Multi-rotor unmanned aerial vehicle synthetic aperture radar high-frequency vibration error compensation method

Abstract

The invention discloses a multi-rotor unmanned aerial vehicle synthetic aperture radar high-frequency vibration error compensation method, which belongs to the technical field of radar data processing, is used for radar signal error processing, and comprises the following steps: establishing a high-frequency vibration error model and a corresponding echo signal model of a multi-rotor unmanned aerial vehicle frequency modulation continuous wave synthetic aperture radar system; analyzing an influence mechanism of the high-frequency vibration error on the imaging quality; the method comprises the following steps of: accurately extracting vibration components by utilizing improved empirical mode decomposition, then estimating vibration parameters by constructing an optimal solution of a correlation function, and finally designing a compensation function and compensating each vibration component one by one through loop iteration. According to the method, the high-frequency vibration error of the frequency-modulated continuous wave synthetic aperture radar system is modeled and analyzed, and the high-frequency vibration error compensation method based on complete ensemble empirical mode decomposition is provided, so that effective compensation of the multi-component high-frequency vibration error is realized, and the suppression effect of a false target caused by the high-frequency vibration error is improved.

Description

TECHNICAL FIELD

[0001] The application discloses a multi-rotor unmanned aerial vehicle synthetic aperture radar high-frequency vibration error compensation method and belongs to the technical field of radar data processing. BACKGROUND

[0002] In a flight process of a multi-rotor unmanned aerial vehicle synthetic aperture radar system, the unmanned aerial vehicle flight platform is prone to periodic vibration due to factors such as high-speed rotation of rotors and motor vibration, and high-frequency vibration errors are generated. Such errors can cause phase modulation of echo signals and introduce paired false targets in imaging results, thereby seriously reducing imaging quality. Generally, the high-frequency vibration error can be approximately expressed as a superposition of a standard sinusoidal signal, multiple harmonic components and part of non-harmonic components, and the vibration amplitude is usually in the millimeter range, so that an inertial measurement unit is difficult to accurately capture. Limited by the precision of sensors carried by the unmanned aerial vehicle and the complex characteristics of the high-frequency vibration error, a traditional synthetic aperture radar imaging algorithm cannot effectively compensate for the high-frequency vibration. Therefore, it is of great significance to carry out research on high-frequency vibration compensation technology.

[0003] In terms of multi-component high-frequency motion errors, the following methods are currently mainly adopted: vibration errors are reconstructed through sinusoidal frequency modulation Fourier transform, so that high-frequency vibration compensation in synthetic aperture radar imaging is realized, the method can effectively extract sinusoidal modulation phase errors under the condition that the maximum phase offset between adjacent sampling points is less than However, the performance of the method significantly decreases in a low signal-to-noise ratio environment; a time-frequency analysis method based on short-time Fourier transform is used to obtain a time-frequency representation of a received signal, and then vibration frequency is estimated, and the accuracy of the time-frequency analysis method depends on the length of a short-time window. A non-parametric paired echo suppression method based on weighted phase gradient self-focusing directly compensates for vibration phase errors through joint estimation of multiple scatterers, and although the non-parametric estimation method avoids the complex process of explicit estimation of vibration parameters and reduces the calculation amount, the compensation accuracy is relatively low. SUMMARY

[0004] The application aims to provide a multi-rotor unmanned aerial vehicle synthetic aperture radar high-frequency vibration error compensation method, so as to solve the problems in the prior art that higher vibration compensation accuracy must be at the cost of greater calculation load, the performance significantly decreases in a low signal-to-noise ratio environment, and the accuracy of a time-frequency analysis method depends on the length of a short-time window.

[0005] A method for compensating for high-frequency vibration errors in a multi-rotor UAV synthetic aperture radar (SAR), comprising: S1, establishing an imaging geometric model of the frequency-modulated continuous wave (FM-CW) SAR system under high-frequency vibration errors and an echo signal model of the FM-CW SAR system under high-frequency vibration errors; S2, performing range migration correction, intra-pulse motion compensation, and azimuth pulse compression on the echo signal to obtain a two-dimensional imaging result of the FM-CW SAR system containing high-frequency vibration errors; S3, based on the two-dimensional imaging result of the FM-CW SAR system with high-frequency vibration errors, constructing a range cell set, extracting the phase information of each azimuth signal to construct a phase set, and adding [variables] to the phase set. Pairs of positive and negative Gaussian white noise are used to generate a signal pair for each phase information. Each signal pair is subjected to empirical mode decomposition and the intrinsic mode components are averaged. The intrinsic mode components obtained from all range cell decompositions are weighted and averaged to obtain the estimated high-frequency vibration components. S4. The frequency of the vibration components is estimated using time-frequency analysis. The basis functions of the vibration components are constructed and fitted based on the minimum mean square error. The objective function is defined and the minimum value of the objective function is obtained through iterative calculation. The vibration components are extracted and the vibration parameters are estimated in sequence. The phase compensation function of the vibration components is constructed and iteratively processed. The vibration suppression convergence threshold is set, and finally the imaging result after high-frequency vibration error compensation is obtained.

[0006] S1 includes, S1.1, establishing the imaging geometric model of the frequency-modulated continuous wave synthetic aperture radar system under high-frequency vibration error, assuming the flight space of the UAV platform is a spatial rectangular coordinate system, and the UAV platform along... Moving along the axial direction, with a speed of Flight time is Flight altitude is , Let the origin of the spatial rectangular coordinate system be, and the ideal trajectory be... The actual flight trajectory is , , To save time, For slow time, ground point Coordinates are , For follow Changing radar and Instantaneous sloping moments between For drone flight platform to The shortest slant distance, along the coordinate system of the UAV flight platform shaft and The high-frequency vibration errors of the shaft are respectively and The high-frequency vibration error of the UAV flight platform is: ; In the formula, is the high frequency vibration error, is the index of the vibration component, is the number of vibration components, is the amplitude of the vibration component, is the amplitude of the th vibration component, is the frequency of the vibration component, is the frequency of the th vibration component, is the initial phase of the vibration component, is the initial phase of the th vibration component.

[0007] S1 includes, S1.2, establishing a frequency modulated continuous wave synthetic aperture radar system echo signal model under high frequency vibration error : ; ; ; ; wherein, , , is a substitution variable, is a rectangular window function, is a natural exponential function, is an imaginary unit, is the pulse duration of the signal, is the instantaneous slant range in ideal case, is the carrier wavelength, , is the speed of light, is the signal center frequency, is the range direction frequency modulation, is the inter-pulse LOS direction high frequency vibration error, is the intra-pulse LOS direction high frequency vibration error, is the instantaneous radial velocity of the radar platform at time caused by high frequency vibration, and are the phase errors caused by vibration of the unmanned aerial vehicle flight platform inter-pulse, are the phase errors caused by vibration of the unmanned aerial vehicle flight platform intra-pulse, LOS is the straight line where the radar beam center optical axis points to the target.

[0008] S2 includes, performing range migration correction, intra-pulse motion compensation and azimuth direction pulse compression on the echo signal to obtain a frequency modulated continuous wave synthetic aperture radar system two-dimensional imaging result containing high frequency vibration error : ; ; ; wherein, , is a substitution variable, is a sine function, is a distance frequency variable, is an azimuth Doppler bandwidth.

[0009] S3 comprises, S3.1, calculating the average energy of each range cell in the synthetic aperture radar echo , extracting the azimuth signals of the top 5% range cells with the highest energy, constructing a range cell set : ; wherein, is the range cell, is the range cell index, is the number of range cells; S3 comprises, S3.2, extracting the phase information of each azimuth signal from the range cell set, performing phase unwrapping, and constructing a phase set : ; wherein, is the phase information of the range cell.

[0010] S3 comprises, S3.3, adding to to form a pair of positive and negative Gaussian white noise to obtain a signal to be processed: ; wherein, , is the signal pair after adding noise, is the Gaussian white noise, is the index of the pair of positive and negative Gaussian white noise; S3 comprises, S3.4, performing empirical mode decomposition on , respectively to obtain intrinsic mode components and , and then averaging and to obtain the final intrinsic mode component of : ; To the average of the results of the second experiment, the final complete set of empirical mode decomposition results of the first distance unit : .

[0011] S3 includes, S3.5, as the weight basis, the weight is normalized, and the estimated high-frequency vibration component is obtained: ; ; In the formula, is the normalized weight, is a vibration component in the high-frequency vibration error, is an index, .

[0012] S4 includes, S4.1, using the extracted vibration component, the frequency of the vibration component is estimated by using the time-frequency analysis method , taking as the known quantity, the basis function of the vibration component is constructed : ; In the formula, is the random amplitude of the vibration component, is the random initial phase of the vibration component.

[0013] S4 includes, S4.2, based on the least mean square error, the target function is defined : ; In the formula, is the number of azimuth sampling points, is the synthetic aperture time, is the absolute value; S4 includes, S4.3, by iterative calculation, find The minimum value corresponding to the minimum value of the parameter is the vibration parameter estimation result: ; In the formula, is the minimum value of the function, is the estimation result of the amplitude of the first vibration component, is the estimation result of the initial phase of the first vibration component.​​

[0014] S4 includes, S4.4, let the first... The phase compensation function is as follows: The vibration components are extracted and the vibration parameters are estimated sequentially, and the phase compensation function of the first vibration component is constructed. : ; S4 includes, S4.5, and will and Multiplication completes the suppression of the first vibrational component: ; ; ; In the formula, and To substitute variables; S4 includes S4.6, which iterates the compensation process, gradually compensating for multiple high-frequency vibration components in the azimuth direction, when... At that time, the vibration suppression reached convergence, and the imaging result after high-frequency vibration compensation was finally obtained. : .

[0015] Compared with existing technologies, this invention has the following advantages: By modeling and analyzing the high-frequency vibration error of a frequency-modulated continuous wave synthetic aperture radar system and employing a high-frequency vibration error compensation method based on complete set empirical mode decomposition, this invention effectively compensates for multi-component high-frequency vibration errors, reducing computational load while improving the suppression effect on false targets caused by high-frequency vibration errors. By adding paired positive and negative Gaussian white noise to the echo signal, it enhances continuity across multiple time scales and optimizes the extreme value distribution. By combining time-frequency analysis and minimum mean square error fitting, it solves the problem of accurate quantization in time-frequency analysis methods and compensates for the dependence of the accuracy of time-frequency analysis methods on the length of short time windows. Attached Figure Description

[0016] Figure 1 This is a flowchart of the technology of this invention; Figure 2 This is a schematic diagram of the imaging geometry model of a frequency-modulated continuous wave synthetic aperture radar system for multi-rotor unmanned aerial vehicles; Figure 3 This is a flowchart of the high-frequency vibration component extraction method; Figure 4 This is a flowchart of a high-frequency vibration error estimation and compensation method; Figure 5 This is a schematic diagram of a simulation scene; Figure 6 This is an image of the imaging result without motion compensation for single-component high-frequency vibration error; Figure 7 This is an image of the existing technology imaging results for single-component high-frequency vibration error; Figure 8 This is an image showing the imaging result of the method of the present invention for single-component high-frequency vibration error; Figure 9 It is a single-component high-frequency vibration error without motion compensation in the azimuth slice; Figure 10 It is a directional slice of existing technology for single-component high-frequency vibration error; Figure 11 This invention relates to a method for azimuth slices of single-component high-frequency vibration error. Figure 12 This is an image of the imaging result without motion compensation for multi-component high-frequency vibration errors; Figure 13 This is an image of the existing technology for imaging multi-component high-frequency vibration errors; Figure 14 This is an image showing the imaging results of the method for multi-component high-frequency vibration error in this invention; Figure 15 The azimuth slice is a multi-component high-frequency vibration error without motion compensation; Figure 16 It is a directional slice of existing technology for multi-component high-frequency vibration error; Figure 17 This invention relates to a method for azimuth-oriented slicing of multi-component high-frequency vibration errors. Figure 18 The measured data was not subjected to motion-compensated azimuth slicing; Figure 19 It is a slice of the existing technology's orientation based on measured data; Figure 20 The measured data is a slice of the azimuth direction of the method of this invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0018] A method for compensating for high-frequency vibration errors in a multi-rotor UAV synthetic aperture radar (SAR), comprising: S1, establishing an imaging geometric model of the frequency-modulated continuous wave (FM-CW) SAR system under high-frequency vibration errors and an echo signal model of the FM-CW SAR system under high-frequency vibration errors; S2, performing range migration correction, intra-pulse motion compensation, and azimuth pulse compression on the echo signal to obtain a two-dimensional imaging result of the FM-CW SAR system containing high-frequency vibration errors; S3, based on the two-dimensional imaging result of the FM-CW SAR system with high-frequency vibration errors, constructing a range cell set, extracting the phase information of each azimuth signal to construct a phase set, and adding [variables] to the phase set. Pairs of positive and negative Gaussian white noise are used to generate a signal pair for each phase information. Each signal pair is subjected to empirical mode decomposition and the intrinsic mode components are averaged. The intrinsic mode components obtained from all range cell decompositions are weighted and averaged to obtain the estimated high-frequency vibration components. S4. The frequency of the vibration components is estimated using time-frequency analysis. The basis functions of the vibration components are constructed and fitted based on the minimum mean square error. The objective function is defined and the minimum value of the objective function is obtained through iterative calculation. The vibration components are extracted and the vibration parameters are estimated in sequence. The phase compensation function of the vibration components is constructed and iteratively processed. The vibration suppression convergence threshold is set, and finally the imaging result after high-frequency vibration error compensation is obtained.

[0019] S1 includes, S1.1, establishing the imaging geometric model of the frequency-modulated continuous wave synthetic aperture radar system under high-frequency vibration error, assuming the flight space of the UAV platform is a spatial rectangular coordinate system, and the UAV platform along... Moving along the axial direction, with a speed of Flight time is Flight altitude is , Let the origin of the spatial rectangular coordinate system be, and the ideal trajectory be... The actual flight trajectory is , , To save time, For slow time, ground point Coordinates are , For follow Changing radar and Instantaneous sloping moments between For drone flight platform to The shortest slant distance, along the coordinate system of the UAV flight platform shaft and The high-frequency vibration errors of the shaft are respectively and The high-frequency vibration error of the UAV flight platform is: ; In the formula, For high-frequency vibration error, For the index of vibration components, The number of vibration components. The amplitude of the vibration component. For the first The amplitude of each vibration component The frequency of the vibration component, For the first The frequency of each vibration component The initial phase of the vibration component. For the first The initial phase of each vibration component.

[0020] S1 includes S1.2, establishing an echo signal model for a frequency-modulated continuous wave synthetic aperture radar system under high-frequency vibration errors. : ; ; ; ; In the formula, , , To replace the variable, For rectangular window functions, It is a natural exponential function. The imaginary unit, The duration of the signal pulse. The instantaneous slant distance under ideal conditions. For carrier wavelength, , At the speed of light, The center frequency of the signal. For range-directed frequency modulation, This refers to the inter-pulse LOS-directed high-frequency vibration error. This refers to the intrapulse LOS-oriented high-frequency vibration error. Caused by high frequency vibration Instantaneous radial velocity of the radar platform at any given moment. and The phase error is caused by the vibration between pulses of the UAV flight platform. The phase error is caused by vibration within the UAV flight platform, and LOS is the straight line from the center optical axis of the radar beam to the target.

[0021] S2 includes performing range migration correction, intra-pulse motion compensation, and azimuth pulse compression on the echo signal to obtain a two-dimensional imaging result of the frequency-modulated continuous wave synthetic aperture radar system containing high-frequency vibration errors. : ; ; ; In the formula, , To replace the variable, For the Singer function, For distance frequency variables, This represents the azimuth Doppler bandwidth.

[0022] S3 includes, S3.1, calculating the average energy of each range cell in the synthetic aperture radar echo. The azimuth signals of the top 5% of range cells with the highest energy are extracted to construct a range cell set. : ; In the formula, For the first One distance unit, For distance cell index, The number of range cells; S3 includes, S3.2, extracting the phase information of each azimuth signal from the range cell set, performing phase unwrapping, and constructing a phase set. : ; In the formula, For the first Phase information of each distance cell.

[0023] S3 includes S3.3, and... Add By constructing pairs of positive and negative Gaussian white noise, the signal to be processed is obtained: ; In the formula, , For the first time after adding noise Group of signal pairs, For the first Gaussian white noise, For the index of paired positive and negative Gaussian white noise; S3 includes, S3.4, pairs of... , Empirical mode decomposition was performed separately to obtain the intrinsic mode components. and Then to and By averaging, we get The final intrinsic mode components : ; right The results of this experiment By averaging, we obtain the first... The final complete set of empirical mode decomposition results for each distance cell : .

[0024] S3 includes, S3.5, and will Using the weights as a basis, the weights are normalized to obtain the estimated high-frequency vibration components: ; ; In the formula, The normalized weights, This is a vibration component in the high-frequency vibration error. For indexing, .

[0025] S4 includes, S4.1, using the extracted vibration components, estimating the frequency of the vibration components using time-frequency analysis. ,by As known quantities, construct the basis functions for the vibrational components. : ; In the formula, The random amplitude of the vibration component. It represents the random initial phase of the vibration component.

[0026] S4 includes S4.2, which involves fitting based on the minimum mean square error and defining the objective function. : ; In the formula, This represents the number of sampling points in the azimuth direction. For the time to synthesize the pore size, For absolute values; S4 includes, S4.3, which is found through iterative calculation. The minimum value, the parameter corresponding to the minimum value. Vibration parameter estimation results: ; In the formula, To find the minimum value of the function, For the first The estimation results of the amplitude of each vibration component For the first The estimation results of the initial phase of each vibration component.

[0027] S4 includes, S4.4, let the first... The phase compensation function is as follows: The vibration components are extracted and the vibration parameters are estimated sequentially, and the phase compensation function of the first vibration component is constructed. : ; S4 includes, S4.5, and will and Multiplication completes the suppression of the first vibrational component: ; ; ; In the formula, and For the substitution variable; S4 includes, S4.6, iterating the compensation process, gradually compensating multiple high-frequency vibration components in the azimuth direction, when At that time, the vibration suppression reached convergence, and the imaging result after high-frequency vibration compensation was finally obtained. : .

[0028] The derivation process of the echo signal model of a frequency-modulated continuous wave synthetic aperture radar system under high-frequency vibration error is as follows: because , Much smaller than the ideal tilt moment, Instantaneous tilt range history for: ; right Perform a Taylor expansion and ignore its second-order terms. , and higher-order terms; thus, an approximate expression is obtained: ; ; ; in: ; ; ; ; In the formula, The angle of incidence of the radar on the target. For radar relative The instantaneous oblique angle, for LOS at time t is the high-frequency vibration error.

[0029] Will exist Perform a first-order Taylor expansion at this point: ; ; ; In the formula, The instantaneous slant range of a conventional pulse-based synthetic aperture radar under ideal conditions. This introduces range offset into the intrapulse motion of the frequency-modulated continuous wave synthetic aperture radar system. For radar and Between Radial velocity on the scale.

[0030] When the radar is performing side-view imaging... It is very small, almost negligible, and according to formula, This can be further expressed as: ; In the formula, , respectively along shaft and The number of vibration components of the shaft; , respectively along shaft and The first axis The amplitude of each vibration component; , respectively along shaft and The first axis The frequency of each vibration component; respectively along shaft and The first axis The initial phase of each vibration component is considered positively when the beam center is perpendicular to the flight direction.

[0031] Based on the principle of harmonic superposition It can be represented as: ; right exist Perform a first-order Taylor expansion at this point: ; ; ; in: ; .

[0032] Suppose that the synthetic aperture radar of a multi-rotor UAV transmits a frequency-modulated continuous wave signal, then the transmitted signal can be expressed as: .

[0033] For any target The echo signal can be represented as: ; RVP cancellation yields the time-domain echo signal: ; ; ; ; In the formula, , , To replace the variable, , , and Caused by high-frequency vibration error, among which and The phase error is caused by the vibration between pulses on the UAV flight platform; the latter two items... and The phase error is caused by vibration within the pulse of the drone flight platform.

[0034] In traditional pulse-based synthetic aperture radar (SAR), due to the extremely short duration of the transmitted pulse, it is typically assumed that the UAV platform remains stationary within a single pulse, thus negligible errors introduced by intra-pulse vibrations (i.e., the last two exponential terms). However, for frequency-modulated continuous-wave SAR systems, the transmitted continuous-wave signal has a longer duration, and the intra-pulse motion of the UAV platform cannot be ignored; therefore, the effects of these terms must be considered. Further analysis shows that for the second-phase term... The magnitude of the phase value it introduces is much smaller than The introduced phase value, therefore, This can be considered a high-order small quantity and neglected from the echo model, ultimately yielding the echo signal model of the frequency-modulated continuous wave synthetic aperture radar system under high-frequency vibration error: ; ; ; ; In the formula, The phase error caused by vibration within the UAV flight platform is also the main reason for the difference between frequency modulated continuous wave synthetic aperture radar system and pulse synthetic aperture radar in high-frequency motion error modeling. The subsequent analysis of high-frequency vibration error and design of motion compensation algorithm will be based on this model.

[0035] To further analyze the impact of high-frequency vibration errors on the imaging results, range migration correction (RCMC), intra-pulse motion compensation, and azimuth pulse compression were applied to the echo signal. After these processing steps, the two-dimensional imaging results of the frequency-modulated continuous wave synthetic aperture radar system containing high-frequency vibration errors are obtained as follows: ; ; ; In the formula, As the envelope function, intrapulse vibration introduces additional phase modulation into the time-domain echo signal, manifested as a frequency shift in the range-frequency domain. The error component in this term... for: ; That is, by and The equivalent frequency shift caused by both factors; the above frequency error can be converted into a range offset. : ; High-frequency vibration errors can be equivalent to sinusoidal modulation phase errors, and their impact depends on the ratio of the vibration amplitude to the operating wavelength. Generally, the amplitude of high-frequency vibration errors is only on the order of millimeters, so the additional phase modulation they cause is small, and the resulting range offset is negligible. Furthermore, when the system's range resolution is greater than the offset caused by high-frequency vibration errors, the envelope shift caused by the vibrations will not lead to significant range defocus, and the image quality is essentially unaffected. This means that the range offset caused by high-frequency vibration errors... It can be ignored.

[0036] To further analyze the sinusoidal modulation phase error caused by high-frequency vibrations to imaging, the Jacobi-Angel identity is introduced. Performing a first-kind Bessel series expansion, we obtain: ; ; ; In the formula, , To replace the variable, The multiplication symbol is used. Let be the order of the Bessel function expansion. for Bessel function of order 1, It is a zero-order Bessel function. Let be the independent variable of the Bessel function. , It is a complex coefficient; This indicates that the main lobe energy of the real target will be affected. The inhibition, of which That is, the zeroth-order Bessel function of all modulation terms. The product of the main lobe amplitude is Scaling causes energy attenuation in the main lobe, resulting in a decrease in target resolution. The term indicates that a single frequency is The vibration will generate an infinite number of harmonic frequency components in the azimuth signal. Introducing a series of coefficients from higher-order Bessel functions Controlled sidelobe components, i.e., each Symmetrical sidebands generated in the azimuth frequency domain Its strength is determined by This leads to the generation of paired false targets. Furthermore, the attenuation of the main lobe energy and the number of side lobes are both affected by the number of vibrational components.

[0037] The following is a further explanation based on the attached diagram, such as... Figure 1 As shown, the method of the present invention first establishes an echo signal model of a frequency-modulated continuous wave synthetic aperture radar system under high-frequency vibration error, performs range migration correction, intra-pulse motion compensation, and azimuth pulse compression on the echo signal to obtain a two-dimensional imaging result of the frequency-modulated continuous wave synthetic aperture radar system containing high-frequency vibration error; then, high-frequency vibration components are extracted based on complete set empirical mode decomposition, and finally, vibration parameters are estimated based on minimum mean square error to obtain high-resolution imaging results; Figure 2 This is the imaging geometric model of a frequency-modulated continuous wave synthetic aperture radar system for a multi-rotor unmanned aerial vehicle (UAV), where the UAV flight platform along... Moving along the axial direction with a speed of Flight altitude is , Let the origin of the spatial rectangular coordinate system be the origin. For ground points, For follow Changing radar and Instantaneous sloping moments between For drone flight platform to The shortest slope distance, The instantaneous slant distance under ideal conditions. The angle of incidence of the radar on the target. The red line represents the instantaneous oblique angle of the radar relative to the target P, while the green line represents the ideal flight trajectory.

[0038] like Figure 3 As shown, high-frequency vibration components are extracted based on complete set empirical mode decomposition. First, the original image is input, a set of range cells is constructed, and then phase information is extracted. The phase information of each azimuth signal is extracted from the set of range cells, phase unwrapping is performed, a phase set is constructed, positive and negative Gaussian white noise pairs are added to the phase set, and then empirical mode decomposition (EMD) is performed and the intrinsic mode components (IMF) are averaged. The IMF of multiple range cells is weighted and averaged to obtain the high-frequency vibration error components.

[0039] like Figure 4 As shown, vibration parameter estimation is performed based on minimum mean square error. First, high-frequency vibration components are extracted based on empirical mode decomposition of the complete set. Vibration parameters are then estimated based on the high-frequency vibration components, including time-frequency analysis to extract vibration frequencies, constructing basis functions for vibration components, and fitting with minimum mean square error (MSE). Next, vibration error compensation is performed, including constructing vibration component compensation functions, iterative processing, and threshold judgment. Finally, high-resolution imaging results are output.

[0040] To verify the effectiveness of the method of the present invention, a simulation experiment was first conducted. The main simulation parameters are shown in Table 1: Table 1. Parameters of UAV Synthetic Aperture Radar System .

[0041] like Figure 5 As shown, the simulation scenario is set to (Range × Azimuth), and a point target is placed at the edge of the scene for imaging performance analysis. In real-world environments, the vibration of multi-rotor UAVs typically exhibits more complex forms, often containing single or multiple vibration frequency components. Therefore, two typical scenarios are designed: a single-component vibration scenario and a multi-component vibration scenario, to comprehensively test the adaptability and effectiveness of the proposed compensation method. First, simulation analysis is conducted on the single-component vibration scenario, and the high-frequency vibration error parameters are shown in Table 2: Table 2. High-frequency vibration error parameters .

[0042] Figure 6 , Figure 7 and Figure 8 The images are shown in the diagrams, respectively, after processing with the uncompensated method, the prior art method, and the method of this invention. The prior art method is a nonparametric paired echo suppression method for helicopter synthetic aperture radar imaging. Figure 6As shown, the uncompensated imaging results exhibit obvious orientation ghosting and false targets, and the image is severely out of focus; Figure 7 The results show that although existing technologies can effectively suppress false targets introduced by single-component high-frequency vibrations, the images still exhibit a certain degree of defocusing due to limited signal decomposition accuracy. In contrast, such as Figure 8 As shown, the method of this invention effectively suppresses false targets and significantly improves the focusing performance of the imaging results by accurately estimating and compensating for single-component high-frequency vibrations. The corresponding high-frequency vibration error parameter estimation results are shown in Table 3. Table 3. Vibration parameter estimation results for single-component vibration scenarios .

[0043] To further verify the effectiveness of the algorithm, Figure 9 , Figure 10 and Figure 11 The image shows azimuth slices of point targets processed by three methods, and Table 4 lists the corresponding azimuth imaging quality parameters, including peak sidelobe ratio (PSLR), integral sidelobe ratio (ISLR), and impulse response width (IRW). Table 4. Azimuth image quality parameters for single-component vibration scenes ; The results show that the peak sidelobe ratio, integral sidelobe ratio, and impulse response width of the prior art are -12.07dB, -6.38dB, and 0.26m, respectively; while the peak sidelobe ratio, integral sidelobe ratio, and impulse response width of the method of the present invention are improved to -12.86dB, -9.38dB, and 0.24m, respectively. Compared with the prior art, the method of the present invention has improved in terms of suppressing sidelobes, improving imaging contrast and resolution, and further verifies its reliability and advantages in single-component high-frequency vibration error scenarios.

[0044] Simulation analysis was conducted for a multi-component high-frequency vibration error scenario. The high-frequency vibration error parameters are shown in Table 2. In this scenario, three vibration components with different frequencies, amplitudes and initial phases were introduced simultaneously in the direction of motion of the UAV flight platform to simulate a more complex actual flight vibration environment. Figure 12 , Figure 13 and Figure 14 The imaging results are shown respectively after processing with the uncompensated method, the prior art method, and the method of this invention. From Figure 12 As can be seen, due to the lack of any high-frequency motion error compensation, the imaging results contain severe defocus and multiple false targets, resulting in a significant decrease in imaging quality. Figure 13The results show that while existing technologies can effectively suppress some vibration errors, their compensation accuracy is limited due to the inability to accurately estimate vibration parameters. Residual errors still result in significant defocusing and false targets in the imaging results. In contrast, Figure 14 The results show that the method of the present invention effectively achieves accurate estimation and compensation of multiple vibration components, significantly improves the focusing performance of imaging results, suppresses false targets, and compares with... Figure 8 and Figure 14 For the same target point, the compensation results for a single vibration component and multiple vibration components differ only in subtle ways, making them difficult to discern with the naked eye. These results verify that the method of this invention still possesses strong robustness and stable adaptability in complex multi-component vibration scenarios. The corresponding high-frequency vibration error parameter estimation results are shown in Table 5. Table 5. Vibration parameter estimation results for multi-component vibration scenarios .

[0045] Similarly, to further verify the effectiveness of the algorithm, Figure 15 , Figure 16 and Figure 17 The image shows azimuth slices of point targets processed by three methods, and Table 6 lists the corresponding azimuth imaging quality parameters, including peak sidelobe ratio, integral sidelobe ratio, and impulse response width. Table 6. Azimuth image quality parameters for multi-component vibration scenes ; The experimental results in Table 6 show that the peak sidelobe ratio, integral sidelobe ratio, and impulse response width of the prior art are -4.17dB, -0.01dB, and 0.29m, respectively; while the peak sidelobe ratio, integral sidelobe ratio, and impulse response width of the method of the present invention are improved to -12.68dB, -9.38dB, and 0.24m, respectively. Compared with the prior art, the method of the present invention has improved in terms of suppressing sidelobes, improving imaging contrast and resolution, further verifying its reliability and advantages in multi-component high-frequency vibration error scenarios.

[0046] from Figure 15 As can be seen, due to the lack of any high-frequency vibration error compensation, the main lobe is significantly widened, the side lobes are significantly raised, false targets are more prominent, and the overall imaging quality is poor. Figure 16 The existing techniques shown can mitigate sidelobe lift caused by vibration errors to some extent, but the main lobe still exhibits significant expansion, resulting in insufficient sidelobe suppression and limited improvement in imaging resolution and contrast. In contrast, Figure 17 The results show that the method proposed in this invention, after effectively estimating and compensating for multi-component vibration errors, achieves better main lobe recovery, significant suppression of side lobes, and a significant improvement in target focusing effect.

[0047] To further verify the effectiveness of the method in a real environment, actual measurement data was used for comparison. The original data used in this invention was collected by a multi-rotor UAV frequency-modulated continuous wave synthetic aperture radar system built by the researchers themselves. The data acquisition scenario was a parking lot. The synthetic aperture radar system operated in the W-band with a carrier frequency of 77 GHz, a bandwidth of 1.79 GHz, a pulse repetition frequency of 1 kHz, and a sampling rate of 10 MHz. The average speed of the UAV during flight was 2 m / s, and the flight altitude was 5 m.

[0048] To quantitatively evaluate imaging quality, under the same flight conditions and radar parameters, the processing results of the uncompensated method and existing techniques were compared with those of the present invention. Typical point targets in the scene were selected, and their azimuth slice results were analyzed. The comparison results are as follows: Figure 18 , Figure 19 and Figure 20 As shown. Figure 18 The image is an azimuth slice without motion compensation processing. Due to motion disturbances during the flight of the UAV, the phase error was not effectively corrected, the main lobe was significantly broadened, the side lobe suppression was poor, the peak energy distribution was not concentrated, and the target focusing performance was insufficient, resulting in low image clarity. Figure 19 This is an azimuth slice image processed using existing technology, and... Figure 18 In comparison, although the main lobe focusing performance has been improved and the side lobe level has been suppressed to some extent, there are still problems such as main lobe widening and insufficient side lobe suppression, resulting in limited improvement in image quality. Figure 20 The image shows the azimuth slice image processed by the method of this invention. It can be seen that the method of this invention significantly reduces the azimuth main lobe width and improves the peak concentration by effectively compensating for platform motion errors, while significantly suppressing side lobes and improving target focusing performance. To better verify the imaging performance, the imaging quality parameters of the corresponding point targets for each method were statistically analyzed, as shown in Table 7. Table 7. Azimuth Image Quality Parameters ; The results show that after processing with the method of this invention, the main lobe width of the point target is significantly narrowed, and the side lobe level is effectively suppressed. Specifically, the peak sidelobe ratio of the point target is optimized from -7.18dB to -11.17dB, the integral sidelobe ratio from -3.67dB to -8.02dB, and the impulse response width from 4.46m to 3.05m. The peak sidelobe ratio, integral sidelobe ratio, and impulse response width of the point target are all significantly improved, demonstrating the effectiveness of this method in improving focusing performance and further verifying the superiority of the proposed method. The high-frequency vibration error parameters estimated using the method of this invention are shown in Table 8. Table 8. Vibration parameter estimation results .

[0049] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for compensating high-frequency vibration errors in synthetic aperture radar for multi-rotor unmanned aerial vehicles, characterized in that, include: S1. Establish the imaging geometric model of the frequency-modulated continuous wave synthetic aperture radar system under high-frequency vibration error and the echo signal model of the frequency-modulated continuous wave synthetic aperture radar system under high-frequency vibration error. S2. Range migration correction, intra-pulse motion compensation, and azimuth pulse compression are performed on the echo signal to obtain the two-dimensional imaging results of the frequency-modulated continuous wave synthetic aperture radar system containing high-frequency vibration errors. S3. Based on the two-dimensional imaging results of the frequency-modulated continuous wave synthetic aperture radar system based on high-frequency vibration error, construct a range cell set, extract the phase information of each azimuth signal to construct a phase set, add pairs of positive and negative Gaussian white noise to the phase set, generate a signal pair for each phase information, perform empirical mode decomposition on each signal pair and average the intrinsic mode components, and perform weighted averaging on the intrinsic mode components obtained from all range cell decompositions to obtain the estimated high-frequency vibration components. S4. The frequency of the vibration component is estimated by time-frequency analysis, the basis function of the vibration component is constructed, and the minimum mean square error is used for fitting. The objective function is defined, and the minimum value of the objective function is obtained by iterative calculation. The vibration component is extracted and the vibration parameter is estimated in sequence. The phase compensation function of the vibration component is constructed and iteratively processed. The vibration suppression convergence threshold is set, and finally the imaging result after high-frequency vibration error compensation is obtained.

2. The method for compensating high-frequency vibration errors of synthetic aperture radar for multi-rotor unmanned aerial vehicles according to claim 1, characterized in that, S1 includes, S1.1, establishing the imaging geometric model of the frequency-modulated continuous wave synthetic aperture radar system under high-frequency vibration error, assuming the flight space of the UAV platform is a spatial rectangular coordinate system, and the UAV platform along... Moving along the axial direction with a speed of Flight time is Flight altitude is , Let the origin of the spatial rectangular coordinate system be, and the ideal trajectory be... The actual flight trajectory is , , To save time, For slow time, ground point Coordinates are , For follow Changing radar and Instantaneous sloping moments between For drone flight platform to The shortest slant distance, along the coordinate system of the UAV flight platform shaft and The high-frequency vibration errors of the shaft are respectively and The high-frequency vibration error of the UAV flight platform is: ； In the formula, For high-frequency vibration error, For the index of vibration components, The number of vibration components. The amplitude of the vibration component. For the first The amplitude of each vibration component The frequency of the vibration component, For the first The frequency of each vibration component The initial phase of the vibration component. For the first The initial phase of each vibration component.

3. The method for compensating high-frequency vibration errors of synthetic aperture radar for multi-rotor unmanned aerial vehicles according to claim 2, characterized in that, S1 includes S1.2, establishing an echo signal model for a frequency-modulated continuous wave synthetic aperture radar system under high-frequency vibration errors. : ； ； ； ； In the formula, , , To replace the variable, For rectangular window functions, It is a natural exponential function. The imaginary unit, The duration of the signal pulse. This represents the instantaneous slant distance under ideal conditions. For carrier wavelength, , At the speed of light, The center frequency of the signal. For range-directed frequency modulation, This refers to the inter-pulse LOS-directed high-frequency vibration error. This refers to the intrapulse LOS-oriented high-frequency vibration error. Caused by high frequency vibration Instantaneous radial velocity of the radar platform at any given moment. and The phase error is caused by the vibration between pulses of the UAV flight platform. The phase error is caused by vibration within the UAV flight platform, and LOS is the straight line from the center optical axis of the radar beam to the target.

4. The method for compensating for high-frequency vibration errors in synthetic aperture radar for multi-rotor unmanned aerial vehicles according to claim 3, characterized in that, S2 includes performing range migration correction, intra-pulse motion compensation, and azimuth pulse compression on the echo signal to obtain a two-dimensional imaging result of the frequency-modulated continuous wave synthetic aperture radar system containing high-frequency vibration errors. : ； ； ； In the formula, , To replace the variable, For the Singer function, For distance frequency variables, This represents the azimuth Doppler bandwidth.

5. A method for compensating high-frequency vibration errors in synthetic aperture radar for multi-rotor unmanned aerial vehicles according to claim 4, characterized in that, S3 includes, S3.1, calculating the average energy of each range cell in the synthetic aperture radar echo. The azimuth signals of the top 5% of range cells with the highest energy are extracted to construct a range cell set. : ； In the formula, For the first One distance unit, For distance cell index, This represents the number of distance units; S3 includes S3.2, extracting the phase information of each azimuth signal from the range cell set, performing phase unwrapping, and constructing a phase set. : ； In the formula, For the first Phase information of each distance cell.

6. The method for compensating high-frequency vibration errors of synthetic aperture radar for multi-rotor unmanned aerial vehicles according to claim 5, characterized in that, S3 includes S3.3, and... Add By constructing pairs of positive and negative Gaussian white noise, the signal to be processed is obtained: ； In the formula, , For the first time after adding noise Group of signal pairs, For the first Gaussian white noise, For paired positive and negative Gaussian white noise index; S3 includes, S3.4, and... , Empirical mode decomposition was performed separately to obtain the intrinsic mode components. and Then to and By averaging, we get The final intrinsic mode components : ； right The results of this experiment By averaging, we obtain the first... The final complete set of empirical mode decomposition results for each distance cell : 。 7. A method for compensating high-frequency vibration errors in synthetic aperture radar for multi-rotor unmanned aerial vehicles according to claim 6, characterized in that, S3 includes, S3.5, and will Using the weights as a basis, the weights are normalized to obtain the estimated high-frequency vibration components: ； ； In the formula, The normalized weights This is a vibration component in the high-frequency vibration error. For indexing, .

8. A method for compensating high-frequency vibration errors in synthetic aperture radar for multi-rotor unmanned aerial vehicles according to claim 7, characterized in that, S4 includes, S4.1, using the extracted vibration components, estimating the frequency of the vibration components using time-frequency analysis. ,by As known quantities, construct the basis functions for the vibration components. : ； In the formula, The random amplitude of the vibration component. It represents the random initial phase of the vibration component.

9. A method for compensating high-frequency vibration errors in synthetic aperture radar for multi-rotor unmanned aerial vehicles according to claim 8, characterized in that, S4 includes S4.2, which involves fitting based on the minimum mean square error and defining the objective function. : ； In the formula, This represents the number of sampling points in the azimuth direction. For the time to synthesize the pore size, It is the absolute value; S4 includes S4.3, which finds the solution through iterative calculation. The minimum value, the parameter corresponding to the minimum value. Vibration parameter estimation results: ； In the formula, To find the minimum value of the function, For the first The estimation results of the amplitude of each vibration component For the first The estimation results of the initial phase of each vibration component.

10. A method for compensating high-frequency vibration errors in synthetic aperture radar for multi-rotor unmanned aerial vehicles according to claim 9, characterized in that, S4 includes, S4.4, let the first... The phase compensation function is as follows: The vibration components are extracted and the vibration parameters are estimated sequentially, and the phase compensation function of the first vibration component is constructed. : ； S4 includes, S4.5, and will and Multiplication completes the suppression of the first vibrational component: ； ； ； In the formula, and To substitute variables; S4 includes S4.6, which iterates the compensation process, gradually compensating for multiple high-frequency vibration components in the azimuth direction, when... At that time, the vibration suppression reached convergence, and the imaging result after high-frequency vibration compensation was finally obtained. : 。

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