CN112305539B - ArcSAR polar coordinate format imaging method based on spherical wave decomposition - Google Patents
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Abstract
The application relates to an ArcSAR polar coordinate format imaging method based on spherical wave decomposition, which comprises the following steps: representing the spherical wave signal of the echo as a plane wave integral form; constructing a filter for scanning the angle direction, and filtering the signal along the angle direction; performing polar coordinate-to-rectangular coordinate interpolation on the filtered signals; and performing two-dimensional inverse Fourier transform on the interpolated signal to obtain a focusing result. The method has the advantages of least residual error retention in theory and suitability for near-far target imaging; the time efficiency of the method is far higher than that of the BP algorithm, and the performance of the method under a near scene is better than that of the RD algorithm.
Description
Technical Field
The application relates to the technical field of foundation synthetic aperture radars with large field of view observation capability, in particular to an ArcSAR polar coordinate format imaging method based on spherical wave decomposition.
Background
GB-SAR uses the principle of synthetic aperture radar imaging, and its system platform is placed on the ground statically, and can actively transmit and receive radar signals to the observed area, and can usually implement scene imaging within a range of several kilometers by using the received echo signals. GB-SAR systems fall into two categories: a linear track system and a circular arc track system. The GB-SAR system based on circular arc orbit is called ArcSAR.
The disclosed ArcSAR imaging algorithms can be divided into three classes. The first type is a Back Projection (BP) algorithm, and the basic principle is to coherently superimpose the distance-compressed echo signals according to an arc track in a two-dimensional time domain. The BP algorithm is characterized by coherent accumulation point by point and is suitable for various complex oblique distance geometries. However, due to the point-by-point coherent accumulation process, the number of scene grid points to be processed becomes very large under the conditions of large field of view, long distance and high resolution, so that the execution efficiency of the BP algorithm is too low. The second type is a range-doppler algorithm, the basic principle is that the range direction adopts pulse compression to focus, the azimuth direction is transformed into the frequency domain, the coupling of the range direction and the azimuth direction is eliminated through range migration correction in the range-doppler domain, and in the general derivation process, the skew is approximate to the second order term of the rotation angle. Because of the oblique approximation of the algorithm, close range targets are often not well focused (the close range depends on different system parameters) and the residual distance space-variant errors cannot be removed. The third type of algorithm is a two-dimensional frequency domain algorithm, in which echo signals are first transformed into a two-dimensional frequency domain, and then coupling between the rotation direction and the distance direction is eliminated through nonlinear mapping. However, as the target slope distance item still exists in the two-dimensional frequency domain phase, the algorithm can only adopt the process of respectively carrying out the Stolt interpolation on targets with different slope distance positions, which can cause the repeated calculation of the Stolt interpolation process, and greatly reduces the processing efficiency.
Disclosure of Invention
In order to overcome the problems existing in the related art to at least a certain extent, the application provides an ArcSAR polar coordinate format imaging method based on spherical wave decomposition.
According to a first aspect of an embodiment of the present application, there is provided an ArcSAR polar coordinate format imaging method based on spherical wave decomposition, including:
representing the spherical wave signal of the echo as a plane wave integral form;
constructing a filter for scanning the angle direction, and filtering the signal along the angle direction;
performing polar coordinate-to-rectangular coordinate interpolation on the filtered signals;
and performing two-dimensional inverse Fourier transform on the interpolated signal to obtain a focusing result.
Further, the method further comprises:
the echo signals are declivated to obtain a signal model expression;
and constructing a compensation function and eliminating modulation terms in the signal model expression.
Further, the signal model expression is:
wherein r is c Is the reference pitch used in declivity, θ is the radar rotation angle, and K is the range wavenumber.
Further, the compensation function is s 1 ＝exp{j[-2πK·r c ]}；
The eliminating the modulation term in the signal model expression comprises:
multiplying the signal model expression with the compensation function to obtain
Further, the method for representing the spherical wave signal of the echo as a plane wave integral form includes:
according to the formula
Representing spherical wave signals as
Wherein,is the propagation vector of the spherical wave at the target; />Is a unit vector with coordinates +.>
Further, the filtering the signal in the angular direction includes:
the spherical wave signal is represented as a convolution of two parts: sS(s) 1 (θ,K)＝f(θ,K)*g(θ,K)；
Using fourier transform in the angular direction
F θ {sS 1 (θ,K)}＝F θ { F (θ, K) ×g (θ, K) } =f (ζ, K) ·g (ζ, K); wherein ζ is the corresponding frequency domain variable of the rotation angle;
after the term transfer, obtain
Performing inverse Fourier transform to obtain signals subjected to azimuth filtering, wherein the signals are as follows:
g(θ,K)＝exp{j·[-2πk x ·x-2πk y ·y]-a }; wherein k is x ＝K·cosθ，k y ＝K·sinθ。
Further, after g (θ, K) completes the polar coordinate to rectangular coordinate interpolation, the signal becomes:
g xy (k x ,k y )＝exp{j·[-2πk x ·x-2πk y ·y]}。
further, performing a two-dimensional inverse fourier transform on the interpolated signal, including:
along k x And k y The two-dimensional inverse Fourier transform is carried out on the direction, and the focusing result of the point target is obtained as follows:
wherein delta x (. Cndot.) and delta y (. Cndot.) is the ambiguity function of the point object P in the X and Y directions, respectively.
According to a second aspect of an embodiment of the present application, there is provided a computer apparatus comprising:
a memory for storing a computer program;
a processor for executing a computer program in said memory to carry out the operational steps of the method as described in any one of the embodiments above.
According to a third aspect of embodiments of the present application, there is provided a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the operational steps of the method according to any of the embodiments above.
The technical scheme provided by the embodiment of the application has the following beneficial effects:
the method has the advantages of least residual error retention in theory and suitability for near-far target imaging; the time efficiency of the method is far higher than that of the BP algorithm, and the performance of the method under a near scene is better than that of the RD algorithm.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application as claimed.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the application and together with the description, serve to explain the principles of the application.
FIG. 1 is a flow chart illustrating an ArcSAR polar format imaging method based on spherical wave decomposition, according to an exemplary embodiment.
Fig. 2 is a schematic diagram of an ArcSAR system scan geometry, according to an example embodiment.
FIG. 3 is a flowchart illustrating a polar format method based on spherical wave decomposition, according to an exemplary embodiment.
Fig. 4 is an ArcSAR spherical wave decomposition schematic.
Fig. 5 is a schematic illustration of the polar to rectangular interpolation process.
Figure 6 is a point target phase map after RVP removal.
Fig. 7 is an angular direction filtered phase diagram.
Fig. 8 (a) is a phase diagram in the rectangular coordinate system after the angular direction filtering.
Fig. 8 (b) is a partial enlarged view of the block position.
Fig. 9 (a) is a schematic diagram of the point target focusing result of the method of the present application.
Fig. 9 (b) is a schematic diagram of the point target focusing result of the BP method.
FIG. 10 is a schematic diagram of a target simulation scenario.
FIG. 11 (a) is a graph showing the response of a 10m target after three methods.
FIG. 11 (b) is a graph showing the response of a target at 30m after three methods.
FIG. 11 (c) is a graph showing the response of a target at 50m after three methods.
Fig. 12 is an actual target scene graph.
Fig. 13 is a graph of the imaging results of the method of the present application for an actual target scene.
Detailed Description
Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, the same numbers in different drawings refer to the same or similar elements, unless otherwise indicated. The implementations described in the following exemplary examples do not represent all implementations consistent with the application. Rather, they are merely examples of methods consistent with aspects of the application as detailed in the accompanying claims.
FIG. 1 is a flow chart illustrating an ArcSAR polar format imaging method based on spherical wave decomposition, according to an exemplary embodiment. The method may comprise the steps of:
step S1: the echo signals are declivated to obtain a signal model expression; and constructing a compensation function and eliminating modulation terms in the signal model expression.
Step S2: the spherical wave signal of the echo is expressed as a plane wave integral form.
Step S3: a filter is constructed that scans the angular direction and filters the signal in the angular direction.
Step S4: and performing polar coordinate-to-rectangular coordinate interpolation on the filtered signals.
Step S5: and performing two-dimensional inverse Fourier transform on the interpolated signal to obtain a focusing result.
The method has the advantages of least residual error retention in theory and suitability for near-far target imaging; the time efficiency of the method is far higher than that of the BP algorithm, and the performance of the method under a near scene is better than that of the RD algorithm.
The scheme of the application is expanded and explained below by combining with specific application scenes.
Fig. 2 is a schematic diagram of the ArcSAR system scan geometry. Where S represents the radar position, P represents the target position, and R represents the target-to-radar distance. The radar performs circular motion by taking the point O as the circle center, and the length of the rotating arm is r.
FIG. 3 is a flow chart of a polar format method based on spherical wave decomposition, first, decomposing an echo spherical wave signal, which is represented as a plane wave integral form; secondly, constructing a filter in the scanning angle direction, and eliminating a high-order phase error in the angle direction by using a convolution theorem of Fourier transformation; further carrying out polar coordinate to rectangular coordinate interpolation on the signals to realize decoupling of the angle direction and the distance direction; finally, the target focusing is realized through two-dimensional inverse Fourier transform. Where RVP is an abbreviation for residual video phase (Residual Video Phase).
The specific imaging algorithm comprises the following steps:
step S1: the signal model expression obtained after the echo signal is declivated (Dechirp) is
Wherein r is c Is the reference pitch used in declivity and is a known parameter. θ is the radar rotation angle, and K is the range wavenumber. The first order compensation function for constructing the distance wavenumber is as follows
s 1 ＝exp{j[-2πK·r c ]} (2)
Using the constructor represented by equation (2), r in the cancellation equation (1) can be compensated for c Modulating the item. Multiplying formula (2) by formula (1) to obtain
The phase in equation (3) is actually the target phase spherical wave form.
Step S2: equation (3) is expressed as a plane wave integral form in the spherical coordinate system, using the following equation
As shown in FIG. 4, in formula (4)Is the propagation vector of spherical waves at the target, and the modulus value of the propagation vector is the slant distance of the target. />Is a unit vector with coordinates +.> Is->Is included in the plane wave component of (a). Because the ArcSAR imaging plane is two-dimensional, the spherical wave decomposition corresponding to ArcSAR systems has only a form of one-fold integration. Formula (3) can be re-expressed as follows from spherical wave decomposition formula (4)
Wherein the method comprises the steps of
In equation (5), the amplitude of the signal is ignored. Equation (5) can be regarded as actually a convolution of two parts, i.e.
sS 1 (θ,K)＝f(θ,K)*g(θ,K) (7)
Wherein,
f(θ,K)＝exp{j·[2πK·r·cos(θ)]} (8)
step S3: fourier transform is applied to the angle direction of (7) to obtain
F θ {sS 1 (θ,K)}＝F θ {f(θ,K)*g(θ,K)}
＝F(ξ,K)·G(ξ,K) (10)
Where ζ is the corresponding frequency domain variance of the rotation angle.
Applying an inverse Fourier transform to (11) to obtain
F in formula (12) θ {sS 1 (θ, K) } can be achieved by fourier transforming the echo data in the angular direction. F (ζ, K) may be implemented using a fourier transform of equation (8) in the angular direction. In this case, g (θ, K) is the azimuthally filtered signal, expressed as
g(θ,K)＝exp{j·[-2πk x ·x-2πk y ·y]} (13)
Wherein the method comprises the steps of
k x ＝K·cosθ，k y ＝K·sinθ (14)
Step S4: under the polar coordinate system, the g (theta, K) expresses the target signal, and decoupling of the angle direction and the distance direction is realized through polar coordinate to rectangular coordinate interpolation, and the specific interpolation process is shown in fig. 5. In FIG. 5, θ 1 And theta 2 The scan start angle and stop angle, respectively. K (K) 1 And K 2 The minimum and maximum wavenumbers, respectively. In fig. 5, the size of the processed data area is determined by the distance wave number and the scanning angle, and when the system parameters are determined, the size of the data area is also determined, and the calculation amount of the algorithm is independent of the size of the scene, which is also different from other methods in the present application.
Step S5: g (theta, K) completes the polar coordinate to rectangular coordinate interpolation, the signal becomes
g xy (k x ,k y )＝exp{j·[-2πk x ·x-2πk y ·y]} (15)
For (15) along k x And k y Performing two-dimensional inverse Fourier transform on the direction to obtain a point target focusing result,
wherein delta x (. Cndot.) and delta y (. Cndot.) is the ambiguity function of the point object P in the X and Y directions, respectively.
Related experiments are carried out by applying the imaging method of the application, and experimental effects are described below.
Table 1 radar parameters
| System carrier frequency | f 0 ＝17.5GHz |
| Pulse time width | T p ＝10μs |
| Scanning angle range | θ 1 ＝-90°，θ 2 ＝90° |
| Azimuth beam-3 dB width | 40° |
| Transmit pulse bandwidth | 1GHz |
| Sampling frequency | 50MHz |
The radar parameters used in performing the experiments are shown in the above table and the processing and results of the method are described below.
First, an RVP-removed echo signal is obtained, and a signal phase diagram is shown in fig. 6. It can be seen that the echo phase has a pronounced spherical wave character.
Next, fig. 6 is filtered in the angular direction, and the filter used is constructed according to equation (8). Fig. 7 shows a phase diagram of the angularly filtered signal.
Next, polar coordinate-to-rectangular coordinate interpolation is performed, and a phase diagram after coordinate conversion is completed is shown in fig. 8 (a). Fig. 8 (b) gives an enlarged view of the box correspondence, and it can be seen that the phase exhibits a plane wave. Further performing a two-dimensional inverse fourier transform on the signal will result in the focusing result of fig. 9 (a). In contrast, fig. 9 (b) gives the focusing result of the BP algorithm.
In addition, comparative experiments of the method of the present application with other methods were also performed.
Point targets are set at 10m,30 m and 50m from the radar respectively, and a scene diagram is shown in fig. 10.
RD (Lee H, chord S J, kim K E.A group-based Arc-scanning synthetic aperture radar (ArcSAR) system and focusing algorithms [ C ]// Geoscience & Remote Sensing symposium.IEEE, 2010.), BP (Lee H, lee J H, kim K E, et al development of a process-moved Arc-Scanning Synthetic Aperture Radar [ J ]. IEEE Transactions on Geoscience and Remote Sensing,2014,52 (5): 2773-2779 ]) and the method of the present application are then used, respectively, and the results are shown in FIG. 11. Three differently labeled curves represent RD, BP and the method of the application, respectively. FIGS. 11 (a), (b) and (c) show the Y-direction response of 10m,30 m and 50m targets, respectively. The target response results of the algorithm are consistent with those of the BP algorithm in both short distance and long distance, but the performance of the RD algorithm in the short distance is obviously reduced.
Time consuming testing was performed using an Intel Xeon server configured as CPU E5-2603, mem 32gb. The time elapsed for the three classes of algorithms is given in table 2. It can be seen that the RD algorithm has a significant advantage in terms of computation time, since BP is very time consuming, taking more than 1 hour in the case of a sampling interval of 0.01m, of course the time can be reduced by increasing the sampling interval, but the application takes only 5 minutes in the case of a sampling interval of 0.004 m.
Table 2 time-consuming comparison of three methods
| The application is that | BP | RD | |
| Time | For 5 minutes | >1 hour | 10 seconds |
| Samplinginterval(m) | 0.004 | 0.01 | 0.01 |
The data related to the experiment are from observation experiments of an ArcSAR system on a large building, the radar carrier frequency is 17.5Hz, the rotating arm length is 1m, and the scanning angle range is 160 degrees. The length of the building is about 300m, and an arch structure with a height of about 100m is arranged at the far end in the X direction, and an actual photograph of the building is shown in fig. 12.
The data is processed by the method, the imaging result is shown in fig. 13, and the image amplitude is expressed by power. The basic outline of the building body can be seen from the imaging results. The arches in the photographs correspond to the imaging result coordinate locations [462m, -18.5m ].
The ArcSAR imaging method based on the spherical wave decomposition polar coordinate format has the following advantages:
1. the resolution is ideal. The method is ideal except that the PLSR value in the Y direction deviates slightly from the ideal value.
2. The algorithm is less time-consuming. The RD algorithm has a significant advantage in terms of computation time, since BP is very time consuming, taking more than 1 hour in case of a sampling interval of 0.01m, of course the time can be reduced by increasing the sampling interval, but the method of the present application takes only 5 minutes in case of a sampling interval of 0.004 m.
3. Compared to other methods. It can be seen that the method is close to the BP algorithm in accuracy, but is much more time efficient than the BP algorithm. Although the method is lower in time efficiency than the RD algorithm, the RD algorithm has a significant decrease in performance in the near range, and the method has better performance in both the near range and the far range.
The present application also provides a computer device comprising: a memory for storing a computer program; a processor for executing the computer program in the memory to implement an ArcSAR polar coordinate format imaging method based on spherical wave decomposition: representing the spherical wave signal of the echo as a plane wave integral form; constructing a filter for scanning the angle direction, and filtering the signal along the angle direction; performing polar coordinate-to-rectangular coordinate interpolation on the filtered signals; and performing two-dimensional inverse Fourier transform on the interpolated signal to obtain a focusing result.
The present application also provides a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements an ArcSAR polar format imaging method based on spherical wave decomposition: representing the spherical wave signal of the echo as a plane wave integral form; constructing a filter for scanning the angle direction, and filtering the signal along the angle direction; performing polar coordinate-to-rectangular coordinate interpolation on the filtered signals; and performing two-dimensional inverse Fourier transform on the interpolated signal to obtain a focusing result.
It is to be understood that the same or similar parts in the above embodiments may be referred to each other, and that in some embodiments, the same or similar parts in other embodiments may be referred to.
It should be noted that in the description of the present application, the terms "first," "second," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance. Furthermore, in the description of the present application, unless otherwise indicated, the meaning of "plurality" means at least two.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and further implementations are included within the scope of the preferred embodiment of the present application in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present application.
It is to be understood that portions of the present application may be implemented in hardware, software, firmware, or a combination thereof. In the above-described embodiments, the various steps or methods may be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, may be implemented using any one or combination of the following techniques, as is well known in the art: discrete logic circuits having logic gates for implementing logic functions on data signals, application specific integrated circuits having suitable combinational logic gates, programmable Gate Arrays (PGAs), field Programmable Gate Arrays (FPGAs), and the like.
Those of ordinary skill in the art will appreciate that all or a portion of the steps carried out in the method of the above-described embodiments may be implemented by a program to instruct related hardware, where the program may be stored in a computer readable storage medium, and where the program, when executed, includes one or a combination of the steps of the method embodiments.
In addition, each functional unit in the embodiments of the present application may be integrated in one processing module, or each unit may exist alone physically, or two or more units may be integrated in one module. The integrated modules may be implemented in hardware or in software functional modules. The integrated modules may also be stored in a computer readable storage medium if implemented in the form of software functional modules and sold or used as a stand-alone product.
The above-mentioned storage medium may be a read-only memory, a magnetic disk or an optical disk, or the like.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present application. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present application have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the application, and that variations, modifications, alternatives and variations may be made to the above embodiments by one of ordinary skill in the art within the scope of the application.
Claims (6)
1. The ArcSAR polar coordinate format imaging method based on spherical wave decomposition is characterized by comprising the following steps of:
representing the spherical wave signal of the echo as a plane wave integral form;
constructing a filter for scanning the angle direction, and filtering the signal along the angle direction;
performing polar coordinate-to-rectangular coordinate interpolation on the filtered signals;
performing two-dimensional inverse Fourier transform on the interpolated signal to obtain a focusing result;
the method further comprises the steps of:
the echo signals are declivated to obtain a signal model expression;
constructing a compensation function, and eliminating modulation items in the signal model expression;
the signal model expression is:
wherein r is c Is the reference skew used in declivity, θ is the radar rotation angle, K is the range wavenumber, W a (θ) represents an angle envelope function, W r (K) Represents a distance envelope function, x represents an abscissa of a target, y represents an ordinate of the target, r represents a radar rotation radius, and a represents an angle direction;
the compensation function is s 1 ＝exp{j[-2πK·r c ]}；
The eliminating the modulation term in the signal model expression comprises:
multiplying the signal model expression with the compensation function to obtain
The method for representing the spherical wave signal of the echo as a plane wave integral form comprises the following steps:
according to the formula
Representing spherical wave signals as
Wherein,is the propagation vector of spherical wave at the target, R represents the propagation distance of spherical wave at the target, R represents the rotation radius of the radar, eta represents the included angle between the sight direction of the radar and the rotation plane of the radar, and +.>Representing the rotation angle in the wavenumber space; />Is a unit vector with coordinates +.>
2. The method of claim 1, wherein the filtering the signal in the angular direction comprises:
the spherical wave signal is represented as a convolution of two parts: sS(s) 1 (θ,K)＝f(θ,K)*g(θ,K)；
Using fourier transform in the angular direction
F θ {sS 1 (θ,K)}＝F θ { F (θ, K) ×g (θ, K) } =f (ζ, K) ·g (ζ, K); wherein ζ is the corresponding frequency domain variable of the rotation angle;
after the term transfer, obtain
Performing inverse Fourier transform to obtain signals subjected to azimuth filtering, wherein the signals are as follows:
g(θ,K)＝exp{j·[-2πk x ·x-2πk y ·y]-a }; wherein k is x ＝K·cosθ，k y ＝K·sinθ。
3. The method of claim 2, wherein g (θ, K) is interpolated from polar to rectangular coordinates, and the signal becomes:
g xy (k x ,k y )＝exp{j·[-2πk x ·x-2πk y ·y]}。
4. a method according to claim 3, wherein performing a two-dimensional inverse fourier transform on the interpolated signal comprises:
along k x And k y The two-dimensional inverse Fourier transform is carried out on the direction, and the focusing result of the point target is obtained as follows:
wherein delta x (. Cndot.) and delta y (. Cndot.) is the ambiguity function of the point object P in the X and Y directions, respectively.
5. A computer device, comprising:
a memory for storing a computer program;
a processor for executing a computer program in the memory to carry out the operational steps of the method of any one of claims 1 to 4.
6. A computer-readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, carries out the operational steps of the method according to any one of claims 1 to 4.
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