SAR motion compensation method for multi-rotor UAV based on wavelet transform

Abstract

The present invention discloses a multi-rotor UAV SAR motion compensation method based on wavelet transform, comprising: obtaining a demodulated echo signal of a multi-rotor UAV airborne radar SAR; performing a wavelet transform on the inertial navigation data collected by the inertial navigation system to remove noise in the data and obtain denoised inertial navigation data; performing motion compensation on the echo signal based on the denoised inertial navigation data; performing PGA compensation on the motion-compensated echo signal; and imaging the PGA-compensated echo signal using a UAV SAR imaging algorithm. The method provided by the present invention can solve the problems of multi-rotor UAV platforms having the largest heading velocity error amplitude and high frequency, and having many high-frequency components of translation error, a complex spectrum, and great compensation difficulty. The method can efficiently estimate the high-frequency motion error of the multi-rotor UAV platform, thereby achieving accurate imaging of the multi-rotor UAV SAR.

Description

Technical Field

[0001] The present invention belongs to the field of radar imaging technology, and in particular relates to a multi-rotor unmanned aerial vehicle (UAV) SAR motion compensation method based on wavelet transform. Background Art

[0002] With the advancement of UAV (Unmanned Aerial Vehicle) technology, drones of all types and functions have sprung up like mushrooms after rain. Micro-SAR, with its small size, light weight, and low power consumption, can be easily mounted on a variety of platforms. However, different platforms vary significantly in terms of size, weight, aerodynamic shape, and power characteristics, and the motion characteristics exhibited by each platform during movement also vary. The differences in flight platforms are primarily reflected in heading speed and attitude stability. Therefore, when a micro-SAR is mounted as a payload on different platforms, targeted motion compensation and real-time imaging processing are required, taking into account the characteristics of the platform and its motion characteristics. During SAR imaging, motion error compensation is crucial for achieving high-resolution SAR imaging. The effectiveness of motion compensation methods is influenced not only by the accuracy of sensor measurement parameters but also by the characteristics of the motion errors. The larger the amplitude and the higher the frequency of the motion errors, the more difficult the compensation becomes.

[0003] Currently, there are two types of conventional SAR motion compensation methods: one is a signal processing method based on echo data, which compensates for motion errors according to the properties of the echo itself and has the ability of adaptive processing. The other is compensation based on the inertial navigation system, which measures the motion parameters of the carrier aircraft through the inertial navigation system to perform compensation. This is more efficient, but is limited by the accuracy of the inertial navigation system. For example, Xidian University disclosed an airborne SAR motion compensation method in its patent application "A Method for Airborne SAR Motion Compensation Based on Inertial Navigation System Parameters" (Publication No. CN 113670301 A). This method is used for airborne SAR motion compensation and improves the imaging quality of the algorithm through a motion compensation method based on inertial navigation system parameters.

[0004] However, because multi-rotor UAVs typically have multiple pairs of rotors, each pair rotates in opposite directions, thereby offsetting the counter-torque forces acting on them. Multi-rotor UAV platforms have the largest heading velocity errors and the highest frequencies. Furthermore, the high-frequency components of translational errors are numerous, resulting in a complex spectrum and significant compensation challenges. Estimating high-frequency phase errors using conventional motion compensation techniques is difficult. For example, directly applying the method described in patent document CN113670301A to multi-rotor UAV SAR systems would result in poor imaging. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a multi-rotor UAV SAR motion compensation method based on wavelet transform. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0006] A multi-rotor UAV SAR motion compensation method based on wavelet transform, comprising:

[0007] Step 1: Obtain the demodulated echo signal of the multi-rotor UAV airborne radar SAR;

[0008] Step 2: Perform wavelet transform on the inertial navigation data collected by the inertial navigation system to remove noise in the data and obtain denoised inertial navigation data;

[0009] Step 3: performing motion compensation on the echo signal based on the denoised inertial navigation data;

[0010] Step 4: Perform PGA compensation on the motion-compensated echo signal;

[0011] Step 5: Use the UAV SAR imaging algorithm to image the echo signal after PGA compensation.

[0012] In one embodiment of the present invention, step 2 includes:

[0013] 2a) Based on the Symlet wavelet basis function, the inertial navigation data collected by the inertial navigation system are decomposed into wavelet coefficients at each scale;

[0014] 2b) Calculate the variance of the noise in each sub-band based on the wavelet coefficients, using the following formula:

[0015] σ u,j =median(d j (k)) / 0.6745

[0016] Among them, σ u,j represents the variance of noise in a certain subband, d j (k) represents the wavelet coefficient in the sub-band, and median() represents arranging the wavelet coefficients in the sub-band by size and taking the middle;

[0017] 2c) Based on the variance, a fixed threshold estimation method is used to determine the noise threshold in the wavelet domain, and the calculation formula is:

[0018]

[0019] Among them, λ represents the threshold of noise in the wavelet domain, N f Indicates the signal length;

[0020] 2d) filtering the wavelet coefficients using a soft threshold denoising method based on the threshold to remove Gaussian noise coefficients;

[0021] 2e) Perform wavelet reconstruction on the filtered wavelet coefficients to obtain denoised inertial navigation data.

[0022] In one embodiment of the present invention, step 3 includes:

[0023] 3a) performing envelope delay compensation on the echo signal in the range frequency domain based on the denoised inertial navigation data;

[0024] 3b) performing phase compensation on the echo signal after envelope delay compensation in the two-dimensional time domain;

[0025] 3c) The phase error of the echo signal after envelope delay compensation is compensated according to each distance unit to obtain a motion compensated echo signal.

[0026] In one embodiment of the present invention, step 3a) comprises:

[0027] Perform Fourier transform on the motion-compensated echo signal in the range direction;

[0028] Calculating the motion error amount based on the denoised inertial navigation data;

[0029] A filter is constructed based on the motion error to perform envelope delay compensation on the Fourier transformed signal; wherein the expression of the filter is as follows:

[0030]

[0031] Among them, f r represents the distance frequency, ΔR represents the amount of motion error, and c represents the speed of light.

[0032] In one embodiment of the present invention, step 3b) comprises:

[0033] Perform inverse Fourier transform on the echo signal after envelope delay compensation to obtain a two-dimensional time domain signal;

[0034] A phase compensation function is constructed based on the motion error to perform phase compensation on the two-dimensional time domain signal; wherein the phase compensation function is:

[0035]

[0036] Where c is the speed of light, λ is the wavelength, and ΔR is the amount of motion error.

[0037] In one embodiment of the present invention, step 4 includes:

[0038] 4a) The residual phase error of the motion-compensated echo signal is expanded into a second-order polynomial of distance, which is expressed as follows:

[0039] Φ(η,R b )=b0(n)+b1(n)Δr+b2(n)Δr 2

[0040] Where η represents the azimuth slow time, Δr represents the difference between the slant range of other target points in the scene and the slant range of the scene center, b0, b1, and b2 represent the constant term, linear term coefficient, and quadratic term coefficient of the phase error, respectively;

[0041] 4b) Divide the motion-compensated data into D range blocks and perform coherent superposition of multiple range samples in each range block to estimate the residual phase error Its expression is as follows:

[0042]

[0043] Where arg is the phase function, J is the number of range samples, h = 1, 2, ..., J is any azimuth position, d = 1, 2, ..., D is the range block position, m d,j is the jth sample unit s in the dth distance block d (j,:) corresponds to the signal-to-clutter ratio weight, conj is the conjugate operation;

[0044] 4c) Calculate Δr corresponding to each distance block;

[0045] 4d) Construct the distance space-varying matrix A based on the Δr calculated in step 4c) b , phase gradient estimation Φ and signal-to-noise ratio weighting matrix W;

[0046] 4e) According to the distance space variable matrix A b , phase gradient estimate Φ and signal-to-noise ratio weighted matrix W to calculate the phase gradient least squares estimate of the distance space-varying polynomial. The calculation formula is:

[0047]

[0048] Where T is the transpose operation, () -1 is the matrix inversion operation;

[0049] 4f) Estimate according to the phase gradient least squares estimation formula The integration obtains b0, b1, and b2, and the space-varying residual phase error is calculated according to the distance unit corresponding to the sample and compensated for the residual phase error to achieve PGA compensation.

[0050] Beneficial effects of the present invention:

[0051] 1. The multi-rotor UAV SAR motion compensation method based on wavelet transform provided by the present invention first uses wavelet transform to process the inertial navigation data, which can automatically adapt to the requirements of time-frequency signal analysis, so as to focus on any detail of the signal; then the PGA algorithm is used to compensate for the motion error, which can estimate the phase error of any order. Through the above two-step motion compensation method, it is possible to solve the problem that the heading velocity error of the multi-rotor UAV platform is the largest and the frequency is high, and the high-frequency components of the translation error are many, the spectrum is complex, and the compensation is difficult. It can efficiently estimate the high-frequency motion error of the multi-rotor UAV platform, thereby achieving accurate imaging of the multi-rotor UAV SAR.

[0052] 2. In the SAR imaging of multi-rotor UAVs, the present invention proposes a data-based phase estimation method, which uses the phase gradient autofocus algorithm to estimate motion parameters and compensate for residual phase errors. The compensation accuracy is higher, meeting the requirements of actual engineering resolution and achieving better imaging effects.

[0053] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 1 is a flow chart of a multi-rotor UAV SAR motion compensation method based on wavelet transform provided by an embodiment of the present invention;

[0055] Figure 2 It is a schematic diagram of the imaging results using the traditional SAR imaging algorithm;

[0056] Figure 3 Schematic diagram of imaging results using the algorithm proposed in the present invention. DETAILED DESCRIPTION

[0057] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0058] Example 1

[0059] See Figure 1 , Figure 1 1 is a flow chart of a multi-rotor UAV SAR motion compensation method based on wavelet transform provided by an embodiment of the present invention, which includes:

[0060] Step 1: Obtain the demodulated echo signal of the multi-rotor UAV's airborne radar SAR.

[0061] Step 2: Perform wavelet transform on the inertial navigation data collected by the inertial navigation system.

[0062] 2a) Based on the Symlet wavelet basis function, the inertial navigation data collected by the inertial navigation system are decomposed into wavelet coefficients at each scale.

[0063] Specifically, this embodiment selects the Symlet (symN) wavelet basis function, where the support range of the symN (N=4) wavelet is 7 and the vanishing moment is 4. It also has good regularity and better symmetry, which can reduce the phase distortion when analyzing and reconstructing the signal to a certain extent.

[0064] 2b) Calculating the variance of the noise in each sub-band based on the wavelet coefficients.

[0065] Specifically, the robust estimator is used to estimate the wavelet coefficients in each subband of the wavelet decomposition signal. The wavelet coefficients in the subband are arranged in order of size, and then the middle one is taken. Then the middle one is divided by 0.6745 to obtain the corresponding variance σ of the noise in a certain subband. u,j , the calculation formula is:

[0066] σ u,j =median(d j (k)) / 0.6745

[0067] Among them, σ u,j represents the variance of noise in a certain subband, d j (k) represents the wavelet coefficient in the band itself, and median() represents arranging the wavelet coefficients in the sub-band in order of size and taking the median value.

[0068] 2c) Based on the variance, a fixed threshold estimation method is used to determine the noise threshold in the wavelet domain, and the calculation formula is:

[0069]

[0070] Among them, λ represents the threshold of noise in the wavelet domain, N f Indicates the signal length;

[0071] 2d) Filtering the wavelet coefficients using a soft threshold denoising method based on the threshold to remove Gaussian noise coefficients.

[0072] Specifically, when the absolute value of the wavelet coefficient is less than a given threshold, it is set to zero; when it is greater than the threshold, it is subtracted from the threshold, that is:

[0073]

[0074] Among them, w represents the wavelet coefficient, w λ Represents the wavelet coefficients obtained after filtering the noise using the soft threshold denoising method.

[0075] 2e) Perform wavelet reconstruction on the filtered wavelet coefficients to obtain denoised inertial navigation data.

[0076] The specific implementation method of wavelet reconstruction can be referred to the existing related technologies, and will not be described in detail in this embodiment.

[0077] Step 3: Perform motion compensation on the echo signal based on the denoised inertial navigation data.

[0078] 3a) performing envelope delay compensation on the echo signal in the range frequency domain based on the denoised inertial navigation data.

[0079] First, the motion-compensated echo signal is Fourier transformed in the range direction.

[0080] Then, the motion error ΔR is calculated based on the denoised inertial navigation data.

[0081] Finally, a filter is constructed based on the motion error to perform envelope delay compensation on the Fourier transformed signal; wherein the expression of the filter is as follows:

[0082]

[0083] Among them, f r represents the distance frequency, ΔR represents the amount of motion error, and c represents the speed of light.

[0084] 3b) performing phase compensation on the envelope delay compensated signal in a two-dimensional time domain;

[0085] Specifically, first, the echo signal after envelope delay compensation is inverse Fourier transformed to obtain a two-dimensional time domain signal;

[0086] Then, a phase compensation function is constructed based on the motion error to perform phase compensation on the two-dimensional time domain signal; wherein the phase compensation function is:

[0087]

[0088] Where c is the speed of light, λ is the wavelength, and ΔR is the amount of motion error.

[0089] 3c) The phase error of the echo signal after envelope delay compensation is compensated according to each distance unit to obtain a motion compensated echo signal.

[0090] Since the distance error is space-variant, the present embodiment compensates the phase error according to each distance unit. The detailed process can be found in the existing related art and will not be described in detail here.

[0091] At this point, the motion compensation of the echo signal is completed, and the motion-compensated echo signal is obtained.

[0092] Step 4: Perform PGA compensation on the motion-compensated echo signal.

[0093] The PGA (Image Gradient Autofocus) algorithm is a more effective motion compensation method. It is not based on a motion model and can estimate phase errors of any order. Therefore, after performing motion compensation on the echo signal, this embodiment also selects PGA compensation to further eliminate phase errors.

[0094] Specifically, step 4 includes:

[0095] 4a) The residual phase error of the motion-compensated echo signal is expanded into a second-order polynomial of distance, which is expressed as follows:

[0096] Φ(η,R b )=b0(n)+b1(n)Δr+b2(n)Δr 2

[0097] Where η represents the azimuth slow time, Δr represents the difference between the slant distance of other target points in the scene and the slant distance of the scene center, b0, b1, and b2 represent the constant term, linear term coefficient, and quadratic term coefficient of the phase error, respectively. The phase error function comprehensively considers the distance variation of the motion error.

[0098] 4b) Divide the motion-compensated data into D range blocks and perform coherent superposition on multiple range samples in each range block to estimate

[0099] Specifically, the motion-compensated data is divided into D distance blocks. The residual phase error in each distance block is considered to be space-invariant. The residual phase error is estimated by coherently superposing multiple distance samples in the dth distance block. The expression is as follows:

[0100]

[0101] Where arg is the phase function, J is the number of range samples, h = 1, 2, ..., J is any azimuth position, d = 1, 2, ..., D is the range block position, m d,j is the jth sample unit s in the dth distance block d (j,:) corresponds to the signal-to-clutter ratio weight, and conj is the conjugate operation.

[0102] 4c) Calculate Δr corresponding to each distance block;

[0103] Specifically, this embodiment is Equivalent calculation, equivalent distance The expression is as follows:

[0104]

[0105] Among them, w dis the weight of the d-th distance block,

[0106] 4d) Construct the distance space-varying matrix A based on the Δr calculated in step 4c) b , phase gradient estimation Φ and signal-to-noise ratio weighting matrix W;

[0107] Specifically, the expressions of each matrix are as follows:

[0108]

[0109]

[0110] W=diag[w1,…,w D ] D*D

[0111] 4e) According to the distance space variable matrix A b , phase gradient estimate Φ and signal-to-noise ratio weighted matrix W to calculate the phase gradient least squares estimate of the distance space-varying polynomial. The calculation formula is:

[0112]

[0113] Where T is the transpose operation, () -1 is the matrix inversion operation;

[0114] 4f) Estimate according to the phase gradient least squares estimation formula The integration obtains b0, b1, and b2, and the space-varying residual phase error is calculated according to the distance unit corresponding to the sample and compensated for the residual phase error to achieve PGA compensation.

[0115] At this point, the PGA compensation of the echo signal is completed.

[0116] Step 5: Use the UAV SAR imaging algorithm to image the echo signal after PGA compensation.

[0117] The wavelet transform-based multi-rotor UAV SAR motion compensation method provided by the present invention first uses wavelet transform to process inertial navigation data, which can automatically adapt to the requirements of time-frequency signal analysis, thereby focusing on any detail of the signal; then, the PGA algorithm is used to compensate for motion errors, capable of estimating phase errors of any order. Through this two-step motion compensation method, the problems of multi-rotor UAV platforms with the largest heading velocity error amplitude and high frequency, and the large number of high-frequency components of translational errors, complex spectrum, and high compensation difficulty can be solved. The high-frequency motion errors of multi-rotor UAV platforms can be efficiently estimated, thereby achieving precise imaging of multi-rotor UAV SAR.

[0118] In addition, the present invention proposes a data-based phase estimation method in multi-rotor UAV SAR imaging, uses the phase gradient autofocus algorithm to estimate motion parameters, and compensates for residual phase errors. The compensation accuracy is higher, meeting the requirements of actual engineering resolution and achieving better imaging effects.

[0119] Example 2

[0120] The method of the present invention is compared with the traditional SAR imaging algorithm through simulation experiments to further illustrate the beneficial effects of the present invention.

[0121] 1. Test conditions

[0122] The parameter settings of this simulation experiment are shown in Table 1.

[0123] Table 1 Simulation parameters

[0124]

[0125]

[0126] 2. Test results and analysis

[0127] The simulation results are shown in Figure 2 and Figure 3 As shown, Figure 2 It is a schematic diagram of the imaging results using the traditional SAR imaging algorithm; Figure 3 Schematic diagram of imaging results using the algorithm proposed in the present invention.

[0128] from Figure 2 and Figure 3 It can be seen that in multi-rotor UAV SAR imaging, the imaging result of the method of the present invention is clearer and the effect is better than that of the traditional SAR imaging algorithm.

[0129] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A multi-rotor UAV SAR motion compensation method based on wavelet transform, characterized in that: include: Step 1: Obtain the demodulated echo signal of the multi-rotor UAV airborne radar SAR; Step 2: Perform wavelet transform on the inertial navigation data collected by the inertial navigation system to remove noise in the data and obtain denoised inertial navigation data; Step 3: performing motion compensation on the echo signal based on the denoised inertial navigation data; Step 4: Perform PGA compensation on the motion-compensated echo signal; Step 5: Use the UAV SAR imaging algorithm to image the echo signal after PGA compensation.

2. The multi-rotor UAV SAR motion compensation method based on wavelet transform according to claim 1 is characterized in that: Step 2 includes: 2a) Based on the Symlet wavelet basis function, the inertial navigation data collected by the inertial navigation system are decomposed into wavelet coefficients at each scale; 2b) Calculate the variance of the noise in each sub-band based on the wavelet coefficients, using the following formula: in, represents the variance of the noise in a certain subband, represents the wavelet coefficients within the subband, It means that the wavelet coefficients in the sub-band are arranged in order of size and the middle is taken; 2c) Based on the variance, a fixed threshold estimation method is used to determine the noise threshold in the wavelet domain, and the calculation formula is: in, represents the threshold of noise in the wavelet domain, Indicates the signal length; 2d) filtering the wavelet coefficients using a soft threshold denoising method based on the threshold to remove Gaussian noise coefficients; 2e) Perform wavelet reconstruction on the filtered wavelet coefficients to obtain denoised inertial navigation data.

3. The multi-rotor UAV SAR motion compensation method based on wavelet transform according to claim 2 is characterized in that: Step 3 includes: 3a) performing envelope delay compensation on the echo signal in the range frequency domain based on the denoised inertial navigation data; 3b) performing phase compensation on the echo signal after envelope delay compensation in the two-dimensional time domain; 3c) The phase error of the echo signal after envelope delay compensation is compensated according to each distance unit to obtain a motion compensated echo signal.

4. The multi-rotor UAV SAR motion compensation method based on wavelet transform according to claim 3 is characterized in that: Step 3a) comprises: Perform Fourier transform on the motion-compensated echo signal in the range direction; Calculating the motion error amount based on the denoised inertial navigation data; A filter is constructed based on the motion error to perform envelope delay compensation on the Fourier transformed signal; wherein the expression of the filter is as follows: in, represents the distance frequency, represents the amount of motion error, Represents the speed of light.

5. The multi-rotor UAV SAR motion compensation method based on wavelet transform according to claim 4 is characterized in that: Step 3b) comprises: Perform inverse Fourier transform on the echo signal after envelope delay compensation to obtain a two-dimensional time domain signal; A phase compensation function is constructed based on the motion error to perform phase compensation on the two-dimensional time domain signal; wherein the phase compensation function is: in, is the wavelength, Represents the amount of motion error.

6. The multi-rotor UAV SAR motion compensation method based on wavelet transform according to claim 1 is characterized in that: Step 4 includes: 4a) The residual phase error of the motion-compensated echo signal is expanded into a second-order polynomial of distance, which is expressed as follows: in, Indicates the direction of slow time, Indicates the difference between the slant distance of other target points in the scene and the slant distance of the scene center. Respectively represent the constant term, linear term coefficient, and quadratic term coefficient of the phase error; 4b) Divide the motion-compensated data into D range blocks and perform coherent superposition of multiple range samples in each range block to estimate the residual phase error , which is expressed as follows: in, is the phase function, is the number of distance samples, For any position, is the distance block position, is the jth sample unit in the dth distance block The corresponding signal-to-noise ratio weight is, To take the conjugate operation; 4c) Calculate the corresponding distance of each block ; 4d) Based on the calculation in step 4c) Constructing distance space-varying matrix , phase gradient estimation and the signal-to-noise ratio weighting matrix ; 4e) According to the distance space variable matrix , phase gradient estimation and the signal-to-noise ratio weighting matrix Calculate the least squares estimate of the phase gradient of the range-varying polynomial, and the calculation formula is: in, T is the transpose operation, is the matrix inversion operation; 4f) Estimate according to the phase gradient least squares estimation formula Points obtained , and calculate the space-varying residual phase error according to the distance unit corresponding to the sample and compensate the residual phase error to achieve PGA compensation.

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