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

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

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CN114609629A
CN114609629A CN202210093131.3A CN202210093131A CN114609629A CN 114609629 A CN114609629 A CN 114609629A CN 202210093131 A CN202210093131 A CN 202210093131A CN 114609629 A CN114609629 A CN 114609629A
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distance
phase
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崔畅
董锡超
胡程
陈志扬
张文滔
李元昊
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Beijing Institute of Technology BIT
Chongqing Innovation Center of Beijing University of Technology
Advanced Technology Research Institute of Beijing Institute of Technology
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Chongqing Innovation Center of Beijing University of Technology
Advanced Technology Research Institute of Beijing Institute of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/904—SAR modes
    • G01S13/9058—Bistatic or multistatic SAR
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section

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Abstract

The invention discloses a GEO satellite-machine bistatic synchronization method based on direct waves and clutter subspaces, which is characterized in that on the basis of direct wave synchronization, in order to realize accurate separation of a direct wave slant distance phase and a synchronization error phase, a cubic phase function is used for extracting a high-order term coefficient of the direct wave slant distance, then a static clutter subspace extracted from a scene is used as an auxiliary calibration source, a Doppler frequency shift error generated by the slant distance phase is estimated from the space, and accurate separation of the direct wave slant distance phase and the synchronization error phase is realized, so that speed measurement and positioning accuracy of a moving target are improved. The method of the invention does not need to obtain high-precision orbit parameters in real time, and reduces the synchronization difficulty.

Description

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 radars, in particular to a GEO satellite-machine bistatic synchronization method based on direct waves and clutter subspaces.
Background
Geosynchronous orbit (GEO) satellite-machine bistatic synthetic aperture radar (GEO SA-BSAR) is a radar system which takes a geosynchronous orbit synthetic aperture radar (GEO SAR) as a radiation source and receives signals by an airborne multi-channel system. The system has good concealment and anti-interference performance, is flexible in configuration, and is an effective means for detecting and monitoring the moving object.
The GEO SA-BSAR system has to face the problem of reduced imaging quality and target detection performance caused by synchronization errors due to the separate arrangement of the transmitting and receiving terminals and the difference between the frequency sources of the transmitting terminal and the receiving terminal. In order to realize synchronization, the airplane receives the GEO SAR direct wave signal and extracts time and phase synchronization errors from the GEO SAR direct wave signal, and the direct wave slant distance phase and the phase synchronization errors need to be accurately separated in the extraction process. The existing synchronization method needs to utilize precise orbit parameters of a satellite to realize the process. The synthetic aperture radar satellite of low orbit can utilize the navigation star to obtain the high-precision orbit position in real time, and the algorithm can better compensate the synchronous error. However, the GEO SAR orbit has a height of about 36000km and is located above the navigation satellites, and it is difficult to obtain high-precision orbit parameters in real time. When the included angle of the GEO and the airplane has an error of 1 degree, the maximum residual Doppler frequency shift error after the algorithm is applied is 6.5Hz, and the influence on the imaging resolution is small. However, for moving target detection, the error may cause a serious target radial velocity estimation bias and affect the positioning performance of the target.
Therefore, a synchronization method is needed to overcome the problem that it is difficult to obtain high-precision orbit parameters in real time, and to implement accurate separation of the direct wave slant distance phase and the synchronization error phase for moving target detection, so as to compensate the synchronization error and improve the positioning precision.
Disclosure of Invention
In view of this, the invention provides a GEO satellite-machine bistatic synchronization method based on direct arrival waves and clutter subspaces, which can realize accurate separation of the direct arrival wave slant distance phase and the synchronization error phase, thereby improving the speed measurement and positioning accuracy of a moving target.
In order to achieve the purpose, the technical scheme of the invention is as follows:
the GEO satellite-machine bistatic synchronization method based on the direct wave and the clutter subspace aims at the synchronous error compensation of the GEO satellite-machine bistatic SAR signal, and comprises the following specific steps:
step 1, extracting direct wave signals and echo signals of a scene of the geosynchronous orbit synthetic aperture radar, and performing distance compression on the direct wave signals and the echo signals.
Performing range migration line estimation on the range-compressed direct wave signal to obtain range migration Rrm(ta) (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 waved(ta) Wherein t isaIs a slow time.
Migration by distance Rrm(ta) Constructing a first reference function, and performing distance alignment on the echo signals after the distance compression; using peak signals s of direct waved(ta) Constructing a first phase compensation function; and multiplying the first phase compensation function by the echo signal after the distance compression to obtain the echo signal after the first phase error compensation.
Step 2, aligning the peak signal s of the direct waved(ta) 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, and obtaining a direct wave peak signal sd(ta) 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; using second order term coefficient, third order term coefficient, fourth order term coefficient and known GEO starCalculating the direct wave slope distance, and constructing a second phase compensation function by using the direct wave slope distance; and multiplying 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.
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; and calculating the Doppler center error according to the base of the clutter subspace, the ideal clutter guide vector, the speed of the airborne platform of the target, the channel interval of the echo signal and the channel number.
Step 4, calculating clutter guide 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.
Further, with range migration Rrm(ta) Constructing a first reference function, and performing distance alignment on the echo signals after distance compression, wherein the specific method comprises the following steps:
first reference function he(fr,ta) The formula of (1) is:
Figure BDA0003489981600000031
wherein f isrIs distance frequency, c is speed of light, taIs the slow time, j is the imaginary number.
And performing Fourier transform on the echo signals after the distance compression, multiplying by a first reference function and performing inverse Fourier transform to obtain the echo signals after the distance alignment.
Further, using the peak signal s of the direct waved(ta) A first phase compensation function is constructed that,the specific method comprises the following steps:
using sd(ta) Constructing a first phase compensation function hf(ta) The formula is as follows:
Figure BDA0003489981600000032
wherein,
Figure BDA0003489981600000033
represents a pair sd(ta) Taking conjugate, | sd(ta) I denotes the pair sd(ta) And (6) taking a mold.
Further, the first phase compensation function is multiplied by the echo signal after the distance compression to obtain the echo signal after the first phase error compensation, and the specific method is as follows: the echo signal is Fourier transformed and converted into a distance frequency domain, and then h is obtainedf(ta) 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.
Further, the peak signal s of the direct waved(ta) 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, and obtaining a direct wave peak signal sd(ta) 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, the direct wave peak value signal sd(ta) Discretizing to obtain discretized direct wave peak signal sd(n) to sd(n) carrying out phase difference processing to obtain a phase reduced function; and 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
Figure BDA0003489981600000041
Slicing n for the second time2Carrying out peak value detection to obtain a second peak value position
Figure BDA0003489981600000042
Where n is the discrete time and Ω is the peak position.
The formula for calculating the third order coefficient and the fourth order coefficient is
Figure BDA0003489981600000043
Wherein, TrThe pulse repetition frequency of the preset discretization direct wave peak value signal.
Discrete direct wave peak signal sd(n) and a reference function sref(n) multiplying and Fourier transforming into frequency domain to obtain transformed signal sPD_de(f) According to sPD_de(f) Calculating the peak value position to obtain the second order coefficient of the direct wave slope distance
Figure BDA0003489981600000044
The formula is as follows:
Figure BDA0003489981600000045
wherein, | SPD_de(f) I is the peak position of the transformed signal and f is the frequency of the radar.
Reference function srefThe formula of (n) is expressed as:
Figure BDA0003489981600000046
where λ is the wavelength of the radar, and p is a delay parameter preset in the phase difference division process.
Step 23, calculating a constant term of the direct wave slant range signal by using the known GEO ephemeris
Figure BDA0003489981600000051
And coefficient of first order term
Figure BDA0003489981600000052
Construction of direct wave slant distance
Figure BDA0003489981600000053
The formula is as follows:
Figure BDA0003489981600000054
using the slant distance of the direct wave
Figure BDA0003489981600000055
Constructing a second phase compensation function hcom(fr,ta) The formula is expressed as:
Figure BDA0003489981600000056
wherein f isrIs the distance frequency, fcIs the speed of light frequency, c is the speed of light, taIs the slow time, j is the 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:
the echo signal after the first phase error compensation is converted into a distance frequency domain and is hcom(fr,ta) Multiplying, and converting back to a two-dimensional time domain to obtain an echo signal after the second phase compensation.
Further, the Doppler center error is calculated according to the characteristic vector, the ideal clutter guide vector, the speed of the airborne platform of the target, the channel interval and the channel number of the echo signal, and the specific method comprises the following steps:
center error of Doppler
Figure BDA0003489981600000057
Is expressed as:
Figure BDA0003489981600000058
wherein v isRThe velocity of the airborne platform as the target, d the channel interval of the echo signal, M the number of channels of the echo signal, pcIs an ideal clutter guide vector, u1Is the base of the clutter subspace.
Wherein the ideal clutter guide vector pcIs expressed as:
Figure BDA0003489981600000059
wherein u isPTUnit vector, v, being the slant range of the target to the satelliteTIs the velocity vector of the satellite or satellites,
Figure BDA00034899816000000510
is the transposed vector of the velocity vector, faIs the azimuth frequency.
Further, the Doppler center error is used as an initial value, and a clutter guide vector containing the Doppler center error is calculated; 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:
Figure BDA0003489981600000061
constructing a cost function J, wherein the formula is expressed as:
Figure BDA0003489981600000062
wherein, U⊥A matrix composed of the bases of the noise subspaces, (U)⊥)HConjugate transpose of matrix composed for noise subspace bases, dfaIs the derivative of the azimuth frequency.
Will be provided with
Figure BDA0003489981600000063
Substituting the cost function J and selecting a symbol that makes J smaller as
Figure BDA0003489981600000064
The symbol of (c).
Step 42, constructing a third phase compensation function hcThe notations are expressed as:
Figure BDA0003489981600000065
further, a 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 converted into a distance frequency domain and is hcMultiplying, and converting back to a two-dimensional time domain to obtain an echo signal after third time phase compensation.
Has the advantages that:
1. the invention provides a synchronization method suitable for detecting a moving target of a geostationary Synthetic Aperture Radar (SAR), which is based on direct wave synchronization and aims to realize accurate separation of a direct wave slant distance phase and a synchronous error phase.
2. The method adopts the existing GEO ephemeris data to calculate the slope distance of the direct wave, carries out the phase compensation of the direct wave, does not need to acquire high-precision orbit parameters in real time, and reduces the synchronization difficulty.
Drawings
FIG. 1 is a flow chart of a synchronization method suitable for GEO SA-BSAR moving target detection.
Fig. 2 is a diagram of the imaging result of the moving object after compensation by the proposed method.
Fig. 3 is a graph of output signal-to-noise ratio.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
Synthetic aperture radars are arranged on both the airplane and the GEO, the receiving end of the synthetic aperture radar is arranged on the airplane, and the transmitting end of the synthetic aperture radar is arranged on the GEO. The frequency sources of the transmitting end and the receiving end are different. The transmitting end of the synthetic aperture radar of the GEO transmits signals, direct wave signals are directly received by the airplane, and echo signals are scattered by the scene and received by the airplane. The echo signals have synchronization errors and need to be compensated.
As shown in fig. 1, aiming at the problem of synchronous error compensation of GEO satellite-base SAR signals, the invention provides a GEO satellite-base synchronization method based on direct waves and clutter subspaces, which comprises the following specific steps:
step 1, extracting direct wave signals and echo signals of a scene of the geosynchronous orbit synthetic aperture radar, and performing distance compression on the direct wave signals and the echo signals. In the embodiment of the invention, the echo signals are multi-channel echo signals, and the number of channels is not less than 3.
Step 11, performing range migration line estimation on the range-compressed direct wave signal to obtain range migration Rrm(ta) (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 waved(ta) Wherein t isaIs a slow time.
Step 12, distance utilizationMigration Rrm(ta) Constructing a first reference function, and performing distance alignment on the echo signals after the distance compression; using peak signals s of direct waved(ta) Constructing a first phase compensation function; and multiplying the first phase compensation function by the echo signal after the distance compression to obtain the echo signal after the first phase error compensation.
First reference function he(fr,ta) The formula of (1) is as follows:
Figure BDA0003489981600000081
wherein f isrIs distance frequency, c is speed of light, taIs the slow time, j is the imaginary number.
And performing Fourier transform on the echo signals after the distance compression, multiplying by a first reference function and performing inverse Fourier transform to obtain the echo signals after the distance alignment.
Step 13, utilizing sd(ta) Constructing a first phase compensation function hf(ta) The formula is as follows:
Figure BDA0003489981600000082
wherein,
Figure BDA0003489981600000083
represents a pair sd(ta) Taking conjugate, | sd(ta) I denotes the pair sd(ta) And (6) taking a mold.
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 hf(ta) 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.
In the embodiment of the invention, as the echo signals are multi-channel echo signals, the echo signals acquired by each channel need to be processed in the same way during processing, and the result after the processing of the mth channel is recorded assm(r,ta)。
Step 2, aligning the peak signal s of the direct waved(ta) 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, and obtaining a direct wave peak signal sd(ta) 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; and multiplying 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 the echo signal synchronization of the scene.
Step 21, the direct wave peak value signal sd(ta) Discretization, denoted sd(n), where n is the number of pulses, satisfies ta＝nTr，TrIs the pulse repetition frequency. Then, for discrete form direct wave peak signal sd(n) carrying out phase difference processing to obtain a phase reduction function PD [ n; p is a radical of]Where p is a delay parameter. For the phase reduction function PD [ n; p is a radical of]And carrying out non-uniform cubic phase function processing, and marking a processing result as a NUCPF function N (N, omega), wherein omega is a slow time frequency domain after transformation.
Step 22, selecting a first time slice n in the NUCPF function1And a second time slice n2(ii) a Slicing the first time n1Carrying out peak value detection to obtain a first peak value position
Figure BDA0003489981600000091
Slicing n for the second time2Carrying out peak value detection to obtain a second peak value position
Figure BDA0003489981600000092
Where n is the discrete time and Ω is the peak position.
The formula for calculating the third order coefficient and the fourth order coefficient is as follows:
Figure BDA0003489981600000093
wherein, TrThe pulse repetition frequency of the preset discretization direct wave peak value signal is 300 Hz.
Discrete direct wave peak signal sd(n) and a reference function sref(n) multiplying and Fourier transforming into frequency domain to obtain transformed signal sPD_de(f) According to sPD_de(f) Calculating the peak value position to obtain the second order coefficient of the direct wave slope distance
Figure BDA0003489981600000094
The formula is as follows:
Figure BDA0003489981600000095
wherein, | sPD_de(f) I is the peak position of the transformed signal and f is the frequency of the radar.
Construction of a reference function sref(n) the formula is:
Figure BDA0003489981600000096
wherein λ is the wavelength of the radar, and p is a delay parameter preset in the phase difference division process, and is 4.
Step 23, calculating a constant term of the direct wave slant range signal by using the known GEO ephemeris
Figure BDA0003489981600000097
And coefficient of first order term
Figure BDA0003489981600000098
Construction of direct wave slant distance
Figure BDA0003489981600000099
The formula is as follows:
Figure BDA00034899816000000910
using the slant distance of the direct wave
Figure BDA00034899816000000911
Constructing a second phase compensation function hcom(fr,ta) The formula is expressed as:
Figure BDA00034899816000000912
wherein f isrIs the distance frequency, fcThe speed of light frequency, and c the speed of light.
The echo signal after the first phase error compensation is converted into a distance frequency domain and is hcom(fr，ta) Multiplying and converting the two-dimensional time domain to obtain the echo signal after the second phase compensation.
Step 3, obtaining the covariance matrix R of the static clutter from the observation dataQFor covariance matrix RQPerforming characteristic value decomposition to obtain a base u of a clutter subspace1Matrix U consisting of (eigenvectors corresponding to large eigenvalues) and the floor of the noise subspace⊥＝[u2,…,uM]Where M is 1,2, …, and M is the eigenvector corresponding to the small eigenvalue. And calculating the Doppler center error according to the base of the clutter subspace, the ideal clutter guide vector, the airborne platform speed of the target, the channel interval of the echo signal and the channel number.
Center error of Doppler
Figure BDA0003489981600000101
Is expressed as:
Figure BDA0003489981600000102
wherein v isRTargeted airborne platformThe stage velocity, d the channel interval of the echo signal, M the number of channels of the echo signal, pcIs an ideal clutter guide vector, u1Is the base of the clutter subspace.
Wherein the ideal clutter guide vector pcIs expressed as:
Figure BDA0003489981600000103
wherein u isPTUnit vector of target-to-satellite slant distance, vTIs the velocity vector of the satellite or satellites,
Figure BDA0003489981600000104
as a transposed vector of the velocity vector, faIs the azimuth frequency.
Step 4, calculating clutter guide 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 complete the third phase compensation.
Step 41, the formula of the clutter guiding vector containing the doppler center error is expressed as:
Figure BDA0003489981600000105
constructing a cost function J, wherein the formula is expressed as:
Figure BDA0003489981600000106
wherein, U⊥A matrix composed of the bases of the noise subspaces, (U)⊥)HConjugate transpose of matrix composed for noise subspace bases, dfaIs the derivative of the azimuth frequency.
Will be provided with
Figure BDA0003489981600000107
Substituting the cost function J and selecting a symbol that makes J smaller as
Figure BDA0003489981600000108
The symbol of (2).
Step 42, constructing a third phase compensation function hcThe notations are expressed as:
Figure BDA0003489981600000111
the echo signal after the second phase error compensation is converted into a distance frequency domain and is hcMultiplying, and then transforming back to the two-dimensional time domain to obtain the echo signal after the third time of phase compensation, as shown in fig. 2.
The invention will be further elucidated with reference to the following specific examples.
In the embodiment of the invention, the parameters of the GEO SA-BSAR system are shown in Table 1.
TABLE 1 GEO SA-BSAR moving target detection system parameter table
Figure BDA0003489981600000112
The background clutter of the GEO SA-BSAR is generated using an existing SAR image, and a multichannel echo signal in the GEO SA-BSAR geometric relationship is generated using the amplitude value of the SAR image of the ALOS PALSAR (band data of a japanese geospatial observation satellite) as a scattering coefficient. Four moving objects are set in the scene, and the object speeds are (-8, -8) m/s, (-5, -5) m/s, (5,5) m/s and (8,8) m/s respectively.
The time and frequency synchronization errors are caused by inaccuracy and instability of the frequency source, and typical frequency accuracy and frequency stability of the high-stability quartz crystal frequency source are shown in table 2, and parameters of the time and frequency synchronization errors are given according to the frequency accuracy and the frequency stability. For time synchronization error, assuming a fixed time offset of 1ns, its linearity errorRelated to frequency accuracy, set to 10-8The random error follows a Gaussian distribution with a mean value of 0, the standard deviation of which is related to the frequency stability and is set to 3X 10-11. For frequency synchronization error, the fixed frequency deviation is related to the frequency accuracy and is set to 10-8fcThe phase noise is generated from the power-law power spectrum.
TABLE 2 table of frequency source parameters and simulation middle time and frequency synchronous error parameters of high-stability quartz crystal
Figure BDA0003489981600000121
The Doppler center estimation method based on the clutter subspace is adopted to estimate and compensate the residual Doppler center error, and the sample number of the clutter covariance matrix is estimated to be 200.
Clutter suppression and beam forming are carried out on the synchronized echo signals by using an STAP method, and output signal-to-noise ratios under different motion parameters are calculated, so that four target speeds are (-8, -8) m/s, (-5, -5) m/s, (5,5) m/s and (8,8) m/s respectively. Finally, the moving object display result obtained by using the object speed is shown in fig. 2, and it can be seen that better moving object imaging performance is also obtained.
Fig. 3 is a graph of the output snr, wherein the dotted line is the output snr curve in the presence of time and frequency synchronization error, the notch position of the curve has a shift and severe broadening compared to the ideal output snr, and the clutter suppression capability is reduced. The compensated snr curve is shown as a solid curve, and it can be seen that the effect of synchronization error is eliminated.
In addition, in order to further verify that the method is carried out a series of Monte Carlo simulation experiments under different signal-to-noise ratios, the simulation times are 100 times, and the signal-to-noise ratios of the echo and direct wave signals after distance compression are respectively set to be 30dB, 20dB, 10dB, 0, -10dB and-20 dB. The doppler center estimation results are shown in table 3, and it can be seen that the residual doppler center of the proposed method is less than 0.01Hz, and has small influence on the radial velocity estimation, and at the same time, the method is verified to have good robustness.
TABLE 3 residual Doppler center frequency estimate and radial velocity deviation table generated by estimation error
Figure BDA0003489981600000131
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in 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 Rrm(ta) (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 waved(ta) Wherein t isaIs a slow time;
migration by distance Rrm(ta) Constructing a first reference function, and performing distance alignment on the echo signals after the distance compression; using peak signals s of direct waved(ta) 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 waved(ta) 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 sd(ta) 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 isrm(ta) 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 he(fr,ta) The formula of (1) is:
Figure FDA0003489981590000021
wherein f isrIs distance frequency, c is speed of light, taSlow 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 usedd(ta) The method for constructing the first phase compensation function comprises the following specific steps:
using sd(ta) Constructing a first phase compensation function hf(ta) The formula is as follows:
Figure FDA0003489981590000022
wherein,
Figure FDA0003489981590000023
represents a pair sd(ta) Taking conjugate, | sd(ta) I denotes the pair sd(ta) 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 hf(ta) 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 sd(ta) 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 sd(ta) 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 sd(ta) Discretizing to obtain discretized direct wave peak signal sd(n) for sd(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
Figure FDA0003489981590000031
Slicing n for the second time2Carrying out peak value detection to obtain a second peak value position
Figure FDA0003489981590000032
Wherein n is discrete time, and Ω is peak position;
the formula for calculating the third order coefficient and the fourth order coefficient is
Figure FDA0003489981590000033
Wherein, TrThe pulse repetition frequency of the preset discretization direct wave peak value signal is obtained;
discrete direct wave peak signal sd(n) and a reference function sref(n) multiplying and Fourier transforming into frequency domain to obtain transformed signal sPD_de(f) According to sPD_de(f) Calculating the peak value position to obtain the second order coefficient of the direct wave slope distance
Figure FDA0003489981590000034
The formula is as follows:
Figure FDA0003489981590000035
wherein, | sPD_de(f) I is the peak position of the transformation signal, and f is the frequency of the radar;
the reference function srefThe formula of (n) is expressed as:
Figure FDA0003489981590000036
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
Figure FDA0003489981590000037
And coefficient of first order term
Figure FDA0003489981590000038
Construction of direct wave slant distance
Figure FDA0003489981590000039
The formula is as follows:
Figure FDA00034899815900000310
using the slant distance of the direct wave
Figure FDA00034899815900000311
Constructing a second phase compensation function hcom(fr,ta) The formula is expressed as:
Figure FDA0003489981590000041
wherein f isrIs the distance frequency, fcIs the speed of light frequency, c is the speed of light, taIs 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 hcom(fr,ta) 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
Figure FDA0003489981590000042
Is expressed as:
Figure FDA0003489981590000043
wherein v isRTarget airborne platform velocity, d channel spacing of echo signals, M number of channels of echo signals, pcIs an ideal clutter guide vector, u1A base that is a clutter subspace;
wherein the ideal clutter guide vector pcIs expressed as:
Figure FDA0003489981590000044
wherein u isPTUnit vector of target-to-satellite slant distance, vTIs the velocity vector of the satellite or satellites,
Figure FDA0003489981590000045
as a transposed vector of the velocity vector, faIs 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:
Figure FDA0003489981590000051
constructing a cost function J, wherein the formula is expressed as:
Figure FDA0003489981590000052
wherein, U⊥A matrix composed of the bases of the noise subspaces, (U)⊥)HConjugate transpose of matrix composed for noise subspace bases, dfaIs the derivative of the azimuth frequency;
will be provided with
Figure FDA0003489981590000053
Substituting the cost function J and selecting a symbol that makes J smaller as
Figure FDA0003489981590000054
The symbol of (a);
step 42, constructing a third phase compensation function hcThe notations are expressed as:
Figure FDA0003489981590000055
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 hcMultiplying, and converting back to a two-dimensional time domain to obtain an echo signal after third time phase compensation.
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Publication number Priority date Publication date Assignee Title
CN116047411A (en) * 2023-02-06 2023-05-02 南京航空航天大学 Signal positioning method and system based on distributed unmanned aerial vehicle under synchronization error
CN116148856A (en) * 2023-04-17 2023-05-23 南京邮电大学 SAR moving target two-dimensional self-focusing imaging processing method

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116047411A (en) * 2023-02-06 2023-05-02 南京航空航天大学 Signal positioning method and system based on distributed unmanned aerial vehicle under synchronization error
CN116047411B (en) * 2023-02-06 2023-11-10 南京航空航天大学 Signal positioning method and system based on distributed unmanned aerial vehicle under synchronization error
CN116148856A (en) * 2023-04-17 2023-05-23 南京邮电大学 SAR moving target two-dimensional self-focusing imaging processing method

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