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CN110445557B - Deep space measurement and control interferometry large-aperture antenna pointing calibration method and device - Google Patents

Deep space measurement and control interferometry large-aperture antenna pointing calibration method and device Download PDF

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CN110445557B
CN110445557B CN201910742956.1A CN201910742956A CN110445557B CN 110445557 B CN110445557 B CN 110445557B CN 201910742956 A CN201910742956 A CN 201910742956A CN 110445557 B CN110445557 B CN 110445557B
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韩松涛
谢剑锋
陈明
陈略
任天鹏
路伟涛
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    • H04BTRANSMISSION
    • H04B17/00Monitoring; Testing
    • H04B17/10Monitoring; Testing of transmitters
    • H04B17/11Monitoring; Testing of transmitters for calibration
    • H04B17/12Monitoring; Testing of transmitters for calibration of transmit antennas, e.g. of the amplitude or phase
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
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Abstract

The invention provides a method and a device for calibrating pointing direction of a deep space measurement and control interferometric large-aperture antenna, wherein the method comprises the following steps: the direction of the fixed large-aperture antenna is fixed, and the direction of the target large-aperture antenna is adjusted in a stepping mode; calculating the directional correction quantity of the fixed large-aperture antenna and the target large-aperture antenna pointing to a plurality of calibration and calibration power supplies according to the following modes: determining the signal-to-noise ratio of interference phases between a first signal received by a fixed large-aperture antenna and a different second signal received by a target large-aperture antenna through step adjustment, and fitting the step amount and the different signal-to-noise ratios to obtain a directional correction amount corresponding to the maximum signal-to-noise ratio; according to the directional correction quantity of the plurality of standard correction power sources and the general antenna directional error model, fitting to obtain a directional correction model parameter; and calibrating the direction of the large-caliber deep space interferometry antenna according to the direction correction model parameters during actual deep space measurement and control. The scheme overcomes the dependence of the traditional antenna pointing calibration method on the sensitivity of radiometer equipment.

Description

Deep space measurement and control interferometry large-aperture antenna pointing calibration method and device
Technical Field
The invention relates to the technical field of information acquisition and processing, in particular to a method and a device for calibrating the pointing direction of a deep space measurement and control interferometric large-aperture antenna.
Background
In order to effectively support deep space exploration (exploration to a wider solar system space on the basis of significant achievement of satellite application and manned space), ground measurement and control resources are generally configured with large-aperture antennas with high system gain sensitivity. The pointing accuracy is an important technical index for measuring the deep space measurement and control large-aperture antenna, and in the physical construction process of the antenna, due to the influence of factors such as mechanical errors, gravity and external environment, the electric axis and the geometric axis of the antenna cannot be ensured to be coincident as much as possible, so that the deviation between the theoretical pointing direction and the actual pointing direction exists, and the efficiency of receiving target signals is influenced.
In the conventional antenna pointing calibration method, an energy radiometer is configured at a receiving end (namely an observation source), a calibration power source is subjected to sky-patrol observation, the pointing direction of each observation source is corrected by observing the change of a radiation count value, and an antenna pointing direction correction model is calculated based on the pointing direction correction values of all the observation sources. This calibration approach is limited by the sensitivity of the radiometer device and the calibration radio power supply current density.
Disclosure of Invention
The embodiment of the invention provides a deep space measurement and control interferometry large-aperture antenna pointing calibration method and device, and solves the technical problem that the traditional antenna pointing calibration method in the prior art depends on the sensitivity of radiometer equipment.
The pointing calibration method for the deep space measurement and control interferometry large-aperture antenna provided by the embodiment of the invention comprises the following steps:
calculating the directional correction amounts of the fixed large-aperture antenna and the target large-aperture antenna pointing to the plurality of calibration and calibration power supplies, wherein the pointing direction of the fixed large-aperture antenna is fixed, and the pointing direction of the target large-aperture antenna is adjusted in a stepping mode;
wherein the directional correction amount for a reference calibration power source is determined as follows: the fixed large-aperture antenna receives a first signal, the target large-aperture antenna receives different second signals through stepping adjustment, the signal-to-noise ratio of interference phases between the first signal and the different second signals is determined, fitting interpolation calculation is carried out on stepping amount and the different signal-to-noise ratios, and the pointing correction amount corresponding to the maximum signal-to-noise ratio is determined;
according to the universal antenna pointing error model, fitting according to the pointing correction quantities of the plurality of calibration and correction power sources to obtain a large-caliber deep space interferometry antenna pointing correction model parameter;
and calibrating the direction of the large-caliber deep space interferometry antenna according to the direction correction model parameters during actual deep space measurement and control.
The pointing calibration device for the deep space measurement and control interferometry large-aperture antenna provided by the embodiment of the invention comprises:
the directional correction quantity calculating module is used for calculating directional correction quantities of the fixed large-aperture antenna and the target large-aperture antenna pointing to the plurality of calibration radio sources, wherein the direction of the fixed large-aperture antenna is fixed, and the direction of the target large-aperture antenna is adjusted in a stepping mode;
wherein the directional correction amount for a reference calibration power source is determined as follows: the fixed large-aperture antenna receives a first signal, the target large-aperture antenna receives different second signals through stepping adjustment, the signal-to-noise ratio of interference phases between the first signal and the different second signals is determined, fitting interpolation calculation is carried out on stepping amount and the different signal-to-noise ratios, and the pointing correction amount corresponding to the maximum signal-to-noise ratio is determined;
the pointing correction model parameter calculation module is used for fitting according to the pointing correction quantity of the plurality of calibration and correction power sources and the universal antenna pointing error model to obtain pointing correction model parameters of the large-caliber deep space interferometry antenna;
and the calibration module is used for calibrating the pointing direction of the large-caliber deep space interferometric antenna according to the pointing direction correction model parameters when actual deep space measurement and control are carried out.
The embodiment of the present invention further provides a computer device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the method when executing the computer program.
The embodiment of the invention also provides a computer readable storage medium, and the computer readable storage medium stores a computer program for executing the method.
In the embodiment of the invention, a double-station linkage type sky-tracking observation standard calibration power supply is adopted, namely, the pointing direction of the other antenna is firstly fixed, the pointing direction of the target antenna is corrected in a stepping mode, the signal-to-noise ratios of interference fringes of received signals corresponding to different stepping quantities are recorded, the peak position of the signal-to-noise ratio is calculated by fitting the stepping quantities and the signal-to-noise ratios, the pointing correction deviation of the antenna in the direction is obtained, and finally, an antenna pointing correction error model is calculated according to deviation correction values of a plurality of sky-tracking pointing directions, so that the calculation quantity of the pointing deviation of the antenna in a certain pointing direction is calculated by fully utilizing interference phase signal-to-noise ratio information of the standard calibration power supply obtained by deep space measurement and control interference measurement. The method overcomes the dependence of the traditional antenna pointing calibration method on the sensitivity of radiometer equipment, improves the flow selection range of the calibration radio source, and has obvious application prospect in the field of deep space measurement and control interferometry.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of a pointing calibration method for a deep space measurement and control interferometry large-aperture antenna provided by an embodiment of the invention;
fig. 2 is a flowchart of a method for obtaining an antenna pointing correction error model coefficient according to an embodiment of the present invention;
FIG. 3 is an exemplary illustration of interference phases of a calibration RF source according to an embodiment of the present invention;
fig. 4 is a structural block diagram of a deep space measurement and control interferometry large-aperture antenna pointing calibration device provided by the embodiment of the invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the embodiment of the present invention, a deep space measurement and control interferometry large-aperture antenna pointing calibration method is provided, as shown in fig. 1 and fig. 2, the method includes:
step 101: calculating the directional correction amounts of the fixed large-aperture antenna and the target large-aperture antenna pointing to the plurality of calibration and calibration power supplies, wherein the pointing direction of the fixed large-aperture antenna is fixed, and the pointing direction of the target large-aperture antenna is adjusted in a stepping mode; wherein the directional correction amount for a reference calibration power source is determined as follows:
step 1011: the fixed large-aperture antenna receives a first signal, and the target large-aperture antenna receives different second signals through stepping adjustment;
step 1012: determining a signal-to-noise ratio of an interference phase between the first signal and the different second signal;
step 1013: fitting interpolation calculation is carried out on the stepping quantity and different signal-to-noise ratios, and the pointing correction quantity corresponding to the maximum signal-to-noise ratio is determined;
step 102: according to the universal antenna pointing error model, fitting according to the pointing correction quantities of the plurality of calibration and correction power sources to obtain a large-caliber deep space interferometry antenna pointing correction model parameter;
step 103: and calibrating the direction of the large-caliber deep space interferometry antenna according to the direction correction model parameters during actual deep space measurement and control.
In the embodiment of the present invention, the step amount is determined as follows:
Figure BDA0002164597280000041
wherein, thetaA_stepStep length in azimuth direction; thetaE_stepStep length in pitching direction; theta is the antenna beam width; λ is wavelength, unit meter; d is the antenna aperture in meters.
In the embodiment of the present invention, 5 (or other ones, set as required) step lengths are respectively adjusted to the azimuth direction and the pitch direction in a successive increment manner according to the positive direction and the negative direction, and the interference fringe (phase) is respectively calculated to calculate the signal-to-noise ratio:
Figure BDA0002164597280000042
Figure BDA0002164597280000043
wherein, SNR is signal-to-noise ratio; rhomaxIs the peak of the resolution function; deltainvIs a resolution function impact factor; n is the number of sub-integration periods; t isintFor integration time, FsIs the sampling bandwidth.
In the embodiment of the invention, for a certain standard calibration power supply, the step amount and different signal-to-noise ratios are subjected to fitting interpolation calculation according to the following modes:
with z, e as independent variables, AsnrFitting a two-dimensional curved surface as a function to obtain an independent variable corresponding to a peak point of the function value, wherein the independent variable is an azimuth correction zδElevation direction eδA correction amount;
wherein,
Figure BDA0002164597280000044
wherein, z ═ z1, z2, z3, z4, z5] represents vectors corresponding to azimuth step;
e ═ e1, e2, e3, e4, e5 denote vectors corresponding to pitch steps;
Zδ=[zδ1,zδ2......zδM];Eδ=[ze1,ze2......zeM]and M is the number of calibration power supplies. Wherein Z isδ、EδAnd 2-4, carrying out operation of the steps on the calibration power supplies in different pointing directions to obtain a series of azimuth and elevation correction values corresponding to different theoretical azimuth and elevation directions.
In the embodiment of the present invention, the general antenna pointing error model is:
Figure BDA0002164597280000051
wherein A is an azimuth pointing angle, Delta A is an azimuth pointing error, E is a pitch pointing angle, Delta E is a pitch pointing error, and parameter C1For azimuth encoder zero error, C2For the zero error, C, of the pitch encoder3Is an azimuth tilt error,
Figure BDA0002164597280000052
An azimuth coordinate in an azimuth inclination direction,
Figure BDA0002164597280000053
Is the included angle between the azimuth axis and the pitch axis, C6Is deviation of electric axis orientation, C7Is deformed by gravity, C8Is refracted to the atmosphere.
Through observation of multiple calibration power supplies, multiple values of A, delta A, E and delta E can be obtained, and parameter C is obtained through least square fitting calculation1、C2、C3、C4、C5、C6、C7、C8
Example (b): and carrying out observation verification by using the antenna of the station 1 and the antenna of the station 2, wherein the direction of the antenna of the station 2 is fixed, and the correction quantity of the direction of the antenna of the station 1 is adjusted step by step. FIG. 3 shows an example of the interference phase of a calibration-calibrated power supply.
By the method and the universal antenna pointing error model, the following correction parameters can be finally obtained:
0.10655、-0.2161、0.00567、155.34、0.0082,0.0065,0.0396,0.0092。
when actual deep space measurement and control are carried out, the pointing directions of the large-caliber deep space interferometric antenna are calibrated by using the parameters.
Based on the same inventive concept, the embodiment of the invention also provides a pointing calibration device for the deep space measurement and control interferometry large-aperture antenna, which is described in the following embodiment. The principle of solving the problems of the deep space measurement and control interferometry large-aperture antenna pointing calibration device is similar to that of the deep space measurement and control interferometry large-aperture antenna pointing calibration method, so the implementation of the deep space measurement and control interferometry large-aperture antenna pointing calibration device can refer to the implementation of the deep space measurement and control interferometry large-aperture antenna pointing calibration method, and repeated parts are not repeated. As used hereinafter, the term "unit" or "module" may be a combination of software and/or hardware that implements a predetermined function. Although the means described in the embodiments below are preferably implemented in software, an implementation in hardware, or a combination of software and hardware is also possible and contemplated.
Fig. 4 is a structural block diagram of a deep space measurement and control interferometry large-aperture antenna pointing calibration device according to an embodiment of the present invention, as shown in fig. 4, including:
the directional correction amount calculation module 401 is configured to calculate directional correction amounts of the fixed large-aperture antenna and the target large-aperture antenna pointing to the multiple calibration radiation sources, where the pointing direction of the fixed large-aperture antenna is fixed, and the pointing direction of the target large-aperture antenna is adjusted in a stepping mode;
wherein the directional correction amount for a reference calibration power source is determined as follows: the fixed large-aperture antenna receives a first signal, the target large-aperture antenna receives different second signals through stepping adjustment, the signal-to-noise ratio of interference phases between the first signal and the different second signals is determined, fitting interpolation calculation is carried out on stepping amount and the different signal-to-noise ratios, and the pointing correction amount corresponding to the maximum signal-to-noise ratio is determined;
the pointing correction model parameter calculation module 402 is configured to obtain a pointing correction model parameter of the large-aperture deep space interferometry antenna according to the universal antenna pointing error model and by fitting pointing correction quantities of the plurality of calibration and calibration power sources;
and the calibration module 403 is configured to calibrate the pointing direction of the large-aperture deep space interferometric antenna according to the pointing direction correction model parameter when performing actual deep space measurement and control.
In this embodiment of the present invention, the directional correction amount calculating module 401 is specifically configured to:
the step size is determined as follows:
Figure BDA0002164597280000061
wherein, thetaA_stepStep length in azimuth direction; thetaE_stepStep length in pitching direction; theta is the antenna beam width; λ is wavelength, unit meter; d is the antenna aperture in meters.
In this embodiment of the present invention, the directional correction amount calculating module 401 is specifically configured to:
the signal-to-noise ratio is determined as follows:
Figure BDA0002164597280000062
Figure BDA0002164597280000063
wherein, SNR is signal-to-noise ratio; rhomaxIs the peak of the resolution function; deltainvIs a resolution function impact factor; n is the number of sub-integration periods; t isintFor integration time, FsIs the sampling bandwidth.
In this embodiment of the present invention, the directional correction amount calculating module 401 is specifically configured to:
and performing fitting interpolation calculation on the stepping quantity and different signal-to-noise ratios according to the following modes:
with z, e as independent variables, AsnrFitting a two-dimensional curved surface as a function to obtain an independent variable corresponding to a peak point of the function value, wherein the independent variable is an azimuth correction zδElevation direction eδA correction amount;
wherein,
Figure BDA0002164597280000064
wherein, z ═ z1, z2, z3, z4, z5] represents vectors corresponding to azimuth step;
e ═ e1, e2, e3, e4, e5 denote vectors corresponding to pitch steps;
Zδ=[zδ1,zδ2......zδM];Eδ=[ze1,ze2......zeM]and M is the number of calibration power supplies.
The embodiment of the present invention further provides a computer device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the method when executing the computer program.
The embodiment of the invention also provides a computer readable storage medium, and the computer readable storage medium stores a computer program for executing the method.
In summary, the two-station linkage type sky observation standard calibration power supply is adopted, namely, the pointing direction of the other antenna is firstly fixed, the pointing direction of the target antenna is corrected in a stepping mode, the signal-to-noise ratios of interference fringes of received signals corresponding to different stepping amounts are recorded, the signal-to-noise ratio peak value position is calculated by fitting the stepping amounts and the signal-to-noise ratios, the pointing correction deviation of the antenna in the direction is obtained, and finally, an antenna pointing correction error model is calculated according to deviation correction values of a plurality of sky observation and control pointing directions, so that the calculation amount of the pointing deviation of the antenna in a certain pointing direction is calculated by fully utilizing interference phase signal-to-noise ratio information of the standard calibration power supply obtained by deep space measurement and control interference measurement. The method overcomes the dependence of the traditional antenna pointing calibration method on the sensitivity of radiometer equipment, improves the flow selection range of the calibration radio source, and has obvious application prospect in the field of deep space measurement and control interferometry.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes may be made to the embodiment of the present invention by those skilled in the art. 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 (8)

1. A deep space measurement and control interferometry large-aperture antenna pointing calibration method is characterized by comprising the following steps:
calculating the directional correction amounts of the fixed large-aperture antenna and the target large-aperture antenna pointing to the plurality of calibration and calibration power supplies, wherein the pointing direction of the fixed large-aperture antenna is fixed, and the pointing direction of the target large-aperture antenna is adjusted in a stepping mode;
wherein the directional correction amount for a reference calibration power source is determined as follows: the fixed large-aperture antenna receives a first signal, the target large-aperture antenna receives different second signals through stepping adjustment, the signal-to-noise ratio of interference phases between the first signal and the different second signals is determined, fitting interpolation calculation is carried out on stepping amount and the different signal-to-noise ratios, and the pointing correction amount corresponding to the maximum signal-to-noise ratio is determined;
according to the universal antenna pointing error model, fitting according to the pointing correction quantities of the plurality of calibration and correction power sources to obtain a large-caliber deep space interferometry antenna pointing correction model parameter;
when actual deep space measurement and control are carried out, the pointing direction of the large-caliber deep space interferometric antenna is calibrated according to the pointing direction correction model parameters;
and performing fitting interpolation calculation on the stepping quantity and different signal-to-noise ratios according to the following modes:
with z, e as independent variables, AsnrFitting a two-dimensional curved surface as a function to obtain an independent variable corresponding to a peak point of the function value, wherein the independent variable is an azimuth correction zδElevation direction eδA correction amount;
wherein,
Figure FDA0003070629840000011
wherein, z ═ z1, z2, z3, z4, z5] represents vectors corresponding to azimuth step;
e ═ e1, e2, e3, e4, e5 denote vectors corresponding to pitch steps;
Zδ=[zδ1,zδ2......zδM];Eδ=[ze1,ze2......zeM]and M is the number of calibration power supplies.
2. The deep space measurement and control interferometry large-aperture antenna pointing calibration method according to claim 1, wherein the step amount is determined according to the following mode:
Figure FDA0003070629840000012
wherein, thetaA_stepStep length in azimuth direction; thetaE_stepStep length in pitching direction; theta is the antenna beam width; λ is wavelength, unit meter; d is the antenna aperture in meters.
3. The deep space measurement and control interferometry large-aperture antenna pointing calibration method according to claim 1, wherein the signal-to-noise ratio is determined as follows:
Figure FDA0003070629840000021
Figure FDA0003070629840000022
wherein, SNR is signal-to-noise ratio; rhomaxIs the peak of the resolution function; deltainvIs a resolution function impact factor; n is the number of sub-integration periods; t isintFor integration time, FsIs the sampling bandwidth.
4. The utility model provides a directional calibration device of deep space measurement and control interferometry large-diameter antenna which characterized in that includes:
the directional correction quantity calculating module is used for calculating directional correction quantities of the fixed large-aperture antenna and the target large-aperture antenna pointing to the plurality of calibration radio sources, wherein the direction of the fixed large-aperture antenna is fixed, and the direction of the target large-aperture antenna is adjusted in a stepping mode;
wherein the directional correction amount for a reference calibration power source is determined as follows: the fixed large-aperture antenna receives a first signal, the target large-aperture antenna receives different second signals through stepping adjustment, the signal-to-noise ratio of interference phases between the first signal and the different second signals is determined, fitting interpolation calculation is carried out on stepping amount and the different signal-to-noise ratios, and the pointing correction amount corresponding to the maximum signal-to-noise ratio is determined;
the pointing correction model parameter calculation module is used for fitting according to the pointing correction quantity of the plurality of calibration and correction power sources and the universal antenna pointing error model to obtain pointing correction model parameters of the large-caliber deep space interferometry antenna;
the calibration module is used for calibrating the pointing direction of the large-caliber deep space interferometric antenna according to the pointing direction correction model parameters when actual deep space measurement and control are carried out;
the directional correction amount calculation module is specifically configured to:
and performing fitting interpolation calculation on the stepping quantity and different signal-to-noise ratios according to the following modes:
with z, e as independent variables, AsnrFitting a two-dimensional curved surface as a function to obtain an independent variable corresponding to a peak point of the function value, wherein the independent variable is an azimuth correction zδElevation direction eδA correction amount;
wherein,
Figure FDA0003070629840000023
wherein, z ═ z1, z2, z3, z4, z5] represents vectors corresponding to azimuth step;
e ═ e1, e2, e3, e4, e5 denote vectors corresponding to pitch steps;
Zδ=[zδ1,zδ2......zδM];Eδ=[ze1,ze2......zeM]and M is the number of calibration power supplies.
5. The deep space measurement and control interferometry large-aperture antenna pointing calibration device according to claim 4, wherein the pointing correction amount calculation module is specifically configured to:
the step size is determined as follows:
Figure FDA0003070629840000031
wherein, thetaA_stepStep length in azimuth direction; thetaE_stepStep length in pitching direction; theta is the antenna beam width; λ is wavelength, unit meter; d is the antenna aperture in meters.
6. The deep space measurement and control interferometry large-aperture antenna pointing calibration device according to claim 4, wherein the pointing correction amount calculation module is specifically configured to:
the signal-to-noise ratio is determined as follows:
Figure FDA0003070629840000032
Figure FDA0003070629840000033
wherein, SNR is signal-to-noise ratio; rhomaxIs the peak of the resolution function; deltainvIs a resolution function impact factor; n is the number of sub-integration periods; t isintFor integration time, FsIs the sampling bandwidth.
7. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the method of any of claims 1 to 3 when executing the computer program.
8. A computer-readable storage medium, characterized in that the computer-readable storage medium stores a computer program for executing the method of any one of claims 1 to 3.
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