A dynamic RCS test system and method based on a UAV

Abstract

The present application relates to the field of RCS test, and more particularly to a dynamic RCS test system and method based on unmanned aerial vehicle.The system comprises an unmanned aerial vehicle platform subsystem, a ground measurement radar subsystem and a comprehensive control and data processing subsystem; the unmanned aerial vehicle platform subsystem is composed of an unmanned aerial vehicle carrier, a target mounting mechanism and a first differential GNSS module; the first differential GNSS module is used to obtain the spatial three-dimensional coordinates, flight speed and heading of the unmanned aerial vehicle and the target; the ground measurement radar subsystem is composed of an RCS measurement radar, a transmitting antenna and a receiving antenna and a second differential GNSS module; the ground measurement radar subsystem is composed of an RCS measurement radar, a transmitting antenna and a receiving antenna and a second differential GNSS module; the comprehensive control and data processing subsystem is composed of a flight control unit, a radar control unit, a data synchronization unit and a data processing and inversion unit.The present application is suitable for RCS test.

Description

Technical Field

[0001] This invention relates to the field of RCS (Radar Cross-Section) testing, specifically to a dynamic RCS testing system and method based on unmanned aerial vehicles (UAVs). Background Technology

[0002] RCS (Radio Scattering Compass) is a key indicator for measuring a target's ability to scatter radar waves, and it is crucial in fields such as stealth technology, target identification, and electromagnetic compatibility. Traditional RCS testing mainly employs the following methods:

[0003] Indoor compressed field testing: Plane waves are generated using precision-machined parabolic mirrors in a microwave anechoic chamber. Advantages include high precision and a controllable environment; disadvantages include extremely high site construction costs, limited test target size, and inability to perform dynamic testing.

[0004] Outdoor testing: A tall tower is erected in an open area, and the target is mounted on a turntable for measurement. The advantage is that larger targets can be tested; the disadvantages are that it is greatly affected by weather, requires a large dedicated area, is difficult to eliminate background clutter interference, and dynamic testing is also not possible.

[0005] The shortcomings of traditional RCS testing:

[0006] Traditional methods are all "static" measurements, meaning the target and the measuring radar are relatively stationary or only undergo simple rotation. However, in real-world scenarios, there are complex relative motions (such as pitch, yaw, and roll) between the target (e.g., aircraft, missiles) and the radar. Traditional methods cannot acquire RCS data under these dynamic attitudes, and the systems are large, inflexible, and costly.

[0007] Therefore, there is an urgent need in this field for a dynamic, multi-angle, low-cost, and highly flexible RCS testing solution. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art and provide a dynamic RCS testing system and method based on UAVs, which realizes efficient and low-cost RCS measurement of targets under different dynamic attitudes.

[0009] The present invention adopts the following technical solution to achieve the above objectives: the present invention provides a dynamic RCS testing system based on unmanned aerial vehicles (UAVs), including an UAV platform subsystem, a ground measurement radar subsystem, and an integrated control and data processing subsystem;

[0010] The unmanned aerial vehicle platform subsystem consists of an unmanned aerial vehicle carrier, a target installation mechanism, and a first differential GNSS module;

[0011] The first differential GNSS (Global Navigation Satellite System) module is used to acquire the spatial three-dimensional coordinates, flight speed and heading of the UAV and the target. The UAV carrier is a UAV with high load capacity, stable flight capability and autopilot function according to preset route. The target mounting mechanism is located below the UAV and is used to fix the target to be tested. The target mounting mechanism includes an attitude adjustment module for changing the pitch, yaw and roll angles of the target during flight.

[0012] The ground measurement radar subsystem consists of an RCS measurement radar, a transmitting antenna and a receiving antenna, and a second differential GNSS module.

[0013] The RCS measurement radar consists of a radar subsystem, an RF transceiver subsystem, and an intermediate frequency signal processing subsystem.

[0014] The radar subsystem is used to generate the radio frequency signal required for RCS testing, receive the target scattered signal, and mix the two to convert them into a lower intermediate frequency signal, which is then output to the intermediate frequency signal processing subsystem.

[0015] The transmitting and receiving antennas are separate antennas, with an azimuth range of ±180° and an elevation range of -10° to 50°. They are supported by a tripod and are height-adjustable.

[0016] The second differential GNSS module shares the base station signal with the first differential GNSS module to achieve time and space synchronization and obtain the phase center position of the radar antenna.

[0017] The integrated control and data processing subsystem consists of a flight control unit, a radar control unit, a data synchronization unit, and a data processing and inversion unit.

[0018] The flight control unit is used to plan the flight path, altitude, and speed of the UAV, and to remotely control the target's attitude adjustment mechanism;

[0019] The radar control unit is used to control the frequency band, power, and scanning mode parameters of the RCS radar, and to trigger data acquisition;

[0020] The data synchronization unit receives and processes differential GNSS data, attitude data, and radar echo data from UAVs and ground radar, ensuring that all data have a unified timestamp.

[0021] Furthermore, the target installation mechanism consists of an azimuth rotation mechanism and a pitch rotation structure. The azimuth rotation mechanism consists of an azimuth turntable frame, a servo drive control unit, and an electrical interface. The pitch rotation structure consists of a pitch rotation frame, an electric push rod, a pitch encoder, and an electrical interface. The azimuth turntable frame serves as the load-bearing component of the whole, undertaking the installation of all built-in components and simultaneously realizing the azimuth rotation of the radar antenna at the load end. The azimuth turntable frame includes a cavity base, an upper cover, a bottom cover, a rotating platform, an antenna radome, a rotating shaft, bearings, internal connecting parts, and fastening screws.

[0022] The servo drive control unit serves as the power output and control of the system, ensuring that the load performs azimuth movement and pitch angle adjustment according to design instructions. It includes a servo controller, azimuth motor, azimuth motor driver, pitch electric actuator, azimuth encoder, pitch encoder, and rotary joint.

[0023] Furthermore, the target mounting mechanism base is fixed on a fixed platform, and the target load is fixed on the rotating table surface. The rotating table is powered by an electrical interface and receives system commands. Driven by a motor inside the rotating table, the motor drives a pair of meshing spur gears through a reducer to rotate the central shaft. The central shaft and the rotating table surface are fixed and rotate synchronously by screws, thereby realizing the 360° rotation of the load radar or antenna fixed on the rotating table surface. The central shaft of the rotating table is also meshed with an absolute encoder. The encoder provides real-time feedback on the speed and position information of the load end, and after being solved by a servo algorithm, a dual closed loop of azimuth speed and position is realized.

[0024] Furthermore, the target mounting mechanism has a fixed mounting flange measuring 240mm × 205mm, with 10 M4 threaded holes on the flange edge for fixing the turntable with M4 screws. The height of the fixed flange from the rotating end face is 79mm. The rotating end face mounting surface is U-shaped and has 10 M4 threaded holes for fixing radar or antenna loads with M4 screws. A top protective cover with a height of 40mm is installed on the rotating end face, and a bottom protective cover with a height of 60mm is installed at the bottom of the fixed flange. The total height of the turntable is 179mm.

[0025] Furthermore, the radar subsystem adopts a hybrid technology combining direct digital frequency synthesis and frequency doubling amplification link. Direct digital frequency synthesis is used to achieve fast frequency switching and high-resolution frequency stepping to meet the requirements of a minimum frequency step of 1kHz and a frequency hopping time of no more than 1µs. The frequency doubling amplification link is responsible for expanding the frequency range and increasing the output power. The frequency doubling amplification link uses a low phase noise crystal oscillator as the reference source and is combined with a high-performance phase noise suppression circuit to control phase noise.

[0026] The radar subsystem consists of a receiving channel, a local oscillator circuit, a transmitting channel power supply, and a control section. The receiving channel consists of an amplification, filtering, and down-conversion circuit. The transmitting channel consists of a direct digital frequency synthesizer, an up-conversion circuit, and an amplification and filtering circuit. The local oscillator circuit uses a phase detector and a voltage-controlled oscillator to lock the output, which is then multiplied, segmented filtered, and amplified before being supplied to the frequency conversion link.

[0027] Furthermore, the RF transceiver subsystem adopts an integrated design, consisting of two separate modules. Each module has one receiving and one transmitting function. Each module receives the RF excitation signal from the radar subsystem and adopts a single transmitting channel design. High-performance transmission is achieved through a three-level core processing link. The transmitting channel mainly consists of a stage 1 pulse modulator, a stage 1 digitally controlled attenuator, a stage 1 temperature-compensated attenuator, a stage 2 selectable attenuator, a stage 2 equalizer, a stage 4 driver amplifier, and a final power amplifier. The receiving channel adopts a single-channel design and uses a low-noise amplifier at the input front end to improve the receiver's sensitivity. The receiving channel consists of a stage 1 limiter, a stage 1 pulse modulator, a stage 1 filter, a stage 1 digitally controlled attenuator, a stage 3 selectable attenuator, a stage 1 equalizer, and a stage 3 low-noise amplifier.

[0028] The multi-channel signal processing module of the intermediate frequency signal processing subsystem includes an FPGA, a cache, a memory, and a multi-core DSP. The FPGA includes a high-speed ADC, a high-speed DAC, and auxiliary circuits.

[0029] Furthermore, the data processing and inversion unit is used to perform the following functions:

[0030] Background cancellation: When the UAV is not carrying a target, it flies along the same route, collects background clutter data, and subtracts it from subsequent measurement data to eliminate environmental interference;

[0031] Coordinate transformation and motion compensation: Using differential GNSS data, the distance and relative velocity between the radar and the target are calculated in real time, and motion compensation is performed on the raw phase data received by the radar to correct the phase error caused by relative motion;

[0032] RCS calculation: The compensated target echo energy is compared with the echo energy of a standard calibration body with known RCS, and the accurate RCS value of the target under test at the set attitude and frequency is finally calculated.

[0033] This invention also provides a dynamic RCS testing method based on unmanned aerial vehicles (UAVs), applied to the aforementioned UAV-based dynamic RCS testing system. This RCS testing method includes:

[0034] Before testing, the system was calibrated using a standard calibrator with a known RCS.

[0035] Control the unmanned aerial vehicle (UAV) without carrying the target to be tested to fly along a predetermined route, and the ground radar collects and records the environmental background echo data;

[0036] The target to be tested is mounted on a drone, and the drone is controlled to fly along a predetermined route while ground radar simultaneously collects data containing the target echo.

[0037] All data is integrated through the data synchronization unit, and background cancellation, RCS calculation, coordinate transformation and motion compensation are performed through the data processing and inversion unit.

[0038] Background cancellation involves collecting background clutter data when the UAV is flying the same route without a target, and then subtracting it from subsequent measurement data to eliminate environmental interference.

[0039] Coordinate transformation and motion compensation include using differential GNSS data to calculate the distance and relative velocity between the radar and the target in real time, performing motion compensation on the raw phase data received by the radar, and correcting the phase error caused by relative motion.

[0040] RCS calculation involves comparing the compensated target echo energy with the echo energy of a standard calibration body with a known RCS, and finally calculating the precise RCS value of the target under test at a set attitude and frequency.

[0041] Furthermore, motion compensation specifically includes:

[0042] S1. Calculate the instantaneous distance history R(t_i);

[0043] For each radar data sampling time t_i, the algorithm calculates the instantaneous two-way distance between the radar and the target based on the synchronized GNSS data, as follows:

[0044] R(t_i) = |[X_tx(t_i), Y_tx(t_i), Z_tx(t_i)] - [X_t(t_i), Y_t(t_i), Z_t(t_i)]| + |[X_rx(t_i), Y_rx(t_i), Z_rx(t_i)] - [X_t(t_i), Y_t(t_i), Z_t(t_i)]|;

[0045] In the formula, (X_t(t_i), Y_t(t_i), Z_t(t_i)) represents the three-dimensional coordinates of each data sampling time t_i from the first differential GNSS module, (X_rx(t_i), Y_rx(t_i), Z_rx(t_i)) represents the three-dimensional coordinates of the phase center of the radar transmitting antenna at each data sampling time t_i from the second differential GNSS module, and (X_tx(t_i), Y_tx(t_i), Z_tx(t_i)) represents the three-dimensional coordinates of the phase center of the receiving antenna at each data sampling time t_i from the second differential GNSS module;

[0046] S2. Construct an ideal reference signal;

[0047] Ideally, if the target remains stationary at a reference position during the measurement, its echo signal will be a stable frequency domain response, thus constructing a phase-compensated reference signal.

[0048] S3. Calculate and apply the phase compensation amount;

[0049] For each sampling time t_i and each frequency point f_j, calculate the difference between the ideal distance and the instantaneous distance:

[0050] ΔR(t_i) = R(t_i) - R_ref;

[0051] In the formula, ΔR(t_i) represents the difference between the ideal distance and the instantaneous distance, and R_ref represents a selected reference distance, which can be the average distance over the entire measurement period or the distance at the midpoint of the flight path.

[0052] The phase delay of the wave is directly related to the propagation distance. Therefore, the phase error caused by the distance difference is calculated as follows:

[0053] Δφ(t_i) = (4π * ΔR(t_i)) / λ;

[0054] In the formula, λ = c / f_j represents the wavelength of the radar at frequency f_j, c represents the speed of light, and Δφ(t_i) represents the phase error;

[0055] The compensation factor is a complex number with an amplitude of 1 and a phase opposite to the error phase. Therefore, the compensation factor is:

[0056] H_comp(t_i, f_j) = exp( -j * Δφ(t_i) ) = exp( -j * (4π * f_j * ΔR(t_i)) / c );

[0057] In the formula, H_comp(t_i, f_j) represents the compensation factor, and j represents the imaginary unit;

[0058] Apply compensation:

[0059] The compensation factor is multiplied by the original frequency domain echo data S_raw(t_i, f_j) as follows:

[0060] S_comp(t_i, f_j) = S_raw(t_i, f_j) * H_comp(t_i, f_j);

[0061] In the formula, S_comp(t_i, f_j) represents the applied phase compensation amount;

[0062] S4, Data Reassembly and Imaging;

[0063] Perform an inverse Fourier transform along the frequency dimension on the compensated S_comp(t_i, f_j) to obtain a high-resolution one-dimensional range image at each time t_i.

[0064] Coherent processing is performed on the range images at different times, and a two-dimensional inverse synthetic aperture radar image of the target is generated by the selected imaging algorithm.

[0065] The beneficial effects of this invention are as follows:

[0066] This invention is based on UAV for dynamic RCS testing. The entire system includes a UAV platform subsystem, a ground measurement radar subsystem, and an integrated control and data processing subsystem. Through the coordination of the three subsystems, dynamic, multi-angle, low-cost, and highly flexible RCS testing can be carried out.

[0067] Unlike traditional motion compensation methods based on signal estimation (such as envelope correlation and distinctive point methods), this invention directly utilizes high-precision external measurement data (differential GNSS) for compensation. It is highly accurate, unaffected by the target scattering characteristics, and applicable to weakly scattering targets.

[0068] This invention enables true dynamic measurement, that is, extracting "static mass" RCS data from "dynamic flight".

[0069] This invention can process any flight trajectory defined by differential GNSS and is applicable to testing in various flight modes such as straight lines, curves, and hovering. Attached Figure Description

[0070] Figure 1 This is a schematic diagram of a dynamic RCS testing system based on an unmanned aerial vehicle (UAV) provided by the present invention.

[0071] Figure 2This is a structural block diagram of the target installation mechanism provided by the present invention;

[0072] Figure 3 This is a structural block diagram of the azimuth turntable structure frame provided by the present invention;

[0073] Figure 4 This is a block diagram of the servo drive control unit structure provided by the present invention;

[0074] Figure 5 This is a schematic diagram of the orientation rotation model of the target installation mechanism provided by the present invention;

[0075] Figure 6 This is a schematic diagram of the two-dimensional turntable pitch model of the target installation mechanism provided by the present invention;

[0076] Figure 7 This is a graph of the filter performance indicators provided by the present invention;

[0077] Figure 8 This is a curve of the filter performance after filtering the 4.35GHz~6GHz signal output provided by the present invention;

[0078] Figure 9 This is a curve of the filter performance after filtering the 6GHz~9GHz signal output provided by this invention;

[0079] Figure 10 This is a curve of the filter performance after filtering the 9GHz~13GHz signal output provided by the present invention;

[0080] Figure 11 This is a curve of the filter performance after filtering the 13GHz~18GHz signal output provided by the present invention;

[0081] Figure 12 This is a block diagram of the transmission channel structure provided by the present invention;

[0082] Figure 13 This is a block diagram of the receiving channel structure provided by the present invention;

[0083] Figure 14 This is a flowchart of the motion compensation algorithm provided by the present invention. Detailed Implementation

[0084] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0085] This invention provides a dynamic RCS testing system based on unmanned aerial vehicles (UAVs), such as... Figure 1 As shown, it includes an unmanned aerial vehicle (UAV) platform subsystem, a ground measurement radar subsystem, and an integrated control and data processing subsystem.

[0086] The UAV platform subsystem consists of the UAV carrier, target mounting mechanism, and first differential GNSS module. The UAV carrier is a UAV with high payload capacity, stable flight capability, and preset flight path autopilot function. The UAV has a battery power supply system; the rotor power (motor) and ESC are powered by the battery pack. The flight control, servo, switch, and engine starter motor are powered by separate batteries.

[0087] Target mounting mechanism: Located below the UAV, it is used to secure the target model under test. This mechanism may include an attitude adjustment module (such as a servo motor-driven gimbal) for precisely changing the target's pitch, yaw, and roll angles during flight.

[0088] like Figure 2 As shown, the target installation mechanism mainly consists of an azimuth rotation mechanism and a pitch rotation mechanism. The azimuth rotation mechanism consists of an azimuth turntable structural frame, a servo drive control unit, and an electrical interface. The pitch rotation mechanism consists of a pitch rotation structural frame, an electric push rod, a pitch encoder, and an electrical interface. It is composed of an airborne radar two-dimensional turntable.

[0089] The azimuth turntable frame, as the overall load-bearing component, not only supports the installation of all built-in components but also enables the azimuth rotation of the radar antenna at the load end. Figure 3 As shown, the azimuth turntable's structural frame mainly includes a cavity base, upper cover, bottom cover, rotating platform, radome, rotating shaft, bearings, internal connectors, and fastening screws. The azimuth turntable's structural frame connects the cavity base and the rotating platform via precision bearings, enabling the core rotation function. The various parts of the outer shell (upper cover and bottom cover) are combined with screws and sealing rings to form a sealed protective cavity. The radar antenna is secured to the rotating platform with high-strength bolts and locating pins to ensure installation accuracy. Internal components are fixed to the base via mounting brackets and screws, together forming a stable, reliable, and precisely operable load-bearing unit.

[0090] The servo drive control unit serves as the system's power output and control, ensuring that the load can perform azimuth and pitch angle adjustments according to design instructions. For example... Figure 4 As shown, the servo drive control unit mainly includes a servo controller, an azimuth motor, an azimuth motor driver, a pitch electric linear actuator, an azimuth encoder, a pitch encoder, and a rotary joint. The servo drive control unit, with the servo controller at its core, sends commands to the azimuth motor driver and the pitch electric linear actuator via cables. The azimuth motor drives the turntable to rotate through a coupling, and its matching azimuth encoder provides real-time position feedback, forming a closed-loop control. The pitch electric linear actuator directly drives the antenna's pitch through the rotary joint, and the pitch encoder detects the angle, together ensuring precise movement following the commands.

[0091] The target mounting mechanism base is fixed to the fixed platform, and the target load is fixed to the rotating table surface. The turntable is powered and receives system commands via an electrical interface. Driven by a motor inside the turntable, the motor, through a reducer, drives a pair of meshing spur gears to rotate the central shaft. The central shaft and the rotating table surface are fixed together by screws and rotate synchronously, thus achieving a 360° rotation of the load radar or antenna fixed on the turntable surface. The turntable's central shaft also meshes with an absolute encoder, which provides real-time feedback on the load's speed and position information. This information, processed by a servo algorithm, achieves a dual closed-loop measurement of azimuth, speed, and position.

[0092] The built-in rotary joint can effectively connect the radio frequency signals, power signals and communication signals of the fixed end and the rotating end, thereby realizing the rotation of the load.

[0093] The target installation mechanism adopts a square flange design to minimize wasted internal space on the turntable while meeting dimensional and weight requirements. The target installation mechanism's orientation and rotation model is shown below. Figure 5 As shown, the two-dimensional turntable pitch model of the target installation mechanism is as follows: Figure 6 As shown.

[0094] The target mounting mechanism has a fixed mounting flange measuring 240mm × 205mm. The flange edge has 10 M4 threaded holes for securing the turntable with M4 screws. The height from the fixed flange to the rotating end face is 79mm. The rotating end face mounting surface is U-shaped and has 10 M4 threaded holes for securing radar or antenna loads with M4 screws. Additionally, there is a top protective cover on the rotating end face with a height of 40mm, and a bottom protective cover at the bottom of the fixed flange with a height of 60mm. The total height of the turntable is 179mm (excluding the height of the aviation connectors and screws).

[0095] The first differential GNSS module is used to accurately acquire the spatial three-dimensional coordinates, flight speed, and heading of UAVs and targets, with positioning accuracy down to the millimeter level.

[0096] The ground measurement radar subsystem consists of an RCS measurement radar, a transmitting antenna and a receiving antenna, and a second differential GNSS module.

[0097] As the core equipment for radar transmission and reception, the RCS measurement radar generates radar waves in the 300MHz-18GHz range and receives echoes. The RCS measurement radar consists of three key subsystems: the radar subsystem, the radio frequency transceiver subsystem, and the intermediate frequency signal processing subsystem, supplemented by auxiliary equipment such as calibration spheres, foam columns, and packaging boxes.

[0098] The main function of the radar subsystem is to generate the radio frequency signal required for RCS testing, receive the target scattering signal, and mix the two to convert them into a lower frequency intermediate frequency signal for output to the intermediate frequency signal processing subsystem.

[0099] The radar subsystem employs a hybrid technology combining a direct digital frequency synthesizer (DDS) and a frequency multiplier amplification link to achieve an ultra-wideband output of 0.3 GHz to 18 GHz. The DDS is used for rapid frequency switching and high-resolution frequency stepping to meet the requirements of a minimum frequency step of 1 kHz and a frequency hopping time of no more than 1 μs. The frequency multiplier is responsible for extending the frequency range and increasing the output power. A low-phase-noise crystal oscillator is selected as the reference source, coupled with a high-performance phase noise suppression circuit, controlling the phase noise to ≤-85 dBc / Hz@1 kHz. Through optimized circuit layout, shielding technology, and high-performance filtering circuits, spurious emission suppression of ≥60 dBc is achieved. Simultaneously, the power amplifier design ensures an output power of ≥10 dBm. This subsystem operates within a temperature range of -40℃ to +50℃ and uses an SMA interface to ensure the stability and reliability of signal transmission.

[0100] The radar subsystem consists of a receiving channel, a local oscillator circuit, and a transmitting channel, along with its power supply and control components. The receiving channel primarily comprises amplification, filtering, and down-conversion circuits. The transmitting channel consists of a direct digital frequency synthesizer, up-conversion, and amplification / filtering circuits. The local oscillator circuit uses a phase detector and a voltage-controlled oscillator (VCO) to lock the output. The output is then multiplied, segmented filtered, and amplified before being supplied to the frequency conversion link.

[0101] In the transmission channel, when the direct digital frequency synthesizer outputs a signal from 0.1GHz to 4.35GHz, the signal is directly amplified and output after being conditioned by the frequency conversion channel. It is then up-converted to 4.35GHz to 18GHz, filtered, attenuated, and conditioned before output. The link functions include mixing, attenuation control, frequency band selection, and amplification. The key performance indicators of the link are spurious suppression and link gain design. When the output signal is 0.1GHz to 4.35GHz, the link directly outputs the signal through amplification and attenuation, and the link does not generate intermodulation spurious signals. When the output signal is 4.35GHz to 18GHz, the link uses a double up-conversion. The first up-conversion outputs an intermediate frequency (IF) of 22GHz. This IF and the local oscillator signal from the frequency hopping high IF are mixed to output the required transmission signal of 4.35GHz to 18GHz. This single up-conversion prevents intermodulation spurious signals from falling within the band.

[0102] Other out-of-band spurious signals mainly include the input intermediate frequency (IF), LO1, 2*IF±LO1, 2*LO1±IF, etc. A two-stage bandpass filter is used in the link design, with specifications as follows: Figure 7 As shown in the figure, the filter specifications show that the filter suppresses near-end spurious signals by more than 50dBc, and the link also uses two-stage filters to ensure the spurious signal suppression requirements after one mixing cycle.

[0103] After the second mixing, other out-of-band spurious signals include RF, 2*RF+LO2, and 2*LO2±RF intermodulation spurious signals. The post-mixing link employs segmented filtering, dividing the 4.35GHz~18GHz signal into four segments: 4.35GHz~6GHz, 6GHz~9GHz, 9GHz~13GHz, and 13GHz~18GHz. These segmented filters are then output to the next stage. The specifications of the segmented filters are as follows: Figures 8 to 11 As shown.

[0104] As can be seen from the segmented filter specifications, it has a good suppression effect on spurious signals outside the band, from 1GHz to 1.5GHz. The link design uses a high local oscillator frequency converter, and the main intermodulation spurious signals are also distributed at a relatively far distance outside the band. Therefore, the suppression of spurious signals by the entire link can meet the specification requirements.

[0105] The RCS measurement radar RF transceiver subsystem adopts an integrated design approach, consisting of two separate modules, each with one receiving and one transmitting channel. The module receives the RF excitation signal from the radar subsystem, employing a 0.3GHz-18GHz, single-transmit channel design, and achieves high-performance transmission through a three-level core processing link (pulse modulation-power control-wideband amplification). The system uses an ultra-wideband multi-stage power amplifier module, based on power combining technology, to achieve ≥40dBm (10W) saturated power output across the entire 0.3GHz-18GHz band, while ensuring an output third-order intermodulation intercept (OIP3) ≥43dBm, guaranteeing linearity under large signals. To adapt to different test targets, the system integrates a 31dB programmable attenuator. The pulse modulation function, based on a high-speed PIN diode switching array and GaNFET driver circuit, combined with nanosecond-level timing control signals generated by an FPGA, ensures pulse rise / fall times ≤15ns and pulse width adjustable within the range of 20ns to 200ns (resolution ≤5ns).

[0106] like Figure 12 As shown, the transmitting channel mainly consists of a stage 1 pulse modulator, a stage 1 digitally controlled attenuator, a stage 1 temperature-compensated attenuator, a stage 1 equalizer, a stage 2 driver amplifier, a stage 2 selectable attenuator, a stage 2 equalizer, a stage 3 driver amplifier, a stage 3 selectable attenuator, a stage 4 driver amplifier, and a final stage power amplifier. When the input signal is ≥-10dBm, the final stage power amplifier of the transmitting channel is in saturated output state, and the output signal power is greater than 34dBm, which meets the system performance requirements.

[0107] like Figure 13 As shown, the receiving channel mainly consists of a first-stage limiter, a first-stage low-noise amplifier, a first-stage selectable attenuator, a first-stage pulse modulator, a first-stage equalizer, a second-stage selectable attenuator, a first-stage filter, a first-stage digitally controlled attenuator, a second-stage low-noise amplifier, a third-stage selectable attenuator, and a third-stage low-noise amplifier.

[0108] The receiving channel employs a single-channel design ranging from 100MHz to 18GHz, utilizing a low-noise amplifier at the input front end to enhance receiver sensitivity and ensure effective reception of weak signals within the 100MHz–18GHz frequency range. Amplifier selection and circuit design fully consider noise figure and linearity to meet the system's signal quality requirements.

[0109] By employing an amplifier and a digitally controlled programmable attenuator, the receiver achieves a dynamic range of ≥80dB@10kHz intermediate frequency bandwidth, ensuring that the signal can be accurately received and processed throughout the entire dynamic range.

[0110] Similar to the transmission subsystem, the hardware gate pulse function is implemented through a high-speed switching circuit. The pulse rise time is guaranteed to be ≤15ns, the pulse width is configurable within the range of 20ns to 2000ns, and the step resolution is ≤5ns. The operating temperature range is -40℃ to +50℃, and the external interface is an SMA interface.

[0111] Intermediate Frequency Signal Processing Subsystem: The multi-channel signal processing module mainly includes one XCZU47DR-2FFVG1517I FPGA, a high-speed cache, a large-capacity memory, one high-performance multi-core DSP (TMS320C6678N), and other auxiliary circuits. The FPGA contains a high-speed ADC, a high-speed DAC, and other auxiliary circuits.

[0112] Transmitting and Receiving Antennas: Separate antennas are used for transmitting and receiving. A large-aperture parabolic antenna is employed to ensure extremely high gain and directivity, which is its core advantage. This allows energy to be focused onto a very small area, enabling ultra-long-distance communication and extremely high-resolution detection. The antenna is pointed towards the airspace where the UAV is flying.

[0113] Antenna azimuth ±180°, elevation: -10°~50°, tripod support, height adjustable. Antenna gain: 1-4GHz: ≥14dB, 4-8GHz: ≥26dB, 8-12GHz: ≥32dB, 12-18GHz: ≥33dB. The parabolic antenna is not only an excellent receiving antenna but also an extremely efficient and powerful transmitting antenna. Its value lies in its ability to efficiently "project" electromagnetic energy to extremely distant targets.

[0114] The second differential GNSS module shares the base station signal with the first differential GNSS module to achieve time and space synchronization and accurately obtain the phase center position of the radar antenna.

[0115] The integrated control and data processing subsystem consists of a flight control unit, a radar control unit, a data synchronization unit, and a data processing and inversion unit.

[0116] Flight control unit: plans the flight path, altitude, and speed of the UAV, and remotely controls the target's attitude adjustment mechanism.

[0117] Radar control unit: controls parameters such as frequency band, power, and scanning mode of the RCS dedicated radar, and triggers data acquisition.

[0118] Data synchronization unit: Receives and processes differential GNSS data, attitude data, and radar echo data from UAVs and ground radar, ensuring that all data have a unified high-precision timestamp.

[0119] Data Processing and Inversion Unit: The core processing module, which performs the following steps:

[0120] Background cancellation: When the UAV is not carrying a target, it flies along the same route, collects background clutter data, and subtracts it from subsequent measurement data to eliminate environmental interference.

[0121] Coordinate transformation and motion compensation: Using high-precision differential GNSS data, the exact distance and relative velocity between the radar and the target are calculated in real time. Motion compensation is performed on the raw phase data received by the radar to correct the phase error caused by relative motion.

[0122] RCS calculation: The compensated target echo energy is compared with the echo energy of a standard calibration body (such as a metal sphere) with known RCS, and finally the accurate RCS value of the target under test at a specific attitude and frequency is calculated.

[0123] System working principle (method):

[0124] The UAV platform subsystem carries the UAV to be measured, an attitude adjustment mechanism for precisely adjusting the target's attitude, and a first differential GNSS module for acquiring the target's precise position information; the ground measurement radar subsystem includes a measurement radar and antenna for transmitting and receiving radar signals, and a second differential GNSS module for acquiring the precise position of the radar antenna's phase center; the integrated control and data processing center includes a flight control unit for controlling the UAV's flight path and the target's attitude, a radar control unit for controlling the measurement radar, a data synchronization unit for synchronizing all data, and a data processing and inversion unit for performing background cancellation and motion compensation processing on the radar echo data and calculating the target's RCS value.

[0125] The detailed testing steps are as follows:

[0126] System calibration: Before testing, the system is calibrated using a standard calibrator with a known RCS.

[0127] Background measurement: Control the UAV (without carrying a target) to fly along a predetermined route, and the ground radar collects and records the environmental background echo data.

[0128] Target measurement: The target is mounted on a UAV, which is then controlled to fly along the exact same flight path. Simultaneously, the attitude adjustment mechanism can be instructed to change the target's attitude according to a preset pattern. Ground radar synchronously acquires data including target echoes.

[0129] Data synchronization and processing: The data synchronization unit merges all data. The data processing unit executes "background cancellation" and "motion compensation" algorithms.

[0130] RCS Extraction and Output: Extract the target's scattering information from the processed data, calculate the dynamic RCS value, and generate a database of RCS variations with attitude angle and frequency.

[0131] The motion compensation algorithm executed by the data processing and inversion unit.

[0132] In traditional static RCS testing, the geometric relationship between the target, transmitting antenna, and receiving antenna remains constant, resulting in a very stable phase history of the radar echo. However, in this system, the UAV carrying the target is in continuous motion relative to the ground radar, which introduces two main problems:

[0133] Range migration: Within a radar frequency sweep cycle (or pulse cycle), the distance between the target and the radar has changed, causing the echo energy to be dispersed across multiple range cells.

[0134] Phase error: Radar RCS measurements are highly dependent on the coherence of the echo phase. Even minute relative motions between the UAV and the radar (even on the millimeter scale) can cause huge phase errors (because radar wavelengths are typically on the centimeter or millimeter scale), making it impossible to accurately reconstruct the target's scattering characteristics.

[0135] Therefore, the core purpose of motion compensation algorithms is:

[0136] Correcting phase errors caused by relative motion between the radar and the target.

[0137] Aligning and compressing the echo signal to make it appear as if it were scattered from a stationary target provides a high-quality data foundation for subsequent accurate RCS calculations.

[0138] like Figure 14 As shown, the motion compensation algorithm is as follows:

[0139] Multi-source data synchronous input:

[0140] Raw radar echo data: usually complex numerical I and Q parameters (frequency domain data) obtained from RCS radar measurements.

[0141] High-precision spatiotemporal synchronized location data:

[0142] From UAV differential GNSS (first differential GNSS module): for each data sampling time t_i, the target's precise three-dimensional coordinates (X_t(t_i), Y_t(t_i), Z_t(t_i)).

[0143] From the ground radar differential GNSS (second differential GNSS module): at each data sampling time t_i, the precise three-dimensional coordinates (X_rx(t_i), Y_rx(t_i), Z_rx(t_i)) and (X_tx(t_i), Y_tx(t_i), Z_tx(t_i)) of the phase center of the radar transmitting antenna and the phase center of the receiving antenna (transmit and receive are separate).

[0144] System timestamp: All data (radar data and GNSS data) must be strictly synchronized using high-precision timestamps (usually provided by GNSS timing, with an accuracy of nanoseconds).

[0145] Calculate the instantaneous distance history R(t_i):

[0146] For each radar data sampling time t_i, the algorithm calculates the instantaneous two-way distance between the radar and the target based on the synchronized GNSS data.

[0147] For a dual-station (transmitter-receiver) system:

[0148] R(t_i) = |[X_tx(t_i), Y_tx(t_i), Z_tx(t_i)] - [X_t(t_i), Y_t(t_i), Z_t(t_i)]| + |[X_rx(t_i), Y_rx(t_i), Z_rx(t_i)] - [X_t(t_i), Y_t(t_i), Z_t(t_i)]|

[0149] Therefore, we can obtain a precise distance curve R(t_i) that varies with time.

[0150] Constructing an ideal reference signal:

[0151] Ideally, if the target remains stationary at a reference position during the measurement (e.g., the position at the start of the flight path at time t0), its echo signal will be a stable frequency domain response. A phase-compensated reference signal can then be constructed based on this.

[0152] Calculate and apply the phase compensation amount:

[0153] This is the core mathematical operation of the algorithm. For each sampling time t_i and each frequency point f_j:

[0154] Calculate the difference between the ideal distance and the instantaneous distance:

[0155] ΔR(t_i) = R(t_i) - R_ref;

[0156] R_ref is a selected reference distance, usually the average distance over the entire measurement period or the distance to the midpoint of the route.

[0157] Calculate the phase error caused by the distance difference:

[0158] The phase delay of radar waves is directly related to the propagation distance. This phase error is given by the following formula:

[0159] Δφ(t_i) = (4π * ΔR(t_i)) / λ

[0160] Where λ = c / f_j is the wavelength of the radar at frequency f_j, and c is the speed of light.

[0161] Formula explanation: 4π comes from two-way propagation (2 * 2π), meaning that a change in distance ΔR will cause a phase change of 4πΔR / λ radians. This is a very sensitive change, requiring centimeter-level GNSS data for calculation.

[0162] Constructing compensation factors:

[0163] The compensation factor is a complex number with an amplitude of 1 and a phase opposite to that of the error.

[0164] H_comp(t_i, f_j) = exp( -j * Δφ(t_i) ) = exp( -j * (4π * f_j * ΔR(t_i)) / c )

[0165] Where j is the imaginary unit;

[0166] Apply compensation:

[0167] Multiply the compensation factor by the original frequency domain echo data S_raw(t_i, f_j):

[0168] S_comp(t_i, f_j) = S_raw(t_i, f_j) * H_comp(t_i, f_j)

[0169] This step directly corrects the phase distortion caused by motion in the frequency domain.

[0170] Data reconstruction and imaging:

[0171] Perform an inverse Fourier transform along the frequency dimension on the compensated frequency domain data S_comp(t_i, f_j) to obtain a high-resolution one-dimensional range image at each time t_i.

[0172] Since the motion has been compensated, the target scattering points have been aligned in the range dimension and are no longer blurred.

[0173] If necessary, the range images at different times can be coherently processed to generate a two-dimensional inverse synthetic aperture radar image of the target through additional imaging algorithms (such as the range-Doppler algorithm).

[0174] The advantages of the motion compensation algorithm of this invention are:

[0175] Accurate compensation based on physical models: Unlike traditional motion compensation based on signal estimation (such as envelope correlation method and distinctive point method), this algorithm directly uses high-precision external measurement data (differential GNSS) for compensation. It has high accuracy, is not affected by the target scattering characteristics, and is applicable to weakly scattering targets.

[0176] Achieving true dynamic measurement: This algorithm is the key to the system's ability to extract "static mass" RCS data from "dynamic flight" and is the core embodiment of the patent's novelty.

[0177] Modularity and flexibility: This algorithm module can handle any flight trajectory defined by differential GNSS and is suitable for testing in various flight modes such as straight lines, curves, and hovering.

[0178] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A dynamic RCS testing system based on unmanned aerial vehicles (UAVs), characterized in that, It includes an unmanned aerial vehicle (UAV) platform subsystem, a ground measurement radar subsystem, and an integrated control and data processing subsystem; The unmanned aerial vehicle platform subsystem consists of an unmanned aerial vehicle carrier, a target installation mechanism, and a first differential GNSS module; The first differential GNSS module is used to acquire the spatial three-dimensional coordinates, flight speed and heading of the UAV and the target. The UAV carrier is a UAV with high load capacity, stable flight capability and autopilot function according to preset route. The target mounting mechanism is located below the UAV and is used to fix the target to be tested. The target mounting mechanism includes an attitude adjustment module for changing the pitch, yaw and roll angles of the target during flight. The ground measurement radar subsystem consists of an RCS measurement radar, a transmitting antenna and a receiving antenna, and a second differential GNSS module. The RCS measurement radar consists of a radar subsystem, an RF transceiver subsystem, and an intermediate frequency signal processing subsystem. The radar subsystem is used to generate the radio frequency signal required for RCS testing, receive the target scattering signal, and mix the two to convert them into a low-frequency intermediate frequency signal, which is then output to the intermediate frequency signal processing subsystem. The transmitting and receiving antennas are separate antennas, with an azimuth range of ±180° and adjustable height. The second differential GNSS module shares the base station signal with the first differential GNSS module to achieve time and space synchronization and obtain the phase center position of the radar antenna. The integrated control and data processing subsystem consists of a flight control unit, a radar control unit, a data synchronization unit, and a data processing and inversion unit. The flight control unit is used to plan the flight path, altitude, and speed of the UAV, and to remotely control the target's attitude adjustment mechanism; The radar control unit is used to control the frequency band, power, and scanning mode parameters of the RCS radar, and to trigger data acquisition; The data synchronization unit receives and processes differential GNSS data, attitude data, and radar echo data from UAVs and ground radar, ensuring that all data have a unified timestamp.

2. The UAV-based dynamic RCS testing system according to claim 1, characterized in that, The target installation mechanism consists of an azimuth rotation mechanism and a pitch rotation mechanism. The azimuth rotation mechanism consists of an azimuth turntable structural frame, a servo drive control unit, and an electrical interface. The pitch rotation mechanism consists of a pitch rotation structural frame, an electric push rod, a pitch encoder, and an electrical interface. The azimuth turntable structural frame serves as the load-bearing component of the whole, undertaking the installation of all built-in components and simultaneously realizing the azimuth rotation of the radar antenna at the load end. The azimuth turntable structural frame includes a cavity base, an upper cover, a bottom cover, a rotating platform, an antenna radome, a rotating shaft, bearings, internal connecting parts, and fastening screws. The servo drive control unit serves as the power output and control of the system, ensuring that the load performs azimuth movement and pitch angle adjustment according to design instructions. It includes a servo controller, azimuth motor, azimuth motor driver, pitch electric actuator, azimuth encoder, pitch encoder, and rotary joint.

3. The UAV-based dynamic RCS testing system according to claim 2, characterized in that, The target mounting mechanism base is fixed on a fixed platform, and the target load is fixed on the rotating table surface. The rotating table is powered by an electrical interface and receives system commands. Driven by a motor inside the rotating table, the motor drives a pair of meshing spur gears through a reducer to rotate the central shaft. The central shaft and the rotating table surface are fixed and rotate synchronously by screws, thereby realizing the 360° rotation of the load radar or antenna fixed on the rotating table surface. The central shaft of the rotating table is also meshed with an absolute encoder. The encoder provides real-time feedback on the speed and position information of the load end, and after being solved by a servo algorithm, a dual closed loop of azimuth speed and position is realized.

4. The UAV-based dynamic RCS testing system according to claim 1, characterized in that, The target mounting mechanism has a fixed mounting flange measuring 240mm × 205mm. The flange edge has 10 M4 threaded holes for fixing the turntable with M4 screws. The height of the fixed flange from the rotating end face is 79mm. The rotating end face mounting surface is U-shaped and has 10 M4 threaded holes for fixing radar or antenna loads with M4 screws. A top protective cover with a height of 40mm is installed on the rotating end face, and a bottom protective cover with a height of 60mm is installed at the bottom of the fixed flange. The total height of the turntable is 179mm.

5. The UAV-based dynamic RCS testing system according to claim 1, characterized in that, The radar subsystem adopts a hybrid technology that combines direct digital frequency synthesis with frequency doubling amplification link. Direct digital frequency synthesis is used to achieve fast frequency switching and high-resolution frequency stepping to meet the requirements of a minimum frequency step of 1kHz and a frequency hopping time of no more than 1µs. The frequency doubling amplification link is responsible for expanding the frequency range and increasing the output power. The frequency doubling amplification link uses a low phase noise crystal oscillator as the reference source and is combined with a high-performance phase noise suppression circuit to control phase noise. The radar subsystem consists of a receiving channel, a local oscillator circuit, a transmitting channel power supply, and a control section. The receiving channel consists of an amplification, filtering, and down-conversion circuit. The transmitting channel consists of a direct digital frequency synthesizer, an up-conversion circuit, and an amplification and filtering circuit. The local oscillator circuit uses a phase detector and a voltage-controlled oscillator to lock the output, which is then multiplied, segmented filtered, and amplified before being supplied to the frequency conversion link.

6. The UAV-based dynamic RCS testing system according to claim 1, characterized in that, The radio frequency transceiver subsystem adopts an integrated design, consisting of two separate modules. Each module has one receiving and one transmitting function. Each module receives the radio frequency excitation signal from the radar subsystem and adopts a single transmitting channel design. High-performance transmission is achieved through a three-level core processing link. The transmitting channel mainly consists of a stage 1 pulse modulator, a stage 1 digitally controlled attenuator, a stage 1 temperature-compensated attenuator, a stage 2 selectable attenuator, a stage 2 equalizer, a stage 4 driver amplifier, and a final power amplifier. The receiving channel adopts a single-channel design and uses a low-noise amplifier at the input front end to improve the receiver's sensitivity. The receiving channel consists of a stage 1 limiter, a stage 1 pulse modulator, a stage 1 filter, a stage 1 digitally controlled attenuator, a stage 3 selectable attenuator, a stage 1 equalizer, and a stage 3 low-noise amplifier. The multi-channel signal processing module of the intermediate frequency signal processing subsystem includes an FPGA, a cache, a memory, and a multi-core DSP. The FPGA includes a high-speed ADC, a high-speed DAC, and auxiliary circuits.

7. The UAV-based dynamic RCS testing system according to claim 1, characterized in that, The data processing and inversion unit is used to perform the following functions: Background cancellation: When the UAV is not carrying a target, it flies along the same route, collects background clutter data, and subtracts it from subsequent measurement data to eliminate environmental interference; Coordinate transformation and motion compensation: Using differential GNSS data, the distance and relative velocity between the radar and the target are calculated in real time, and motion compensation is performed on the raw phase data received by the radar to correct the phase error caused by relative motion; RCS calculation: The compensated target echo energy is compared with the echo energy of a standard calibration body with known RCS, and the accurate RCS value of the target under test at the set attitude and frequency is finally calculated.

8. A dynamic RCS testing method based on unmanned aerial vehicles (UAVs), applied to the dynamic RCS testing system based on UAVs as described in any one of claims 1-7, characterized in that, The RCS testing method includes: Before testing, the system was calibrated using a standard calibrator with a known RCS. Control the unmanned aerial vehicle (UAV) without carrying the target to be tested to fly along a predetermined route, and the ground radar collects and records the environmental background echo data; The target to be tested is mounted on a drone, and the drone is controlled to fly along a predetermined route while ground radar simultaneously collects data containing the target echo. All data is integrated through the data synchronization unit, and background cancellation, RCS calculation, coordinate transformation and motion compensation are performed through the data processing and inversion unit. Background cancellation involves collecting background clutter data when the UAV is flying the same route without a target, and then subtracting it from subsequent measurement data to eliminate environmental interference. Coordinate transformation and motion compensation include using differential GNSS data to calculate the distance and relative velocity between the radar and the target in real time, performing motion compensation on the raw phase data received by the radar, and correcting the phase error caused by relative motion. RCS calculation involves comparing the compensated target echo energy with the echo energy of a standard calibration body with a known RCS, and finally calculating the precise RCS value of the target under test at a set attitude and frequency.

9. The dynamic RCS testing method based on unmanned aerial vehicles according to claim 8, characterized in that, Exercise compensation specifically includes: S1. Calculate the instantaneous distance history R(t_i); For each radar data sampling time t_i, the algorithm calculates the instantaneous two-way distance between the radar and the target based on the synchronized GNSS data, as follows: R(t_i) = |[X_tx(t_i), Y_tx(t_i), Z_tx(t_i)] - [X_t(t_i), Y_t(t_i), Z_t(t_i)]| + |[X_rx(t_i), Y_rx(t_i), Z_rx(t_i)] - [X_t(t_i), Y_t(t_i), Z_t(t_i)]|; In the formula, (X_t(t_i), Y_t(t_i), Z_t(t_i)) represents the three-dimensional coordinates of each data sampling time t_i from the first differential GNSS module, (X_rx(t_i), Y_rx(t_i), Z_rx(t_i)) represents the three-dimensional coordinates of the phase center of the radar transmitting antenna at each data sampling time t_i from the second differential GNSS module, and (X_tx(t_i), Y_tx(t_i), Z_tx(t_i)) represents the three-dimensional coordinates of the phase center of the receiving antenna at each data sampling time t_i from the second differential GNSS module; S2. Construct an ideal reference signal; Ideally, if the target remains stationary at a reference position during the measurement, its echo signal will be a stable frequency domain response, thus constructing a phase-compensated reference signal. S3. Calculate and apply the phase compensation amount; For each sampling time t_i and each frequency point f_j, calculate the difference between the ideal distance and the instantaneous distance: ΔR(t_i) = R(t_i) - R_ref; In the formula, ΔR(t_i) represents the difference between the ideal distance and the instantaneous distance, and R_ref represents a selected reference distance, which can be the average distance over the entire measurement period or the distance at the midpoint of the flight path. The phase delay of the wave is directly related to the propagation distance. Therefore, the phase error caused by the distance difference is calculated as follows: Δφ(t_i) = (4π * ΔR(t_i)) / λ; In the formula, λ = c / f_j represents the wavelength of the radar at frequency f_j, c represents the speed of light, and Δφ(t_i) represents the phase error; The compensation factor is a complex number with an amplitude of 1 and a phase opposite to the error phase. Therefore, the compensation factor is: H_comp(t_i, f_j) = exp( -j * Δφ(t_i) ) = exp( -j * (4π * f_j * ΔR(t_i)) / c ); In the formula, H_comp(t_i, f_j) represents the compensation factor, and j represents the imaginary unit; Apply compensation: The compensation factor is multiplied by the original frequency domain echo data S_raw(t_i, f_j) as follows: S_comp(t_i, f_j) = S_raw(t_i, f_j) * H_comp(t_i, f_j); In the formula, S_comp(t_i, f_j) represents the applied phase compensation amount; S4, Data Reassembly and Imaging; Perform an inverse Fourier transform along the frequency dimension on the compensated S_comp(t_i, f_j) to obtain a high-resolution one-dimensional range image at each time t_i. Coherent processing is performed on the range images at different times, and a two-dimensional inverse synthetic aperture radar image of the target is generated by the selected imaging algorithm.

Images