CN114609629A - A GEO satellite-machine bistatic synchronization method based on direct wave and clutter subspace - Google Patents

Abstract

The invention discloses a GEO satellite-machine bistatic synchronization method based on direct wave and clutter subspace. On the basis of direct wave synchronization, in order to realize the precise separation of direct wave slant range phase and synchronization error phase, the synchronization method firstly utilizes the third phase The function extracts the high-order term coefficient of the direct wave slant range, and then uses the stationary clutter subspace extracted in the scene as an auxiliary calibration source, and estimates the Doppler frequency shift error generated by the slant range phase from this space, and realizes the direct wave slope. Accurate separation of distance phase and synchronization error phase, thereby improving the speed measurement and positioning accuracy of moving objects. The method of the invention does not require real-time acquisition of high-precision orbit parameters, thereby reducing synchronization difficulty.

Description

A GEO satellite-machine bistatic synchronization method based on direct wave and clutter subspace

technical field

The invention relates to the technical field of synthetic aperture radar, in particular to a GEO satellite-machine bistatic synchronization method based on direct wave and clutter subspace.

Background technique

Geosynchronous orbit (GEO) satellite-based bistatic synthetic aperture radar (GEO SA-BSAR) is a radar system that uses geosynchronous orbit synthetic aperture radar (GEO SAR) as a radiation source to receive signals from an airborne multi-channel system. The system has good concealment and anti-interference, and is flexible in configuration. It is an effective means of reconnaissance and surveillance of moving targets.

The GEO SA-BSAR system has to face the problem of degraded imaging quality and target detection performance caused by synchronization errors due to the separation of transceivers and the difference in frequency sources between the transmitter and the receiver. In order to achieve synchronization, the aircraft receives the GEO SAR direct wave signal, and extracts the time and phase synchronization errors from it. Existing synchronization methods need to use precise orbital parameters of satellites to achieve this process. Synthetic aperture radar satellites in low orbit can obtain high-precision orbital positions in real time using navigation satellites, and the above algorithms can better compensate for synchronization errors. However, the orbital height of GEO SAR is about 36000km, which is located above the navigation star, so it is difficult to obtain high-precision orbital parameters in real time. When there is a 1° error in the velocity angle between the GEO and the aircraft, the residual Doppler frequency shift error after applying the above algorithm is at most 6.5 Hz, which has little effect on the imaging resolution. However, for moving target detection, this error will lead to serious target radial velocity estimation deviation and affect the target localization performance.

Therefore, there is an urgent need for a synchronization method, which can overcome the problem of difficult to obtain high-precision orbit parameters in real time, and realize the precise separation of the direct wave slant range phase and the synchronization error phase for moving target detection, so as to compensate the synchronization error and improve the positioning accuracy.

SUMMARY OF THE INVENTION

In view of this, the present invention provides a GEO satellite-machine bistatic synchronization method based on the direct wave and clutter subspace, which can realize the precise separation of the direct wave slant range phase and the synchronization error phase, thereby improving the speed measurement and positioning accuracy of the moving target.

In order to realize the above-mentioned purpose of the invention, the technical scheme of the present invention is:

A GEO satellite-machine bistatic synchronization method based on the direct wave and clutter subspace, the method aims at the synchronization error compensation of the GEO satellite-machine bistatic SAR signal, and the specific steps of the method include:

Step 1: Extract the direct wave signal of the geosynchronous orbit synthetic aperture radar and the echo signal of the scene, and perform distance compression on the direct wave signal and the echo signal.

Perform the distance migration line estimation on the direct wave signal after range compression to obtain the distance migration R _rm (t _a ); extract the peak signal of the direct wave signal after the distance migration line estimation to obtain the direct wave peak signal s _d ( t _a ), where t _a is slow time.

The first reference function is constructed with the range migration R _rm (t _a ), and the range-compressed echo signal is distance-aligned; the first phase compensation function is constructed with the direct wave peak signal s _d (t _a ); the first phase compensation The function is multiplied by the range-compressed echo signal to obtain a first phase error compensated echo signal.

Step 2. Perform non-uniform cubic phase function processing on the direct wave peak signal s _d (t _a ) to obtain the third-order term coefficient and the fourth-order term coefficient of the direct-wave slant range; use the third-order term coefficient, the fourth-order term coefficient The term coefficient constructs a second reference function, which is multiplied with the direct wave peak signal s _d (t _a ) and transformed to the frequency domain, and the second-order term coefficient of the direct-wave slant distance is obtained according to the peak position of the obtained signal; coefficient, third-order term coefficient, fourth-order term coefficient and known GEO ephemeris to calculate the direct wave slant range, and use the direct wave slant range to construct the second phase compensation function; the second phase compensation function and the first phase error compensation The latter echo signals are multiplied to obtain the echo signal after the second phase compensation.

Step 3. Obtain the covariance matrix of the range-Doppler domain from the echo signal after the second phase compensation, and perform eigenvalue decomposition on the covariance matrix of the range-Doppler domain to obtain the base sum of the clutter subspace. The base of the noise subspace; the Doppler center error is calculated according to the base of the clutter subspace and the ideal clutter steering vector, the target's airborne platform velocity, the channel spacing and number of channels of the echo signal.

Step 4. Using the Doppler center error as the initial value, calculate the clutter steering vector including the Doppler center error; construct a cost function according to the clutter steering vector and the base of the noise subspace; select the one that minimizes the value of the cost function. The clutter steering vector is used to construct the third phase compensation function; the third phase compensation function is multiplied by the echo signal after the second phase error compensation to obtain the echo signal after the third phase compensation, and the echo signal of the scene is realized Synchronize.

Further, a first reference function is constructed by using the distance migration R _rm (t _a ) to perform distance alignment on the distance-compressed echo signals. The specific method is as follows:

The formula of the first reference function he (f _r , _{t a} ) is:

where _fr is the distance frequency, _c is the speed of light, ta is the slow time, and j is an imaginary number.

Fourier transform is performed on the distance-compressed echo signal, multiplied by the first reference function and inverse Fourier transform to obtain the echo signal after distance alignment.

Further, the first phase compensation function is constructed with the direct wave peak signal s _d (t _a ), and the specific method is:

Use s _d (t _a ) to construct the first phase compensation function h _f (t _a ), the formula is:

表示对s_d(t_a)取共轭，|s_d(t_a)|表示对s_d(t_a)取模。in,

means taking the conjugate of s _d (t _a ), and |s _d (t _a )| means taking the modulo of s _d (t _a ).

Further, the first phase compensation function is multiplied by the range-compressed echo signal to obtain the echo signal after the first phase error compensation. The specific method is: performing Fourier transform on the echo signal and converting it to the range frequency domain. After multiplication with h _f (t _a ), and through inverse Fourier transformation back to the original two-dimensional time domain, the echo signal after the first phase error compensation is obtained.

Further, the non-uniform cubic phase function processing is performed on the direct wave peak signal s _d (t _a ) to obtain the third-order term coefficient and the fourth-order term coefficient of the direct-wave slope distance; The term coefficient constructs a second reference function, which is multiplied with the direct wave peak signal s _d (t _a ) and transformed to the frequency domain, and the second-order term coefficient of the direct-wave slant distance is obtained according to the peak position of the obtained signal; The coefficient, the coefficient of the third-order term, the coefficient of the fourth-order term and the known GEO ephemeris are used to calculate the direct wave slope distance, and the second phase compensation function is constructed by using the direct wave slope distance. The specific method is as follows:

Step 21: Discretize the direct wave peak signal s _d (t _a ) to obtain a discretized direct wave peak signal s _d (n), perform phase difference processing on s _d (n), and obtain a phase reduction function; The non-uniform cubic phase function is processed by the phase depreciation function, and the processing result is recorded as the NUCPF function N(n,Ω).

对第二时间切片n₂进行峰值检测，得到第二峰值位置

其中，n为离散时间，Ω为峰值位置。Step 22: Select the first time slice n ₁ and the second time slice n ₂ in the NUCPF function N(n,Ω); perform peak detection on the first time slice n ₁ to obtain the first peak position

Perform peak detection on the second time slice n ₂ to obtain the second peak position

where n is the discrete time and Ω is the peak position.

The formula for calculating the coefficient of the third-order term and the coefficient of the fourth-order term is

Wherein, _Tr is the pulse repetition frequency of the preset discretized direct wave peak signal.

公式为：Multiply the discretized direct wave peak signal s _d (n) by the reference function s _ref (n) and Fourier transform to the frequency domain to obtain the transformed signal s _{PD_de} (f), according to the peak position of s _{PD_de} (f) Calculate the coefficient of the second-order term of the direct wave slope distance

The formula is:

where |S _{PD_de} (f)| is the peak position of the transformed signal, and f is the frequency of the radar.

The formula for the reference function s _ref (n) is expressed as:

Among them, λ is the wavelength of the radar, and p is the preset delay parameter in the phase difference processing.

和第一阶项系数

构建直达波斜距

公式为：Step 23. Using the known GEO ephemeris, calculate the constant term of the direct wave slant range signal

and the first-order term coefficients

Constructing the direct wave slope distance

The formula is:

构建第二相位补偿函数h_com(f_r,t_a)，公式表达为：Utilize the direct wave slant range

Construct the second phase compensation function h _com ( _{f r} , ta ), the formula is expressed as:

Among them, _fr is the distance frequency, f _c is the frequency of the speed of light, _c is the speed of light, ta is the slow time, and j is an imaginary number.

Further, the second phase compensation function is multiplied by the echo signal after the first phase error compensation to complete the second phase compensation, and the specific method is as follows:

Transform the echo signal after the first phase error compensation to the range frequency domain and multiply it by h _com ( _{f r} , ta ), and then transform it back to the two-dimensional time domain to obtain the echo signal after the second phase compensation .

Further, the Doppler center error is calculated according to the eigenvector and the ideal clutter steering vector, the speed of the airborne platform of the target, the channel interval and number of channels of the echo signal, and the specific method is as follows:

的公式表达为：Doppler center error

The formula is expressed as:

Among them, v _R is the airborne platform velocity of the target, d is the channel interval of the echo signal, M is the channel number of the echo signal, p _c is the ideal clutter steering vector, and u ₁ is the base of the clutter subspace.

Among them, the formula of ideal clutter steering vector p _c is expressed as:

为速度矢量的转置矢量，f_a为方位频率。Among them, u _PT is the unit vector of the slant distance from the target to the satellite, v _T is the velocity vector of the satellite,

is the transposed vector of the velocity vector, and f _a is the azimuth frequency.

Further, take the Doppler center error as the initial value, calculate the clutter steering vector including the Doppler center error; construct the cost function according to the matrix composed of the clutter steering vector and the base of the noise subspace; The clutter steering vector with the smallest value is used to construct the third phase compensation function. The specific method is as follows:

Step 41. The formula of the clutter steering vector including the Doppler center error is expressed as:

Construct the cost function J, which is expressed as:

Among them, U ^⊥ is the matrix composed of the base of the noise subspace, (U ^⊥ ) ^H is the conjugate transpose of the matrix composed of the base of the noise subspace, and df _a is the differential of the azimuth frequency.

代入代价函数J，并选择使J更小的符号，作为

的符号。Will

Substitute into the cost function J, and choose a symbol that makes J smaller, as

symbol.

Step 42, construct a third phase compensation function h _c , which is expressed as:

Further, the third phase compensation function is multiplied by the echo signal after the second phase error compensation to complete the third phase compensation, and the specific method is as follows:

The echo signal after the second phase error compensation is transformed into the range frequency domain and multiplied by h _c , and then transformed back to the two-dimensional time domain to obtain the echo signal after the third phase compensation.

Beneficial effects:

1. The present invention provides a synchronization method suitable for GEO satellite-borne bistatic SAR moving target detection. The synchronization method is based on the synchronization of the direct wave. The cubic phase function extracts the high-order term coefficient of the slant range of the direct wave, and then uses the stationary clutter subspace extracted in the scene as an auxiliary calibration source, and estimates the Doppler frequency shift error generated by the slant range phase from this space, realizing the direct Accurate separation of wave slant range phase and synchronization error phase, thereby improving the speed measurement and positioning accuracy of moving objects.

2. The method of the present invention uses the existing GEO ephemeris data to calculate the slant distance of the direct wave, performs phase compensation of the direct wave, does not need to acquire high-precision orbit parameters in real time, and reduces the difficulty of synchronization.

Description of drawings

Figure 1 is a flowchart of a synchronization method suitable for GEO SA-BSAR moving target detection.

Figure 2 is a graph of the imaging results of moving objects after compensation by the proposed method.

Figure 3 is a graph of the output signal-to-noise ratio.

Detailed ways

The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

There are synthetic aperture radars on both aircraft and GEO. The aircraft is the receiving end of the synthetic aperture radar, and the GEO is the transmitting end of the synthetic aperture radar. There is a difference in the frequency sources at the transmitter and receiver. The transmitter of GEO's synthetic aperture radar transmits signals, which are directly received by the aircraft are direct wave signals, and those scattered by the scene and received by the aircraft are echo signals. There is a synchronization error in the echo signal, which needs to be compensated.

As shown in Figure 1, in view of the problem of synchronization error compensation of GEO satellite-based bistatic SAR signals, the present invention provides a GEO satellite-based bistatic synchronization method based on direct wave and clutter subspace, and the specific steps include:

Step 1: Extract the direct wave signal of the geosynchronous orbit synthetic aperture radar and the echo signal of the scene, and perform distance compression on the direct wave signal and the echo signal. In the embodiment of the present invention, the echo signal is a multi-channel echo signal, and the number of channels is not less than three.

Step 11. Perform distance migration line estimation on the direct wave signal after distance compression to obtain the distance migration R _rm (t _a ); perform peak signal extraction on the direct wave signal after distance migration line estimation to obtain the direct wave peak signal s _d ( _ta ), where _ta is slow time.

Step 12, construct a first reference function with distance migration R _rm (t _a ), and perform distance alignment on the echo signal after distance compression; construct a first phase compensation function with direct wave peak signal s _d (t _a ); A phase compensation function is multiplied by the range-compressed echo signal to obtain a first phase error compensated echo signal.

The formula of the first reference function he (f _r , _{t a} ) is:

where _fr is the distance frequency, _c is the speed of light, ta is the slow time, and j is an imaginary number.

Fourier transform is performed on the distance-compressed echo signal, multiplied by the first reference function and inverse Fourier transform to obtain the echo signal after distance alignment.

Step 13. Use s _d (t _a ) to construct a first phase compensation function h _f (t _a ), the formula is:

表示对s_d(t_a)取共轭，|s_d(t_a)|表示对s_d(t_a)取模。in,

means taking the conjugate of s _d (t _a ), and |s _d (t _a )| means taking the modulo of s _d (t _a ).

The echo signal is subjected to Fourier transform, converted to the distance frequency domain, multiplied by h _f (t _a ), and converted back to the original two-dimensional time domain by inverse Fourier transform to obtain the first phase error compensation after echo signal.

In the embodiment of the present invention, since the echo signal is a multi-channel echo signal, the echo signal obtained by each channel needs to be processed in the same way, and the processed result of the mth channel is denoted as s _m (r , t _a ).

Step 2. Perform non-uniform cubic phase function processing on the direct wave peak signal s _d (t _a ) to obtain the third-order term coefficient and the fourth-order term coefficient of the direct-wave slant range; use the third-order term coefficient, the fourth-order term coefficient The term coefficient constructs a second reference function, which is multiplied with the direct wave peak signal s _d (t _a ) and transformed to the frequency domain, and the second-order term coefficient of the direct-wave slant distance is obtained according to the peak position of the obtained signal; coefficient, third-order term coefficient, fourth-order term coefficient and known GEO ephemeris to calculate the direct wave slant range, and use the direct wave slant range to construct the second phase compensation function; the second phase compensation function and the first phase error compensation The latter echo signals are multiplied to obtain the echo signals after the second phase compensation, so as to realize the synchronization of the echo signals of the scene.

Step 21: Discretize the direct wave peak signal s _d (t _a ), denoted as s _d (n), where _n is the number of pulses, satisfying _ta = _nTr , and Tr is the pulse repetition frequency. Then, the phase difference processing is performed on the discrete form of the direct wave peak signal s _d (n) to obtain a phase reduction function PD[n; p], where p is a delay parameter. The non-uniform cubic phase function processing is performed on the phase reduction function PD[n; p], and the processing result is recorded as the NUCPF function N(n, Ω), where Ω is the transformed slow-time frequency domain.

对第二时间切片n₂进行峰值检测，得到第二峰值位置

其中，n为离散时间，Ω为峰值位置。Step 22: Select the first time slice n ₁ and the second time slice n ₂ in the NUCPF function; perform peak detection on the first time slice n ₁ to obtain the first peak position

Perform peak detection on the second time slice n ₂ to obtain the second peak position

where n is the discrete time and Ω is the peak position.

The formula for calculating the coefficient of the third-order term and the coefficient of the fourth-order term is:

Wherein, _Tr is the preset pulse repetition frequency of the discretized direct wave peak signal, which is 300 Hz.

公式为：Multiply the discretized direct wave peak signal s _d (n) by the reference function s _ref (n) and Fourier transform to the frequency domain to obtain the transformed signal s _{PD_de} (f), according to the peak position of s _{PD_de} (f) Calculate the coefficient of the second-order term of the direct wave slope distance

The formula is:

where |s _{PD_de} (f)| is the peak position of the transformed signal, and f is the frequency of the radar.

Construct the reference function s _ref (n), which is expressed as:

Among them, λ is the wavelength of the radar, and p is the preset delay parameter in the phase difference processing, which is 4.

和第一阶项系数

构建直达波斜距

公式为：Step 23. Using the known GEO ephemeris, calculate the constant term of the direct wave slant range signal

and the first-order term coefficients

Constructing the direct wave slope distance

The formula is:

构建第二相位补偿函数h_com(f_r,t_a)，公式表达为：Utilize the direct wave slant range

Construct the second phase compensation function h _com ( _{f r} , ta ), the formula is expressed as:

Among them, _fr is the distance frequency, f _c is the frequency of the speed of light, and c is the speed of light.

Transform the echo signal after the first phase error compensation to the range frequency domain and multiply it with h _com ( _{f r} , ta ), and then transform it back to the two-dimensional time domain to obtain the echo signal after the second phase compensation .

Step 3. Obtain the covariance matrix R _Q of the stationary clutter from the observation data, and perform eigenvalue decomposition on the covariance matrix R _Q to obtain the base u ₁ of the clutter subspace (the eigenvector corresponding to the large eigenvalue) and the noise subspace The matrix U ^⊥ =[u ₂ ,...,u _M ] composed of the basis of , where m=1,2,...,M is the eigenvector corresponding to the small eigenvalue. The Doppler center error is calculated based on the base of the clutter subspace and the ideal clutter steering vector, the target's airborne platform velocity, the channel spacing and number of channels of the echo signal.

的公式表达为：Doppler center error

The formula is expressed as:

Among them, v _R is the airborne platform velocity of the target, d is the channel interval of the echo signal, M is the channel number of the echo signal, p _c is the ideal clutter steering vector, and u ₁ is the base of the clutter subspace.

Among them, the formula of ideal clutter steering vector p _c is expressed as:

为速度矢量的转置矢量，f_a为方位频率。Among them, u _PT is the unit vector of the slant distance from the target to the satellite, v _T is the velocity vector of the satellite,

is the transposed vector of the velocity vector, and f _a is the azimuth frequency.

Step 4. Using the Doppler center error as the initial value, calculate the clutter steering vector including the Doppler center error; construct a cost function according to the clutter steering vector and the base of the noise subspace; select the one that minimizes the value of the cost function. The clutter steering vector is used to construct a third phase compensation function; the third phase compensation function is multiplied by the echo signal after the second phase error compensation to complete the third phase compensation.

Step 41. The formula of the clutter steering vector including the Doppler center error is expressed as:

Construct the cost function J, which is expressed as:

Among them, U ^⊥ is the matrix composed of the base of the noise subspace, (U ^⊥ ) ^H is the conjugate transpose of the matrix composed of the base of the noise subspace, and df _a is the differential of the azimuth frequency.

代入代价函数J，并选择使J更小的符号，作为

的符号。Will

Substitute into the cost function J, and choose a symbol that makes J smaller, as

symbol.

Step 42, construct a third phase compensation function h _c , which is expressed as:

The echo signal after the second phase error compensation is transformed into the range frequency domain and multiplied by h _c , and then transformed back to the two-dimensional time domain to obtain the echo signal after the third phase error compensation, as shown in Figure 2.

The present invention will be further described below in conjunction with specific embodiments.

In the embodiment of the present invention, the parameters of the GEO SA-BSAR system are shown in Table 1.

Table 1 Parameters of GEO SA-BSAR moving target detection system

The background clutter of GEO SA-BSAR is generated by using the existing SAR image, and the amplitude value of the SAR image of ALOS PALSAR (band data of Japan's earth observation satellite) is used as the scattering coefficient to generate the multi-dimensional data under the geometric relationship of GEO SA-BSAR. Channel echo signal. Four moving targets are set in the scene, and the target speeds are (-8,-8)m/s, (-5,-5)m/s, (5,5)m/s and (8,8)m /s.

Both the time and frequency synchronization errors originate from the inaccuracy and instability of the frequency source. For a high-stable quartz crystal frequency source, the typical frequency accuracy and frequency stability are shown in Table 2, and the time and frequency are given accordingly. Synchronization error parameter. For the time synchronization error, assuming that the fixed time deviation is 1ns, the linear error is related to the frequency accuracy, set to 10 ^-8 , the random error obeys a Gaussian distribution with a mean of 0, and its standard deviation is related to the frequency stability, set to 3× ^10-11 . For frequency synchronization error, whose fixed frequency deviation is related to frequency accuracy, set to 10 ^-8 f _c , the phase noise is generated according to the power-law power spectrum.

Table 2 High-stable quartz crystal frequency source parameters and time and frequency synchronization error parameters in simulation

The Doppler center estimation method based on the clutter subspace proposed by the present invention is used to estimate and compensate the residual Doppler center error, and the number of samples used to estimate the clutter covariance matrix is 200.

Using the STAP method to perform clutter suppression and beamforming on the synchronized echo signals, and calculate the output signal-to-noise ratio under different motion parameters, the four target velocities are (-8,-8)m/s, (-5,-5)m/s, (5,5)m/s and (8,8)m/s. Finally, the moving target display result obtained by using the target speed is shown in Figure 2, which shows that a better moving target imaging performance is also obtained.

Figure 3 is the output signal-to-noise ratio curve graph, in which the dotted line is the output signal-to-noise ratio curve when there are time and frequency synchronization errors. Decreased wave suppression capability. The compensated signal-to-noise ratio curve is shown as the solid line curve, and it can be seen that the influence of the synchronization error is eliminated.

In addition, in order to further verify the proposed method under different signal-to-noise ratios, a series of Monte Carlo simulation experiments are carried out. The number of simulations is 100 times. 30dB, 20dB, 10dB, 0, -10dB and -20dB. The Doppler center estimation results are shown in Table 3. It can be seen that the residual Doppler center of the proposed method is less than 0.01 Hz, and has little influence on the radial velocity estimation. At the same time, it verifies that the method has good robustness .

Table 3 The residual Doppler center frequency estimation results and the radial velocity deviation caused by the estimation error

To sum up, the above are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims (9)

1. The GEO satellite-machine bistatic synchronization method based on the direct wave and the clutter subspace is characterized in that the method aims at the synchronous error compensation of the GEO satellite-machine bistatic SAR signals, and the method specifically comprises the following steps:

step 1, extracting a direct wave signal and an echo signal of a scene of a geosynchronous orbit synthetic aperture radar, and performing distance compression on the direct wave signal and the echo signal;

performing range migration line estimation on the range-compressed direct wave signal to obtain range migration R_rm(t_a) (ii) a Extracting the peak value signal of the direct wave after the estimation of the range migration line to obtain a peak value signal s of the direct wave_d(t_a) Wherein t is_aIs a slow time;

migration by distance R_rm(t_a) Constructing a first reference function, and performing distance alignment on the echo signals after the distance compression; using peak signals s of direct wave_d(t_a) Constructing a first phase compensation function; multiplying the first phase compensation function by the echo signal after the distance compression to obtain an echo signal after the first phase error compensation;

step 2, aligning the peak signal s of the direct wave_d(t_a) Carrying out non-uniform cubic phase function processing to obtain a third order coefficient and a fourth order coefficient of the direct wave slant distance; using the third order coefficient and the fourth order coefficient to constructEstablishing a second reference function and a direct wave peak signal s_d(t_a) Multiplying and transforming to a frequency domain, and obtaining a second order term coefficient of the direct wave slant distance according to the peak position of the obtained signal; calculating the direct wave slope distance by using the second order coefficient, the third order coefficient, the fourth order coefficient and the known GEO ephemeris, and constructing a second phase compensation function by using the direct wave slope distance; the second phase compensation function is multiplied by the echo signal after the first phase error compensation to obtain an echo signal after the second phase compensation;

step 3, obtaining a covariance matrix of a distance-Doppler domain from the echo signal after the second phase compensation, and performing characteristic value decomposition on the covariance matrix of the distance-Doppler domain to obtain a clutter subspace substrate and a noise subspace substrate; calculating Doppler center error according to the base of clutter subspace, ideal clutter guide vector, airborne platform speed of the target, and channel interval and channel number of echo signals;

step 4, calculating clutter guiding vectors containing the Doppler center errors by taking the Doppler center errors as initial values; constructing a cost function according to the clutter guide vector and the base of the noise subspace; selecting a clutter guide vector which minimizes the value of the cost function, and constructing a third phase compensation function; and multiplying the third phase compensation function by the echo signal after the second phase error compensation to obtain the echo signal after the third phase compensation, thereby realizing the echo signal synchronization of the scene.

2. The method of claim 1, further wherein the distance migration R is_rm(t_a) Constructing a first reference function, and performing distance alignment on the echo signals after distance compression, wherein the specific method comprises the following steps:

the first reference function h_e(f_r,t_a) The formula of (1) is:

wherein f is_rIs distance frequency, c is speed of light, t_aSlow time, j is an imaginary number;

and performing Fourier transform on the echo signals after the distance compression, multiplying the echo signals by the first reference function and performing inverse Fourier transform to obtain the echo signals after the distance alignment.

3. The method of claim 1, wherein the direct peak signal s is used_d(t_a) The method for constructing the first phase compensation function comprises the following specific steps:

using s_d(t_a) Constructing a first phase compensation function h_f(t_a) The formula is as follows:

wherein,

represents a pair s_d(t_a) Taking conjugate, | s_d(t_a) I denotes the pair s_d(t_a) And (6) taking a mold.

4. The method of claim 1, wherein the first phase compensation function is multiplied by the range-compressed echo signal to obtain a first phase error compensated echo signal by: fourier transform is carried out on the echo signal, and the echo signal is converted into a distance frequency domain and then is summed with h_f(t_a) Multiplying, and converting back to the original two-dimensional time domain through inverse Fourier transform to obtain the echo signal after the first phase error compensation.

5. The method of claim 1, wherein the pair of direct arrival peak signals s_d(t_a) Carrying out non-uniform cubic phase function processing to obtain a third order coefficient and a fourth order coefficient of the direct wave slant distance; constructing a second reference function by using the third order coefficient and the fourth order coefficient, andwave arrival peak signal s_d(t_a) Multiplying and converting the signal into a frequency domain, and obtaining a second order term coefficient of the direct wave slant distance according to the peak position of the obtained signal; calculating the direct wave slope distance by using the second order coefficient, the third order coefficient, the fourth order coefficient and the known GEO ephemeris, and constructing a second phase compensation function by using the direct wave slope distance, wherein the specific method comprises the following steps:

step 21, direct wave peak value signal s_d(t_a) Discretizing to obtain discretized direct wave peak signal s_d(n) for s_d(n) carrying out phase difference processing to obtain a phase reduced function; carrying out non-uniform cubic phase function processing on the phase reduction function, and recording the processing result as a NUCPF function N (N, omega);

step 22, selecting a first time slice N in the NUCPF function N (N, Ω)₁And a second time slice n₂(ii) a Slicing the first time n₁Carrying out peak value detection to obtain a first peak value position

Slicing n for the second time₂Carrying out peak value detection to obtain a second peak value position

Wherein n is discrete time, and Ω is peak position;

the formula for calculating the third order coefficient and the fourth order coefficient is

Wherein, T_rThe pulse repetition frequency of the preset discretization direct wave peak value signal is obtained;

discrete direct wave peak signal s_d(n) and a reference function s_ref(n) multiplying and Fourier transforming into frequency domain to obtain transformed signal s_{PD_de}(f) According to s_{PD_de}(f) Calculating the peak value position to obtain the second order coefficient of the direct wave slope distance

The formula is as follows:

wherein, | s_{PD_de}(f) I is the peak position of the transformation signal, and f is the frequency of the radar;

the reference function s_refThe formula of (n) is expressed as:

wherein lambda is the wavelength of the radar, and p is a delay parameter preset in the phase difference division;

step 23, calculating a constant term of the direct wave slant range signal by using the known GEO ephemeris

And coefficient of first order term

Construction of direct wave slant distance

The formula is as follows:

using the slant distance of the direct wave

Constructing a second phase compensation function h_com(f_r,t_a) The formula is expressed as:

wherein f is_rIs the distance frequency, f_cIs the speed of light frequency, c is the speed of light, t_aIs the slow time, j is the imaginary number.

6. The method of claim 5, wherein the second phase compensation function is multiplied by the echo signal after the first phase error compensation to complete the second phase compensation by:

the echo signal after the first phase error compensation is converted into a distance frequency domain and is h_com(f_r,t_a) Multiplying, and converting back to a two-dimensional time domain to obtain an echo signal after the second phase compensation.

7. The method of claim 1, wherein the doppler center error is calculated based on the eigenvector and the ideal clutter guide vector, the airborne platform velocity of the target, the channel spacing and the number of channels of the echo signal by:

the Doppler center error

Is expressed as:

wherein v is_RTarget airborne platform velocity, d channel spacing of echo signals, M number of channels of echo signals, p_cIs an ideal clutter guide vector, u₁A base that is a clutter subspace;

wherein the ideal clutter guide vector p_cIs expressed as:

wherein u is_PTUnit vector of target-to-satellite slant distance, v_TIs the velocity vector of the satellite or satellites,

as a transposed vector of the velocity vector, f_aIs the azimuth frequency.

8. The method of claim 7, wherein the clutter guide vector containing the doppler center error is calculated using the doppler center error as an initial value; constructing a cost function according to a matrix formed by the clutter guide vector and the base of the noise subspace; selecting a clutter guide vector which minimizes the value of the cost function, and constructing a third phase compensation function, wherein the specific method comprises the following steps:

step 41, the formula of the clutter guiding vector containing the doppler center error is expressed as:

constructing a cost function J, wherein the formula is expressed as:

wherein, U^⊥A matrix composed of the bases of the noise subspaces, (U)^⊥)^HConjugate transpose of matrix composed for noise subspace bases, df_aIs the derivative of the azimuth frequency;

will be provided with

Substituting the cost function J and selecting a symbol that makes J smaller as

The symbol of (a);

step 42, constructing a third phase compensation function h_cThe notations are expressed as:

9. the method of claim 8, wherein the third phase compensation function is multiplied by the echo signal after the second phase error compensation to complete the third phase compensation, and the method comprises:

the echo signal after the second phase error compensation is converted into a distance frequency domain and is h_cMultiplying, and converting back to a two-dimensional time domain to obtain an echo signal after third time phase compensation.

Images