CN112305539A - ArcSAR polar coordinate format imaging method based on spherical wave decomposition - Google Patents

ArcSAR polar coordinate format imaging method based on spherical wave decomposition Download PDF

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CN112305539A
CN112305539A CN202011021821.5A CN202011021821A CN112305539A CN 112305539 A CN112305539 A CN 112305539A CN 202011021821 A CN202011021821 A CN 202011021821A CN 112305539 A CN112305539 A CN 112305539A
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张远
王彦平
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North China University of Technology
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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 in a scanning angle direction, and filtering signals along the angle direction; carrying out polar coordinate to rectangular coordinate interpolation on the filtered signals; and carrying out two-dimensional inverse Fourier transform on the interpolated signal to obtain a focusing result. The method has the advantages of being minimum in residual error retention theoretically and suitable for near-distance and far-distance target imaging; the time efficiency of the method is far higher than that of a BP algorithm, and the performance of the method is superior to that of an RD algorithm in a short-distance scene.

Description

ArcSAR polar coordinate format imaging method based on spherical wave decomposition
Technical Field
The application relates to the technical field of foundation synthetic aperture radars with large visual field observation capability, in particular to an ArcSAR polar coordinate format imaging method based on spherical wave decomposition.
Background
The GB-SAR adopts a synthetic aperture radar imaging principle, a system platform of the GB-SAR is statically placed on the ground, radar signals can be actively transmitted and received to an observed area, and scene imaging within a range of several kilometers can be generally realized by utilizing received echo signals. GB-SAR systems fall into two categories: linear rail systems and circular arc rail systems. The GB-SAR system based on the circular arc orbit is called ArcSAR.
The disclosed ArcSAR imaging algorithms can be divided into three categories. The first type is the Back Projection (BP) algorithm, whose basic principle is to add distance to the compressed echo signal in accordance with the coherence of the arc orbit in the two-dimensional time domain. The BP algorithm is characterized in that coherent accumulation is carried out point by point, and the method is suitable for various complex skew distance geometries. However, due to the point-by-point coherent accumulation processing, under the conditions of large field of view, long distance and high resolution, the number of scene grid points to be processed becomes very large, thereby causing the execution efficiency of the BP algorithm to be too low. The second type is a range-doppler algorithm, the basic principle is that the range direction is focused by adopting pulse compression, the azimuth direction is converted into a frequency domain, the range direction and the azimuth direction coupling are eliminated in the range-doppler domain through range migration correction, and in the general derivation process, the slant distance is approximate to a second-order term of a rotation angle. Due to the fact that the algorithm has the slope distance approximation, a short-distance target cannot be well focused (the short-distance range depends on different system parameters), and in addition, residual distance space-variant errors cannot be removed. The third type of algorithm is a two-dimensional frequency domain algorithm, which transforms the echo signal to a two-dimensional frequency domain, and then eliminates the coupling between the rotation direction and the distance direction through nonlinear mapping. However, because the target slant range item still exists in the two-dimensional frequency domain phase, the algorithm can only adopt the processing of performing Stolt interpolation on targets at different slant range positions respectively, which inevitably causes repeated calculation in the Stolt interpolation process, and greatly reduces the processing efficiency.
Disclosure of Invention
To overcome, at least to some extent, the problems in the related art, the present application provides an ArcSAR polar format imaging method based on spherical wave decomposition.
According to a first aspect of embodiments of the present application, there is provided an ArcSAR polar 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 in a scanning angle direction, and filtering signals along the angle direction;
carrying out polar coordinate to rectangular coordinate interpolation on the filtered signals;
and carrying out two-dimensional inverse Fourier transform on the interpolated signal to obtain a focusing result.
Further, the method further comprises:
obtaining a signal model expression after the echo signal is deskewed;
and constructing a compensation function, and eliminating a modulation term in the signal model expression.
Further, the signal model expression is as follows:
Figure RE-GDA0002799128250000021
wherein r iscIs a reference slant pitch used in deskewing, θ is a radar rotation angle, and K is a distance wave number.
Further, the compensation function is s1＝exp{j[-2πK·rc]}；
The elimination of the modulation term in the signal model expression comprises:
multiplying the signal model expression by the compensation function to obtain
Figure RE-GDA0002799128250000022
Further, the representing the spherical wave signal of the echo as a plane wave integral form includes:
according to the formula
Figure RE-GDA0002799128250000023
Representing spherical wave signals as
Figure RE-GDA0002799128250000024
Wherein,
Figure RE-GDA0002799128250000031
is the propagation vector of the spherical wave at the target;
Figure RE-GDA0002799128250000032
is a unit vector with coordinates of
Figure RE-GDA0002799128250000033
Figure RE-GDA0002799128250000034
Further, the filtering the signal in the angular direction includes:
the spherical wave signal is represented as a convolution of two parts: sS1(θ,K)＝f(θ,K)*g(θ,K)；
Derived using Fourier transform along the angular direction
Fθ{sS1(θ,K)}＝Fθ{ F (θ, K) × G (θ, K) } ═ F (ξ, K) · G (ξ, K); where ξ is the corresponding frequency domain variable of the rotation angle;
after item shifting to obtain
Figure RE-GDA0002799128250000035
And performing inverse Fourier transform to obtain signals subjected to azimuth filtering as follows:
g(θ,K)＝exp{j·[-2πkx·x-2πky·y]}; wherein k isx＝K·cosθ，ky＝K·sinθ。
Further, after g (θ, K) completes the polar-to-rectangular interpolation, the signal becomes:
gxy(kx,ky)＝exp{j·[-2πkx·x-2πky·y]}。
further, performing a two-dimensional inverse fourier transform on the interpolated signal, comprising:
edge kxAnd kyAnd performing two-dimensional inverse Fourier transform on the direction to obtain a point target focusing result as follows:
Figure RE-GDA0002799128250000036
wherein, deltax(. and. delta.)y(. cndot.) is a function of the ambiguity of the point target P in the X and Y directions, respectively.
According to a second aspect of embodiments of the present application, there is provided a computer apparatus comprising:
a memory for storing a computer program;
a processor for executing the computer program in the memory to implement the operational steps of the method according to any of the above embodiments.
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 one of the above embodiments.
The technical scheme provided by the embodiment of the application has the following beneficial effects:
the method has the advantages of being minimum in residual error retention theoretically and suitable for near-distance and far-distance target imaging; the time efficiency of the method is far higher than that of a BP algorithm, and the performance of the method is superior to that of an RD algorithm in a short-distance scene.
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.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and together with the description, serve to explain the principles of the application.
Fig. 1 is a flowchart 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 shown in accordance with an exemplary embodiment.
FIG. 3 is a flowchart illustrating a polar format method based on spherical wave decomposition in accordance with an exemplary embodiment.
Fig. 4 is a schematic diagram of ArcSAR spherical wave decomposition.
Fig. 5 is a schematic diagram of a polar to rectangular interpolation process.
Figure 6 is a plot of the target phase after RVP removal.
Fig. 7 is a phase diagram after angular direction filtering.
Fig. 8(a) is a phase diagram in a rectangular coordinate system after filtering in the angular direction.
Fig. 8(b) is a partially enlarged view of the position of the block.
FIG. 9(a) is a schematic illustration of the point target focusing results of the method of the present application.
Fig. 9(b) is a schematic view 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 diagram showing the response of a target at 10m after the target has been processed by three methods.
FIG. 11(b) is a diagram showing the response of the target at 30m after being processed by three methods.
FIG. 11(c) is a diagram showing the response of a target at 50m after being processed by three methods.
Fig. 12 is a diagram of an actual target scene.
FIG. 13 is a graph of the results of the method of the present application with respect to the imaging of an actual target scene.
Detailed Description
Reference will now be made in detail to the exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, like numbers in different drawings represent the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present application. Rather, they are merely examples of methods consistent with aspects of the present application, as detailed in the appended claims.
Fig. 1 is a flowchart 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: obtaining a signal model expression after the echo signal is deskewed; and constructing a compensation function, and eliminating a modulation term in the signal model expression.
Step S2: the spherical wave signal of the echo is represented as a plane wave integral.
Step S3: and constructing a filter for scanning the angle direction, and filtering the signal along the angle direction.
Step S4: and carrying out polar coordinate to rectangular coordinate interpolation on the filtered signals.
Step S5: and carrying out two-dimensional inverse Fourier transform on the interpolated signal to obtain a focusing result.
The method has the advantages of being minimum in residual error retention theoretically and suitable for near-distance and far-distance target imaging; the time efficiency of the method is far higher than that of a BP algorithm, and the performance of the method is superior to that of an RD algorithm in a short-distance scene.
The following describes the scheme of the present application in an expanded manner with reference to a specific application scenario.
Fig. 2 is a schematic view of the scanning geometry of the ArcSAR system. Where S represents the radar position, P represents the target position, and R represents the target-to-radar distance. The radar makes circular motion by taking the point O as the center of a circle, 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, spherical wave signals of echoes are decomposed and represented in 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 utilizing the convolution theorem of Fourier transform; further carrying out polar coordinate-to-rectangular coordinate interpolation on the signals to realize decoupling of the angle direction and the distance direction; and finally, realizing target focusing through two-dimensional inverse Fourier transform. Where RVP is an abbreviation for Residual Video Phase.
The specific imaging algorithm comprises the following steps:
step S1: the expression of a signal model obtained after the echo signal is deskewed (Decirp) is as follows
Figure RE-GDA0002799128250000061
Wherein r iscIs a reference slope distance used in deskewing and is a known parameter. θ is the radar rotation angle, and K is the range wavenumber. Constructional distanceThe first order compensation function of the ionization number is as follows
s1＝exp{j[-2πK·rc]} (2)
The constructor expressed by the formula (2) can compensate and eliminate r in the formula (1)cAnd modulating the item. Multiplying formula (2) by formula (1) to obtain
Figure RE-GDA0002799128250000062
The phase in equation (3) is actually a target phase spherical wave form.
Step S2: expression (3) is expressed as a plane wave integral form in a spherical coordinate system, and the following expression is used
Figure RE-GDA0002799128250000063
As shown in FIG. 4, in the formula (4)
Figure RE-GDA0002799128250000064
Is the propagation vector of the spherical wave at the target, and the module value is the slope distance of the target.
Figure RE-GDA0002799128250000065
Is a unit vector, and has coordinates in a three-dimensional space coordinate system OXYZ of
Figure RE-GDA0002799128250000066
Figure RE-GDA0002799128250000067
Figure RE-GDA0002799128250000068
Is composed of
Figure RE-GDA0002799128250000069
Of the plane wave component. Since the ArcSAR imaging plane is two-dimensional, the spherical wave decomposition for the ArcSAR system has only a one-fold form. Formula (3) can be expressed asIs re-expressed as formula (4) according to spherical wave decomposition
Figure RE-GDA00027991282500000610
Wherein
Figure RE-GDA00027991282500000611
In equation (5), the amplitude of the signal is ignored. Equation (5) can be viewed as a convolution of two parts in practice, i.e.
sS1(θ,K)＝f(θ,K)*g(θ,K) (7)
Wherein,
f(θ,K)＝exp{j·[2πK·r·cos(θ)]} (8)
Figure RE-GDA0002799128250000071
step S3: obtained by Fourier transform in the angular direction for equation (7)
Fθ{sS1(θ,K)}＝Fθ{f(θ,K)*g(θ,K)}
＝F(ξ,K)·G(ξ,K) (10)
Where ξ is the corresponding frequency domain variable of the rotation angle.
Figure RE-GDA0002799128250000072
Applying an inverse Fourier transform to equation (11) to obtain
Figure RE-GDA0002799128250000073
F in formula (12)θ{sS1(θ, K) } may be realized by fourier transform of the echo data in the angular direction. F (xi, K) can be represented by the formula(8) Fourier transform implementation along the angular direction. In this case, g (θ, K) is an azimuth-filtered signal and is expressed as
g(θ,K)＝exp{j·[-2πkx·x-2πky·y]} (13)
Wherein
kx＝K·cosθ，ky＝K·sinθ (14)
Step S4: g (theta, K) expresses that the target signal is in a polar coordinate system, and the decoupling of the angle direction and the distance direction needs to be realized by the interpolation from the polar coordinate to the rectangular coordinate, and the specific interpolation process is shown in fig. 5. In FIG. 5, θ1And theta2Respectively a scanning start angle and a stop angle. K1And K2The minimum and maximum wave numbers, respectively. In fig. 5, the size of the processed data region is determined by the distance wave number and the scanning angle, and when the system parameters are determined, the size of the data region is also determined, and the calculation amount of the algorithm is independent of the size of the scene, which is also the difference between the method and other methods.
Step S5: g (theta, K) after completing the interpolation of polar coordinates to rectangular coordinates, the signal becomes
gxy(kx,ky)＝exp{j·[-2πkx·x-2πky·y]} (15)
Pair formula (15) edge kxAnd kyTwo-dimensional inverse Fourier transform is carried out on the direction to obtain a point target focusing result,
Figure RE-GDA0002799128250000081
wherein deltax(. and. delta.)y(. cndot.) is a function of the ambiguity of the point target P in the X and Y directions, respectively.
Relevant experiments are carried out by applying the imaging method of the application, and the experimental effect is explained below.
TABLE 1 Radar parameters
System carrier frequency f0＝17.5GHz
Pulse width of transmission Tp＝10μs
Range of scanning angles θ1＝-90°，θ2＝90°
Azimuth beam-3 dB width 40°
Bandwidth of transmitted pulse 1GHz
Sampling frequency 50MHz
The radar parameters used to perform the experiments are shown in the table above, and the processing and results of the method are described below.
First, the echo signal with RVP removed is obtained, and a signal phase diagram is given in FIG. 6. It can be seen that the echo phase has a pronounced spherical wave character.
The angular filtering of fig. 6 is then performed using a filter constructed according to equation (8). Fig. 7 shows a phase diagram of the angular direction filtered signal.
Next, polar-to-rectangular interpolation is performed, and a phase diagram after coordinate conversion is shown in fig. 8 (a). Fig. 8(b) shows an enlarged view corresponding to the box, and it can be seen that the phase exhibits a plane wave. Further, performing a two-dimensional inverse fourier transform on the signal will yield the focusing result of fig. 9 (a). By 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 respectively arranged at the positions 10m,30 m and 50m away from the radar, and a scene schematic diagram is shown in FIG. 10.
RD (Lee H, Cho S J, Kim K E.A group-based Arc-Scanning perspective Radar (ArcSAR) system and focusing algorithm [ C ]// Sensing & moving Sensing symposium. IEEE,2010.), BP ((Lee H, Lee J H, Kim K E, et al. development of a Truck-Mounted Arc-Scanning perspective Radar [ J ]. IEEE Transactions on geometry and moving Sensing, 201473.)) and the inventive method were then used, respectively, with the results shown in FIG. 11. The three curves with different markers represent RD, BP and the method of the invention, respectively. FIGS. 11(a), (b) and (c) show the Y-direction responses of 10m,30 m and 50m targets, respectively. The target response result of the algorithm is consistent with that of the BP algorithm no matter in near distance or far distance, but the performance of the RD algorithm in the near distance is obviously reduced.
Time consuming tests were performed using an Intel Xeon server, configured as CPU E5-2603, MEM 32 GB. Table 2 gives the time consumption of the three types of algorithms. It can be seen that the RD algorithm has a significant advantage in terms of computation time, since BP is very time consuming, which is more than 1 hour at a sampling interval of 0.01m, although the time can be reduced by increasing the sampling interval, the invention also takes only 5 minutes at a sampling interval of 0.004 m.
TABLE 2 comparison of time consumption of the three methods
The invention BP RD
Time 5 minutes >1 hour 10 seconds
Samplinginterval(m) 0.004 0.01 0.01
The data related to the above experiment are from the observation experiment of the ArcSAR system on large buildings, the radar carrier frequency is 17.5Hz, the rotating arm length is 1m, and the scanning angle range is 160 degrees. The building length is about 300m, and an arch structure with the height of about 100m exists at the far end in the X direction, and the actual picture of the building is shown in figure 12.
The data were processed using the method of the present invention, the imaging results are shown in fig. 13, with the image amplitude in power. The basic outline of the building body can be seen from the imaging result. The arch in the photograph corresponds to the imaging result coordinate positions 462m, -18.5 m.
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 very ideal in all other indexes except that the PLSR value in the Y direction slightly deviates from the ideal value.
2. The algorithm consumes less time. The RD algorithm has a significant advantage in computation time, since BP is very time-consuming, and takes more than 1 hour at a sampling interval of 0.01m, it is of course possible to reduce the time by increasing the sampling interval, but the method of the present application also takes only 5 minutes at a sampling interval of 0.004 m.
3. Compared with other methods. It can be seen that the method is close to the BP algorithm in accuracy, but much more time efficient than the BP algorithm. Although the method is lower than the RD algorithm in time efficiency, the performance of the RD algorithm is obviously reduced at a close distance, and the method has better performance at a close distance and a far distance.
The present application further provides a computer device, comprising: a memory for storing a computer program; a processor for executing a computer program in the memory to implement a spherical wave decomposition based ArcSAR polar format imaging method: representing the spherical wave signal of the echo as a plane wave integral form; constructing a filter in a scanning angle direction, and filtering signals along the angle direction; carrying out polar coordinate to rectangular coordinate interpolation on the filtered signals; and carrying out two-dimensional inverse Fourier transform on the interpolated signal to obtain a focusing result.
The present application further provides a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements a spherical wave decomposition-based ArcSAR polar format imaging method: representing the spherical wave signal of the echo as a plane wave integral form; constructing a filter in a scanning angle direction, and filtering signals along the angle direction; carrying out polar coordinate to rectangular coordinate interpolation on the filtered signals; and carrying out two-dimensional inverse Fourier transform on the interpolated signal to obtain a focusing result.
It is understood that the same or similar parts in the above embodiments may be mutually referred to, and the same or similar parts in other embodiments may be referred to for the content which is not described in detail in some embodiments.
It should be noted that, in the description of the present application, the terms "first", "second", etc. are used for descriptive purposes only and are not to be construed as indicating or implying relative importance. Further, in the description of the present application, the meaning of "a plurality" means at least two unless otherwise specified.
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 the scope of the preferred embodiments of the present application includes other implementations 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 should be understood that portions of the present application may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.
It will be understood by those skilled in the art that all or part of the steps carried by the method for implementing the above embodiments may be implemented by hardware related to instructions of a program, which may be stored in a computer readable storage medium, and when the program is executed, the program includes one or a combination of the steps of the method embodiments.
In addition, functional units in the embodiments of the present application may be integrated into one processing module, or each unit may exist alone physically, or two or more units are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. The integrated module, if implemented in the form of a software functional module and sold or used as a stand-alone product, may also be stored in a computer readable storage medium.
The storage medium mentioned above may be a read-only memory, a magnetic or optical disk, etc.
In the description herein, reference to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," 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 application. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Although embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application, and that variations, modifications, substitutions and alterations may be made to the above embodiments by those of ordinary skill in the art within the scope of the present application.

Claims (10)

1. An ArcSAR polar coordinate format imaging method based on spherical wave decomposition is characterized by comprising the following steps:
representing the spherical wave signal of the echo as a plane wave integral form;
constructing a filter in a scanning angle direction, and filtering signals along the angle direction;
carrying out polar coordinate to rectangular coordinate interpolation on the filtered signals;
and carrying out two-dimensional inverse Fourier transform on the interpolated signal to obtain a focusing result.
2. The method of claim 1, further comprising:
obtaining a signal model expression after the echo signal is deskewed;
and constructing a compensation function, and eliminating a modulation term in the signal model expression.
3. The method of claim 2, wherein the signal model expression is:
Figure RE-FDA0002799128240000011
wherein r iscIs a reference slant pitch used in deskewing, θ is a radar rotation angle, and K is a distance wave number.
4. The method of claim 3,
the compensation function is s1＝exp{j[-2πK·rc]}；
The elimination of the modulation term in the signal model expression comprises:
multiplying the signal model expression by the compensation function to obtain
Figure RE-FDA0002799128240000012
5. The method of claim 4, wherein said representing the spherical wave signal of the echo as a plane wave integral form comprises:
according to the formula
Figure RE-FDA0002799128240000013
Representing spherical wave signals as
Figure RE-FDA0002799128240000014
Wherein,
Figure RE-FDA0002799128240000015
is the propagation vector of the spherical wave at the target;
Figure RE-FDA0002799128240000016
is a unit vector with coordinates of
Figure RE-FDA0002799128240000017
Figure RE-FDA0002799128240000021
η∈[0,π/2]；
Figure RE-FDA0002799128240000022
6. The method of claim 5, wherein the filtering the signal in the angular direction comprises:
the spherical wave signal is represented as a convolution of two parts: sS1(θ,K)＝f(θ,K)*g(θ,K)；
Derived using Fourier transform along the angular direction
Fθ{sS1(θ,K)}＝Fθ{ F (θ, K) × G (θ, K) } ═ F (ξ, K) · G (ξ, K); where ξ is the corresponding frequency domain variable of the rotation angle;
after item shifting to obtain
Figure RE-FDA0002799128240000023
And performing inverse Fourier transform to obtain signals subjected to azimuth filtering as follows:
g(θ,K)＝exp{j·[-2πkx·x-2πky·y]}; wherein k isx＝K·cosθ，ky＝K·sinθ。
7. The method of claim 6, wherein after g (θ, K) completes the polar to rectangular interpolation, the signal becomes:
gxy(kx,ky)＝exp{j·[-2πkx·x-2πky·y]}。
8. the method of claim 7, wherein performing a two-dimensional inverse fourier transform on the interpolated signal comprises:
edge kxAnd kyAnd performing two-dimensional inverse Fourier transform on the direction to obtain a point target focusing result as follows:
Figure RE-FDA0002799128240000024
wherein, deltax(. and. delta.)y(. cndot.) is a function of the ambiguity of the point target P in the X and Y directions, respectively.
9. A computer device, comprising:
a memory for storing a computer program;
a processor for executing the computer program in the memory to carry out the operational steps of the method of any one of claims 1 to 8.
10. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the operating steps of the method according to any one of claims 1 to 8.
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