to obtain the impact of electromagnetic interference on the radar effect, and then simulate the impact of the radar effect on the landing of the UAV.

[0085] Since the actual radar system always has various losses, the loss correction should be introduced, and the loss factor L should be used to correct the received echo power to obtain the corrected received echo power to reflect the actual situation where the effective received power is reduced due to losses. By considering the actual losses and environmental factors, the received echo power equation taking into account the two influencing factors is given to obtain the impact of electromagnetic interference on the radar effect, and then simulate the impact of the radar effect on the landing of the UAV. L represents the loss factor added to the denominator of the received echo power. L is a value greater than 1 and is expressed in positive decibels. The corrected received echo power is expressed as:

[0086]

[0087] Then, the radar signal-to-noise ratio (SNR) is calculated based on the corrected received echo power and the instantaneous power of the composite electromagnetic interference signal, according to the following formula:

[0088]

[0089] Calculation steps for the root mean square of angle measurement and distance measurement errors: Calculate the root mean square of angle measurement error based on the signal-to-noise ratio, radar antenna aperture, and wavelength, and calculate according to the following formula:

[0090]

[0091] In the above formula, SNR is the signal-to-noise ratio of the radar, D is the radar antenna aperture, and λ is the wavelength.

[0092] The RMS of the ranging error is calculated based on the signal-to-noise ratio and the RMS bandwidth, and is calculated according to the following formula:

[0093]

[0094] In the above formula, B c represents the RMS bandwidth of the radar transmit signal, SNR is the radar’s signal-to-noise ratio, and c is the speed of light.

[0095] Angle measurement and ranging error generation steps: The angle measurement error root mean square and the ranging error root mean square are respectively input into the random number generator, and the angle measurement error and the ranging error are output to realize the measurement of radar error.

[0096] Specifically, a random number generator is used to generate an angle measurement error that obeys a normal distribution with a mean of 0 and a standard deviation of the angle measurement error root mean square at each moment, and a random number generator is used to generate a ranging error that obeys a normal distribution with a mean of 0 and a standard deviation of the ranging error root mean square at each moment. And because the signal-to-noise ratio corresponding to different moments is different, radar errors (angle measurement errors and ranging errors) that meet different conditions (i.e., meet 0 mean and root mean square) are generated at each moment.

[0097] The present invention also relates to a radar error measurement system under composite electromagnetic interference, which corresponds to the radar error measurement method under composite electromagnetic interference, and can be understood as a system for implementing the method. The system includes a parameter acquisition module, a Gaussian white noise interference signal instantaneous amplitude generation module, a clutter interference signal instantaneous amplitude generation module, a noise amplitude modulation and frequency modulation interference signal instantaneous amplitude calculation module, an instantaneous power calculation module, a signal-to-noise ratio calculation module, an angle measurement and ranging error root mean square calculation module, and an angle measurement and ranging error generation module, which are connected in sequence. Specifically,

[0098] The parameter acquisition module acquires radar characteristic parameters and carrier-based aircraft characteristic parameters, wherein the radar characteristic parameters include the carrier voltage, wavelength, root mean square bandwidth, center frequency and amplitude of the carrier signal, radar transmission power, radar transmission antenna gain, radar receiving antenna gain and radar antenna aperture of the electromagnetic wave transmitted by the radar; and the carrier-based aircraft characteristic parameters include the scattering cross-sectional area of ​​the carrier-based aircraft and the distance between the carrier-based aircraft and the radar;

[0099] The Gaussian white noise interference signal instantaneous amplitude generation module uses a random number generator to generate random numbers that obey a normal distribution with specific parameters for all time points within a certain time period, thereby forming a random number sequence to simulate the Gaussian white noise interference signal within the time period, and uses the random number at each time point in the random number sequence as the instantaneous amplitude of the Gaussian white noise interference signal at the corresponding time point; and then performs band-limiting processing on each random number representing the Gaussian white noise interference signal in the random number sequence to obtain Gaussian band-limited white noise;

[0100] The clutter interference signal instantaneous amplitude generation module uses a random number generator to generate random numbers that obey Rayleigh distribution with specific scale parameters for all time points within a certain time period, thereby forming a random number sequence to simulate the clutter interference signal within the time period, and uses the random number at each time point in the random number sequence as the instantaneous amplitude of the clutter interference signal at the corresponding time point;

[0101] The noise AM and FM interference signal instantaneous amplitude calculation module calculates the instantaneous amplitude of the noise AM interference signal according to the carrier voltage, Gaussian band-limited white noise and the center frequency of the carrier signal; and calculates the instantaneous amplitude of the noise FM interference signal according to the amplitude of the carrier signal, Gaussian band-limited white noise and the center frequency of the carrier signal;

[0102] The instantaneous power calculation module calculates the amplitude of the composite electromagnetic interference signal according to the instantaneous amplitude of the Gaussian white noise interference signal, the instantaneous amplitude of the clutter interference signal, the instantaneous amplitude of the noise amplitude modulation interference signal, and the instantaneous amplitude of the noise frequency modulation interference signal, and then calculates the instantaneous power of the composite electromagnetic interference signal according to the amplitude of the composite electromagnetic interference signal;

[0103] The signal-to-noise ratio calculation module calculates the radar receiving echo power based on the radar transmitting power, the radar transmitting antenna gain, the radar receiving antenna gain, the wavelength, the scattering cross-sectional area and the distance between the carrier-based aircraft and the radar, and calculates the radar signal-to-noise ratio according to the receiving echo power and the instantaneous power of the composite electromagnetic interference signal;

[0104] The angle measurement and distance measurement error root mean square calculation module calculates the angle measurement error root mean square according to the signal-to-noise ratio, radar antenna aperture and wavelength, and calculates the distance measurement error root mean square according to the signal-to-noise ratio and root mean square bandwidth;

[0105] The angle measurement and ranging error generation module inputs the angle measurement error root mean square and the ranging error root mean square into a random number generator respectively, and outputs the angle measurement error and the ranging error to achieve radar error measurement.

[0106] Preferably, in the signal-to-noise ratio calculation module, after calculating the received echo power of the radar, the received echo power is corrected using the loss factor to obtain the corrected received echo power to reflect the reduction in effective received power due to loss in actual situations.

[0107] Preferably, in the noise amplitude modulation and frequency modulation interference signal instantaneous amplitude calculation module, digital signal processing technology is also used to refine the instantaneous amplitude of the noise amplitude modulation and frequency modulation interference signal respectively to obtain the instantaneous amplitude with higher resolution; the digital signal processing technology includes wavelet transform or Fourier transform.

[0108] Preferably, the radar characteristic parameters also include the effective receiving areas of the radar receiving antenna and the transmitting antenna, the electromagnetic wave propagation speed, and the time delay of receiving the echo of a signal after the radar transmits a certain signal; the radar receiving antenna gain is calculated according to the effective receiving area and wavelength of the radar receiving antenna; the radar transmitting antenna gain is calculated according to the effective receiving area and wavelength of the radar transmitting antenna; the distance between the carrier-based aircraft and the radar is calculated according to the electromagnetic wave propagation speed and the time delay of receiving the echo of the signal after the radar transmits a certain signal.

[0109] The present invention provides an objective and scientific radar error measurement method and system under composite electromagnetic interference. Based on radar characteristic parameters and carrier-based aircraft characteristic parameters, a composite electromagnetic interference signal including Gaussian white noise, clutter, noise amplitude modulation and noise frequency modulation is generated by using simulation means and mathematical modeling, and a radar signal-to-noise ratio, a root mean square of an angle measurement error and a root mean square of a distance measurement error are calculated by using a specific calculation method. Then, an angle measurement error and a distance measurement error are generated by a random number generator, so that the radar error measurement has higher accuracy, can more accurately evaluate the working performance of the radar in a complex electromagnetic environment, and is helpful to improve the landing safety of carrier-based UAVs.

[0110] It should be noted that the above-described specific implementations can enable those skilled in the art to more fully understand the invention, but do not limit the invention in any way. Therefore, although this specification has described the invention in detail with reference to the drawings and embodiments, those skilled in the art should understand that the invention can still be modified or replaced by equivalents. In short, all technical solutions and improvements that do not deviate from the spirit and scope of the invention should be included in the protection scope of the patent for the invention.

Claims

1. A radar error measurement method under composite electromagnetic interference, characterized in that: The following steps are involved: Parameter acquisition step: acquiring radar characteristic parameters and carrier-based aircraft characteristic parameters, wherein the radar characteristic parameters include carrier voltage, wavelength, root mean square bandwidth, center frequency and amplitude of carrier signal, radar transmit power, radar transmit antenna gain, radar receive antenna gain and radar antenna aperture of electromagnetic waves transmitted by the radar; and the carrier-based aircraft characteristic parameters include scattering cross-sectional area of ​​the carrier-based aircraft and the distance between the carrier-based aircraft and the radar; The instantaneous amplitude generation step of the Gaussian white noise interference signal is as follows: a random number generator is used to generate random numbers that obey a normal distribution with specific parameters for all time points within a certain time period, thereby forming a random number sequence to simulate the Gaussian white noise interference signal within the time period, and the random number at each time point in the random number sequence is used as the instantaneous amplitude of the Gaussian white noise interference signal at the corresponding time point; and each random number representing the Gaussian white noise interference signal in the random number sequence is subjected to band-limiting processing to obtain Gaussian band-limited white noise; The instantaneous amplitude generation step of the clutter interference signal is as follows: a random number generator is used to generate random numbers that obey the Rayleigh distribution with a specific scale parameter for all time points within a certain time period, thereby forming a random number sequence to simulate the clutter interference signal within the time period, and the random number at each time point in the random number sequence is used as the instantaneous amplitude of the clutter interference signal at the corresponding time point; The instantaneous amplitude calculation steps of the noise AM and FM interference signals are as follows: the instantaneous amplitude of the noise AM interference signal is calculated according to the carrier voltage, the Gaussian band-limited white noise and the center frequency of the carrier signal; and the instantaneous amplitude of the noise FM interference signal is calculated according to the amplitude of the carrier signal, the Gaussian band-limited white noise and the center frequency of the carrier signal; Instantaneous power calculation step: the amplitude of the composite electromagnetic interference signal is calculated according to the instantaneous amplitude of the Gaussian white noise interference signal, the instantaneous amplitude of the clutter interference signal, the instantaneous amplitude of the noise amplitude modulation interference signal and the instantaneous amplitude of the noise frequency modulation interference signal, and then the instantaneous power of the composite electromagnetic interference signal is calculated according to the amplitude of the composite electromagnetic interference signal; SNR calculation steps: Calculate the radar received echo power based on radar transmit power, radar transmit antenna gain, radar receive antenna gain, wavelength, scattering cross-section, and the distance between the carrier-based aircraft and the radar; Calculate the radar signal-to-noise ratio based on the received echo power and the instantaneous power of the composite electromagnetic interference signal; Calculation steps of angle measurement and distance measurement error root mean square: Calculate the angle measurement error root mean square according to the signal-to-noise ratio, radar antenna aperture and wavelength, and calculate the distance measurement error root mean square according to the signal-to-noise ratio and root mean square bandwidth; Angle measurement and ranging error generation steps: The angle measurement error root mean square and the ranging error root mean square are respectively input into the random number generator, and the angle measurement error and the ranging error are output to realize the measurement of radar error.

2. The radar error measurement method under composite electromagnetic interference according to claim 1, characterized in that: In the signal-to-noise ratio calculation step, after calculating the received echo power of the radar, the received echo power is corrected using the loss factor to obtain the corrected received echo power to reflect the reduction in effective received power due to loss in actual situations.

3. The radar error measurement method under composite electromagnetic interference according to claim 1, characterized in that: In the instantaneous amplitude generation step of the Gaussian white noise interference signal, using a random number generator to generate random numbers that obey a normal distribution with specific parameters for all time points within a certain time period specifically includes: A random time seed with a normal distribution that obeys a first specific parameter is generated by a random number generator in MATLAB software, and the random time seed is input into a SIMULINK model in MATLAB software. The SIMULINK model generates random numbers with a normal distribution that obey a second specific parameter for all time points within a certain time period.

4. The radar error measurement method under composite electromagnetic interference according to claim 1, characterized in that: In the parameter acquisition step, the radar characteristic parameters also include the effective receiving area of ​​the radar receiving antenna and the transmitting antenna, the electromagnetic wave propagation speed, and the time delay of receiving the signal echo after the radar transmits a signal; the radar receiving antenna gain is calculated based on the effective receiving area and wavelength of the radar receiving antenna; the radar transmitting antenna gain is calculated based on the effective receiving area and wavelength of the radar transmitting antenna.

5. The radar error measurement method under composite electromagnetic interference according to claim 1, characterized in that: In the step of calculating the instantaneous amplitude of the noise AM and FM interference signals, digital signal processing technology is also used to refine the instantaneous amplitude of the noise AM and FM interference signals respectively to obtain higher resolution instantaneous amplitudes; the digital signal processing technology includes wavelet transform or Fourier transform.

6. The radar error measurement method under composite electromagnetic interference according to claim 4, characterized in that: The distance between the carrier-based aircraft and the radar is calculated based on the propagation speed of electromagnetic waves and the time delay of receiving the echo of a signal after the radar transmits it.

7. A radar error measurement system under composite electromagnetic interference, characterized in that: It includes a parameter acquisition module, a Gaussian white noise interference signal instantaneous amplitude generation module, a clutter interference signal instantaneous amplitude generation module, a noise amplitude modulation and frequency modulation interference signal instantaneous amplitude calculation module, an instantaneous power calculation module, a signal-to-noise ratio calculation module, an angle measurement and distance measurement error root mean square calculation module, and an angle measurement and distance measurement error generation module, which are connected in sequence. The parameter acquisition module acquires radar characteristic parameters and carrier-based aircraft characteristic parameters, wherein the radar characteristic parameters include the carrier voltage, wavelength, root mean square bandwidth, center frequency and amplitude of the carrier signal, radar transmission power, radar transmission antenna gain, radar receiving antenna gain and radar antenna aperture of the electromagnetic wave transmitted by the radar; and the carrier-based aircraft characteristic parameters include the scattering cross-sectional area of ​​the carrier-based aircraft and the distance between the carrier-based aircraft and the radar; The Gaussian white noise interference signal instantaneous amplitude generation module uses a random number generator to generate random numbers that obey a normal distribution with specific parameters for all time points within a certain time period, thereby forming a random number sequence to simulate the Gaussian white noise interference signal within the time period, and uses the random number at each time point in the random number sequence as the instantaneous amplitude of the Gaussian white noise interference signal at the corresponding time point; and then performs band-limiting processing on each random number representing the Gaussian white noise interference signal in the random number sequence to obtain Gaussian band-limited white noise; The clutter interference signal instantaneous amplitude generation module uses a random number generator to generate random numbers that obey Rayleigh distribution with specific scale parameters for all time points within a certain time period, thereby forming a random number sequence to simulate the clutter interference signal within the time period, and uses the random number at each time point in the random number sequence as the instantaneous amplitude of the clutter interference signal at the corresponding time point; The noise AM and FM interference signal instantaneous amplitude calculation module calculates the instantaneous amplitude of the noise AM interference signal according to the carrier voltage, Gaussian band-limited white noise and the center frequency of the carrier signal; and calculates the instantaneous amplitude of the noise FM interference signal according to the amplitude of the carrier signal, Gaussian band-limited white noise and the center frequency of the carrier signal; The instantaneous power calculation module calculates the amplitude of the composite electromagnetic interference signal according to the instantaneous amplitude of the Gaussian white noise interference signal, the instantaneous amplitude of the clutter interference signal, the instantaneous amplitude of the noise amplitude modulation interference signal, and the instantaneous amplitude of the noise frequency modulation interference signal, and then calculates the instantaneous power of the composite electromagnetic interference signal according to the amplitude of the composite electromagnetic interference signal; The signal-to-noise ratio calculation module calculates the radar receiving echo power based on the radar transmitting power, the radar transmitting antenna gain, the radar receiving antenna gain, the wavelength, the scattering cross-sectional area and the distance between the carrier-based aircraft and the radar, and calculates the radar signal-to-noise ratio according to the receiving echo power and the instantaneous power of the composite electromagnetic interference signal; The angle measurement and distance measurement error root mean square calculation module calculates the angle measurement error root mean square according to the signal-to-noise ratio, radar antenna aperture and wavelength, and calculates the distance measurement error root mean square according to the signal-to-noise ratio and root mean square bandwidth; The angle measurement and ranging error generation module inputs the angle measurement error root mean square and the ranging error root mean square into a random number generator respectively, and outputs the angle measurement error and the ranging error to achieve radar error measurement.

8. The radar error measurement system under composite electromagnetic interference according to claim 7, characterized in that: In the signal-to-noise ratio calculation module, after calculating the received echo power of the radar, the received echo power is corrected using the loss factor to obtain the corrected received echo power to reflect the reduction in effective received power due to loss in actual situations.

9. The radar error measurement system under composite electromagnetic interference according to claim 7, characterized in that: In the Gaussian white noise interference signal instantaneous amplitude generation module, using a random number generator to generate random numbers that obey a normal distribution of specific parameters for all time points within a certain time period specifically includes: A random time seed with a normal distribution that obeys a first specific parameter is generated by a random number generator in MATLAB software, and the random time seed is input into a SIMULINK model in MATLAB software. The SIMULINK model generates random numbers with a normal distribution that obey a second specific parameter for all time points within a certain time period.

10. The radar error measurement system under composite electromagnetic interference according to claim 7, characterized in that: The radar characteristic parameters also include the effective receiving areas of the radar receiving antenna and the transmitting antenna, the electromagnetic wave propagation speed, and the time delay of receiving the echo of a signal after the radar transmits a certain signal; the radar receiving antenna gain is calculated according to the effective receiving area and wavelength of the radar receiving antenna; the radar transmitting antenna gain is calculated according to the effective receiving area and wavelength of the radar transmitting antenna; the distance between the carrier-based aircraft and the radar is calculated according to the electromagnetic wave propagation speed and the time delay of receiving the echo of the signal after the radar transmits a certain signal.

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