CN118131221A - Space target resolution imaging method of step frequency radar based on MS-GRFT under low signal-to-noise ratio - Google Patents
Space target resolution imaging method of step frequency radar based on MS-GRFT under low signal-to-noise ratio Download PDFInfo
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Abstract
The invention discloses a space target resolution imaging method of a step frequency radar under low signal to noise ratio based on multi-sub-band (MS) -generalized Ladong Fourier transform (GRFT). Firstly, rough GRFT of single sub-band data is used for obtaining a rough motion parameter range and rough motion compensation, fine GRFT of parallel processing is used for obtaining a parameter estimation result of each sub-band data, then CFAR and non-coherent accumulation screening part of motion parameters are used for taking sharpness as an objective function for estimating sub-band phase errors, and an analysis solution is obtained; finally, the GRFT results for the multiple subbands are error compensated, and the CFAR is again used to extract motion parameters and perform range-instantaneous doppler imaging. The invention aims to provide a high-resolution imaging algorithm which is suitable for correcting subband phase errors and space-variant errors caused by complex movement of a target under long-time observation under the condition of low signal-to-noise ratio, and can be expected to be applied to the fields of ground-based radar and space target observation.
Description
Technical Field
The invention relates to a step frequency radar space target imaging method based on MS-GRFT, and belongs to the technical field of synthetic aperture radars.
Background
The ground-based radar is an effective means for detecting and imaging the space-sky targets, improves the resolution, can acquire more target detail information, and is convenient for classification and identification. Achieving high resolution requires the ability of the radar to transmit large bandwidth signals, and if instantaneous large bandwidth signals are transmitted, a higher sampling rate matching the nyquist sampling theorem needs to be achieved, which is a great challenge for system hardware such as analog-to-digital conversion and direct digital synthesis. The frequency stepping signal has the advantages of instantaneous narrow band and synthesized broadband, and has wide application in the radar field.
However, high resolution imaging of spatial targets using step-frequency techniques of ground-based radar mainly faces three difficulties: 1. the distance between the space targets is far, so that the signal-to-noise ratio of the echo is low; 2. in the distance dimension, a large bandwidth signal is required to be obtained by using a step frequency technology, but a step frequency system has a sub-band phase error; 3. in the Doppler dimension, a large synthetic aperture is required to be obtained by long-time observation, so that errors caused by the movement of the target are more complex.
The generalized Lato Fourier transform (GRFT) algorithm is a traditional parametric coherent accumulation algorithm, a parameterized model of a target echo is accumulated, the target echo energy is focused into a parameter space through envelope phase joint compensation, a focused peak is formed, and coherent accumulation is completed.
However, the conventional imaging method is prone to failure due to the low signal-to-noise ratio and complex motion of the target under complex long-time observation which increase processing difficulty. In addition, although the step frequency technology can improve the resolution, extra inter-subband phase errors are introduced to influence the imaging quality, the pulse repetition frequency is reduced, the difficulty of error estimation and compensation is increased, and meanwhile, the inter-subband phase errors also influence the imaging quality.
Therefore, there is a need to develop a GRFT imaging method that can be used for step-frequency radar observation of complex moving objects at low signal-to-noise ratios.
Disclosure of Invention
In order to solve the problems of low signal-to-noise ratio, step frequency sub-band phase error and image degradation caused by complex motion error under long-time observation in space target resolution imaging, the method for imaging the space target resolution by the step frequency radar under the low signal-to-noise ratio based on multi-sub-band (MS) -generalized Ladong Fourier transform (GRFT) is provided.
The invention is realized by the following technical scheme:
Step one, carrying out large-range parameter estimation and coarse compensation through coarse GRFT of a single sub-band, reducing parameter search space, and then carrying out parallel GRFT of all sub-bands to obtain accurate motion parameters of a target.
Step two, using CFAR and non-coherent accumulation screening part motion parameters, summing the motion parameters, using sharpness as an evaluation standard of subband error estimation and compensation, and combining a gradient descent method for multiple iterations to realize coherent accumulation after the error compensation of a plurality of subbands, so as to improve the distance resolution;
and thirdly, performing error compensation and synthesis on GRFT results of a plurality of sub-bands, extracting motion parameters again by using CFAR, and realizing distance-instantaneous Doppler high-resolution imaging.
Advantageous effects
1. The method and the device are applicable to imaging of the step frequency radar on the space target under the low signal-to-noise ratio, can realize coherent accumulation of each sub-band data, improve the signal-to-noise ratio, simultaneously operate different sub-band data in a parallel processing mode, and save calculation time.
2. The method is applicable to azimuth high-resolution imaging of the stepping frequency radar on the space target, and the parameters of the plurality of sub-bands after coherent accumulation are extracted through the constant false alarm technology, so that instantaneous distance-Doppler information of the parameters is obtained, and azimuth high-resolution imaging is realized.
Drawings
FIG. 1 is a schematic view of the observation geometry;
FIG. 2 is a schematic diagram of a subband GRFT amplitude accumulation algorithm;
FIG. 3 is a schematic diagram of broadband synthesis;
FIG. 4 is a flow chart of MS-GRFT algorithm processing;
Fig. 5 (a) to 5 (d) are simulation experiment models and observation tracks, wherein fig. 5 (a) is a simulation point target model, fig. 5 (b) is an observation geometry, fig. 5 (c) is a satellite model simulation track, and fig. 5 (d) is a motion process of each point of the satellite model relative to the center of the satellite model;
FIG. 6 is a graph of results of GRFT peaks, where (a-d) is a two-dimensional and one-dimensional plot of results for a first sub-band, (e-h) is a two-dimensional and one-dimensional plot of results of incoherent accumulation for all sub-bands, (i-l) is a two-dimensional and one-dimensional plot of results of coherent accumulation for all sub-bands without sub-band error calibration, and (m-p) is a two-dimensional and one-dimensional plot of MS-GRFT;
FIG. 7 shows instantaneous imaging results, wherein (a-b) is the instantaneous imaging result of the first sub-band at the false alarm rates of 10 -6 and 10 -5, (e-h) is the instantaneous imaging result of the non-coherent accumulation of all sub-bands at the false alarm rates of 10 -6 and 10 -5, (i-l) is the instantaneous imaging result of the coherent accumulation of all sub-bands without sub-band error calibration at the false alarm rates of 10 -6 and 10 -5, and (m-p) is the instantaneous imaging result of the MS-GRFT at the false alarm rates of 10 -6 and 10 -5.
Detailed Description
Embodiments of the method of the present invention will now be described with reference to the accompanying drawings and examples.
The radar observation geometry is shown in figure 1 and can be divided into a translational component and a translational componentAnd rotational component/>I.e.
AndThe translational distance components of all scattering points of the target are uniform, which does not contribute to imaging, while the rotational distance components of different scattering points differ, which is the basis of ISAR imaging.
To reduce the solution difficulty, it can be re-modeled as according to the taylor series
In the middle ofAnd/>The calculated distance from the ephemeris and the residual distance of the qth scattering point, b p,k is the kth element of the parameterized vector b p, and b p,0、bp,1、bp,2 represents distance, velocity and acceleration, respectively. The order of model selection is related to the accumulation time t a, and the range-doppler algorithm generally considers a first order approximation to be possible in a short time.
The distance time domain multi-component signal after the carrier frequency removal and the matched filtering treatment can be approximated as
Where σ p is the scattering intensity of the p-th scattering point,Is the amplitude gain from the pulse pressure. After pulse compression, the waveform becomes sinc form, and the position and phase of the echo of each scattering point can be seen to be consistent, namely, the echo is consistent with that of each scattering pointIn the related art, non-ideal factors exist in each link of the actual radar system, such as an amplifier, a filter and a mixer all introduce systematic errors, errors exist between the actual value and the nominal value of a frequency source for generating a transmitting and sampling trigger signal, the errors affect the amplitude frequency and the phase frequency response of the system, and partial errors can be calibrated in advance before experiments. However, since the step frequency radar achieves a high resolution by synthesizing a large bandwidth signal with a plurality of sub-band bandwidths, the influence of phase errors between sub-bands on imaging must be considered, and since the target distance is long, the target signal power is small and noise must be considered. Signal writing taking into account subband phase errors and noise
Here, theFor the phase error of the q-th subband,/>Is complex gaussian white noise.
Aiming at the low signal-to-noise ratio step frequency multi-component signal of the formula (4), a high-resolution imaging method based on MS-GRFT is provided:
Firstly, rough GRFT of single sub-band data is used for obtaining a rough motion parameter range and rough motion compensation, fine GRFT of parallel processing is used for obtaining a parameter estimation result of each sub-band data, then CFAR and non-coherent accumulation screening part of motion parameters are used for taking sharpness as an objective function for estimating sub-band phase errors, and an analysis solution is obtained; finally, the GRFT results for the multiple subbands are error compensated, and the CFAR is again used to extract motion parameters and perform range-instantaneous doppler imaging.
Step one, carrying out large-range parameter estimation and coarse compensation through coarse GRFT of a single sub-band, reducing parameter search space, and then carrying out parallel GRFT of all sub-bands to obtain accurate motion parameters of a target.
Because of the sub-band errors, it is not feasible to directly perform wideband synthesis on pulse-pressed data, and at the same time, the spatial targets are usually non-cooperative, and the accuracy required by imaging cannot be achieved by means of ephemeris or tracking radar compensation accuracy, so that the signal to noise ratio must be improved by coherent accumulation. GRFT is an effective motion parameter estimation method, and for step frequency radar data, parallel GRFT can be performed on multiple sub-bands, and GRFT of each sub-band is defined as
H q (b) is a parameter search spaceTime domain-frequency domain joint filter on the upper part,/>And/>For/>The upper and lower bounds of the kth element of (b), H q (b) are defined as
Where delta (·) is the impulse function, lambda q＝c/fq is the wavelength of the q-th subband, as shown in figure 2,After multiplication with H q (b), the phase is compensated and projected onto the parameter space via azimuthal accumulation.
If the amplitude-phase fluctuation characteristic of the target is not considered, when the parameters are matched and the accumulation is optimal, the amplitude is increased to
Where A a＝PRF·Ta/Nf is the azimuth gain, PRF, T a and N f are the pulse repetition frequency, azimuth accumulation time and frequency count, respectively. It can be seen that GRFT improves signal to noise ratio through azimuthal coherent accumulation.
In the step, large-range parameter estimation is performed through coarse GRFT of a single sub-band and coarse compensation is performed, at the moment, most motion components are compensated, the parameter searching space of the GRFT is reduced, parallel GRFT of all sub-bands is performed, and accurate motion parameters of a target are acquired in a finer parameter space.
And secondly, using CFAR and non-coherent accumulation screening part motion parameters, summing the motion parameters, using sharpness as an evaluation standard for estimating and compensating the subband errors, and combining a gradient descent method for multiple iterations to realize coherent accumulation after the error compensation of a plurality of subband data and improve the distance resolution.
Through parallel GRFT, the parameter search result of Q sub-bands can be obtained, the step frequency Lei Datong always keeps redundant information of frequency bands in the system design, namely, overlapping parts exist between different frequency bands, redundant information is generated by direct broadband synthesis, grating lobes are easy to cause, and therefore windowing is needed for each sub-band. The window W q selected herein is a trapezoidal window that ensures that the spectrum is still flat after wideband synthesis for multiple subbands. If the q-th sub-band phase error isThe ideal full-band signal spectrum is
And full band signalsGRFT writeable of corresponding time-domain signals
In the middle ofIs an inverse fourier transform operator. The broadband problem under low signal-to-noise ratio is converted into the problem of performing coherent accumulation to improve the signal-to-noise ratio and performing broadband splicing in a parameter domain through exchanging integration and summation sequences, so that the processing difficulty is reduced, and the method is as follows
Because the parameter matrix G q (b) contains a large number of scattered points which are not optimally coherent and accumulated, the magnitudes of the points are small, and the imaging is not assisted, the CFAR technology can be used for threshold detection, fewer points are screened out, the calculated amount is reduced, and meanwhile, the influence of useless points is avoided.
It is worth noting that, due to the existence of sub-band phase errors, the coherent accumulation between sub-bands cannot be realized temporarily, and the limited signal to noise ratio can be improved by utilizing the non-coherent accumulation, so that the motion parameters can be detected by utilizing the CFAR. GRFT of non-coherent accumulation is defined as
To estimate the phase error of a subband, the sharpness of the parameter matrix after wideband synthesis can be used as an objective function, the sharpness of G (b) being defined as
For any set of parameter vectors on parameter space b. It should be noted that, sharpness is to use energy information of multiple points, and since two-dimensional accumulation is not performed after distance compression, the sharpness-based envelope alignment method is easy to fail under low signal-to-noise ratio, and indexes such as entropy and contrast are similar. The GRFT is needed to realize two-dimensional accumulation, improve the signal to noise ratio, and the CFAR is used for screening out partial motion parameters, so that the influence of invalid points is avoided, and the sharpness can be used for estimating the phase error of the sub-band, which is similar to the idea of extracting the estimation error of the isolated strong scattering points in SAR imaging.
The subband error estimation problem can thus be modeled as
Directly deriving the derivative to zero to obtain the optimal solution
In the middle of
As shown in fig. 3, the subband error is obtained by equation (14) and compensated, and the wideband synthesis is completed by coherent accumulation of a plurality of subband data, so that a GRFT result G all (b) with a higher signal-to-noise ratio, which is a high resolution, is obtained. It should be noted that, although coherent accumulation is performed in the parameter domain, GRFT is also equivalent to frequency domain wideband synthesis because it is a linear transform.
The method comprises the steps of firstly carrying out non-coherent accumulation on GRFT results of a plurality of sub-bands, then extracting motion parameters by using a CFAR technology after improving the signal to noise ratio, summing the parameter extraction results of the plurality of sub-bands, taking sharpness as an evaluation standard of sub-band error estimation and compensation precision, carrying out multiple iterations by combining a gradient descent method, realizing step frequency sub-band error estimation and compensation, and improving the distance resolution in a mode of coherent accumulation of a plurality of sub-band data.
And thirdly, performing error compensation and synthesis on GRFT results of a plurality of sub-bands, extracting motion parameters again by using CFAR, and realizing distance-instantaneous Doppler high-resolution imaging.
The GRFT result G all (b) of all the subbands is more accurate than the parameter estimation result of the GRFT result G q (b) of a single subband, more subband data are utilized, the signal to noise ratio is higher, and therefore the CFAR detection strategy is used again to obtainAt this time the signal amplitude becomes
Where a s is the gain due to wideband synthesis, if the target is a point target, a s＝Ball/B＝Ts/Tp, i.e. the accumulated gain in azimuth time, is equivalent to the accumulated gain in bandwidth, and T s is the equivalent accumulated time after wideband synthesis.
N b is the number of points after CFAR detection, consisting ofN b distance-speed information can be obtained, optionally at some point/>The instantaneous distance-velocity history can be expressed as
Here, theFor/>The nth b th set of k th order polynomial coefficients. Thus, the range-instantaneous Doppler image can be reconstructed as
Here, theIs the wavelength corresponding to the center frequency after broadband synthesis.
The method extracts high-resolution GRFT results after the error compensation of a plurality of sub-bands by using the CFAR technology, obtains high-precision motion parameters, obtains distance-Doppler information corresponding to the instant time of the motion parameters, and realizes azimuth high-resolution imaging.
In summary, the MS-GRFT space target resolution imaging method can be obtained, and the processing flow is shown in figure 4. The echo is first input for range-wise pulse compression and ephemeris-based motion calibration, signal-to-noise ratio is improved and most of the errors are calibrated. And then carrying out coarse GRFT, carrying out coarse compensation and obtaining a parameter range, then using parallel GRFT, estimating a sub-band phase error by using the sharpness summed by the parallel GRFT as an objective function, and carrying out broadband synthesis in the parameter range to obtain an accurate estimation result. And finally, detecting by using CFAR, projecting the extracted motion parameters onto an instantaneous range-Doppler plane, and obtaining a high-resolution RID image.
Example 1
The observation target of the experiment is a satellite lattice consisting of 70 points, as shown in fig. 5 (a), the relative positions of the target and the radar are shown in fig. 5 (b), the track of the satellite is obtained according to STK simulation, as shown in fig. 5 (c), the motion process of each point of the satellite model relative to the center of the satellite model is shown in fig. 5 (d), and other experimental parameters are shown in table 1.
Table 1 simulation experiment parameters
| Radar parameters | Numerical value | Unit (B) |
| Number of subbands | 8 | Personal (S) |
| Pulse count | 256 | Personal (S) |
| Bandwidth of a communication device | 125 | MHz |
| Frequency step size | 80 | MHz |
| Sampling rate | 160 | MHz |
| Pulse repetition frequency | 400 | Hz |
| Pulse width | 7.81 | us |
| Initial center frequency | 4.5 | GHz |
| Target distance | 720 | km |
| Target speed | 1600 | m/s |
| Acceleration of | 34 | m/s2 |
| Signal to noise ratio | -28 | dB |
For the purpose of correcting motion errors, the echo data of the first frequency point is used, and coherent accumulation is performed by GRFT in a coarse parameter space, and the parameter space is set as shown in table 2. And searching a peak value after coarse GRFT, and intercepting along the acceleration dimension of the parameter matrix to obtain a coarse estimated value with the distance of 359.8438m, the speed of 1.2297m/s and the acceleration of 0.0843m/s 2 so as to perform motion coarse compensation.
TABLE 2 coarse GRFT parameter search Range
| Parameters (parameters) | Maximum value | Minimum value | Spacing of | Unit (B) |
| Distance of | 228.12 | 509.14 | 0.4688 | m |
| Speed of speed | -3 | 3 | 0.018 | m/s |
| Acceleration of | -0.2 | 0.2 | 0.0015 | m/s2 |
After the parameter rough compensation, parallel GRFT processing can be used near the compensated motion parameters. The parameter range settings for the parallel GRFT are shown in table 3.
TABLE 3 parallel GRFT parameter search Range
| Parameters (parameters) | Maximum value | Minimum value | Spacing of | Unit (B) |
| Distance of | 10.3 | 57.1 | 0.5 | m |
| Speed of speed | -1 | 1 | 0.0018 | m/s |
| Acceleration of | -0.02 | 0.02 | 0.0002 | m/s2 |
As shown in fig. 6 (a-d), the signal to noise ratio is low, which is less than 10dB, so that it is difficult to obtain the motion parameters, and it is also difficult to extract the peak value from the tangential plane of three dimensions of distance, speed and acceleration. Non-coherent accumulation is performed by using all sub-bands, and the result is shown in fig. 6 (e-h), the signal to noise ratio is improved only to a limited extent, but the distance, speed and acceleration section can extract peak values, so that the CFAR technique is required to be used for extracting effective motion parameters based on the result to realize sub-band error estimation. Fig. 6 (i-l) and fig. 6 (m-p) are the results of coherent accumulation of parameters before and after calibration of the subband errors, respectively. Obviously, the result before the sub-band error is calibrated is interfered by the error, and although the signal to noise ratio is improved, the motion parameters are difficult to extract. The result after the subband error is calibrated has a better signal-to-noise ratio of about 15dB, the peak value is more obviously compared with the background, and in the dimensions of distance, speed and acceleration, the peak value is more obvious, and the motion parameters are more easily extracted.
CFAR detection of the results in fig. 6 is followed by projection onto the RD plane to obtain RID images. Fig. 7 (a-b) are RID imaging results for a single subband at different false alarm rates. Because of the low signal-to-noise ratio, the detected parameters cannot delineate the true structure of the target. Fig. 7 (c-d) shows RID imaging results after non-coherent accumulation, which brings about signal-to-noise ratio improvement and makes noise distribution more concentrated, so that multiple real motion parameters can be detected, but under the condition of low false alarm rate, false alarm can occur, and under the condition of high false alarm rate, some points with closer distances can not be separated due to lower resolution. Fig. 7 (e-f) shows RID imaging results of wideband synthesis without correcting subband errors, which result in a large number of false alarm targets, and difficulty in acquiring target structure information. Fig. 7 (g-h) shows the result of RID imaging after the proposed algorithm, that is, the subband error is calibrated, it can be seen that, due to the coherent accumulation of all the subbands GRFT, the signal-to-noise ratio is improved, the resolution is enhanced, and the CFAR can extract the target parameters more accurately, so as to obtain a better imaging effect.
In summary, the above embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. The space target resolution imaging method of the step frequency radar based on the MS-GRFT under the low signal-to-noise ratio is characterized by comprising the following steps:
Step one, carrying out large-range parameter estimation and coarse compensation through coarse GRFT of a single sub-band, reducing parameter search space, and then carrying out parallel GRFT of all sub-bands to obtain accurate motion parameters of a target.
Step two, using CFAR and non-coherent accumulation screening part motion parameters, summing the motion parameters, using sharpness as an evaluation standard of subband error estimation and compensation, and combining a gradient descent method for multiple iterations to realize coherent accumulation after the error compensation of a plurality of subbands, so as to improve the distance resolution;
and thirdly, performing error compensation and synthesis on GRFT results of a plurality of sub-bands, extracting motion parameters again by using CFAR, and realizing distance-instantaneous Doppler high-resolution imaging.
2. The method for space-target-resolved imaging of step-frequency radar based on MS-GRFT at low signal-to-noise ratio of claim 1 wherein in step one parallel GRFT is performed on multiple subbands, the GRFT for each subband being defined as
H q (b) is a parameter search spaceTime domain-frequency domain joint filter on the upper part,/>And/>For/>The upper and lower bounds of the kth element of (b), H q (b) are defined as
Here δ (·) is the impulse function and λ q＝c/fq is the wavelength of the q-th subband.
3. The method for spatially resolved imaging of a step-frequency radar based on MS-GRFT at low signal-to-noise ratio of claim 1 wherein the full-band signal in step twoGRFT for corresponding time domain signal
In the middle ofIs an inverse fourier transform operator.
4. The method for spatially resolved imaging of a step-frequency radar based on MS-GRFT at low signal-to-noise ratio of claim 1 wherein the GRFT of the non-coherent accumulation in step two is defined as
To estimate the phase error of a subband, the sharpness of the parameter matrix after wideband synthesis can be used as an objective function, the sharpness of G (b) being defined as
For any set of parameter vectors on parameter space b.
5. The method for space-target-resolved imaging of MS-GRFT-based step-frequency radar at low signal-to-noise ratio of claim 1, wherein the sub-band error estimation problem in step two is modeled as
Directly deriving the derivative to zero to obtain the optimal solution
In the middle of
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