Error analysis method and device for constellation cluster geometry cross calibration

Abstract

The present application relates to a kind of error analysis method and device for constellation constellation geometry intersection calibration, comprising: simulating the original echo data corresponding to main image and slave image;According to the intersection region between main image and slave image, virtual control point is extracted;According to original echo data, virtual control point and simulation error, auxiliary star is geometrically calibrated, and calibration result is obtained;Wherein, simulation error includes one or more of position error, velocity error and / or atmospheric delay;According to calibration result and simulation error, error analysis is carried out.Through the above technical scheme, the problem that error data simulation is difficult in constellation constellation geometry intersection calibration is solved.With the present application, various errors can be simulated intuitively and accurately for the data of intersection analysis between multiple stars, without the need to specially find image data containing various specific errors, and without the need to simulate various errors from existing images, which greatly reduces the research cost of personnel engaged in constellation research.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of synthetic aperture radar imaging detection, in particular to an error analysis method and device for constellation star group geometric cross calibration. BACKGROUND

[0002] Synthetic aperture radar (SAR) is a microwave imaging radar system, which is not limited by weather and light conditions. Existing ground-based, airborne and satellite-based systems have been widely used in environmental monitoring, topographic mapping, resource exploration and other fields.

[0003] With the gradual deepening of SAR related technology research, the demand for SAR data of researchers is also rising. According to the needs of each link, the SAR echo required by independent simulation plays an important role in solving such problems. Research on SAR echo simulation of the whole chain can greatly reduce the demand for SAR data acquisition, development of experimental SAR systems and other needs.

[0004] Geometric calibration refers to correcting the geometric parameters of the imaging system by using model analysis or high-precision control data, so as to achieve more accurate positioning performance. Due to the platform height, observation geometry and other reasons, the influence of system error on satellite SAR is greater than that on airborne SAR system. Therefore, it is necessary to calibrate the geometry of satellite SAR system.

[0005] In recent years, satellite launches in various countries have shown a rapid and large-scale trend, and satellite networking is the goal. For image acquisition and geographic information mapping in a large range of the world, it is of great significance to quickly realize the geometric calibration of each satellite in the star constellation scenario. Through cross geometric calibration, the calibration of each satellite is quickly realized to achieve high-precision positioning, and through comprehensive and rapid error analysis, the calibration of each type of satellite is simulated and analyzed. At present, it is difficult to obtain SAR data of the star constellation, and it is difficult to perform comprehensive error analysis of cross geometric calibration. It is an indispensable work to realize the simulation of full-link SAR echo data and the targeted error analysis of cross geometric calibration. SUMMARY

[0006] In order to solve the above problems in the prior art, the present application provides an error analysis method and device for constellation star group geometric cross calibration.

[0007] According to a first aspect of an embodiment of the present application, an error analysis method for constellation star group geometric cross calibration is provided, the method comprising:

[0008] Simulating the original echo data corresponding to the main star and the auxiliary star;

[0009] extracting a virtual control point according to a cross region between a main image and a slave image, wherein the main image is obtained according to the main star, and the slave image is obtained according to the auxiliary star;

[0010] geometrically calibrating the auxiliary star according to the original echo data, the virtual control point and a simulated error to obtain a calibration result, wherein the simulated error comprises one or more of a position error, a velocity error and / or an atmospheric delay;

[0011] performing error analysis according to the calibration result and the simulated error.

[0012] Optionally, the original echo data corresponding to the simulated main star and auxiliary star comprises:

[0013] The original echo data is obtained by using a range frequency domain pulse coherence method.

[0014] The original echo data is expressed in a form of frequency domain calculation according to a convolution distribution property, so as to obtain the original echo data in the form of frequency domain calculation.

[0015] Optionally, the extracting the virtual control point according to the cross region between the main image and the slave image comprises:

[0016] Respective target points corresponding to the same geographical position in the main image and the slave image are obtained as feature points.

[0017] The feature points in the cross region are extracted as initial virtual points.

[0018] The virtual control point is obtained by screening the initial virtual points.

[0019] Optionally, after the virtual control point is obtained by screening the initial virtual points, the method further comprises:

[0020] A joint error equation is established according to orbit parameters of the main star and the auxiliary star.

[0021] A fitting coefficient is calculated according to the joint error equation.

[0022] Specific coordinates of the virtual control point are obtained according to initial coordinates of the virtual control point and the fitting coefficient.

[0023] Optionally, the geometrically calibrating the auxiliary star according to the original echo data, the virtual control point and a simulated error to obtain a calibration result comprises:

[0024] Orbit information is calculated by using the original echo data.

[0025] adding errors to the orbit information by using the simulation errors, to obtain the orbit information after adding errors;

[0026] geometrically calibrating the secondary satellite by using a range-Doppler model, specific coordinates of the virtual control point and the orbit information after adding errors.

[0027] Optionally, the position error is as follows:

[0028]

[0029]

[0030] wherein Δx1 represents a position error along a track direction in the position error, ΔR x represents a range error along the track, R e represents an equatorial radius of the earth, H represents a flight height of the secondary satellite, ΔR e represents a position error perpendicular to the track direction in the position error, ΔR y represents a range error perpendicular to the track.

[0031] Optionally, the velocity error is as follows:

[0032]

[0033] wherein Δ x represents a velocity error, θ s represents a squint angle of a beam center of the secondary satellite, γ represents a downward angle of the beam center of the secondary satellite, ΔV x represents a velocity error along the track, ΔV y represents a velocity error perpendicular to the track, ΔV z represents a velocity error along a radial direction, V r represents a fitting velocity of the secondary satellite, V g represents an observed velocity of the secondary satellite, R s is a slant range from a radar on the secondary satellite to the virtual control point.

[0034] Optionally, the atmospheric delay includes an ionospheric delay and a tropospheric delay, and the ionospheric delay is as follows:

[0035]

[0036] wherein n e represents an electron density in the atmosphere, K is a constant, K = e 2 / 8πε0m e = 40.28 m 3 / s 2 , ε0 represents a dielectric constant, me represents the electron mass, TEC represents the integral of the electron density along the propagation path, TEC = ∫n e ds, f com represents the frequency of the current dispersion component.

[0037] Optionally, the tropospheric delay is as follows:

[0038] p0 = ∫v dτ ≈ cΔτ vac - ∫(n e -1)ds;

[0039] wherein p0 represents the true distance of signal propagation of the secondary star, v represents the propagation speed of the electromagnetic wave in the troposphere, dτ represents a time infinitesimal, Δτ vac represents the time of the signal passing through p0 in vacuum, ds is an infinitesimal of the propagation path, ∫(n e -1)ds represents the tropospheric delay, and c represents the propagation speed of the electromagnetic wave in vacuum.

[0040] According to a second aspect of the embodiments of the present application, an error analysis device for constellation star group geometric cross calibration is provided, and the device comprises:

[0041] a data simulation module configured to simulate original echo data corresponding to a primary image and a secondary image; wherein the primary image is obtained according to a primary star, and the secondary image is obtained according to a secondary star;

[0042] a control point extraction module configured to extract a virtual control point according to a cross region between the primary image and the secondary image;

[0043] a geometric calibration module configured to perform geometric calibration on the secondary star according to the original echo data, the virtual control point and a simulation error to obtain a calibration result; wherein the simulation error comprises one or more of a position error, a velocity error, an atmospheric delay, a slant range measurement error and a virtual control point position transfer error;

[0044] an error analysis module configured to perform error analysis according to the calibration result and the simulation error.

[0045] The technical scheme provided by the embodiments of the present application can include the following beneficial effects:

[0046] In the technical solution, the original echo data corresponding to the simulation main image and the slave image is obtained; the main image is obtained according to the main star, and the slave image is obtained according to the auxiliary star; the virtual control points are extracted according to the intersection area between the main image and the slave image; the auxiliary star is geometrically calibrated according to the original echo data, the virtual control points and the simulation error to obtain the calibration result; the simulation error includes one or more of the position error, the speed error and / or the atmospheric delay; and the error analysis is performed according to the calibration result and the simulation error. Through the technical solution, the problem of difficult error data simulation in the geometric intersection calibration of the constellation star group is solved. With the application, the simulation of various errors for the data analyzed in the intersection between the multiple stars can be intuitively and accurately performed, the image data containing various specific errors no longer needs to be specially searched, and various errors no longer needs to be simulated from the existing images, so that the research cost of the staff engaged in the research of the star group constellation is greatly reduced.

[0047] Other features and advantages of the present application will be described in detail in the following specific embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0048] The accompanying drawings are included to provide a further understanding of the application, and constitute a part of the specification, and are used together with the following specific embodiments to explain the application, but do not constitute a limitation on the application. In the drawings:

[0049] Figure 1 is a flowchart of an error analysis method for geometric intersection calibration of a constellation star group according to an exemplary embodiment.

[0050] Figure 2 is a schematic diagram of a main star and an auxiliary star according to an exemplary embodiment.

[0051] Figure 3 is a schematic diagram of a satellite position measurement error module according to an exemplary embodiment.

[0052] Figure 4 is a schematic diagram of a satellite speed measurement error module according to an exemplary embodiment.

[0053] Figure 5 is a schematic diagram of an ionosphere and troposphere influence module according to an exemplary embodiment.

[0054] Figure 6 is a flowchart of an error analysis device for geometric intersection calibration of a constellation star group according to an exemplary embodiment. DETAILED DESCRIPTION

[0055] Figure 1 is a flowchart of an error analysis method for geometric intersection calibration of a constellation star group according to an exemplary embodiment, asFigure 1 As shown, the method comprises the following steps.

[0056] S101, simulating original echo data corresponding to the main star and the auxiliary star.

[0057] It can be understood that the original echo data corresponding to the main star and the auxiliary star simulated in the application is the echo data of a simulated synthetic aperture radar (SAR). If other radar echo data needs to be simulated, it is determined according to the actual situation.

[0058] S102, extracting a virtual control point according to the intersection area between the main image and the slave image; wherein the main image is obtained according to the main star, and the slave image is obtained according to the auxiliary star.

[0059] It can be understood that before the virtual control point is extracted according to the intersection area between the main image and the slave image, the main star can be geometrically calibrated, and it is necessary to ensure that the slant range of the main star calibration is better than the accuracy threshold, for example, 4 meters.

[0060] S103, geometrically calibrating the auxiliary star according to the original echo data, the virtual control point and the simulated error to obtain a calibration result; wherein the simulated error includes one or more of the position error, the velocity error and / or the atmospheric delay.

[0061] It can be understood that in the process of geometrically calibrating the auxiliary star, one or more simulated errors are added to the data in the calibration process, so as to simulate interference for the geometric calibration of the auxiliary star. The type of simulated error to be added is determined according to the actual situation.

[0062] S104, error analysis according to the calibration result and the simulated error.

[0063] It can be understood that the obtained calibration result is the result affected by the simulated error, so the calibration result can be analyzed, and the analysis result is compared with the simulated error.

[0064] Optionally, S101 can comprise:

[0065] Using the range frequency domain pulse coherence method, the original echo data is obtained;

[0066] According to the convolution distribution property, the original echo data is expressed in the form of frequency domain calculation, and the original echo data in the form of frequency domain calculation is obtained.

[0067] It can be understood that the primary star and the secondary star are used to produce the primary image and the secondary image respectively. Using the range frequency pulse coherence (RFPC), the time shift term in the signal is expressed in the form of convolution with an impulse signal, and the original echo data of any target point (m, n) in the primary image or the secondary image is:

[0068]

[0069] Wherein, ξ and τ are slow time and fast time respectively, f t is the carrier frequency of the transmitted signal, σ c (m, n) is the bistatic scattering coefficient of the target point, W(ξ; m, n) is the comprehensive loss parameter, which is affected by the radar transmitting power, the transmitting and receiving antenna gain, etc., τ d is the echo time delay, and p0(τ) is the baseband linear frequency modulation signal.

[0070] According to the convolution distribution property, the following can be obtained:

[0071]

[0072] Wherein, Further, s r (ξ, τ; m, n) is expressed in the form of frequency domain calculation:

[0073] s r (ξ, τ; m, n) = IFFT{FFT[h(ξ, τ; m, n)]·FFT[p0(τ)]}.

[0074] Optionally, S102 can include:

[0075] Respectively, the target points corresponding to the same geographical position in the primary image and the secondary image are obtained as feature points;

[0076] The feature points in the cross region are extracted as initial virtual points;

[0077] The virtual control points are obtained by screening the initial virtual points.

[0078] Optionally, after the virtual control points are obtained by screening the initial virtual points, the method further includes:

[0079] A joint error equation is established according to the orbit parameters of the primary star and the secondary star;

[0080] The fitting coefficients are calculated according to the joint error equation;

[0081] The specific coordinates of the virtual control points are obtained according to the initial coordinates of the virtual control points and the fitting coefficients.

[0082] It can be understood that, in the master, the slave image data is searched for feature points, that is, target points corresponding to the same geographical position, and the direction of the feature points is calculated, and the initial virtual control points of the intersection area are extracted, which can be mainly based on the corner points, edge points, bright points and dark points. Each feature point corresponds to three elements of position, scale and direction. The initial virtual points between the master image and the slave image are matched by identifying adjacent points, and after a certain condition is screened, a certain number of virtual control points are determined. For the virtual control points obtained by intersection, a joint error equation is established according to the track parameters, and the fitting coefficients are solved, and the virtual control point coordinates are output and judged according to the set threshold. Finally, the specific coordinates of a certain number of virtual control points are obtained. According to the obtained virtual control point coordinates, the slave image is geometrically calibrated in combination with the track data of the auxiliary star.

[0083] In an example, in the embodiment, the multi-star data is simulated by two images, one is the ascending track image, and the other is the descending track image. The ascending track image is regarded as the master image, and the descending track image is regarded as the slave image. The intersection area is about 30%. And 25 virtual control points are uniformly arranged in the overlapping area of the two images. The longitude range of the slave image is 115.59516662-115.68336596, and the latitude range is 40.94207267-41.15662709.

[0084] Optionally, S103 can include:

[0085] The track information is calculated by using the original echo data;

[0086] The track information is added with errors by using the simulation errors, to obtain the track information after adding errors;

[0087] The auxiliary star is geometrically calibrated by using the range-Doppler model, the specific coordinates of the virtual control points and the track information after adding errors.

[0088] It can be understood that, Figure 2 is a schematic diagram of a master star and an auxiliary star according to an example embodiment, as Figure 2 As shown, the blue triangle in the intersection area of the master image and the slave image represents the virtual control point, and the yellow triangle represents the target point in the master image. In the pre-calibration of the master star, the range-Doppler model can also be used. Taking the master star as an example, in the case of self-transmission and self-reception of the master star, the geometric calibration model of the master star is as follows:

[0089] |R m1 |=|P t -P sat1_T |+R equ1 ;

[0090] |R m1 |=|P t -P sat1_T|+R equ1 ;

[0091]

[0092] Among them, P t P is the position vector of the target point. sat1_T It is the position vector at the moment of primary star pulse emission, P sat1_R R is the position vector at the moment the primary star pulse is received. equ1 and R equ2 These are the slant range errors caused by the primary and secondary satellite systems and the equivalent slant range error caused by atmospheric delay, R. m1 R is the slant distance from the primary satellite's launch point to the target point. m2 V is the slant range from the primary satellite to the target point at the moment of reception, θ is the angle between the satellite velocity vector and the slant range vector, and V sat1_T With V sat1_R These are the velocity vectors at the moments of primary star emission and reception of pulses, f. d Let be the Doppler frequency corresponding to the target point in the scene. When initially calculating the parameters in the above geometric model, the corresponding imaging time is calculated based on the pixel coordinates (m,n) of the target point, and then combined with the nearest slant range R of the main image. near The slant distance of the target point in the main image is calculated, and the platform position and velocity information at the corresponding time are derived by the least squares method.

[0093] In one implementation, satellite position measurement errors affect the estimation of the satellite's equivalent velocity, which in turn affects the estimation of the azimuth modulation frequency and the azimuth Doppler center frequency based on orbital data. The satellite position error is decomposed into three error components: along the track, perpendicular to the track, and radial. These three directions of error have different impacts on the target's positioning accuracy. Errors along the track primarily affect the target's azimuth positioning accuracy, while errors perpendicular to the track primarily affect the target's range positioning accuracy. Under direct viewing conditions, radial position measurement errors can be ignored. The position errors generated along the track and perpendicular to the track are as follows:

[0094]

[0095]

[0096] Where Δx1 represents the position error along the flight path in the position error, ΔR x R represents the distance error along the flight path. e ΔR represents the Earth's equatorial radius, H represents the secondary star's altitude, and ΔR represents the orbital radius of the secondary star. e ΔR represents the position error perpendicular to the track direction within the position error. y This represents the distance error perpendicular to the flight path.

[0097] The satellite velocity measurement error only affects the determination of the Doppler plane, and since the Doppler plane only affects the positioning accuracy in the azimuth direction, the platform velocity measurement error also only affects the positioning accuracy in the azimuth direction, and the velocity error is shown in the following formula:

[0098]

[0099] wherein, Δ x represents the velocity error, θ s represents the slant angle of the beam center of the secondary satellite, γ represents the downward angle of the beam center of the secondary satellite, ΔV x represents the velocity error along the track, ΔV y represents the velocity error perpendicular to the track, ΔV z represents the velocity error along the radial direction, V r represents the fitting velocity of the secondary satellite, V g represents the observed velocity of the secondary satellite, R s is the slant range from the radar on the secondary satellite to the virtual control point.

[0100] The influence of the atmosphere on the echo signal mainly reflects in the ionosphere and the troposphere, and the atmospheric delay includes the ionospheric delay and the tropospheric delay, and the ionospheric delay is shown in the following formula:

[0101]

[0102] wherein, n e represents the electron density in the atmosphere, K is a constant, K = e 2 / 8πε0m e = 40.28 m 3 / s 2 , ε0 represents the dielectric constant, m e represents the electron mass, TEC represents the integral of the electron density along the propagation path, TEC = ∫n e ds, f com represents the frequency of the current dispersion component.

[0103] The tropospheric delay is shown in the following formula:

[0104] ρ0 = ∫vdτ ≈ cΔτ vac - ∫(n e - 1)ds;

[0105] wherein, ρ0 represents the true distance of the signal propagation of the secondary satellite, v represents the propagation speed of the electromagnetic wave in the troposphere, dτ represents the time infinitesimal, Δτ vac represents the time of the signal passing through ρ0 in vacuum, ds is the infinitesimal of the propagation path, ∫(n e - 1)ds represents the tropospheric delay, and c represents the propagation speed of the electromagnetic wave in vacuum.

[0106] It can be understood that, in addition to position error, speed error and atmospheric delay, slant range measurement error and virtual control point position transfer error can also be added by using prior art solutions. For the above-mentioned errors, independent error adding modules can be respectively set. In the design of the satellite platform module, satellite position measurement error and satellite speed measurement error can be added. In the design of the transmission link module, the effects of ionosphere and troposphere can be respectively set, Figure 3 is a schematic diagram of a satellite position measurement error module according to an example embodiment, Figure 4 is a schematic diagram of a satellite speed measurement error module according to an example embodiment, Figure 5 is a schematic diagram of an ionosphere and troposphere effect module according to an example embodiment. In actual cases, the simulation error can be controlled by adjusting the parameters of each module.

[0107] In an implementation, it is assumed that the main image has completed calibration, and the slant range positioning accuracy is better than 4m. Therefore, in the error adding part, the error simulation is not performed for the main image and its related parameters, and the errors that may occur in the calibration process of the slave image are mainly analyzed.

[0108] The position error and the speed error mainly have two points, one is the error generated by the satellite itself when flying, and the other is the measurement error when measuring the position and speed of the satellite. In the WGS84 coordinate system, the error in each coordinate axis direction is fitted by using a polynomial, and the result is superimposed on the ideal satellite trajectory position and speed parameter, so as to complete the error addition. In this embodiment, the position error range is [-10-10] (unit, m), and the speed error range is [-5-5] (unit, m / s).

[0109] The auxiliary satellite slant range measurement error can be mapped to the satellite position error, or can be directly simulated in the processing process. The slant range measurement error is taken as [-10-10] (unit, m).

[0110] For ionospheric delay, the signal is divided into blocks according to the apparent angle, and Fourier transform is performed along the distance direction, and the phase delay of the corresponding block is multiplied to add the dispersion delay error.

[0111] The commonly used calculation model of tropospheric delay Δρ drop =∫(n e -1)ds has Hopfield model, Saastanmoinen model, Black model, EGNOS model, etc. The target point temperature T s , target point air pressure P ds in the model can be directly measured, and the target point water vapor partial pressure e ws can be calculated from the relative humidity RH:

[0112]

[0113] The tropospheric delay calculated above is in zenith direction, and the zenith tropospheric delay can be projected to the direction of the propagation path accurately by using the UNBabc model.

[0114] The tropospheric influence is independent of frequency but dependent on the propagation path, and can be added directly in the time domain. In the simulation process of the original echo data, the error can be calculated once when the response of each target point is calculated.

[0115] The coordinates of the virtual control points are obtained by cross transfer, and it is assumed that the pixel coordinates of the virtual control points obtained by transfer are (m+e m , n+e n ), wherein (e m , e n ) is the deviation of the transfer result relative to the ideal pixel coordinates, and the deviation value is set in the range of 5*5 around the ideal pixel coordinates, so as to be used as the result of adding the coordinate error of the virtual control point.

[0116] It can be understood that, when the error analysis is performed according to the calibration result and the simulation error, the virtual control points are extracted according to the cross transfer method, and the geometric calibration is performed on the auxiliary star.

[0117] The corresponding inter-satellite geometric cross-calibration error analysis is performed based on the present application. The above steps are performed on the embodiments, and the corresponding inter-satellite geometric cross-calibration result errors are as follows:

[0118] Table 1

[0119]

[0120]

[0121] In the present embodiment, when the trajectory position error and the trajectory velocity error change linearly in a single axis, the calibration result errors generated are also approximately linearly changed. According to the result data of the present embodiment, the effects of each error on each virtual control point are highly approximate, and the dispersion coefficients are all within 3.

[0122] In the present embodiment, the trajectory position error, the trajectory velocity error, the atmospheric delay, the slant range measurement error and the virtual control point coordinate error are added respectively by using the present device, the influence of a specific error source on the multi-satellite cross-calibration result is quickly and quantitatively analyzed, and the error consistency of the multi-virtual control points on the calibration result is verified.

[0123] By the technical scheme, the problem of difficulty in error data simulation in constellation star group geometric intersection calibration is solved. With the application, various errors of the data for intersection analysis among multiple stars can be simulated intuitively and accurately, and there is no need to specially search for image data containing various specific errors or to simulate various errors from the existing image, so that the research cost of the staff engaged in star group constellation research is greatly reduced.

[0124] Figure 6 is a flow chart of an error analysis device for constellation star group geometric intersection calibration according to an example embodiment, as shown in Figure 6 The device 600 comprises:

[0125] A data simulation module 601 is configured to simulate original echo data corresponding to a main image and a slave image. The main image is obtained according to a main star, and the slave image is obtained according to an auxiliary star.

[0126] A control point extraction module 602 is configured to extract a virtual control point according to an intersection area between the main image and the slave image.

[0127] A geometric calibration module 603 is configured to perform geometric calibration on the auxiliary star according to the original echo data, the virtual control point and a simulated error to obtain a calibration result. The simulated error comprises one or more of a position error, a velocity error, an atmospheric delay, a slant range measurement error and a virtual control point position transfer error.

[0128] An error analysis module 604 is configured to perform error analysis according to the calibration result and the simulated error.

[0129] As to the device in the above embodiment, the specific manner in which each module performs operations has been described in detail in the embodiment of the method, and will not be described in detail here.

[0130] The preferred embodiments of the application are described in detail above with reference to the drawings, but the application is not limited to the specific details in the above embodiments. Within the technical concept of the application, various simple modifications can be made to the technical scheme of the application, and these simple modifications all belong to the protection scope of the application.

[0131] In addition, it should be noted that each specific technical feature described in the above specific embodiments can be combined in any appropriate manner without contradiction, and to avoid unnecessary repetition, the application will not describe various possible combinations.

[0132] In addition, various different embodiments of the application can be combined in any appropriate manner, as long as it does not deviate from the technical concept of the application, and it should be considered as disclosed by the application.

Claims

1. A method for error analysis of constellation cluster geometry cross-calibration, characterized in that, The method comprises: simulating original echo data corresponding to a primary satellite and a secondary satellite; extracting a virtual control point according to an intersection region between a primary image and a secondary image, wherein the primary image is obtained according to the primary satellite, and the secondary image is obtained according to the secondary satellite; geometrically calibrating the secondary satellite according to the original echo data, the virtual control point and simulated errors to obtain a calibration result, wherein the simulated errors include one or more of a position error, a velocity error and / or an atmospheric delay; performing error analysis according to the calibration result and the simulated errors.

2. The method for error analysis of constellation cluster geometric cross-calibration according to claim 1, characterized in that, The original echo data corresponding to the simulated primary satellite and the secondary satellite comprises: obtaining the original echo data by using a range-frequency domain pulse coherence method; expressing the original echo data in a form of frequency domain calculation according to a convolution distribution property to obtain the original echo data in the form of frequency domain calculation.

3. The method for error analysis of constellation cluster geometric cross-calibration according to claim 1, characterized in that, The extracting of the virtual control point according to the intersection region between the primary image and the secondary image comprises: respectively obtaining target points corresponding to the same geographical position in the primary image and the secondary image as feature points; extracting the feature points in the intersection region as initial virtual points; obtaining the virtual control point through the initial virtual points.

4. The method for error analysis of constellation cluster geometric cross-calibration according to claim 3, characterized in that, After the virtual control point is obtained through the initial virtual points, the method further comprises: establishing a joint error equation according to orbit parameters of the primary satellite and the secondary satellite; calculating fitting coefficients according to the joint error equation; obtaining specific coordinates of the virtual control point according to initial coordinates of the virtual control point and the fitting coefficients.

5. The method for error analysis of constellation cluster geometric cross-calibration according to claim 4, characterized in that, The geometrically calibrating of the secondary satellite according to the original echo data, the virtual control point and the simulated errors to obtain the calibration result comprises: calculating orbit information by using the original echo data; adding errors to the orbit information by using the simulated errors to obtain the orbit information after the errors are added; geometrically calibrating the secondary satellite by using a range-Doppler model, the specific coordinates of the virtual control point and the orbit information after the errors are added.

6. The method for error analysis of constellation cluster geometric cross-calibration according to claim 1, wherein, The position error is shown in the following formula: where Δx1represents a position error along a track direction in the position error, ΔR x represents a distance error along a track, R e represents an equatorial radius of the earth, H represents a flight altitude of the secondary satellite, ΔR e represents a position error perpendicular to a track direction in the position error, ΔR y represents a distance error perpendicular to a track.

7. The method for error analysis of constellation cluster geometric cross-calibration according to claim 1, wherein, The velocity error is shown in the following formula: where ΔV x represents the velocity error, θ s represents the slant angle of the beam center of the secondary star, γ represents the downward angle of the beam center of the secondary star, ΔV x represents the velocity error along the track, ΔV y represents the velocity error perpendicular to the track, ΔV z represents the velocity error along the radial, V r represents the fitted velocity of the secondary star, V g represents the observed velocity of the secondary star, R s is the slant range from the radar on the secondary star to the virtual control point.

8. The method for error analysis of constellation cluster geometric cross-calibration according to claim 1, wherein, The atmospheric delay includes an ionospheric delay and a tropospheric delay, the ionospheric delay is shown in the following formula: where n e represents the electron density in the atmosphere, K is a constant, K = e 2 / 8πε0m e = 40.28 m 3 / s 2 , ε0represents the dielectric constant, m e represents the electron mass, TEC represents the integral of the electron density along the propagation path, TEC = ∫n e ds, f com represents the frequency of the current dispersion component.

9. The method for error analysis of constellation cluster geometric cross-calibration according to claim 8, characterized in that, The tropospheric delay is shown in the following formula: p0= ∫v dτ ~ cΔτ vac -∫(n e -1)ds; where p0represents the true distance of signal propagation of the secondary star, v represents the propagation speed of electromagnetic waves in the troposphere, dτ represents a time infinitesimal, Δτ vac represents the time of signal passing through p0in vacuum, ds is an infinitesimal of the propagation path, ∫(n e -1)ds represents the tropospheric delay, and c represents the propagation speed of electromagnetic waves in vacuum.

10. An error analysis device for constellation cluster geometry cross-calibration, characterized in that, The device comprises: a data simulation module configured to simulate original echo data corresponding to a primary image and a secondary image, wherein the primary image is obtained according to a primary satellite, and the secondary image is obtained according to a secondary satellite; a control point extraction module configured to extract a virtual control point according to an intersection region between the primary image and the secondary image; a geometric calibration module configured to geometrically calibrate the secondary satellite according to the original echo data, the virtual control point and simulated errors to obtain a calibration result, wherein the simulated errors include one or more of a position error, a velocity error, an atmospheric delay, a slant range measurement error and a virtual control point position transfer error; an error analysis module configured to perform error analysis according to the calibration result and the simulated errors.

Images