A GEO satellite-to-aircraft dual-base synchronization method based on direct wave and clutter subspace

Abstract

This invention discloses a GEO satellite-to-satellite dual-base synchronization method based on direct wave and clutter subspace. Based on direct wave synchronization, this synchronization method first uses a cubic phase function to extract the high-order coefficients of the direct wave slant range to achieve precise separation of the direct wave slant range phase and the synchronization error phase. Then, using the stationary clutter subspace extracted from the scene as an auxiliary calibration source, the Doppler shift error generated by the slant range phase is estimated from this space. This achieves precise separation of the direct wave slant range phase and the synchronization error phase, thereby improving the velocity measurement and positioning accuracy of moving targets. This method does not require real-time acquisition of high-precision orbital parameters, reducing the difficulty of synchronization.

Description

Technical Field

[0001] The present invention relates to the technical field of synthetic aperture radar, and in particular to a GEO satellite-machine dual-base synchronization method based on direct wave and clutter subspace. Background Art

[0002] The Geosynchronous Orbit (GEO) Satellite-Aircraft Bistatic Synthetic Aperture Radar (GEO SA-BSAR) is a radar system that uses a Geosynchronous Orbit Synthetic Aperture Radar (GEO SAR) as a radiation source and an airborne multi-channel system to receive signals. This system offers excellent concealment and anti-interference capabilities, along with flexible configuration, making it an effective means of detecting and monitoring moving targets.

[0003] Due to the separate transmission and reception locations, GEO SA-BSAR systems face synchronization errors that degrade image quality and target detection performance due to differences in the frequency sources between the transmitter and receiver. To achieve synchronization, an aircraft receives the GEO SAR direct-arrival signal and extracts the time and phase synchronization errors. This extraction process requires precise separation of the direct-arrival slant range phase and phase synchronization errors. Existing synchronization methods utilize precise satellite orbit parameters to achieve this. Synthetic aperture radar satellites in low Earth orbit (LEO) can obtain high-precision orbital positions in real time using navigation satellites, and the aforementioned algorithm effectively compensates for synchronization errors. However, GEO SAR orbits are located at an altitude of approximately 36,000 km, above the navigation satellites, making it difficult to obtain high-precision orbit parameters in real time. When the velocity angle between the GEO and the aircraft is 1°, the residual Doppler shift error after applying the aforementioned algorithm is a maximum of 6.5 Hz, which has minimal impact on imaging resolution. However, for moving target detection, this error can lead to significant bias in target radial velocity estimation and compromise target positioning performance.

[0004] Therefore, there is an urgent need for a synchronization method that can overcome the problem of difficulty in obtaining high-precision orbit parameters in real time, and for moving target detection, achieve accurate separation of the direct wave slant range phase and the synchronization error phase to compensate for the synchronization error and improve positioning accuracy. Summary of the Invention

[0005] In view of this, the present invention provides a GEO satellite-machine dual-base synchronization method based on the direct wave and clutter subspace, which can achieve accurate separation of the direct wave slant range phase and the synchronization error phase, thereby improving the speed measurement and positioning accuracy of moving targets.

[0006] In order to achieve the above-mentioned object of the invention, the technical solution of the present invention is:

[0007] A GEO satellite-based bistatic synchronization method based on direct wave and clutter subspace is proposed. This method aims to compensate for the synchronization error of GEO satellite-based bistatic SAR signals. The specific steps of this method include:

[0008] 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.

[0009] The range migration line of the direct wave signal after range compression is estimated to obtain the range migration R rm (t a ) ; Extract the peak signal of the direct wave signal after the distance migration line is estimated to obtain the direct wave peak signal s d (t a ), where t a For slow time.

[0010] Migrate by distance R rm (t a ) Construct the first reference function to align the echo signal after range compression; use the direct wave peak signal s d (t a ) construct a first phase compensation function; multiply the first phase compensation function by the echo signal after distance compression to obtain the echo signal after the first phase error compensation.

[0011] Step 2: Direct peak signal s d (t a ) is processed with a non-uniform cubic phase function to obtain the third-order coefficient and the fourth-order coefficient of the direct wave slant range; the third-order coefficient and the fourth-order coefficient are used to construct a second reference function, which is compared with the direct wave peak signal s d (t a ) and transform it into the frequency domain, and obtain the second-order coefficient of the direct wave slant range based on the peak position of the obtained signal; calculate the direct wave slant range using the second-order coefficient, third-order coefficient, fourth-order coefficient and known GEO ephemeris, and construct a second phase compensation function using the direct wave slant range; multiply the second phase compensation function by the echo signal after the first phase error compensation to obtain the echo signal after the second phase compensation.

[0012] Step 3: Obtain a range-Doppler domain covariance matrix from the echo signal after the second phase compensation, perform eigenvalue decomposition on the range-Doppler domain covariance matrix, and obtain a basis of the clutter subspace and a basis of the noise subspace; calculate the Doppler center error based on the basis of the clutter subspace and the ideal clutter guidance vector, the target airborne platform speed, and the channel spacing and number of channels of the echo signal.

[0013] 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 based on the clutter steering vector and the basis of the noise subspace; select the clutter steering vector that minimizes the value of the cost function and construct a third phase compensation function; multiply 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 achieving echo signal synchronization of the scene.

[0014] Furthermore, using distance migration R rm (t a ) Construct a first reference function to perform distance alignment on the echo signal after range compression. The specific method is as follows:

[0015] The first reference function h e (f r ,t a ) is:

[0016]

[0017] Among them, f r is the distance frequency, c is the speed of light, t a is the slow time, and j is an imaginary number.

[0018] The echo signal after range compression is Fourier transformed, multiplied by the first reference function and inversely Fourier transformed to obtain the echo signal after range alignment.

[0019] Furthermore, using the direct peak signal s d (t a ) Construct the first phase compensation function, the specific method is:

[0020] Utilize s d (t a ) Construct the first phase compensation function h f (t a ), the formula is:

[0021]

[0022] in, Indicates s d (t a ) takes conjugate, |s d (t a )| indicates s d (t a ) modulus.

[0023] Furthermore, the first phase compensation function is multiplied with the echo signal after range compression to obtain the echo signal after first phase error compensation. The specific method is: the echo signal is Fourier transformed, converted to the range frequency domain, and then compared with hf (t a ) and return it to the original two-dimensional time domain through inverse Fourier transform to obtain the echo signal after the first phase error compensation.

[0024] Furthermore, for the direct peak signal s d (t a ) is processed with a non-uniform cubic phase function to obtain the third-order coefficient and the fourth-order coefficient of the direct wave slant range; the third-order coefficient and the fourth-order coefficient are used to construct a second reference function, which is compared with the direct wave peak signal s d (t a ) and transform it into the frequency domain. The second-order coefficient of the direct wave slant range is obtained according to the peak position of the obtained signal. The direct wave slant range is calculated using the second-order coefficient, the third-order coefficient, the fourth-order coefficient and the known GEO ephemeris. The second phase compensation function is constructed using the direct wave slant range. The specific method is:

[0025] Step 21: Direct peak signal s d (t a ) is discretized to obtain the discretized direct wave peak signal s d (n), for s d (n) is subjected to phase difference processing to obtain a phase reduction function; the phase reduction function is subjected to non-uniform cubic phase function processing, and the processing result is recorded as NUCPF function N(n,Ω).

[0026] Step 22: Select the first time slice n1 and the second time slice n2 in the NUCPF function N(n,Ω); perform peak detection on the first time slice n1 to obtain the first peak position Perform peak detection on the second time slice n2 to obtain the second peak position Where n is the discrete time and Ω is the peak position.

[0027] The formula for calculating the third-order coefficient and the fourth-order coefficient is

[0028]

[0029] Among them, T r is the pulse repetition frequency of the preset discretized direct wave peak signal.

[0030] The discretized direct peak signal s d (n) and the reference function s ref (n) multiply and Fourier transform to the frequency domain to obtain the transformed signal s PD_de (f), according to s PD_de The second-order coefficient of the direct wave slant distance is calculated from the peak position of (f) The formula is:

[0031]

[0032] Among them, |s PD_de (f)| is the peak position of the transformed signal, and f is the frequency of the radar.

[0033] Reference function s ref The formula for (n) is:

[0034]

[0035] Where λ is the wavelength of the radar, and p is the delay parameter preset in the phase difference processing.

[0036] Step 23: Using the known GEO ephemeris, calculate the constant term of the direct wave slant range signal and the first-order coefficient Constructing direct wave slant distance The formula is:

[0037]

[0038] Direct wave slant distance Construct the second phase compensation function h com (f r ,t a ), the formula is:

[0039]

[0040] Among them, f r is the distance frequency, f c is the light speed frequency, c is the light speed, t a is the slow time, and j is an imaginary number.

[0041] Furthermore, the second phase compensation function is multiplied by the echo signal after the first phase error compensation to complete the second phase compensation. The specific method is:

[0042] The echo signal after the first phase error compensation is transformed into the range frequency domain and compared with h com (f r ,t a ) and then transformed back to the two-dimensional time domain to obtain the echo signal after the second phase compensation.

[0043] Furthermore, the Doppler center error is calculated based on the eigenvector and the ideal clutter guidance vector, the target airborne platform speed, the channel spacing and the number of channels of the echo signal. The specific method is:

[0044] Doppler center error The formula is:

[0045]

[0046] Among them, v R is the target airborne platform speed, d is the channel spacing of the echo signal, M is the number of channels of the echo signal, p c is the ideal clutter steering vector, and u1 is the basis of the clutter subspace.

[0047] Among them, the ideal clutter steering vector p c The formula is:

[0048]

[0049] Among them, u PT is the unit vector of the slant range from the target to the satellite, v T is the satellite's velocity vector, is the transposed vector of the velocity vector, f a is the azimuth frequency.

[0050] Furthermore, the Doppler center error is used as the initial value to calculate the clutter steering vector including the Doppler center error. A cost function is constructed based on the matrix composed of the clutter steering vector and the basis of the noise subspace. The clutter steering vector that minimizes the cost function is selected to construct the third phase compensation function. The specific method is as follows:

[0051] Step 41: The formula for the clutter steering vector including the Doppler center error is expressed as:

[0052]

[0053] Construct the cost function J, the formula is expressed as:

[0054]

[0055] Among them, U ⊥ is the matrix composed of the basis of the noise subspace, (U ⊥ ) H is the conjugate transpose of the matrix composed of the noise subspace basis, df a is the differential of the azimuth frequency.

[0056] Will Substitute the cost function J and choose the symbol that makes J smaller as symbol.

[0057] Step 42: Construct the third phase compensation function h c , the public expression is:

[0058]

[0059] Furthermore, the third phase compensation function is multiplied by the echo signal after the second phase error compensation to complete the third phase compensation. The specific method is:

[0060] The echo signal after the second phase error compensation is transformed into the range frequency domain and compared with h c Multiply them and then transform back to the two-dimensional time domain to obtain the echo signal after the third phase compensation.

[0061] Beneficial effects:

[0062] 1. The present invention provides a synchronization method suitable for GEO satellite-based bistatic SAR moving target detection. Based on direct wave synchronization, the synchronization method first uses a cubic phase function to extract the high-order term coefficients of the direct wave slant range in order to achieve accurate separation of the direct wave slant range phase and the synchronization error phase. Then, the stationary clutter subspace extracted from the scene is used as an auxiliary calibration source. The Doppler frequency shift error caused by the slant range phase is estimated from the stationary clutter subspace, thereby achieving accurate 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.

[0063] 2. The method of the present invention uses existing GEO ephemeris data to calculate the direct wave slant range and perform phase compensation of the direct wave. It does not require real-time acquisition of high-precision orbit parameters, thus reducing the difficulty of synchronization. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 The flowchart of the synchronization method suitable for GEO SA-BSAR moving target detection.

[0065] Figure 2 Figure 2 is the imaging result of the moving target after compensation using the proposed method.

[0066] Figure 3 The output signal-to-noise ratio curve is shown in Figure 2. DETAILED DESCRIPTION

[0067] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0068] Both aircraft and GEO satellites have synthetic aperture radars (SARs). The aircraft is the receiver, while the GEO is the transmitter. The frequency sources of the transmitter and receiver differ. The GEO SAR transmitter transmits a signal. The direct wave signal is directly received by the aircraft, while the echo signal is scattered by the scene and received by the aircraft. The echo signal contains synchronization errors that need to be compensated.

[0069] like Figure 1 As shown, to address the problem of GEO satellite-based bistatic SAR signal synchronization error compensation, the present invention provides a GEO satellite-based bistatic synchronization method based on direct wave and clutter subspace, the specific steps of which include:

[0070] 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 with a number of channels of not less than 3.

[0071] Step 11: Estimating the range migration line of the direct wave signal after range compression to obtain the range migration R rm (t a ) ; Extract the peak signal of the direct wave signal after the distance migration line is estimated to obtain the direct wave peak signal s d (t a ), where t a For slow time.

[0072] Step 12: Migrate R using distance rm (t a ) Construct the first reference function to align the echo signal after range compression; use the direct wave peak signal s d (t a ) construct a first phase compensation function; multiply the first phase compensation function by the echo signal after distance compression to obtain the echo signal after the first phase error compensation.

[0073] The first reference function h e (f r ,t a ) is:

[0074]

[0075] Among them, f r is the distance frequency, c is the speed of light, t a is the slow time, and j is an imaginary number.

[0076] The echo signal after range compression is Fourier transformed, multiplied by the first reference function and inversely Fourier transformed to obtain the echo signal after range alignment.

[0077] Step 13, use s d (t a ) Construct the first phase compensation function h f (t a ), the formula is:

[0078]

[0079] in, Indicates s d (t a ) takes conjugate, |s d (t a )| indicates sd (t a ) modulus.

[0080] The echo signal is Fourier transformed and converted to the range frequency domain and then compared with h f (t a ) and return it to the original two-dimensional time domain through inverse Fourier transform to obtain the echo signal after the first phase error compensation.

[0081] In the embodiment of the present invention, since the echo signal is a multi-channel echo signal, the echo signal obtained from each channel needs to be processed in the same way during processing. The result after processing the mth channel is recorded as s m (r,t a ).

[0082] Step 2: Direct peak signal s d (t a ) is processed with a non-uniform cubic phase function to obtain the third-order coefficient and the fourth-order coefficient of the direct wave slant range; the third-order coefficient and the fourth-order coefficient are used to construct a second reference function, which is compared with the direct wave peak signal s d (t a ) and transform it into the frequency domain, and obtain the second-order coefficient of the direct wave slant range based on the peak position of the obtained signal; use the second-order coefficient, third-order coefficient, fourth-order coefficient and known GEO ephemeris to calculate the direct wave slant range, and use the direct wave slant range to construct a second phase compensation function; multiply the second phase compensation function by the echo signal after the first phase error compensation to obtain the echo signal after the second phase compensation, thereby realizing echo signal synchronization of the scene.

[0083] Step 21: Direct peak signal s d (t a ) is discretized and recorded as s d (n), where n is the number of pulses, satisfying t a =nT r , T r is the pulse repetition frequency. Then the direct peak signal s in discrete form is d (n) is subjected to phase difference processing to obtain the phase reduction function PD[n;p], where p is the delay parameter. The phase reduction function PD[n;p] is subjected to non-uniform cubic phase function processing, and the processing result is recorded as NUCPF function N(n,Ω), where Ω is the slow time frequency domain after transformation.

[0084] Step 22: Select the first time slice n1 and the second time slice n2 in the NUCPF function; perform peak detection on the first time slice n1 to obtain the first peak position Perform peak detection on the second time slice n2 to obtain the second peak position Where n is the discrete time and Ω is the peak position.

[0085] The formulas for calculating the third-order coefficients and the fourth-order coefficients are:

[0086]

[0087] Among them, T r The pulse repetition frequency of the preset discretized direct wave peak signal is 300 Hz.

[0088] The discretized direct peak signal s d (n) and the reference function s ref (n) multiply and Fourier transform to the frequency domain to obtain the transformed signal s PD_de (f), according to s PD_de The second-order coefficient of the direct wave slant distance is calculated from the peak position of (f) The formula is:

[0089]

[0090] Among them, |s PD_de (f)| is the peak position of the transformed signal, and f is the frequency of the radar.

[0091] Construct reference function s ref (n), the formula is:

[0092]

[0093] Where λ is the wavelength of the radar, and p is the delay parameter preset in the phase difference processing, which is 4.

[0094] Step 23: Using the known GEO ephemeris, calculate the constant term of the direct wave slant range signal and the first-order coefficient Constructing direct wave slant distance The formula is:

[0095]

[0096] Direct wave slant distance Construct the second phase compensation function h com (f r ,t a ), the formula is:

[0097]

[0098] Among them, f r is the distance frequency, f c is the frequency of the speed of light, and c is the speed of light.

[0099] The echo signal after the first phase error compensation is transformed into the range frequency domain and compared with h com (f r , t a ) and then transformed back to the two-dimensional time domain to obtain the echo signal after the second phase compensation.

[0100] Step 3: Get the covariance matrix R of the stationary clutter from the observed data Q , for the covariance matrix R Q Perform eigenvalue decomposition to obtain the matrix U composed of the basis u1 of the clutter subspace (eigenvector corresponding to the large eigenvalue) and the basis of the noise subspace ⊥ =[u2,…,u M ], where m = 1, 2, …, M is the eigenvector corresponding to the smallest eigenvalue. The Doppler center error is calculated based on the basis of the clutter subspace and the ideal clutter guidance vector, the target airborne platform speed, the channel spacing and the number of channels of the echo signal.

[0101] Doppler center error The formula is:

[0102]

[0103] Among them, v R is the target airborne platform speed, d is the channel spacing of the echo signal, M is the number of channels of the echo signal, p c is the ideal clutter steering vector, and u1 is the basis of the clutter subspace.

[0104] Among them, the ideal clutter steering vector p c The formula is:

[0105]

[0106] Among them, u PT is the unit vector of the slant range from the target to the satellite, v T is the satellite's velocity vector, is the transposed vector of the velocity vector, f a is the azimuth frequency.

[0107] 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 based on the clutter steering vector and the basis of the noise subspace; select the clutter steering vector that minimizes the value of the cost function and construct a third phase compensation function; multiply the third phase compensation function by the echo signal after the second phase error compensation to complete the third phase compensation.

[0108] Step 41: The formula for the clutter steering vector including the Doppler center error is expressed as:

[0109]

[0110] Construct the cost function J, the formula is expressed as:

[0111]

[0112] Among them, U ⊥ is the matrix composed of the basis of the noise subspace, (U ⊥ ) H is the conjugate transpose of the matrix composed of the noise subspace basis, df a is the differential of the azimuth frequency.

[0113] Will Substitute the cost function J and choose the symbol that makes J smaller as symbol.

[0114] Step 42: Construct the third phase compensation function h c , the public expression is:

[0115]

[0116] The echo signal after the second phase error compensation is transformed into the range frequency domain and compared with h c Multiply and transform back to the two-dimensional time domain to obtain the echo signal after the third phase compensation, as shown in Figure 2 shown.

[0117] The present invention will be further described below with reference to specific embodiments.

[0118] In the embodiment of the present invention, the parameters of the GEO SA-BSAR system are shown in Table 1.

[0119] Table 1 GEO SA-BSAR moving target detection system parameters

[0120]

[0121] The GEO SA-BSAR background clutter is generated using existing SAR images. The amplitude values ​​of the ALOS PALSAR (band data from Japan's Earth observation satellite) SAR image are used as scattering coefficients to generate multi-channel echo signals based on the GEO SA-BSAR geometry. Four moving targets are set in the scene, with speeds of (-8, -8) m / s, (-5, -5) m / s, (5, 5) m / s, and (8, 8) m / s, respectively.

[0122] Time and frequency synchronization errors are caused by the inaccuracy and instability of the frequency source. For a high-stability quartz crystal frequency source, its typical frequency accuracy and frequency stability are shown in Table 2, and the parameters of time and frequency synchronization errors are given accordingly. For the time synchronization error, assuming a fixed time deviation of 1ns, its linear error is related to the frequency accuracy and is set to 10 -8 The random error follows a Gaussian distribution with a mean of 0, and its standard deviation is related to the frequency stability and is set to 3×10 -11 For frequency synchronization error, the fixed frequency deviation is related to the frequency accuracy and is set to 10 -8 f c , the phase noise is generated according to the power-law power spectrum.

[0123] Table 2 High-stability quartz crystal frequency source parameters and time and frequency synchronization error parameters in simulation

[0124]

[0125] The Doppler center estimation method based on clutter subspace proposed in the present invention is used to estimate and compensate for the residual Doppler center error. The number of samples used to estimate the clutter covariance matrix is ​​200.

[0126] The synchronized echo signal is subjected to clutter suppression and beamforming using the STAP method, and the output signal-to-noise ratio under different motion parameters is calculated. The four target speeds are obtained as (-8,-8) m / s, (-5,-5) m / s, (5,5) m / s, and (8,8) m / s. Finally, the moving target display results obtained using the target speed are shown as follows: Figure 2 As shown, it can be seen that good moving target imaging performance is also achieved.

[0127] Figure 3 Figure 2 shows the output SNR curve. The dotted line represents the output SNR curve when time and frequency synchronization errors are present. Compared to the ideal output SNR, the notch in the curve is offset and significantly broadened, resulting in reduced clutter suppression. The compensated SNR curve is shown as the solid line, demonstrating that the effects of synchronization errors are eliminated.

[0128] To further validate the proposed method under different signal-to-noise ratios (SNRs), a series of 100 Monte Carlo simulations were conducted. The SNRs of the range-compressed echo and direct wave signals were set to 30 dB, 20 dB, 10 dB, 0, -10 dB, and -20 dB, respectively. 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 impact on the radial velocity estimation, demonstrating the robustness of the proposed method.

[0129] Table 3 Residual Doppler center frequency estimation results and radial velocity deviation caused by estimation error

[0130]

[0131] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A GEO satellite-machine dual-base synchronization method based on direct wave and clutter subspace is characterized by: This method aims at compensating the synchronization error of GEO satellite-based bistatic SAR signals. The specific steps of the method include: Step 1: extracting the direct wave signal of the geosynchronous orbit synthetic aperture radar and the echo signal of the scene, and performing distance compression on the direct wave signal and the echo signal; The range migration line of the direct wave signal after range compression is estimated to obtain the range migration R rm (t a ) ; Extract the peak signal of the direct wave signal after the distance migration line is estimated to obtain the direct wave peak signal s d (t a ), where t a For slow time; Migrate by distance R rm (t a ) Construct the first reference function to align the echo signal after range compression; use the direct wave peak signal s d (t a ) constructing a first phase compensation function; multiplying the first phase compensation function by the echo signal after range compression to obtain an echo signal after first phase error compensation; Step 2: Direct peak signal s d (t a ) is processed with a non-uniform cubic phase function to obtain the third-order coefficient and the fourth-order coefficient of the direct wave slant range; the third-order coefficient and the fourth-order coefficient are used to construct a second reference function, which is compared with the direct wave peak signal s d (t a ) and transform it into the frequency domain, obtaining a second-order coefficient of the direct wave slant range based on the peak position of the obtained signal; calculating the direct wave slant range 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 using the direct wave slant range; multiplying the second phase compensation function by the echo signal after the first phase error compensation to obtain an echo signal after the second phase compensation; Step 3: Obtain a range-Doppler domain covariance matrix from the echo signal after the second phase compensation, perform eigenvalue decomposition on the range-Doppler domain covariance matrix to obtain a basis of the clutter subspace and a basis of the noise subspace; calculate the Doppler center error based on the basis of the clutter subspace and the ideal clutter guidance vector, the target airborne platform speed, the channel spacing and the number of channels of the echo signal; Step 4: Using the Doppler center error as an initial value, calculate a clutter steering vector including the Doppler center error; construct a cost function based on the clutter steering vector and the basis of the noise subspace; select the clutter steering vector that minimizes the value of the cost function and construct a third phase compensation function; multiply 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 achieving echo signal synchronization of the scene.

2. The GEO satellite-machine bistatic synchronization method based on direct wave and clutter subspace according to claim 1, characterized in that: The distance migration R rm (t a ) Construct a first reference function to perform distance alignment on the echo signal after range compression. The specific method is as follows: The first reference function h e (f r ,t a ) is: Among them, f r is the distance frequency, c is the speed of light, t a is the slow time, j is an imaginary number; The echo signal after range compression is subjected to Fourier transformation, multiplied by the first reference function and inversely Fourier transformed to obtain the echo signal after range alignment.

3. The GEO satellite-machine bistatic synchronization method based on direct wave and clutter subspace according to claim 1, characterized in that: Use the direct peak signal s d (t a ) Construct the first phase compensation function, the specific method is: Utilize s d (t a ) Construct the first phase compensation function h f (t a ), the formula is: in, Indicates s d (t a ) takes conjugate, |s d (t a )| indicates s d (t a ) modulus.

4. The GEO satellite-machine bistatic synchronization method based on direct wave and clutter subspace according to claim 1, characterized in that: The first phase compensation function is multiplied by the echo signal after range compression to obtain the echo signal after the first phase error compensation. The specific method is: the echo signal is Fourier transformed, converted to the range frequency domain, and then multiplied by the first phase compensation function h f (t a ) and return it to the original two-dimensional time domain through inverse Fourier transform to obtain the echo signal after the first phase error compensation.

5. The GEO satellite-machine bistatic synchronization method based on direct wave and clutter subspace according to claim 1, characterized in that: The direct wave peak signal s d (t a ) is processed with a non-uniform cubic phase function to obtain the third-order coefficient and the fourth-order coefficient of the direct wave slant range; the third-order coefficient and the fourth-order coefficient are used to construct a second reference function, which is compared with the direct wave peak signal s d (t a ) and transform it into the frequency domain. The second-order coefficient of the direct wave slant range is obtained according to the peak position of the obtained signal. The direct wave slant range is calculated using the second-order coefficient, the third-order coefficient, the fourth-order coefficient and the known GEO ephemeris. The second phase compensation function is constructed using the direct wave slant range. The specific method is: Step 21: Direct peak signal s d (t a ) is discretized to obtain the discretized direct wave peak signal s d (n), for s d (n) performing phase difference processing to obtain a phase reduction function; The phase reduction function is processed by a non-uniform cubic phase function, and the processing result is recorded as a NUCPF function n(n,Ω); Step 22: Select the first time slice n1 and the second time slice n2 in the NUCPF function n(n,Ω); Perform peak detection on the first time slice n1 to obtain the first peak position Perform peak detection on the second time slice n2 to obtain the second peak position Where n is the discrete time, Ω is the peak position; The formula for calculating the third-order coefficient and the fourth-order coefficient is Among them, T r is the pulse repetition frequency of the preset discretized direct wave peak signal; The discretized direct peak signal s d (n) and the reference function s ref (n) multiply and Fourier transform to the frequency domain to obtain the transformed signal s PD_de (f), according to s PD_de The second-order coefficient of the direct wave slant distance is calculated from the peak position of (f) The formula is: Among them, |s PD_de (f)| is the peak position of the transformed signal, and f is the frequency of the radar; The reference function s ref The formula for (n) is: Where λ is the wavelength of the radar, and p is the delay parameter preset in the phase difference processing; Step 23: Using the known GEO ephemeris, calculate the constant term of the direct wave slant range signal and the first-order coefficient Constructing direct wave slant distance The formula is: Direct wave slant distance Construct the second phase compensation function h com (f r ,t a ), the formula is: Among them, f r is the distance frequency, f c is the light speed frequency, c is the light speed, t a is the slow time, and j is an imaginary number.

6. The GEO satellite-machine bistatic synchronization method based on direct wave and clutter subspace according to claim 5, characterized in that: The second phase compensation function is multiplied by the echo signal after the first phase error compensation to complete the second phase compensation. The specific method is: The echo signal after the first phase error compensation is transformed into the range frequency domain and compared with h com (f r ,t a ) and then transformed back to the two-dimensional time domain to obtain the echo signal after the second phase compensation.

7. The GEO satellite-machine bistatic synchronization method based on direct wave and clutter subspace according to claim 1, characterized in that: The Doppler center error is calculated based on the basis of the clutter subspace and the ideal clutter guidance vector, the target airborne platform speed, the channel spacing and the number of channels of the echo signal. The specific method is: The Doppler center error The formula is: Among them, v R is the target airborne platform speed, d is the channel spacing of the echo signal, M is the number of channels of the echo signal, p c is the ideal clutter steering vector, u1 is the basis of the clutter subspace; Among them, the ideal clutter steering vector p c The formula is: Among them, u PT is the unit vector of the slant range from the target to the satellite, v T is the satellite's velocity vector, is the transposed vector of the velocity vector, f a is the azimuth frequency.

8. The GEO satellite-machine bistatic synchronization method based on direct wave and clutter subspace according to claim 7, characterized in that: The Doppler center error is used as an initial value to calculate a clutter steering vector including the Doppler center error; a cost function is constructed according to a matrix composed of the clutter steering vector and the basis of the noise subspace; and a clutter steering vector that minimizes the value of the cost function is selected to construct a third phase compensation function. The specific method is as follows: Step 41: The formula for the clutter steering vector including the Doppler center error is expressed as: Construct the cost function J, the formula is expressed as: Among them, U ⊥ is the matrix composed of the basis of the noise subspace, (U ⊥ ) H is the conjugate transpose of the matrix composed of the noise subspace basis, df a is the differential of the azimuth frequency; Will Substitute the cost function J and choose the symbol that makes J smaller as Symbols; Step 42: Construct the third phase compensation function h c , the public expression is: Among them, f r is the distance frequency, f c is the frequency of the speed of light, and c is the speed of light.

9. The GEO satellite-machine bistatic synchronization method based on direct wave and clutter subspace according to claim 8, characterized in that: The third phase compensation function is multiplied by the echo signal after the second phase error compensation to complete the third phase compensation. The specific method is: The echo signal after the second phase error compensation is transformed into the range frequency domain and compared with h c Multiply them and then transform back to the two-dimensional time domain to obtain the echo signal after the third phase compensation.

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