A method for compensating high-frequency vibration errors in synthetic aperture radar for multi-rotor UAVs

Abstract

This invention discloses a high-frequency vibration error compensation method for a multi-rotor UAV synthetic aperture radar, belonging to the field of radar data processing technology. It is used for radar signal error processing, including establishing a high-frequency vibration error model and corresponding echo signal model for a multi-rotor UAV frequency-modulated continuous-wave synthetic aperture radar system, analyzing the impact mechanism of high-frequency vibration error on imaging quality; using improved empirical mode decomposition to accurately extract vibration components; subsequently estimating vibration parameters by constructing the optimal solution of the correlation function; and finally designing a compensation function and iteratively compensating each vibration component one by one. This invention, through modeling and analyzing the high-frequency vibration error of a frequency-modulated continuous-wave synthetic aperture radar system, proposes a high-frequency vibration error compensation method based on complete set empirical mode decomposition, achieving effective compensation for multi-component high-frequency vibration errors and improving the suppression effect on false targets caused by high-frequency vibration errors.

Description

Technical Field

[0001] This invention discloses a method for high-frequency vibration error compensation of synthetic aperture radar for multi-rotor unmanned aerial vehicles, belonging to the field of radar data processing technology. Background Technology

[0002] During flight, multi-rotor UAV synthetic aperture radar (SAR) systems are prone to periodic vibrations due to factors such as high-speed rotor rotation and motor vibration, resulting in high-frequency vibration errors. These errors cause phase modulation of the echo signal, introducing pairs of false targets into the imaging results and severely degrading image quality. Typically, high-frequency vibration errors can be approximated as a superposition of a standard sine wave, its multiple harmonic components, and some non-harmonic components. The vibration amplitude is usually in the millimeter range, making it difficult for inertial measurement units (IMUs) to accurately capture. Limited by the accuracy of the sensors onboard the UAV and the complex characteristics of high-frequency vibration errors, traditional SAR imaging algorithms cannot effectively compensate for such high-frequency vibrations. Therefore, research on high-frequency vibration compensation technology is of great significance.

[0003] Regarding multi-component high-frequency motion errors, the following methods are currently mainly adopted: Vibration errors are reconstructed through sinusoidal frequency-modulated Fourier transform, thereby achieving high-frequency vibration compensation in synthetic aperture radar imaging. This method can achieve a maximum phase shift of less than [value missing] between adjacent sampling points. Under certain conditions, it effectively extracts sinusoidal modulation phase error, but its performance degrades significantly in low signal-to-noise ratio environments. A time-frequency analysis method based on short-time Fourier transform is used to obtain the time-frequency representation of the received signal and then estimate the vibration frequency. The accuracy of this time-frequency analysis method depends on the length of the short time window. A non-parametric paired echo suppression method based on weighted phase gradient self-focusing directly compensates for vibration phase error through joint estimation of multiple scatterers. While this method avoids the complex process of explicit estimation of vibration parameters and reduces computational load, its compensation accuracy is relatively low. Summary of the Invention

[0004] The purpose of this invention is to provide a high-frequency vibration error compensation method for synthetic aperture radar of multi-rotor UAVs, in order to solve the problems in the prior art, such as higher vibration compensation accuracy must come at the cost of greater computational load, significant performance degradation in low signal-to-noise ratio environments, and the accuracy of time-frequency analysis methods depending on the length of short time windows.

[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:

[0007] ;

[0008] 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.

[0009] S1 includes S1.2, establishing an echo signal model for a frequency-modulated continuous wave synthetic aperture radar system under high-frequency vibration errors. :

[0010] ;

[0011] ;

[0012] ;

[0013] ;

[0014] 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.

[0015] 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. :

[0016] ;

[0017] ;

[0018] ;

[0019] In the formula, , To replace the variable, For the Singer function, For distance frequency variables, This represents the azimuth Doppler bandwidth.

[0020] S3 includes, S3.1, calculating the average energy of each range cell in the synthetic aperture radar echo. Extract the azimuth signals of the top 5% of range cells with the highest energy to construct a range cell set. :

[0021] ;

[0022] In the formula, For the first One distance unit, For distance cell index, This represents the number of distance units;

[0023] 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. :

[0024] ;

[0025] In the formula, For the first Phase information of each distance cell.

[0026] S3 includes S3.3, and... Add By constructing pairs of positive and negative Gaussian white noise, the signal to be processed is obtained:

[0027] ;

[0028] 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;

[0029] 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 :

[0030] ;

[0031] 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 :

[0032] .

[0033] S3 includes, S3.5, and will Using the weights as a basis, the weights are normalized to obtain the estimated high-frequency vibration components:

[0034] ;

[0035] ;

[0036] In the formula, The normalized weights, This is a vibration component in the high-frequency vibration error. For indexing, .

[0037] 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. :

[0038] ;

[0039] In the formula, The random amplitude of the vibration component. It represents the random initial phase of the vibration component.

[0040] S4 includes S4.2, which involves fitting based on the minimum mean square error and defining the objective function. :

[0041] ;

[0042] 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;

[0043] 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:

[0044] ;

[0045] 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.

[0046] 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. :

[0047] ;

[0048] S4 includes, S4.5, and will and Multiplication completes the suppression of the first vibrational component:

[0049] ;

[0050] ;

[0051] ;

[0052] In the formula, and To substitute variables;

[0053] 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. :

[0054] .

[0055] 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

[0056] Figure 1 This is a flowchart of the technology of this invention;

[0057] 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;

[0058] Figure 3 This is a flowchart of the high-frequency vibration component extraction method;

[0059] Figure 4 This is a flowchart of a high-frequency vibration error estimation and compensation method;

[0060] Figure 5 This is a schematic diagram of a simulation scene;

[0061] Figure 6 This is an image of the imaging result without motion compensation for single-component high-frequency vibration error;

[0062] Figure 7 This is an image of the existing technology imaging results for single-component high-frequency vibration error;

[0063] Figure 8 This is an image showing the imaging result of the method of the present invention for single-component high-frequency vibration error;

[0064] Figure 9 It is a single-component high-frequency vibration error without motion compensation in the azimuth slice;

[0065] Figure 10 It is a directional slice of existing technology for single-component high-frequency vibration error;

[0066] Figure 11 This invention relates to a method for azimuth slices of single-component high-frequency vibration error.

[0067] Figure 12This is an image of the imaging result without motion compensation for multi-component high-frequency vibration errors;

[0068] Figure 13 This is an image of the existing technology for imaging multi-component high-frequency vibration errors;

[0069] Figure 14 This is an image showing the imaging results of the method for multi-component high-frequency vibration error in this invention;

[0070] Figure 15 The azimuth slice is a multi-component high-frequency vibration error without motion compensation;

[0071] Figure 16 It is a directional slice of existing technology for multi-component high-frequency vibration error;

[0072] Figure 17 This invention relates to a method for azimuth-oriented slicing of multi-component high-frequency vibration errors.

[0073] Figure 18 The measured data was not subjected to motion-compensated azimuth slicing;

[0074] Figure 19 It is a slice of the measured data in the existing technology orientation.

[0075] Figure 20 The measured data are azimuth slices of the method of this invention. Detailed Implementation

[0076] 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.

[0077] 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.

[0078] 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:

[0079] ;

[0080] 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.

[0081] S1 includes S1.2, establishing an echo signal model for a frequency-modulated continuous wave synthetic aperture radar system under high-frequency vibration errors. :

[0082] ;

[0083] ;

[0084] ;

[0085] ;

[0086] 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.

[0087] 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. :

[0088] ;

[0089] ;

[0090] ;

[0091] In the formula, , To replace the variable, For the Singer function, For distance frequency variables, This represents the azimuth Doppler bandwidth.

[0092] S3 includes, S3.1, calculating the average energy of each range cell in the synthetic aperture radar echo. Extract the azimuth signals of the top 5% of range cells with the highest energy to construct a range cell set. :

[0093] ;

[0094] 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. :

[0095] ;

[0096] In the formula, For the first Phase information of each distance cell.

[0097] S3 includes S3.3, and... Add By constructing pairs of positive and negative Gaussian white noise, the signal to be processed is obtained:

[0098] ;

[0099] 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 :

[0100] ;

[0101] 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 :

[0102] .

[0103] S3 includes, S3.5, and will Using the weights as a basis, the weights are normalized to obtain the estimated high-frequency vibration components:

[0104] ;

[0105] ;

[0106] In the formula, The normalized weights, This is a vibration component in the high-frequency vibration error. For indexing, .

[0107] 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. :

[0108] ;

[0109] In the formula, The random amplitude of the vibration component. It represents the random initial phase of the vibration component.

[0110] S4 includes S4.2, which involves fitting based on the minimum mean square error and defining the objective function. :

[0111] ;

[0112] 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:

[0113] ;

[0114] 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.

[0115] 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. :

[0116] ;

[0117] S4 includes, S4.5, and will and Multiplication completes the suppression of the first vibrational component:

[0118] ;

[0119] ;

[0120] ;

[0121] 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. :

[0122] .

[0123] 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:

[0124] because , Much smaller than the ideal tilt moment, Instantaneous tilt range history for:

[0125] ;

[0126] right Perform a Taylor expansion and ignore its second-order terms. , and higher-order terms; thus, an approximate expression is obtained:

[0127] ;

[0128] ;

[0129] ;

[0130] in:

[0131] ;

[0132] ;

[0133] ;

[0134] ;

[0135] 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.

[0136] Will exist Perform a first-order Taylor expansion at this point:

[0137] ;

[0138] ;

[0139] ;

[0140] 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.

[0141] When the radar is performing side-view imaging... It is very small, almost negligible, and according to formula, This can be further expressed as:

[0142] ;

[0143] 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.

[0144] Based on the principle of harmonic superposition It can be represented as:

[0145] ;

[0146] right exist Perform a first-order Taylor expansion at this point:

[0147] ;

[0148] ;

[0149] ;

[0150] in:

[0151] ;

[0152] .

[0153] 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:

[0154] .

[0155] For any target The echo signal can be represented as:

[0156] ;

[0157] RVP cancellation yields the time-domain echo signal:

[0158] ;

[0159] ;

[0160] ;

[0161] ;

[0162] 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.

[0163] 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:

[0164] ;

[0165] ;

[0166] ;

[0167] ;

[0168] 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.

[0169] 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:

[0170] ;

[0171] ;

[0172] ;

[0173] In the formula, As the envelope function, intrapulse vibrations introduce 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:

[0174] ;

[0175] That is, by and The equivalent frequency shift caused by both factors; the above frequency error can be converted into a range offset. :

[0176] ;

[0177] 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.

[0178] 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:

[0179] ;

[0180] ;

[0181] ;

[0182] 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.

[0183] 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.

[0184] 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.

[0185] 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.

[0186] 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:

[0187] Table 1. Parameters of UAV Synthetic Aperture Radar System

[0188] .

[0189] 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:

[0190] Table 2. High-frequency vibration error parameters

[0191] .

[0192] Figure 6 , Figure 7 and Figure 8 The imaging results are shown respectively after processing by the uncompensated method, the prior art, and the method of this invention. The prior art is a nonparametric paired echo suppression method for helicopter synthetic aperture radar imaging. Figure 6 As 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.

[0193] Table 3. Vibration parameter estimation results for single-component vibration scenarios

[0194] .

[0195] 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).

[0196] Table 4. Azimuth image quality parameters for single-component vibration scenes

[0197] ;

[0198] 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.

[0199] 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 by 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 13 The 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.

[0200] Table 5. Vibration parameter estimation results for multi-component vibration scenarios

[0201] .

[0202] 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.

[0203] Table 6. Azimuth image quality parameters for multi-component vibration scenes

[0204] ;

[0205] 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.

[0206] 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.

[0207] 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.

[0208] 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 20The 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.

[0209] Table 7. Azimuth Image Quality Parameters

[0210] ;

[0211] 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.

[0212] Table 8. Vibration parameter estimation results

[0213] .

[0214] 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 high frequency vibration error compensation of a multi-copter unmanned aerial vehicle synthetic aperture radar, characterized in that, The method comprises the following steps: S1, establishing an imaging geometry model of a frequency-modulated continuous wave synthetic aperture radar system under high-frequency vibration error and an echo signal model of the frequency-modulated continuous wave synthetic aperture radar system under high-frequency vibration error; 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 frequency-modulated continuous wave synthetic aperture radar system containing high-frequency vibration error; S3, based on the two-dimensional imaging result of the frequency-modulated continuous wave synthetic aperture radar system under high-frequency vibration error, constructing a distance cell set, extracting phase information of each azimuth signal to construct a phase set, adding a pair of positive and negative Gaussian white noises in the phase set, generating a group of signal pairs for each phase information, performing empirical mode decomposition on each group of signal pairs and averaging the intrinsic mode components, performing weighted averaging on the intrinsic mode components obtained by decomposing all distance cells to obtain an estimated high-frequency vibration component; S4, estimating the frequency of the vibration component by using a time-frequency analysis method, constructing a basis function of the vibration component, fitting based on minimum mean square error, defining an objective function, obtaining a minimum value of the objective function through iterative calculation, sequentially performing vibration component extraction and vibration parameter estimation, constructing a phase compensation function of the vibration component and iteratively processing, setting a vibration suppression convergence threshold, and finally obtaining an imaging result after high-frequency vibration error compensation.

2. The method of claim 1, wherein, 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 of claim 2, wherein the method further comprises: S1 comprises, S1.2, establishing a frequency modulated continuous wave synthetic aperture radar system return 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 a signal pulse duration, is an instantaneous slant range in ideal case, is a carrier wavelength, , is a light speed, is a signal center frequency, is a range-rate, is an inter-pulse LOS high-frequency vibration error, is an intra-pulse LOS high-frequency vibration error, is a radar platform instantaneous radial velocity at time caused by high-frequency vibration, is a phase error caused by vibration of the UAV flight platform inter-pulse, and is a phase error caused by vibration of the UAV flight platform intra-pulse, is a straight line in which the radar beam center optical axis points to the target.

4. The method of claim 3, wherein the method further comprises: S2 includes, on the echo signal, range migration correction, intra-pulse motion compensation and azimuth pulse compression, to obtain a frequency-modulated continuous wave synthetic aperture radar system two-dimensional imaging result containing high-frequency vibration errors : ； ； ； wherein , is a substitution variable, is a sine function, is a distance frequency variable, is an azimuth Doppler bandwidth.

5. The method of claim 4, wherein the method further comprises: 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, and constructing a range cell set : ； In the formula, is the first distance unit, is the second distance unit, is the distance unit index, is the distance unit quantity; S3 comprises, S3.2, extracting phase information of each azimuth signal from the set of distance units, performing phase unwrapping, constructing a set of phases : ； In the formula, is the phase information of the first distance unit.

6. The method of claim 5, wherein the method further comprises: S3 comprises, S3.3, adding to a pair of positive and negative Gaussian white noise to obtain a signal to be processed:​ ； In the formula, , is the first group of signal pairs after adding noise, is the first Gaussian white noise, is the index of the pair of positive and negative Gaussian white noise; S3 comprises, S3.4, obtaining , respectively by empirical mode decomposition to obtain intrinsic mode components and and :​​​ ； To The results of the second experiment The average of the first The final ensemble empirical mode decomposition results of the distance unit : 。 7. The method of claim 6, wherein the method further comprises: S3 comprises, S3.5, determining The high frequency vibration component is estimated by normalizing the weights, based on the weights: ； ； wherein is the normalized weight, is one of the oscillation components in the high-frequency oscillation error, is the index, .

8. The method of claim 7, wherein the method further comprises: S4 comprises, S4.1, using the extracted vibration component, a frequency of the vibration component is estimated by a time-frequency analysis method , and as a known quantity, a basis function of the vibration component is constructed : ； wherein is the random amplitude of the vibration component, is the random initial phase of the vibration component.

9. The method of claim 8, wherein the method further comprises: S4 comprises, S4.2, fitting based on minimum mean square error, defining an objective function : ； In the formula, is the number of azimuth sampling points, is the synthetic aperture time, is the absolute value; S4 comprises, S4.3, finding the minimum of the parameters corresponding to the minimum as the vibration parameter estimate: ； wherein is the minimum of the function, is the estimate of the amplitude of the th vibration component, is the estimate of the initial phase of the th vibration component.

10. The method of claim 9, wherein the method further comprises: 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 comprises, S4.5, multiplying with to complete the suppression of the first vibration component: ； ； ； wherein and are substitution variables; S4 comprises, S4.6, iteratively compensating the azimuthal multiple high-frequency vibration components step by step, when the vibration suppression reaches convergence, and finally obtaining the imaging result after high-frequency vibration compensation : 。

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