A method for compensating high-frequency vibration of a SAR platform in a terahertz wave band

Abstract

The application relates to a high-frequency vibration compensation method for a SAR platform in a terahertz wave band, and aims to solve the problem of platform high-frequency vibration error compensation in the imaging process of a terahertz SAR, which can seriously affect the imaging quality, cause defocusing along the azimuth direction and result in the problem of platform high-frequency vibration error compensation in the imaging process of the terahertz SAR. The process comprises the following steps: 1, obtaining a sinusoidal frequency modulation signal; 2, obtaining a time-frequency distribution function to determine the corresponding relationship between discrete time points and frequency points; 3, extracting an instantaneous frequency by using a Viterbi algorithm; 4, estimating an instantaneous frequency error parameter introduced by high-frequency vibration of a SAR platform by using a nonlinear least square method; and 5, constructing a compensation function by using the estimated instantaneous frequency error parameter introduced by high-frequency vibration, compensating the high-frequency vibration of the SAR platform by using the compensation function and obtaining a final imaging result. The application is used in the field of radar technology.

Description

Technical Field

[0001] This invention belongs to the field of radar technology and relates to a method for compensating for high-frequency vibrations of a platform during SAR imaging in the terahertz band. Background Technology

[0002] Compared to traditional microwave-band synthetic aperture radar (SAR) imaging, terahertz SAR, with its smaller wavelength, more easily achieves high range resolution. Therefore, terahertz SAR imaging is widely used in various fields, including civilian and military applications. However, the wavelength of terahertz SAR is comparable to or even much smaller than the amplitude of high-frequency platform vibrations. Therefore, high-frequency vibration errors that are negligible in traditional bands are no longer negligible in the terahertz band. Traditional microwave SAR imaging algorithms, such as the range-Doppler (RD) algorithm, can still be used for terahertz SAR imaging, but due to the non-negligible high-frequency vibrations in terahertz SAR imaging, these algorithms cannot compensate for them. Therefore, researching how to compensate for the high-frequency platform vibration errors in terahertz SAR is particularly important.

[0003] Currently, the main methods for high-frequency vibration compensation in terahertz SAR platforms are to first extract the vibration error through time-frequency analysis, then estimate the parameters of the high-frequency vibration, and finally construct a compensation function for compensation. Therefore, in terahertz SAR imaging, accurately extracting the high-frequency vibration error and estimating the high-frequency vibration error parameters is crucial for compensating for high-frequency vibration and suppressing azimuth ambiguity in terahertz SAR imaging. Summary of the Invention

[0004] The purpose of this invention is to solve the problem that high-frequency vibration of the platform can seriously affect the imaging quality and cause defocus along the azimuth direction during terahertz SAR imaging, resulting in a non-negligible high-frequency vibration error compensation problem in terahertz SAR imaging. Therefore, a high-frequency vibration compensation method for SAR platforms in the terahertz band is proposed.

[0005] The specific process of a high-frequency vibration compensation method for SAR platforms in the terahertz band is as follows:

[0006] Step 1: Perform range compression on the echo signal received by the terahertz SAR operating in front-side-looking mode to obtain a hybrid linear-sinusoidal frequency-modulated signal. Then, delinearly modulate the hybrid linear-sinusoidal frequency-modulated signal to obtain the sinusoidal frequency-modulated signal s. SFM (n);

[0007] Step 2: Use the short-time Fourier transform to analyze the sinusoidal frequency-modulated signal s from Step 1. SFM (n) Perform time-frequency analysis to obtain the time-frequency distribution function STFT(n,ω) to determine the correspondence between discrete time points and frequency points;

[0008] Step three: extracting instantaneous frequency by using Viterbi algorithm;

[0009] Step four: estimating instantaneous frequency error parameters introduced by high frequency vibration of SAR platform by using nonlinear least square method;

[0010] Step five: compensating high frequency vibration of SAR platform by using estimated instantaneous frequency error parameters introduced by high frequency vibration Constructing compensation function s ref (n), compensating high frequency vibration of SAR platform by using compensation function, and obtaining final imaging result.

[0011] The present application has the following beneficial effects:

[0012] Since the wavelength of terahertz SAR is small, high imaging resolution is obtained, and at the same time, platform high frequency vibration error cannot be ignored. In view of the problem that the traditional SAR imaging algorithm cannot compensate for the high frequency vibration error, the present application proposes a platform high frequency vibration compensation algorithm for SAR in the terahertz band. The present application firstly linear frequency modulation is carried out on the echo signal after distance compression to obtain a sinusoidal frequency modulation signal; then, the short-time Fourier transform is used to obtain the time-frequency analysis diagram corresponding to the sinusoidal frequency modulation signal; after obtaining the corresponding relationship between the discrete time points and the frequency points, the instantaneous frequency is estimated by using Viterbi algorithm; finally, the instantaneous frequency error introduced by high frequency vibration is estimated based on the principle of nonlinear least square method, and the compensation function is constructed for compensation. The present application can suppress the defocusing along the azimuth direction in the terahertz SAR imaging, so as to obtain good focusing imaging effect. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 The present application is a specific embodiment flowchart;

[0014] Figure 2 The present application is a model diagram of a scattering point target;

[0015] Figure 3 The present application is a terahertz SAR imaging diagram before high frequency vibration compensation under the condition of 10dB;

[0016] Figure 4 The present application is a time-frequency analysis diagram obtained by short-time Fourier transform under the condition of 10dB;

[0017] Figure 5 The present application is an instantaneous frequency diagram extracted by using Viterbi algorithm under the condition of 10dB;

[0018] Figure 6 The present application is an instantaneous frequency diagram reconstructed by using nonlinear least square method under the condition of 10dB;

[0019] Figure 7The THz SAR imaging graph after high-frequency vibration compensation under the condition of 10dB;

[0020] Figure 8 The THz SAR imaging graph before high-frequency vibration compensation under the condition of 5dB;

[0021] Figure 9 The time-frequency analysis graph obtained by short-time Fourier transform under the condition of 5dB;

[0022] Figure 10 The instantaneous frequency graph extracted by Viterbi algorithm under the condition of 5dB;

[0023] Figure 11 The instantaneous frequency graph reconstructed by nonlinear least squares method under the condition of 5dB;

[0024] Figure 12 The THz SAR imaging graph after high-frequency vibration compensation under the condition of 5dB. DETAILED DESCRIPTION

[0025] Specific implementation one: combined with Figure 1 In this embodiment, the specific process of a high-frequency vibration compensation method for a SAR platform in a THz band is as follows:

[0026] Step one: distance compression is performed on echo signals received by a THz SAR working in a forward-looking mode, a mixed linear-sinusoidal frequency modulation signal is obtained, and then the mixed linear-sinusoidal frequency modulation signal is de-linear frequency modulated to obtain a sinusoidal frequency modulation signal s SFM (n).

[0027] Step two: time-frequency analysis is performed on the sinusoidal frequency modulation signal s SFM (n) in step one by using short-time Fourier transform to obtain a time-frequency distribution function STFT(n, ω) to determine the corresponding relationship between a discrete time point and a frequency point;

[0028] Step three: the instantaneous frequency is extracted by using Viterbi algorithm;

[0029] Step four: the instantaneous frequency error parameter introduced by high-frequency vibration of the SAR platform is estimated by using nonlinear least squares method;

[0030] Step five: the instantaneous frequency error parameter introduced by high-frequency vibration is estimated to construct a compensation function s ref (n), the compensation function is used to compensate the high-frequency vibration of the SAR platform, and a final imaging result with good focusing is obtained;

[0031] wherein, is an amplitude estimation value of the instantaneous frequency error introduced by high-frequency vibration, a frequency estimation value of the instantaneous frequency error introduced by the high frequency vibration, an initial phase estimation value of the instantaneous frequency error introduced by the high frequency vibration.

[0032] Specific implementation two: the difference between this embodiment and the first embodiment is that the step one is to perform range compression on the echo signal received by the terahertz SAR working in the forward-looking mode to obtain a mixed linear-sinusoidal frequency modulation signal, and then linear frequency modulation is performed on the mixed linear-sinusoidal frequency modulation signal to obtain a sinusoidal frequency modulation signal s SFM (n); the specific process is as follows:

[0033] It is assumed that there is a point target P in the imaging scene, and the coordinates of the point target P are (x p ,y p ,0);

[0034] The echo signal received by the terahertz SAR working in the forward-looking mode is range compressed to obtain a mixed linear-sinusoidal frequency modulation signal; the expression is as follows:

[0035] Wherein, σ represents the amplitude of the echo signal, B is the signal bandwidth, τ is the fast time in the range direction, n is the discrete time, n ∈ (n1, n2), N is the length of the terahertz SAR echo signal, R Ap (n) is the slant range between the target point and the phase center of the terahertz SAR, c is the speed of light, j is the imaginary unit, j 2 =-1; is the Doppler frequency modulation, V is the speed of the SAR platform, is the shortest slant range between the SAR platform and the target point, H is the height of the SAR platform, λ is the wavelength of the terahertz SAR signal, and ΔR is the high frequency vibration error of the SAR platform;

[0036] The mixed linear-sinusoidal frequency modulation signal is de-linear frequency modulated to obtain a sinusoidal frequency modulation signal s SFM (n):

[0037]

[0038] Wherein, is the time-varying complex amplitude of the sinusoidal frequency modulation signal; I is the number of sinusoidal components in the high frequency vibration error, a i is the amplitude of the high frequency vibration error of the SAR platform, f i is the frequency of the high frequency vibration error of the SAR platform, is the initial phase of the high frequency vibration error of the SAR platform;

[0039] As can be seen from (2), the instantaneous frequency error introduced by the high frequency vibration of the platform is

[0040] The other steps and parameters are the same as in Embodiment One.

[0041] Embodiment Three: The difference between this embodiment and Embodiment One or Two is that the high-frequency vibration is specifically:

[0042] When the following condition is met, the SAR platform vibration is considered to be SAR platform high-frequency vibration:

[0043] |f×t s |≥1 (3)

[0044] Wherein, f is the SAR platform vibration frequency, t s is the synthetic aperture time.

[0045] The other steps and parameters are the same as in Embodiment One or Two.

[0046] Embodiment Four: The difference between this embodiment and any one of Embodiments One to Three is that the SAR platform high-frequency vibration error ΔR is expressed as:

[0047] The platform high-frequency vibration error of the terahertz SAR can be modeled as a simple harmonic motion, so the SAR platform high-frequency vibration error in can be expressed as:

[0048]

[0049] The other steps and parameters are the same as in any one of Embodiments One to Three.

[0050] Embodiment Five: The difference between this embodiment and any one of Embodiments One to Four is that in Step Two, the short-time Fourier transform is used to perform time-frequency analysis on the sinusoidal frequency modulation signal s SFM (n) in Step One to obtain the time-frequency distribution function STFT(n, ω) to determine the correspondence between the discrete time points and the frequency points; the specific process is:

[0051] The short-time Fourier transform is used to perform time-frequency analysis on the sinusoidal frequency modulation signal s SFM (n) obtained in Step One to obtain the time-frequency analysis function STFT(n, ω):

[0052]

[0053] Wherein, ω is the frequency, h(m) is the window function, and m is the discrete time;

[0054] The correspondence between the discrete time points and the frequency points can be obtained through STFT(n, ω) so as to further extract the instantaneous frequency by using the Viterbi algorithm.

[0055] The other steps and parameters are the same as in any one of Embodiments One to Four.

[0056] Sixth embodiment: Different from the first to fifth embodiments, the step three uses Viterbi algorithm to extract the instantaneous frequency; the specific process is as follows:

[0057] For the time point n i , find the corresponding each frequency point (one time point corresponds to multiple frequency points) and the sum of the penalty functions of all frequency points corresponding to the previous time point n i , and record the local optimal path with the minimum sum of the penalty functions; for the time point n i-1 , calculate the local optimal path based on the local optimal path of the time point before n i ; i

[0058] Calculate the penalty functions of all recorded paths, find the point with the minimum sum of the penalty functions, and calculate the final optimal path based on the recorded local optimal paths in turn; the final optimal path is the instantaneous frequency extracted by the Viterbi algorithm.

[0059] The expression is as follows:

[0060] The penalty function Φ(x, y) can be expressed as:

[0061]

[0062] Wherein, c is the weight of the penalty function, Δ is the threshold value; x and y are variables.

[0063] For the time-frequency analysis function value STFT(n, ω), arrange the time-frequency analysis function value STFT(n, ω) in non-increasing order:

[0064] STFT(n, ω1) ≥ STFT(n, ω2) ≥ … ≥ STFT(n, ω j ) … ≥ STFT(n, ω p ) (7)

[0065] Wherein, j = 1, 2, … p is the position in the sequence.

[0066] The penalty function Γ(x) can be expressed as:

[0067] Γ(STFT(n, ω j )) = j-1 (8)

[0068] The path with the minimum sum of the penalty functions is the instantaneous frequency extracted by the Viterbi algorithm:

[0069] ​

[0070] wherein n is discrete time, n∈(n1,n2), K represents all paths between n1 and n2, and k(n) is a path.

[0071] The other steps and parameters are the same as one of the first to fifth embodiments.

[0072] The seventh embodiment is different from one of the first to sixth embodiments in that the step four estimates the instantaneous frequency error parameter introduced by the high-frequency vibration of the SAR platform by using a nonlinear least square method; the specific process is as follows:

[0073] First, a model of the sinusoidal signal is established:

[0074]

[0075] wherein A i is the amplitude of the i-th component of the sinusoidal signal, F i is the frequency of the i-th component of the sinusoidal signal, Ψ i is the initial phase of the i-th component of the sinusoidal signal, and S is the number of the sinusoidal signal;

[0076] The value of S can be obtained by performing Fourier transform on the extracted instantaneous frequency and estimating the number of peaks;

[0077] The instantaneous frequency error parameter introduced by the high-frequency vibration of the SAR platform can be estimated by using the nonlinear least square method, and the corresponding objective function can be expressed as:

[0078]

[0079] wherein is the instantaneous frequency extracted by the Viterbi algorithm, and |||2 is the 2-norm;

[0080] The instantaneous frequency error parameter introduced by the high-frequency vibration of the SAR platform can be estimated by estimating the minimum value of the objective function, that is:

[0081]

[0082] The other steps and parameters are the same as one of the first to sixth embodiments.

[0083] The eighth embodiment is different from one of the first to seventh embodiments in that the step five compensates the high-frequency vibration of the SAR platform by using the estimated instantaneous frequency error parameter to construct a compensation function s ref (n), and the compensation function is used to compensate the high-frequency vibration of the SAR platform to obtain a final imaging result with good focusing; the specific process is as follows:

[0084] Instantaneous frequency error parameter introduced by estimated high-frequency vibration Construct the compensation function s ref (n):

[0085]

[0086] Finally, by using a compensation function to compensate for the high-frequency vibration of the SAR platform, a final imaging result with good focusing can be obtained.

[0087] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0088] The beneficial effects of the present invention are verified using the following embodiments:

[0089] Example 1:

[0090] In this embodiment, the effectiveness of the high-frequency vibration error compensation algorithm for the terahertz SAR platform mentioned in this invention is verified using simulation experimental data of terahertz SAR. The high-frequency vibration parameters of the platform in the simulation experiment are shown in Table 1.

[0091] Table 1 High-frequency vibration error parameters of the terahertz SAR platform

[0092]

[0093] Under a signal-to-noise ratio of 10dB, the model of the scattering point target is as follows: Figure 2 As shown. The imaging results of the terahertz SAR echo before high-frequency vibration compensation are as follows. Figure 3 As shown. The time-frequency analysis diagram obtained through short-time Fourier transform is as follows. Figure 4 As shown. After obtaining the time-frequency analysis plot, the instantaneous frequency is extracted using the Viterbi algorithm, as follows. Figure 5 As shown. Finally, the extracted instantaneous frequency is reconstructed by estimating the parameters using the nonlinear least squares method, as shown in the figure. Figure 6 As shown. After reconstructing the instantaneous frequency, a compensation function is constructed to compensate for the high-frequency vibration error of the platform, finally obtaining an imaging result with good focusing, as shown. Figure 7 As shown.

[0094] Under the condition of a signal-to-noise ratio of 5dB, the same method is used. Figure 2 The point target model shown, the terahertz SAR imaging results before high-frequency vibration compensation are as follows: Figure 8 As shown. Using short-time Fourier transform, time-frequency analysis of the echo signal is performed, and the resulting time-frequency analysis graph is shown below. Figure 9 As shown. Then, the Viterbi algorithm is used to extract the instantaneous frequency, and the extracted signal is as follows. Figure 10The parameters of the instantaneous frequency error introduced by the high-frequency vibration can be estimated by the nonlinear least square method, and the corresponding compensation function can be constructed. Figure 11 Finally, the compensation function is used to compensate the high-frequency vibration error of the platform, and the imaging result after compensation is shown in FIG. 6. Figure 12

[0095] It can be seen from the implementation examples that, under the conditions of signal-to-noise ratios of 10 dB and 5 dB, the high-frequency vibration error of the platform in the terahertz SAR imaging process can be well suppressed. After the high-frequency vibration compensation, the imaging effect of the terahertz SAR is obviously improved. And the defocusing along the azimuth direction caused by the high-frequency vibration error of the platform is also well suppressed. Therefore, the high-frequency vibration error of the platform in the terahertz SAR imaging process can be well compensated by the present application, and the imaging result with good focusing property can be obtained.

[0096] The present application also has other various embodiments, and those skilled in the art can make various corresponding changes and modifications according to the present application without departing from the spirit and essence of the present application. However, these corresponding changes and modifications should all belong to the protection scope of the claims attached to the present application.​

Claims

1. A method for compensating high-frequency vibration of a SAR platform in a terahertz band, characterized in that: The method comprises the following steps: Step one: the echo signal received by the terahertz SAR working in the forward-looking mode is range-compressed to obtain a mixed linear-sinusoidal frequency modulation signal, and then the mixed linear-sinusoidal frequency modulation signal is de-linear frequency modulated to obtain a sinusoidal frequency modulation signal s SFM (n); Step two: using short-time Fourier transform on the sinusoidal frequency modulation signal s SFM (n) performing time-frequency analysis to obtain a time-frequency distribution function STFT(n, ω) to determine the correspondence between discrete time points and frequency points; Step three: extracting the instantaneous frequency by using the Viterbi algorithm; Step four: estimating the instantaneous frequency error parameter introduced by the high-frequency vibration of the SAR platform by using the nonlinear least square method; Step five: introducing the instantaneous frequency error parameter caused by the estimated high frequency vibration Constructing the compensation function s ref (n), compensating the high frequency vibration of the SAR platform by using the compensation function, and obtaining the final imaging result; wherein an amplitude estimate of the instantaneous frequency error introduced by the high frequency oscillation, a frequency estimate of the instantaneous frequency error introduced by the high frequency oscillation, an initial phase estimate of the instantaneous frequency error introduced by the high frequency oscillation.

2. The method according to claim 1, wherein the method is characterized in that: The step one is to compress the distance of the echo signal received by the terahertz SAR working in the positive side-looking mode to obtain a mixed linear-sinusoidal frequency modulation signal, and then linear frequency modulation is performed on the mixed linear-sinusoidal frequency modulation signal to obtain a sinusoidal frequency modulation signal s SFM (n); the specific process is as follows: Assume that there is a point target P in the imaging scene, and the coordinates of the point target P are (x p ,y p ,0). The echo signal received by the terahertz SAR working in the forward-looking mode is subjected to range compression to obtain a mixed linear-sinusoidal frequency modulation signal, and the expression is: wherein, σ represents the amplitude of echo signal, B is the signal bandwidth, τ is the range fast time, n is the discrete time, n∈(n1, n2), N is the length of terahertz SAR echo signal, R Ap (n) is the slant range of the target point and the phase center of terahertz SAR, c is the speed of light, j is the imaginary unit, j 2 =-1; is the Doppler frequency, V is the SAR platform speed, is the shortest slant range between the SAR platform and the target point, H is the SAR platform height, λ is the wavelength of terahertz SAR signal, and ΔR is the SAR platform high frequency vibration error. linear frequency modulation signal s SFM (n): wherein, is the time-varying complex amplitude of the sinusoidal frequency modulation signal; I is the number of sinusoidal components in the high frequency vibration error, a i is the amplitude of the high frequency vibration error of the SAR platform, f i is the frequency of the high frequency vibration error of the SAR platform, is the initial phase of the high frequency vibration error of the SAR platform; As can be seen from (2), the instantaneous frequency error introduced by the platform high-frequency vibration is 3. The method of claim 2, wherein the method is characterized by: The high-frequency vibration specifically refers to: When the following condition is met, the SAR platform vibration is considered as the high-frequency vibration of the SAR platform: |f×t s |≥1 (3) where f is the SAR platform vibration frequency, t s is the synthetic aperture time.

4. The method according to claim 3, wherein the method is characterized in that: The SAR platform high-frequency vibration error ΔR is expressed as:

5. The method of claim 4, wherein the method is characterized by: The step two uses short-time Fourier transform to the sinusoidal frequency modulation signal s SFM (n) performing time-frequency analysis to obtain time-frequency distribution function STFT(n, ω) to determine the corresponding relationship between discrete time points and frequency points; The specific process is: The sinusoidal frequency-modulated signal s obtained in step one is analyzed using a short-time Fourier transform SFM (n) performing a time-frequency analysis to obtain a time-frequency analysis function STFT(n, ω): Wherein, ω is the frequency, h(m) is the window function, and m is the discrete time; The corresponding relationship between the discrete time point and the frequency point can be obtained by STFT(n, ω).

6. The method of claim 5, wherein the method is characterized by: In step three, the instantaneous frequency is extracted by using the Viterbi algorithm, and the specific process is: For time point n i Find time point n i Each corresponding frequency point and the previous time point n i-1 Find the path that minimizes the sum of the penalty functions among all frequency points, and record these locally optimal paths; The penalty function of all recorded paths is calculated, the point with the minimum sum of penalty functions is found, and the final optimal path is calculated based on the local optimal path recorded, and the final optimal path is obtained. The optimal path extracted by the Viterbi algorithm is the instantaneous frequency; The expression is: The penalty function Φ(x, y) can be expressed as: Wherein, c is the weight of the penalty function, and Δ is the threshold; x and y are variables; For the time-frequency analysis function value STFT(n, ω), the time-frequency analysis function value STFT(n, ω) is arranged in a non-increasing order: STFT(n,ω1)≥STFT(n,ω2)≥…≥STFT(n,ω j )…≥STFT(n,ω p ) (7) Wherein, j=1, 2, … p is the position in the sequence; The penalty function Γ(x) can be expressed as: Γ(STFT(n, ω j )) = j-1 (8) The path with the minimum sum of penalty functions is the instantaneous frequency finally extracted by the Viterbi algorithm: Wherein, n is the discrete time, n∈(n1, n2), K represents all paths between n1 and n2, and k(n) is the path.

7. The method of claim 6, wherein the method is characterized by: In step four, the instantaneous frequency error parameter introduced by the high-frequency vibration of the SAR platform is estimated by using the nonlinear least square method, and the specific process is: Firstly, the model of the sinusoidal signal is established: where A i is the amplitude of the i-th component of the sinusoidal signal, F i is the frequency of the i-th component of the sinusoidal signal, ψ i is the initial phase of the i-th component of the sinusoidal signal, and S is the number of components of the sinusoidal signal. The number of peaks can be obtained by performing Fourier transform on the extracted instantaneous frequency and estimating the number of peaks. The instantaneous frequency error parameter introduced by the high-frequency vibration of the SAR platform can be estimated by using the nonlinear least square method, and the corresponding objective function can be expressed as: wherein is the instantaneous frequency extracted for the Viterbi algorithm, and || ||2is the 2-norm. By estimating the minimum value of the objective function, the instantaneous frequency error parameter introduced by the high-frequency vibration of the SAR platform can be estimated, that is, 8. The method according to claim 7, wherein the method is characterized in that: The estimated high-frequency vibration-induced instantaneous frequency error parameter in the fifth step Constructing the compensation function s ref (n), and compensating the SAR platform high-frequency vibration by using the compensation function to obtain the final imaging result; The specific process is: Utilizing estimated high frequency vibration induced instantaneous frequency error parameters Constructing a compensation function s ref (n): Finally, the high-frequency vibration of the SAR platform is compensated by using the compensation function, and the final imaging result with good focusing can be obtained.

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