A multi-station synchronization method for distributed synthetic aperture radar

Abstract

The present invention relates to a distributed synthetic aperture radar multi-station synchronization method, which belongs to the field of distributed radar imaging technology. First, direct wave signals are transmitted between each station to establish a synchronization link, the synchronization error is extracted from the direct wave signal, and the echo is compensated to achieve dual-base distributed synchronization. Then, the residual time-invariant time and phase errors of the dual-base synchronization are eliminated through isolated strong point calibration, thereby achieving multi-base distributed time and phase synchronization. The proposed method aims to provide a distributed synthetic aperture radar time and phase synchronization solution suitable for various platforms and application scenarios. It is expected to be applicable to the field of distributed radar imaging. The method can solve the residual π ambiguity problem in multi-base distributed SAR phase synchronization and the problem caused by the unconsidered system link delay in dual-base distributed SAR synchronization.

Description

Technical Field

[0001] The present invention relates to a distributed synthetic aperture radar (SAR) multi-station synchronization method, belonging to the technical field of distributed radar imaging. Background Art

[0002] Distributed SAR is a system composed of multiple identical sub-radars, each housed on a separate mobile platform and using independent crystal oscillators to provide local clocks and frequencies. Compared to monostatic radars, bistatic and multistatic distributed SAR configurations enable multi-angle observation, giving the system anti-interference and anti-stealth capabilities. They also enable long-baseline and multi-baseline observation, enabling high-resolution, time-sensitive three-dimensional imaging. Distributed SAR can achieve all-day, all-weather imaging of areas of interest or targets, and is widely used in battlefield reconnaissance, terrain telemetry, and other fields. Consequently, distributed radar imaging technology has become a growing research hotspot.

[0003] However, because each distributed SAR station uses an independent crystal oscillator to generate its clock signal and its hardware links are not completely consistent, time and phase errors, as well as system link delay errors, exist between substations. Taking distributed SAR 3D imaging as an example, initial clock differences and system link errors lead to time-invariant time errors between substations; accumulated clock errors lead to time-varying time errors; system link delay errors and initial phase differences lead to time-invariant phase errors; and accumulated frequency source errors and phase noise lead to time-invariant phase errors. These non-ideal factors can cause 3D SAR image offset and defocus, thus affecting the imaging results.

[0004] To address the time and phase synchronization issues in bistatic distributed radar systems, existing technologies utilize a synchronization link to alternately transmit and receive direct wave signals between two stations. This direct wave signal extracts synchronization information, which is then used to adjust the sampling gate and compensate for echo phase errors to achieve time and phase synchronization. However, this method leaves residual π phase ambiguity during phase synchronization and fails to account for the impact of link errors. While this does not affect bistatic distributed SAR imaging, for multistatic distributed SAR, the residual constant time delay and phase error between each bistatic SAR group can cause the echoes from each station to lose coherence. Summary of the Invention

[0005] The technical problem solved by the present invention is to overcome the shortcomings of the existing technology and propose a distributed synthetic aperture radar multi-station synchronization method. This method can synchronize the time and phase of multi-base distributed SAR. It is a distributed time and phase synchronization method based on alternating direct wave propagation and strong point calibration. In order to achieve time and phase synchronization between stations, the direct wave signal is first propagated between each station to establish a synchronization link, the synchronization error is extracted from the direct wave signal, and the echo is compensated to achieve bistatic distributed synchronization. Then, the residual time-invariant time and phase errors of bistatic synchronization are eliminated through isolated strong point calibration, thereby achieving multistatic distributed time and phase synchronization. The proposed method aims to provide a distributed synthetic aperture radar time and phase synchronization solution suitable for various platforms and application scenarios. It is expected to be applicable to the field of distributed radar imaging. This method can solve the residual π ambiguity problem in multistatic distributed SAR phase synchronization and the problem caused by the unaccounted system link delay in bistatic distributed SAR synchronization.

[0006] The method of the present invention is achieved through the following technical solutions:

[0007] A distributed synthetic aperture radar multi-station synchronization method, wherein the distributed synthetic aperture radar is a system composed of M identical sub-radars, wherein the sub-radars in the system are station 1, station 2, ..., station i, ..., station j, ..., station M, and station i and station j are defined as a pair of stations DS ij , for example, station 1 and station 2 form a double station DS 12 , Station 3 and Station 4 form a pair of station DS 34 , the method comprises the following steps:

[0008] Step 1: Station i and station j transmit and receive synchronization signals to each other, and demodulate the received signals respectively;

[0009] Among them, the signal transmitted by station i passes through τ ij The signal arrives at station j with a time delay and is demodulated by station j. The demodulated signal model is:

[0010]

[0011] Among them, w(t j +Δt ij -d i，t -τ ij -d j，r -t0) is the envelope of the transmission signal of station i at time t, t j is the apparent time of station j, t i is the apparent time at station i, Δt ij =t i- t jis the apparent time difference between station i and station j, t0 is the starting time of the signal transmission, then the apparent time of station j at time t0 is t i -Δt ij ;d i，t is the transmission link delay of station i, d j，r is the receiving link delay of station j; f0 is the nominal carrier frequency of the system, Δf ij =Δf i0 -Δf j0 is the time-invariant frequency offset between station i and station j, Δf i0 is the difference between the actual frequency of station i and the nominal carrier frequency, Δf j0 is the difference between the actual frequency and the nominal carrier frequency at station j, This is the initial phase of station i, is the initial phase of station j, n i (t j ) is the phase noise of station i, n j (t j ) is the phase noise of station j;

[0012] The signal transmitted by station j passes through τ ji The signal arrives at station i with a time delay and is demodulated by station i. The demodulated signal model is:

[0013]

[0014] Among them, w(t i -Δt ij -d j，t -τ ji -d i，r -t0) is the envelope of the transmission signal of station j at time t, d j，t is the transmission link delay of station j, d i，r is the receiving link delay of station i;

[0015] Step 2: Extract the time-varying time synchronization error and the time-varying phase synchronization error of station i and station j. The specific method is:

[0016] The demodulated signal model s after step 1 Tij (t j ; t0) and s Tji (t i ; t0) perform pulse compression and extract the peak time and phase of the signal after pulse compression;

[0017] to s Tij (t j ; t0) The peak moment of the signal after pulse compression is

[0018] t P，ij =-Δtij +d i，t +d j，r +t0;

[0019] to s Tij (t j ; t0) The peak phase of the signal after pulse compression is:

[0020]

[0021] to s Tji (t i ; t0) The peak moment of the signal after pulse compression is:

[0022] t P，ji =Δt ij +d j，t +d i，r +τ ij +t0

[0023] to s Tji (t i ; t0) The peak phase of the signal after pulse compression is:

[0024]

[0025] Then the estimated value of the time-varying time synchronization error is:

[0026]

[0027] The estimated value of the time-varying phase synchronization error is:

[0028]

[0029] Step 3: Use the time-varying time synchronization error and the time-varying phase synchronization error obtained in step 2 to compensate the demodulated signal model obtained in step 1.

[0030] When the demodulated signal model is compensated for the time-varying time synchronization error, the compensation is performed by shifting the distance unit or multiplying the linear phase term of the distance-frequency in the distance frequency domain. The compensated signal envelope is:

[0031]

[0032] Among them, ρ t It is the fast time resolution after the distance pulse pressure;

[0033] When compensating for the time-varying phase synchronization error of the demodulated signal model, the backscattered echo is multiplied by a conjugate phase term. The compensated phase is:

[0034]

[0035] Among them, k ij is an integer representing the fuzzy number of π;

[0036] Step 4: Eliminate the double-station DS in the signal model after compensation in step 3 ij The time-invariant time synchronization error and the time-invariant phase synchronization error between stations 1 and 2 are eliminated. 12 Dual-station DS formed by stations 3 and 4 34 The time-invariant time and phase error between

[0037] Then the method to determine the estimated value of the time-invariant time synchronization error is:

[0038] (1) Estimation is performed by minimizing the entropy of the two-dimensional image:

[0039]

[0040] in, is the estimate of the residual time error, is the true value of the residual time error, E ij It is the entropy of the two-dimensional image. The optimization process can be achieved through a variety of optimization algorithms, such as traversal search. Through minimum entropy estimation, a relatively accurate fast time error can be obtained, but more accurate multi-base time synchronization based on isolated strong points is also required;

[0041] (2) Select any strong point on the two-dimensional image with the minimum entropy, and then image the selected strong point using the three-dimensional BP imaging algorithm to obtain the coordinates of the strong point in the three-dimensional grid. The residual time-invariant time synchronization error The estimation is based on the following formula:

[0042]

[0043] Where, the subscript ref indicates the selected reference strong point, t P (x ref ,y ref , z ref ) is the peak value measured by the fast time of the reference strong point, t M (x ref ,y ref , z ref ) is the fast time delay calculated from the radar position measurements and the strong point positions;

[0044] (3) The time-invariant time synchronization error is By compensating the time-invariant time synchronization error in the signal model, time synchronization of multiple stations of a distributed synthetic aperture radar can be achieved.

[0045] The estimated value of the time-invariant phase synchronization error is:

[0046]

[0047] in, To use the current phase A three-dimensional back-projection image obtained by compensating the phase in the real three-dimensional back-projection image;

[0048] The real 3D back-projection image is:

[0049]

[0050] is the three-dimensional back-projection image of the echo transmitted by station i and received by station j in the presence of a time-invariant phase error, z ij (n) is the three-dimensional back-projected image of the echo transmitted by station i and received by station j when there is no time-invariant phase error; n represents the pixel number in the three-dimensional back-projected image, is the true value of the time-invariant phase error;

[0051] The estimation process of the time-invariant phase synchronization error is an N-dimensional optimization problem, where N is the vector The length of the optimization problem can be solved by using the coordinate descent method to transform the initial problem into N one-dimensional optimization problems. Each one-dimensional optimization can be achieved by algorithms such as traversal search.

[0052] By compensating the estimated value of this time-invariant phase synchronization error in the signal model, phase synchronization of multiple stations in a distributed synthetic aperture radar can be achieved to realize accurate three-dimensional imaging.

[0053] Beneficial effects

[0054] (1) The method of the present invention divides multiple stations into multiple groups of two-station synchronization, first performing time-varying error compensation for the two stations, and then performing time-invariant error compensation between the multiple groups of two stations. Compared with existing distributed system time and phase synchronization methods, this method can effectively improve synchronization accuracy. This method is used in the field of synthetic aperture radar imaging and can significantly improve image focusing.

[0055] (2) The method of the present invention transmits the signal transmitted by station i through τ ij The signal arrives at station j with a time delay and is demodulated by station j, which outputs the demodulated signal model and describes the structure of the signal model in detail, making the output of the signal model more specific.

[0056] (3) The method of the present invention transmits the signal transmitted by station j through τ jiThe signal arrives at station i with a time delay and is demodulated by station i, which outputs the demodulated signal model and describes the structure of the signal model in detail, making the output of the signal model more specific.

[0057] (4) The method of the present invention obtains the time-varying time synchronization error and the time-varying phase synchronization error of station i and station j based on the extracted peak time and phase, and describes the form of the error in detail;

[0058] (5) The method of the present invention is based on the presence of the dual-station DS in the compensated signal model. ij The time-invariant time synchronization error and the time-invariant phase synchronization error are calculated and the estimated value of the time-invariant time synchronization error is obtained. The specific calculation method of the estimated value and the formal expression of the result are explained.

[0059] (6) Compared with the existing distributed system time and phase synchronization methods, the method of the present invention not only compensates for time-varying time and phase errors, but also takes into account the Pi ambiguity problem during phase synchronization and the time-invariant time and phase errors caused by system link errors, which is beneficial to improving the consistency of each station in the distributed system. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 The diagram below shows the bidirectional signal transmission in a distributed system (taking a four-station system as an example).

[0061] Figure 2 Schematic diagram of the method flow of the present invention;

[0062] Figure 3 The UAV platform and lattice geometry of Example 1;

[0063] Figure 4 Comparison between the estimated value of the time-invariant phase error and the true value in Example 1;

[0064] Figure 5 This is the three-dimensional imaging result of the traditional dual-warning synchronization method for the dot matrix target in Example 1;

[0065] Figure 6 This is the three-dimensional imaging result of the method of the present invention for the dot matrix target in Example 1. DETAILED DESCRIPTION

[0066] The following describes in detail the implementation of the method of the present invention in conjunction with the accompanying drawings and examples.

[0067] Step 1: Stations transmit and receive synchronization signals to each other

[0068] Assume that stations i and j transmit and receive synchronization signals to each other, such as Figure 1 As shown. Among them, the signal transmitted by station i passes through τ ijThe signal arrives at station j with a time delay and is demodulated by station j. The demodulated signal model is

[0069]

[0070] Where w(·) is the envelope of the transmitted signal at time t, t j is the apparent time of station j, t i is the apparent time of station i, Δt ij =t i -t j is the apparent time difference between station i and station j, t0 is the starting time of the signal transmission of station i, then the apparent time t of station j at the same time is i -Δt ij ;d i，t with d j，r are the transmission link delay of station i and the receiving link delay of station j respectively; f0 is the nominal carrier frequency of all substations, Δf ij =Δf i0 -Δf j0 is the time-invariant frequency offset between station i and station j; and are the initial phases of station i and station j respectively; n i (t j ) and n j (t j ) are the phase noises of station i and station j respectively.

[0071] Similarly, the signal transmitted by station j, received by station i, and demodulated by station i is:

[0072]

[0073] Step 2: Time-varying time and phase synchronization error extraction

[0074] After pulse compression of the received direct wave, the peak moments of the direct wave pulse pressure at station i transmitting and station j receiving, and at station j transmitting and station i receiving can be extracted respectively: t P，ij =-Δt ij +d i，t +d j，r +t0' t P，ji =Δt ij +d j，t +d i，r +τ ij +t0; the pulse pressure peak phase is:

[0075]

[0076]

[0077] Therefore, the time-varying time synchronization error can be estimated as:

[0078]

[0079] The time-varying phase synchronization error can be estimated as:

[0080]

[0081] Step 3: Multiple groups of dual stations perform time-varying time and phase error compensation

[0082] The time-varying time error between the two stations can be compensated by shifting the distance unit or multiplying the linear phase term of the distance-frequency in the distance-frequency domain. After the two stations are synchronized, the signal envelope transmitted by station i and received by station j is:

[0083]

[0084] Among them, ρ t It is the fastest time resolution after the range pulse compression. It can be seen that there is still a time-invariant time error in the signal caused by the internal delay error of the system, which needs further compensation.

[0085] The time-varying phase error of the two stations can be compensated by multiplying a conjugate phase term at the backscatter echo. However, since the phase error term calculated by formula (6) has the step of dividing the phase by 2, the estimated phase error has π ambiguity. The direct wave peak phase after compensation is:

[0086]

[0087] Among them, k ij is an integer representing the π ambiguity number. It can be seen that after the time-varying phase error is compensated, the time-invariant phase error caused by the system internal delay error and π ambiguity still exists.

[0088] Step 4: Use isolated strong point calibration to eliminate the time-invariant time and phase errors between multiple pairs of stations

[0089] The residual bistatic time-invariant error can be estimated by minimizing the entropy of the two-dimensional image:

[0090]

[0091] in, and are the estimated value and true value of the residual time error respectively. E ij The optimization process can be achieved through various optimization algorithms, such as traversal search. Minimum entropy estimation can obtain relatively accurate fast time errors, but more accurate multi-base time synchronization based on isolated strong points is still required.

[0092] First, a strong point is selected on the two-dimensional image, and then the selected strong point is imaged using the three-dimensional BP imaging algorithm to obtain the coordinates of the strong point in the three-dimensional grid. It can be estimated based on the following formula:

[0093]

[0094] Where, the subscript ref indicates the selected reference strong point, t P (x ref ,y ref , z ref ) is the peak value measured by the fast time of the reference strong point, t M (x ref ,y ref , z ref ) is the fast time delay calculated from the radar position measurement and the strong point position.

[0095] According to (9) and (10), the total time-invariant time error is By compensating for this time-invariant time error, the multistatic echo envelopes can be aligned.

[0096] After multi-base time synchronization, it is necessary to estimate and eliminate the residual time-invariant phase error. The basic strategy is to add a constant phase to the echo at each phase center to maximize the 3D image intensity of isolated strong points. The 3D backprojection image with time-invariant phase error before multi-base phase synchronization is:

[0097]

[0098] in, With z ij (n) are the three-dimensional back-projection images of the echo transmitted by station i and received by station j when there is and does not exist a time-invariant phase error, respectively. n represents the pixel number in the three-dimensional back-projection image. is the true value of the time-invariant phase error.

[0099] If the unknown time-invariant phase error in the echo can be completely eliminated, the 3D image of the isolated strong point in the scene can obtain the maximum energy. Therefore, the multi-base time-invariant phase error estimate can be expressed as:

[0100]

[0101] in:

[0102]

[0103] in, and They are and The vectors composed of represent the true value, estimated value and current compensation value of the multi-base phase error respectively.

[0104] The above estimation process is an N-dimensional optimization problem, where N is the vector The optimization problem can be solved by transforming the initial problem into N one-dimensional optimization problems using coordinate descent. Each one-dimensional optimization can be achieved using algorithms such as traversal search. The estimated time-invariant phase error is then compensated in the echo to achieve accurate three-dimensional imaging.

[0105] So far, a distributed time and phase synchronization method based on alternating direct wave and strong point calibration has been realized. The processing block diagram is as follows: Figure 2 shown.

[0106] Example 1

[0107] The effectiveness of the proposed method is verified by computer simulation using a four-station distributed P-band radar mounted on a UAV platform. A total of 10 virtual flight paths enable 3D imaging, eliminating the overlap seen in single-station 2D imaging. Bidirectional direct wave signals are simulated, accounting for link delay errors. Time and phase synchronization is performed on the simulated echoes. A 3x3 dot matrix is used for imaging. The geometric relationship between the UAV platform and the dot matrix target is shown in Figure 3. The dot matrix imaging effect is used to compare the synchronization between the two.

[0108] In this simulation, the four stations transmit and receive linear frequency modulation pulse signals to each other and transmit and receive linear frequency modulation pulse signals to the scene at the same time. The time-varying frequency error is simulated based on the crystal oscillator phase noise model to obtain the time-varying time error and phase error, and the time-varying frequency deviation Δf is added. ij , the apparent time deviation of each station Δt ij , the initial phase difference of each station and the system link delay d i，t d j，t (Assume that the transmission link delay is equal to the reception link delay.) The main parameters in the simulation are shown in Table 1.

[0109] Table 1. Time and phase synchronization simulation parameters of the UAV platform P-band four-station distributed radar in Example 1

[0110] Parameter / Unit value Carrier frequency / MHz 425 Pulse width / us 2.5 Bandwidth / MHz 60 Sampling rate / MHz 160 Synchronous rate / Hz 625 Direct wave signal-to-noise ratio / dB 17

[0111] By performing time and phase synchronization processing on the simulated echo, the time-invariant phase error estimation values of multiple phase centers can be obtained. The comparison between the true value and the estimated value is as follows: Figure 4This method estimates it, and the estimated result is close to the true value with an error of about 0.02rad(1σ). Figure 5 The three-dimensional imaging results of the traditional dual-station synchronization method for the array target are shown in Figure 2. Figure 6 The three-dimensional imaging results of the method of the present invention are shown in FIG. 3D images of a point array target. After comparison, the method takes into account the time-invariant time and phase errors between multiple groups of dual stations, so the three-dimensional imaging results are well focused, proving that the proposed method has better synchronization effect than the comparative method.

Claims

1. A distributed synthetic aperture radar multi-station synchronization method, characterized by: The distributed synthetic aperture radar is a system composed of M identical sub-radars, wherein the sub-radars in the system are station 1, station 2, ..., station i, ..., station j, ..., station M, and station i and station j are defined as a pair of stations DS ij , the method comprises the following steps: Step 1: Station i and station j transmit and receive synchronization signals to each other, and demodulate the received signals to obtain the demodulated signal model; suppose the signal transmitted by station i passes through τ ij The signal arrives at station j with a time delay and is demodulated by station j. The demodulated signal model is s Tij (t j ; t0); Assume that the signal transmitted by station j passes through τ ji The signal arrives at station i with a time delay and is demodulated by station i. The demodulated signal model is s Tji (t i ; t0); Step 2: Pulse compress the signal model demodulated in step 1, extract the peak moment and phase of the pulse compressed signal, and then obtain the time-varying time synchronization error and time-varying phase synchronization error of station i and station j based on the extracted peak moment and phase; Estimation of time-varying time synchronization error and the estimated value of the time-varying phase synchronization error for: Among them, t P,ji and Represents the signal model s after demodulation in step 1 Tji (t i ; t0) the peak time and peak phase of the signal after pulse compression, t P,ij and Represents the signal model s after demodulation in step 1 Tij (t j ; t0) the peak time and peak phase of the signal after pulse compression; Step 3: Using the time-varying time synchronization error and the time-varying phase synchronization error obtained in step 2, the demodulated signal model obtained in step 1 is time compensated and phase compensated; Step 4: Eliminate the time-invariant time synchronization error and the time-invariant phase synchronization error between the two stations in the signal model after compensation in Step 3, and complete the multi-station synchronization of the distributed synthetic aperture radar; In step 4, the method for determining the time-invariant time synchronization error estimate and the time-varying phase synchronization error estimate is: (1) Estimation is performed by minimizing the entropy of the two-dimensional image: in, is the estimated value of the residual time error, is the true value of the residual time error, E ij is the 2D image entropy; (2) Select any strong point on the two-dimensional image with the minimum entropy, and then image the selected strong point using the three-dimensional BP imaging algorithm to obtain the coordinates of the strong point in the three-dimensional grid. The residual time-invariant time synchronization error The estimation is based on the following formula: Where, the subscript ref indicates the selected reference strong point, t P (x ref ,y ref ,z ref ) is the peak value measured by the fast time of the reference strong point, t M (x ref ,y ref ,z ref ) is the fast time delay calculated from the radar position measurements and the strong point positions; (3) The time-invariant time synchronization error is By compensating the time-invariant time synchronization error in the signal model, time synchronization of multiple stations of a distributed synthetic aperture radar can be achieved. The estimated value of the time-invariant phase synchronization error is: in, To use the current phase A three-dimensional back-projection image obtained by compensating the phase in the real three-dimensional back-projection image; The real 3D back-projection image is: is the three-dimensional back-projection image of the echo transmitted by station i and received by station j in the presence of a time-invariant phase error, z ij (n) is the three-dimensional back-projected image of the echo transmitted by station i and received by station j when there is no time-invariant phase error; n represents the pixel number in the three-dimensional back-projected image, is the true value of the time-invariant phase error.

2. The distributed synthetic aperture radar multi-station synchronization method according to claim 1, characterized in that: In the step 1, the signal transmitted by station i passes through τ ij The signal arrives at station j with a time delay and is demodulated by station j. The demodulated signal model is: Among them, w(t j +Δt ij -d i,t -τ ij -d j,r -t0) is the envelope of the transmission signal of station i at time t, t j is the apparent time of station j, t i is the apparent time at station i, Δt ij =t i -t j is the apparent time difference between station i and station j, t0 is the starting time of the signal transmission, then the apparent time of station j at time t0 is t i -Δt ij ;d i,t is the transmission link delay of station i, d j,r is the receiving link delay of station j; f0 is the nominal carrier frequency of the system, Δf ij =Δf i0 -Δf j0 is the time-invariant frequency offset between station i and station j, Δf i0 is the difference between the actual frequency of station i and the nominal carrier frequency, Δf j0 is the difference between the actual frequency and the nominal carrier frequency at station j, This is the initial phase of station i, is the initial phase of station j, n i (t j ) is the phase noise of station i, n j (t j ) is the phase noise of station j.

3. The distributed synthetic aperture radar multi-station synchronization method according to claim 2, characterized in that: In the step 1, the signal transmitted by station j passes through τ ji The signal arrives at station i with a time delay and is demodulated by station i. The demodulated signal model is: Among them, w(t i -Δt ij -d j,t -τ ji -d i,r -t0) is the envelope of the transmission signal of station j at time t, d j,t is the transmission link delay of station j, d i,r is the receiving link delay of station i.

4. A distributed synthetic aperture radar multi-station synchronization method according to any one of claims 1 to 3, characterized in that: In step 2, the specific method for obtaining the time-varying time synchronization error and the time-varying phase synchronization error of station i and station j based on the extracted peak time and phase is: The demodulated signal model s after step 1 Tij (t j ; t0) and s Tji (t i ; t0) perform pulse compression and extract the peak time and phase of the signal after pulse compression; to s Tij (t j ; t0) The peak moment of the signal after pulse compression is t P,ij =-Δt ij +d i,t +d j,r +t0; to s Tij (t j ; t0) The peak phase of the signal after pulse compression is: to s Tji (t i ; t0) The peak moment of the signal after pulse compression is: t P,ji =Δt ij +d j,t +d i,r +τ ij +t0 to s Tji (t i ; t0) The peak phase of the signal after pulse compression is:

5. The distributed synthetic aperture radar multi-station synchronization method according to claim 4, characterized in that: In the step 3, the method for compensating the demodulated signal model obtained in step 1 using the time-varying time synchronization error and the time-varying phase synchronization error obtained in step 2 is: When the demodulated signal model is compensated for the time-varying time synchronization error, the compensation is performed by shifting the distance unit or multiplying the linear phase term of the distance-frequency in the distance frequency domain. The compensated signal envelope is: Among them, ρ t It is the fast time resolution after the distance pulse pressure.

6. The distributed synthetic aperture radar multi-station synchronization method according to claim 5, characterized in that: When compensating for the time-varying phase synchronization error of the demodulated signal model, the backscattered echo is multiplied by a conjugate phase term. The compensated phase is: Among them, k ij is an integer representing the fuzzy number of π.

Images