A time synchronization error imaging influence analysis method suitable for bi-geo sar

Abstract

The application provides a time synchronization error imaging influence analysis method suitable for Bi-GEO SAR, wherein the method comprises the following steps: obtaining echo signal data of Bi-GEO SAR, determining position parameters of a platform and a target to be measured according to the echo signal data; calculating a position deviation of the target to be measured according to a preset linear time synchronization error term coefficient and the position parameters; calculating a phase error of a time domain imaging algorithm according to the position parameters and the position deviation; calculating a phase error of a frequency domain imaging algorithm according to the position deviation; calculating an integral sidelobe ratio of an imaging result according to a preset random phase error standard deviation and the position parameters; and judging the time synchronization error imaging influence according to the phase error of the time domain imaging algorithm, the phase error of the frequency domain imaging algorithm and the integral sidelobe ratio of the imaging result.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of synthetic aperture radar, and particularly relates to a time synchronization error imaging influence analysis method suitable for Bi-GEO SAR. BACKGROUND

[0002] With the development of radar technology, bistatic spaceborne synthetic aperture radar has become an important earth observation sensor. The geosynchronous orbit synthetic aperture radar works in an orbit of 36500 kilometers, has the advantages of short revisit time, wide coverage, etc., and is also a very promising earth observation concept. The Bi-GEO SAR, which is born by combining the two concepts, has great potential in fast imaging, interferometric measurement, tomographic imaging, etc., and therefore has attracted widespread attention.

[0003] The time synchronization error is an error introduced due to the use of different clocks by the transmitter and receiver, and is a unique error factor in Bi-SAR, which is mainly composed of three parts of fixed term, linear term and random term. The time synchronization error will seriously affect the imaging of Bi-SAR, and its influence has been widely studied in low earth orbit and airborne SAR systems, however, these studies do not consider the curved trajectory and long synthetic aperture time, and are not suitable for the time synchronization error imaging influence analysis of Bi-GEO SAR. SUMMARY

[0004] Therefore, it is necessary to provide a time synchronization error imaging influence analysis method suitable for Bi-GEO SAR in view of the above technical problems.

[0005] A time synchronization error imaging influence analysis method suitable for Bi-GEO SAR, comprising the following steps:

[0006] Obtaining echo signal data of the Bi-GEO SAR, and determining position parameters of a platform and a target to be measured according to the echo signal data;

[0007] Calculating a range migration of the target to be measured according to a preset linear time synchronization error term coefficient and the position parameters;

[0008] Calculating a phase error of a time domain imaging algorithm according to the position parameters and the range migration;

[0009] Calculating a phase error of a frequency domain imaging algorithm according to the range migration;

[0010] Calculating an integral sidelobe ratio of an imaging result according to a preset random phase error standard deviation and the position parameters;

[0011] Judging the time synchronization error imaging influence according to the phase error of the time domain imaging algorithm, the phase error of the frequency domain imaging algorithm and the integral sidelobe ratio of the imaging result.

[0012] In one embodiment, the azimuthal displacement of the target is calculated according to the preset linear time synchronization error term coefficient and the position parameter, comprising:

[0013] A high-order slant range history model is determined according to the preset linear time synchronization error term coefficient and the position parameter, comprising:

[0014] R(t a ) = R0+ k1t a + k2t a 2 + k3t a 3 + k4t a 4

[0015] R(t a ) represents the high-order slant range history model, R0represents the slant range between the target and the platform at the aperture center time, t a represents the azimuthal slow time, k1represents the first-order term coefficient of the high-order slant range history model, k2represents the second-order term coefficient of the high-order slant range history model, k3represents the third-order term coefficient of the high-order slant range history model, and k4represents the fourth-order term coefficient of the high-order slant range history model;

[0016] A Doppler centroid displacement is calculated according to the linear term coefficient change of the high-order slant range history model, comprising:

[0017]

[0018] Wherein, Δf dk represents the Doppler centroid displacement, β represents the preset linear time synchronization error term coefficient, f0represents the signal carrier frequency, v represents the platform speed, θ represents the position relationship between the platform and the target to calculate the squint angle, Δθ represents the squint angle change amount caused by the target displacement, λ represents the wavelength, and R0represents the slant range between the target and the platform at the aperture center time.

[0019] The azimuthal displacement of the target is calculated according to the Doppler centroid displacement by the following formula:

[0020]

[0021] Wherein, Δy a represents the azimuthal displacement of the target, β represents the preset linear time synchronization error term coefficient, R0represents the slant range between the target and the platform at the aperture center time, v represents the platform speed, θ represents the position relationship between the platform and the target to calculate the squint angle, and c represents the speed of light.

[0022] In one of the embodiments, calculating a phase error of a time-domain imaging algorithm according to the position parameter and the azimuth offset comprises:

[0023] The phase error of the time-domain imaging algorithm is calculated according to the following formula:

[0024]

[0025]

[0026] wherein QPE BP represents a quadratic phase error of the time-domain imaging algorithm, λ represents a wavelength, a represents an acceleration, a represents an acceleration vector, Δy a represents an azimuth offset of a target to be measured, V represents a platform velocity vector, T s represents a synthetic aperture time, R0 represents a slant range between the target to be measured and the platform at a time of an aperture center, R0 represents a slant range vector between the target to be measured and the platform at the time of the aperture center, CPE BP represents a cubic phase error of the time-domain imaging algorithm, b represents a jerk, and b represents a jerk vector.

[0027] In one of the embodiments, calculating a phase error of a frequency-domain imaging algorithm according to the azimuth offset comprises:

[0028] performing a fourth-order fitting on a high-order slant history model with respect to a slow time to obtain coefficients of first-order to fourth-order terms;

[0029] calculating the phase error of the frequency-domain imaging algorithm according to the coefficients of the first-order to fourth-order terms.

[0030] In one of the embodiments, calculating the phase error of the frequency-domain imaging algorithm according to the coefficients of the first-order to fourth-order terms comprises:

[0031] The phase error of the frequency-domain imaging algorithm is calculated according to the following formula:

[0032]

[0033]

[0034] wherein QPE RD represents a quadratic phase error of the frequency-domain imaging algorithm, CPE RD represents a cubic phase error of the frequency-domain imaging algorithm, k1 represents a first-order term coefficient of the high-order slant history model, k2 represents a second-order term coefficient of the high-order slant history model, k3 represents a third-order term coefficient of the high-order slant history model, k4 represents a fourth-order term coefficient of the high-order slant history model, c represents a speed of light, β represents a preset linear time synchronization error term coefficient, f0 represents a signal carrier frequency, T s represents a synthetic aperture time.

[0035] In one embodiment, the integral side lobe ratio of the imaging result is calculated according to the preset random phase error standard deviation and the position parameter, and the integral side lobe ratio of the imaging result is calculated according to the following formula:

[0036] The integral side lobe ratio of the imaging result is calculated according to the following formula:

[0037]

[0038]

[0039] Wherein, ISLR represents the integral side lobe ratio of the imaging result after introducing the random time synchronization error, ISLR0 represents the ideal integral side lobe ratio of the imaging result, N s represents the number of selected side lobes, N a represents the number of azimuth sampling points, c represents the speed of light, and σ represents the random phase error standard deviation.

[0040] The second object of the present application is to provide a computer device, comprising a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor implements the method as described above when executing the computer program.

[0041] The third object of the present application is to provide a computer readable storage medium, which stores a computer program, wherein the computer program is executed by a processor to implement the method as described above.

[0042] Compared with the prior art, the present application has the advantages and beneficial effects that the present application can analyze and compare the causes of defocusing in time domain and frequency domain imaging algorithms, and gives the theoretical secondary phase error derivation process. For random time synchronization error, based on the idea of time domain integral, the calculation method of integral side lobe ratio is given, which can analyze the influence of random time synchronization error on imaging according to the number of pulses, and has high calculation precision. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 It is a flowchart of a time synchronization error imaging influence analysis method suitable for Bi-GEO SAR in one embodiment;

[0044] Figure 2 It is a Bi-GEO SAR distribution diagram in one embodiment;

[0045] Figure 3 It is a diagram showing the degree of image azimuth deviation caused by preset linear time synchronization error in one embodiment;

[0046] Figure 4 It is a diagram showing the influence of preset linear time synchronization error on azimuth focusing in different imaging algorithms in one embodiment;

[0047] Figure 5 Fig. 2 is a schematic diagram of the influence of preset random phase error on the azimuth focusing of Bi-GEO SAR and Bi-LEO SAR in an embodiment;

[0048] Figure 6A Fig. 3 is a schematic diagram of the azimuth ISLR theoretical calculation value in an embodiment;

[0049] Figure 6B Fig. 4 is a schematic diagram of the azimuth ISLR simulation calculation value in an embodiment. DETAILED DESCRIPTION

[0050] Before the specific embodiment of the present application is described, the overall concept of the present application is described as follows:

[0051] The present application is mainly developed based on the imaging influence analysis process of time synchronization error of Bi-GEO SAR. The linear time synchronization error will cause the azimuth defocusing of the image, which is due to the coupling linear term of the residual range frequency and Doppler frequency in the signal spectrum. The image will also be azimuthally offset due to the Doppler centroid shift. The random time synchronization error can be modeled as a Gaussian random variable, and the influence of the random time synchronization error on imaging is mainly studied through numerical simulation.

[0052] The inventor found that the main reason for the above problems is that the current analysis method is based on a straight line trajectory for linear synchronization error, which cannot reveal the influence of a curved trajectory. For random synchronization error, the current method is based on numerical simulation or continuous signal analysis, without considering the number of azimuth sampling points. Therefore, the present application proposes a time synchronization error imaging influence analysis method suitable for Bi-GEO SAR. For linear time synchronization error, the method compares the reasons for defocusing in the time domain and frequency domain imaging algorithms, and gives the theoretical secondary phase error derivation process. For random time synchronization error, based on the idea of time domain integration, the calculation method of the deteriorated integration sidelobe ratio is given, which can analyze the influence of random time synchronization error on imaging according to the number of pulses, and has high calculation accuracy.

[0053] It should be noted that, unless otherwise defined, technical or scientific terms used in one or more embodiments of the present disclosure should be understood as having the same meaning as commonly understood by one of ordinary skill in the art to which the present disclosure belongs. The terms "first", "second", and similar terms used in one or more embodiments of the present disclosure do not denote any order, quantity, or importance, but are only used to distinguish different components. The terms "include" or "contain" and similar terms mean that the elements or objects before the terms encompass the elements or objects listed after the terms and their equivalents, and do not exclude other elements or objects. The terms "connected" or "connected" and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up", "down", "left", "right", and the like are only used to represent relative positional relationships, and when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0054] For the convenience of understanding, the terms involved in the embodiments of the present application are explained as follows:

[0055] SAR: Synthetic Aperture Radar, an active ground observation system, which can be installed on a flight platform such as an airplane, a satellite, a spacecraft, etc., to implement observation on the ground at all times and in all weather, and has a certain ground penetration capability.

[0056] Bi-SAR: bistatic synthetic aperture radar, a SAR system in which the transmitter and receiver are located on different platforms.

[0057] GEO SAR: Geosynchronous Orbit Synthetic Aperture Radar.

[0058] ISLR: Integrated Side Lobe Ratio, the ratio of main lobe energy to side lobe energy in profile.

[0059] In one embodiment, as shown in Figure 1 , a time synchronization error imaging influence analysis method suitable for Bi-GEO SAR is provided, comprising the following steps:

[0060] Step S101, obtaining echo signal data of Bi-GEO SAR, and determining position parameters of the platform and the target to be measured according to the echo signal data.

[0061] Specifically, a plurality of Bi-GEO SARs operate at the same height, and the specific distribution diagram is shown in Figure 2 , obtaining echo signal data of Bi-GEO SAR, and determining position parameters of the platform and the target to be measured according to the echo signal data, the position parameters including platform trajectory, target to be measured position coordinates, etc., the slant range vector between the target to be measured and the platform at the aperture center time is R0, the platform velocity vector is V, the acceleration vector is a, the jerk vector is b, and the synthetic aperture time is Ts .

[0062] In one embodiment, Bi-GEO SAR along the orbit formation is used. The satellite related parameters are shown in Table 1. The target for SAR imaging is a point target located at 119.938°E, 4.134°N, and each image size is 200 pixels x 200 pixels with a pixel interval of 10 m. The aperture center of the satellite is located close to the equatorial space at the moment. The simulation selection range of time synchronization error is shown in Table 1.

[0063]

[0064]

[0065] Table 1 Simulation selection range of time synchronization error

[0066] In step S102, the azimuth direction offset of the target to be measured is calculated according to the preset linear time synchronization error term coefficient and the position parameter.

[0067] Specifically, the preset linear time synchronization error term coefficient is introduced, and the target to be measured will be offset in the image. According to the position relationship between the platform and the target to be measured, the squint angle θ is calculated, the speed of light is denoted as c, the preset linear time synchronization error term coefficient is denoted as β, the Doppler centroid offset is calculated according to the linear term coefficient change of the slant range, and then the offset of the image of the target to be measured along the azimuth direction is calculated.

[0068] On this basis, the azimuth direction offset of the target to be measured is calculated according to the preset linear time synchronization error term coefficient and the position parameter, including:

[0069] The high-order slant range history model is determined according to the preset linear time synchronization error term coefficient and the position parameter.

[0070] R(t a )=R0+k1t a +k2t a 2 +k3t a 3 +k4t a 4

[0071] R(t a ) represents the high-order slant range history model, R0 represents the slant range between the target to be measured and the platform at the aperture center moment, t a represents the azimuth direction slow time, k1 represents the first-order term coefficient of the high-order slant range history model, k2 represents the second-order term coefficient of the high-order slant range history model, k3 represents the third-order term coefficient of the high-order slant range history model, and k4 represents the fourth-order term coefficient of the high-order slant range history model.

[0072] ​The Doppler centroid shift is calculated according to the linear term coefficient variation of the high-order slant range history model:

[0073]

[0074] Wherein, Δf dk represents the Doppler centroid shift, β represents the preset linear time synchronization error term coefficient, f0 represents the signal carrier frequency, v represents the platform speed, θ represents the platform and the target to be measured position relationship calculation angle of sight, Δθ represents the angle of sight change amount caused by the target to be measured offset, and λ represents the wavelength.

[0075] The azimuth direction offset of the target to be measured is calculated according to the Doppler centroid shift by the following formula:

[0076]

[0077] Wherein, Δy a represents the azimuth direction offset of the target to be measured, β represents the preset linear time synchronization error term coefficient, R0 represents the slant range between the target to be measured and the platform at the aperture center moment, v represents the platform speed, θ represents the platform and the target to be measured position relationship calculation angle of sight, and c represents the light speed.

[0078] Specifically, the linear time synchronization error term coefficient is set, and the position parameter with the preset linear time synchronization error term coefficient is modeled. Let the light speed be c, the platform speed be v, the distance direction and azimuth direction envelopes of the time domain signal be A r and A a , the distance direction fast time and azimuth direction slow time be t r and t a , the signal frequency modulation be K r , the preset linear time synchronization error term coefficient be β, the signal carrier frequency be f0, and the wavelength be λ. The expression of the echo signal time domain is as follows:

[0079]

[0080] Wherein, S t (t r ,t a ; β) represents the echo signal time domain expression, A r represents the distance direction envelope of the time domain signal, t r represents the distance direction fast time, c represents the light speed, R(t a ) represents the high-order slant range history model, β represents the preset linear time synchronization error term coefficient, t a represents the azimuth direction slow time, A a represents the azimuth direction envelope of the time domain signal, exp() represents the exponential function with the natural constant e as the base, j represents the imaginary unit, and K rf0 represents the signal carrier frequency.

[0081] Then, the high-order slant range history model is determined according to the preset linear time synchronization error term coefficient and the position parameter:

[0082] R(t a ) = R0+ k1t a + k2t a 2 + k3t a 3 + k4t a 4

[0083] R(t a ) represents the high-order slant range history model, R0 represents the slant range between the target to be measured and the platform at the aperture center moment, t a represents the azimuth slow time, k1 represents the first-order term coefficient of the high-order slant range history model, k2 represents the second-order term coefficient of the high-order slant range history model, k3 represents the third-order term coefficient of the high-order slant range history model, and k4 represents the fourth-order term coefficient of the high-order slant range history model.

[0084] The Doppler centroid shift is calculated according to the linear term coefficient change of the high-order slant range history model, and the Doppler centroid shift is Δf dk = -βf0, and the Doppler centroid shift can also be expressed as:

[0085]

[0086] Δf dk represents the Doppler centroid shift, β represents the preset linear time synchronization error term coefficient, f0 represents the signal carrier frequency, v represents the platform speed, θ represents the position relationship between the platform and the target to be measured to calculate the squint angle, Δθ represents the squint angle change amount caused by the target to be measured to shift, λ represents the wavelength, and R0 represents the slant range between the target to be measured and the platform at the aperture center moment.

[0087] The two expressions of the Doppler centroid shift are combined to obtain the azimuth shift of the target to be measured as:

[0088]

[0089] Δy a represents the azimuth shift of the target to be measured, β represents the preset linear time synchronization error term coefficient, R0 represents the slant range between the target to be measured and the platform at the aperture center moment, v represents the platform speed, θ represents the position relationship between the platform and the target to be measured to calculate the squint angle, and c represents the speed of light.

[0090] In step S103, the phase error of the time-domain imaging algorithm is calculated according to the position parameter and the azimuth shift.

[0091] Specifically, a linear time synchronization error term coefficient is set, and a QPE and a CPE of a time domain imaging algorithm generated after a linear time synchronization error is introduced are calculated according to a position parameter and the azimuth deviation to which the preset linear time synchronization error term coefficient is introduced.

[0092] On this basis, a phase error of the time domain imaging algorithm is calculated according to the position parameter and the azimuth deviation, and the phase error includes:

[0093] The phase error of the time domain imaging algorithm is calculated according to the following formula:

[0094]

[0095]

[0096] wherein, QPE BP represents a quadratic phase error of the time domain imaging algorithm, λ represents a wavelength, a represents an acceleration, a represents an acceleration vector, Δy a represents an azimuth deviation of the target to be measured, V represents a platform velocity vector, T s represents a synthetic aperture time, R0 represents a slant range between the target to be measured and the platform at a time of an aperture center, R0 represents a slant range vector between the target to be measured and the platform at the time of the aperture center, CPE BP represents a cubic phase error of the time domain imaging algorithm, b represents a jerk, and b represents a jerk vector.

[0097] Specifically, the time domain imaging algorithm is time domain matched filtering on the echo of the target to be measured, and therefore, a residual phase error after imaging can be represented as:

[0098]

[0099]

[0100] wherein, QPE BP represents a quadratic phase error of the time domain imaging algorithm, CPE BP represents a cubic phase error of the time domain imaging algorithm, k′2 and k′3 respectively represent second-order and third-order expansion coefficients of a slant range history model of the target to be measured after a preset linear time synchronization error term coefficient offset is introduced, λ represents a wavelength, k2 represents a second-order term coefficient of a high-order slant range history model, k3 represents a third-order term coefficient of the high-order slant range history model, T s represents a synthetic aperture time.

[0101] The second-order and third-order expansion coefficients of the real high-order slant range history model of the target to be measured are calculated according to the following formula:

[0102]

[0103]

[0104] wherein k2 represents the second-order expansion coefficient of the real high-order slant range history model of the target to be measured, k3 represents the third-order expansion coefficient of the real high-order slant range history model of the target to be measured, R0 represents the slant range between the target to be measured and the platform at the time of the center of the aperture, R0 represents the slant range vector between the target to be measured and the platform at the time of the center of the aperture, v represents the platform velocity, a represents the acceleration vector, b represents the jerk vector, V represents the platform velocity vector, and T represents the transpose calculation.

[0105] Under the influence of the preset linear time synchronization error term coefficient, the slant range vector of the target to be measured is:

[0106]

[0107] wherein R'0 represents the slant range vector of the target to be measured, R0 represents the slant range vector between the target to be measured and the platform at the time of the center of the aperture, Ay represents the azimuth direction offset of the target to be measured, and V represents the platform velocity vector. a wherein v represents the platform velocity.

[0108] The second-order and third-order expansion coefficients k'2 and k'3 of the slant range history model of the target to be measured after the introduction of the preset linear time synchronization error term coefficient offset can be calculated by bringing the slant range vector of the target to be measured into the second-order and third-order expansion coefficient formulas of the real high-order slant range history model of the target to be measured.

[0109] In one embodiment, since the slant range R0 between the target to be measured and the platform at the time of the center of the aperture of the Bi-GEO SAR to the target to be measured is 35000 km or above, the preset linear time synchronization error term coefficient β is not more than 1x10 -8 order of magnitude, the corresponding offset of the target to be measured in the image is not more than 100 kilometers, and the offset is mainly along the direction of the velocity V. Therefore, the influence of the change of R0 caused by the offset of the target to be measured in the second-order and third-order expansion coefficients of the real high-order slant range history model of the target to be measured can be ignored. Therefore,

[0110]

[0111] Since Therefore V T R0 = vR0sinθ, the following formula is obtained:

[0112]

[0113] Since the view angle of Bi-GEO SAR is usually 1.5°-7.5°, tanθ≈θ, cosθ≈1. Considering a L-band Bi-GEO SAR system with 10m resolution and 16° inclination angle, the orbit velocity is 850m / s, then the synthetic aperture time T s is usually no more than 500s, according to the formula The magnitude of each quantity is no more than 4×10 -6 , and it is known that the term can be ignored. Thus Therefore, the quadratic phase error of the time-domain imaging algorithm can be obtained as

[0114]

[0115] where QPE BP represents the quadratic phase error of the time-domain imaging algorithm, λ represents the wavelength, Δy a represents the azimuth displacement of the target to be measured, V represents the platform velocity vector, T s represents the synthetic aperture time, and R0 represents the slant range between the target to be measured and the platform at the aperture center time.

[0116] From the same calculation idea, it can be obtained that

[0117]

[0118] Therefore, the cubic phase error of the time-domain imaging algorithm can be obtained as

[0119]

[0120] where CPE BP represents the cubic phase error of the time-domain imaging algorithm, λ represents the wavelength, Δy a represents the azimuth displacement of the target to be measured, V represents the platform velocity vector, T s represents the synthetic aperture time, R0 represents the slant range between the target to be measured and the platform at the aperture center time, R0 represents the slant range vector between the target to be measured and the platform at the aperture center time, b represents the jerk vector, and a represents the acceleration vector.

[0121] In step S104, the phase error of the frequency-domain imaging algorithm is calculated according to the azimuth displacement.

[0122] On this basis, the phase error of the frequency-domain imaging algorithm is calculated according to the azimuth displacement, and the method comprises the steps of:

[0123] A fourth-order fitting about the slow time is performed on the high-order slant range history model to obtain the coefficients of the first-order to fourth-order terms;

[0124] The phase error of the frequency-domain imaging algorithm is calculated according to the coefficients of the first-order to fourth-order terms.

[0125] Specifically, a fourth-order fitting is performed on the high-order slant-range history model with respect to the slow time, and the coefficients of the first to fourth-order terms are denoted as k1, k2, k3, and k4, respectively. Denote the carrier frequency as f0. According to the calculation of the frequency-domain imaging algorithm, the phase error is obtained.

[0126] In one embodiment, according to the echo signal time domain, a two-dimensional spectrum of the position parameter of the preset linear time synchronization error term coefficient is obtained by using the series inversion method. The phase of the two-dimensional spectrum is:

[0127]

[0128] wherein, φ(f r ,f a ; β) represents the phase of the two-dimensional spectrum, K r represents the signal frequency, f r represents the distance frequency, f a represents the Doppler frequency, f0 represents the signal carrier frequency, R0 represents the slant range between the target to be measured and the platform at the aperture center moment, k1 represents the first-order term coefficient of the high-order slant-range history model, k2 represents the second-order term coefficient of the high-order slant-range history model, k3 represents the third-order term coefficient of the high-order slant-range history model, k4 represents the fourth-order term coefficient of the high-order slant-range history model, c represents the speed of light, and β represents the preset linear time synchronization error term coefficient.

[0129] According to the principle of the matched filtering of the frequency-domain imaging algorithm, the calculation method of the residual phase error after the processing of the frequency-domain imaging algorithm is:

[0130] φ error (f r ,f a ; β) = φ(f r ,f a ; β) - φ(f r ,f a ; 0)

[0131] Therefore, the phase error of the frequency-domain imaging algorithm can be calculated as:

[0132]

[0133]

[0134] wherein, QPE RD represents the quadratic phase error of the frequency-domain imaging algorithm, and CPE RDk1, k2, k3, k4, c, β, f0, T s represents a synthetic aperture time.

[0135] In step S105, the integral side lobe ratio of the imaging result is calculated according to the preset random phase error standard deviation and the position parameter.

[0136] Specifically, a preset random phase error is introduced, and the azimuth focusing performance deteriorates. Let the number of side lobes selected when calculating the integral side lobe ratio be N s , the number of azimuth sampling points be N a , and the preset random phase error standard deviation introduced by the random time synchronization error be σ. The integral side lobe ratio of the imaging result is calculated according to the above data.

[0137] On this basis, the integral side lobe ratio of the imaging result is calculated according to the preset random phase error standard deviation and the position parameter, and includes:

[0138] The integral side lobe ratio of the imaging result is calculated according to the following formula:

[0139]

[0140]

[0141] Where ISLR represents the integral side lobe ratio of the imaging result after introducing the random time synchronization error, ISLR0 represents the ideal integral side lobe ratio of the imaging result, N s represents the number of selected side lobes, c represents the speed of light, and σ represents the random phase error standard deviation.

[0142] In one embodiment, the calculation formula of the integral side lobe ratio is obtained according to the following operation. First, the azimuth time domain expression of the echo signal introducing the random phase error standard deviation is obtained:

[0143]

[0144] Where s(t a ) represents the azimuth time domain of the echo signal introducing the random phase error, T s represents the synthetic aperture time, λ represents the wavelength, j represents the imaginary unit, R(t a ) represents the high-order slant range history model, t a represents the azimuth slow time, exp() represents the exponential function with the natural constant e as the base, φ n(t a ) ~ N(0, σ 2 ) represents a random phase error term introduced by random time synchronization error.

[0145] The pixel point energy at the position of the slow time interval τ from the center of the platform after imaging is:

[0146] q(τ) = ∫s(t a ) exp[-jπK a (t a - τ) 2 ]dt a

[0147] wherein q(τ) represents the pixel point energy at the position of the slow time interval τ from the center of the platform after imaging, s(t a ) represents the azimuth time domain of the echo signal introducing random phase error, exp() represents an exponential function with the natural constant e as the base, j represents an imaginary unit, K a represents an azimuth frequency modulation, τ represents a slow time interval, and t a represents an azimuth slow time.

[0148] The imaging result is expressed by power as follows:

[0149]

[0150] wherein p(τ) represents the power of the imaging result, q(τ) represents the pixel point energy at the position of the slow time interval τ from the center of the platform after imaging, T a represents a synthetic aperture time, t a represents an azimuth slow time, j represents an imaginary unit, K a represents an azimuth frequency modulation, τ represents a slow time interval, exp() represents an exponential function with the natural constant e as the base, φ n (t a ) ~ N(0, σ 2 ) represents a random phase error term introduced by random time synchronization error.

[0151] Let t a -t′ a =u, and it can be obtained that,

[0152]

[0153] The calculation formula of the average power of the pixel point is:

[0154]

[0155] wherein K a represents an azimuth frequency modulation, χ(u, ta ) represents exp[jφ n (t a )] autocorrelation function, which is calculated as:

[0156]

[0157] Since the actual signal is often discrete, we have:

[0158] E[p(τ)]=N a exp(-σ 2 )sinc 2 (T p K a τ)+1-exp(-σ 2 )

[0159] where E[p(τ)] represents the average power of the pixel point, N a represents the number of sampling points in the azimuth direction, exp() represents the exponential function with the natural constant e as the base, σ represents the standard deviation of the random phase error, and c represents the speed of light.

[0160] Let T p K a τ=x, the integral sidelobe ratio of the imaging result is calculated according to the following formula:

[0161]

[0162]

[0163] Step S106, judging the imaging influence of the time synchronization error according to the phase error of the time-domain imaging algorithm, the phase error of the frequency-domain imaging algorithm, and the integral sidelobe ratio of the imaging result.

[0164] Specifically, generating a shadow image according to the phase error of the time-domain imaging algorithm, the phase error of the frequency-domain imaging algorithm, and the integral sidelobe ratio of the imaging result, and analyzing the imaging influence of the time synchronization error according to the shadow image.

[0165] In one embodiment, Figure 3 The degree of image azimuth direction deviation caused by introducing a preset linear time synchronization error is shown, and the theoretical calculation of the deviation amount is basically consistent with the simulation result. Figure 4 The influence of a preset linear time synchronization error on the azimuth focusing of Bi-GEO SAR using different imaging algorithms is shown, and it can be seen that the time-domain imaging algorithm is more sensitive to the preset linear time synchronization error, and the theoretical calculation result of the boundary value is basically consistent with the simulation situation. Figure 5 The influence of introducing a preset random phase error on the azimuth focusing of Bi-GEO SAR and Bi-LEO SAR is shown,Figure 6A The azimuth ISLR theoretical calculation value is shown, Figure 6B The azimuth ISLR simulation calculation value is shown, and comparison between the two can show that the deterioration degree of the random time synchronization error on the azimuth focusing will gradually weaken with the increase of the azimuth sampling points

[0166] The application provides a time synchronization error imaging influence analysis method suitable for Bi-GEO SAR, can analyze and compare the causes of defocusing in time domain and frequency domain imaging algorithms, and gives the theoretical three-phase error derivation process. For the random time synchronization error, based on the idea of time domain integration, the calculation method of integral sidelobe ratio is given, the influence of the random time synchronization error on imaging can be analyzed according to the number of pulses, and has high calculation precision.

[0167] Those skilled in the art should understand that the above discussion of any embodiment is only exemplary and is not intended to limit the scope (including claims) of the present application to these examples; under the idea of the present application, the above embodiments or technical features in different embodiments can also be combined, the steps can be implemented in any order, and there are many other changes of different aspects of the embodiments of the present application as described above, which are not provided in details for the sake of simplicity.

[0168] Any process or method descriptions or any other descriptions herein can be understood as representing modules, segments, or portions of code that include one or more executable instructions for implementing specific logic functions or steps, and the scope of the preferred embodiments of the present application includes additional implementation in which the functions are carried out in different orders, in substantially simultaneous fashion, or in reverse order, as will be understood by those skilled in the art of the embodiments of the present application.

[0169] In addition, in order to simplify the description and discussion, and so as not to make the embodiments of the present application difficult to understand, the well-known power / ground connections of integrated circuit (IC) chips and other components can or can not be shown in the provided drawings. In addition, the devices can be shown in the form of block diagrams in order to avoid making the embodiments of the present application difficult to understand, and this also takes into account the fact that the details of the implementation of these block diagram devices are highly dependent on the platform to be implemented (i.e. these details should be fully within the understanding of those skilled in the art). Where specific details (e.g. circuits) are set forth in order to describe the exemplary embodiments of the present application, it will be apparent to those skilled in the art that the embodiments of the present application can be implemented without these specific details or with variations on these specific details. Therefore, these descriptions should be considered illustrative rather than limiting.

[0170] While the application has been described in terms of particular embodiments, many alternatives, modifications and variations will be apparent to those skilled in the art from the foregoing description. For example, other memory architectures (e.g., dynamic RAM (DRAM)) can use the embodiments discussed.

[0171] Embodiments of the application are intended to cover all such alternatives, modifications, and variations as come within the scope of the appended claims. Accordingly, any and all such alternatives, modifications, equivalents, improvements and the like are intended to be encompassed by the present application.

Claims

1. A method for analyzing the impact of time synchronization error imaging on Bi-GEO SAR, characterized in that, include: Acquire Bi-GEO SAR echo signal data, and determine the position parameters of the platform and the target under test based on the echo signal data; The azimuth offset of the target under test is calculated based on the preset linear time synchronization error term coefficient and the position parameters. The phase error of the temporal imaging algorithm is calculated based on the position parameters and the azimuth offset; The phase error of the frequency domain imaging algorithm is calculated based on the azimuth offset. The integral sidelobe ratio of the imaging result is calculated based on the preset random phase error standard deviation and the position parameters; The impact of time synchronization error on imaging is determined based on the phase error of the time-domain imaging algorithm, the phase error of the frequency-domain imaging algorithm, and the integral sidelobe ratio of the imaging result.

2. The method for analyzing the impact of time synchronization error imaging on Bi-GEO SAR according to claim 1, characterized in that, The calculation of the azimuth offset of the target under test based on the preset linear time synchronization error term coefficient and the position parameters includes: The higher-order slant range history model is determined based on the preset linear time synchronization error term coefficients and the position parameters: R(t a )=R0+k1t a +k2t a 2 +k3t a 3 +k4t a 4 R(t a ) represents the high-order slant range history model, R0 represents the slant range between the target and the platform at the aperture center time, and t a The azimuth slow time is represented by k1, k2, k3, and k4. The first-order coefficient of the higher-order slant range history model is represented by k1, k2 by k2, k3 by k3, and k4 by k4. The Doppler centroid shift is calculated based on the changes in the linear term coefficients of the higher-order slant range history model: Where, Δf dk denoted by Doppler centroid shift, β represents the coefficient of the preset linear time synchronization error term, f0 represents the signal carrier frequency, v represents the platform speed, θ represents the angle of view for calculating the positional relationship between the platform and the target under test, Δθ represents the change in angle of view caused by the shift of the target under test, λ represents the wavelength, and R0 represents the slant distance between the target under test and the platform at the aperture center time. The azimuth offset of the target under test is calculated based on the Doppler centroid offset using the following formula: Where, Δy a β represents the azimuth offset of the target under test, β represents the coefficient of the preset linear time synchronization error term, R0 represents the slant distance between the target under test and the platform at the aperture center time, v represents the platform velocity, θ represents the angle of view for calculating the positional relationship between the platform and the target under test, and c represents the speed of light.

3. The method for analyzing the impact of time synchronization error imaging on Bi-GEO SAR according to claim 2, characterized in that, The phase error of the temporal imaging algorithm calculated based on the position parameters and the azimuth offset includes: The phase error of the temporal imaging algorithm is calculated using the following formula: Among them, QPE BP Let λ represent the quadratic phase error of the time-domain imaging algorithm, λ represent the wavelength, a represent the acceleration, and a represent the acceleration vector. Δy a V represents the azimuth offset of the target under test, V represents the platform velocity vector, and T represents the position of the target. s Represents the synthetic aperture time, R0 represents the slant distance between the target and the platform at the aperture center time, and CPE represents the slant distance vector between the target and the platform at the aperture center time. BP denoted by , where represents the cubic phase error of the time-domain imaging algorithm, b represents the jerkiness, and b represents the jerkiness vector.

4. The method for analyzing the impact of time synchronization error imaging on Bi-GEO SAR according to claim 2, characterized in that, The phase error of the frequency domain imaging algorithm calculated based on the azimuth offset includes: A fourth-order fitting of the high-order slant range history model with respect to slow time was performed to obtain the coefficients of the first to fourth orders. The phase error of the frequency domain imaging algorithm is calculated based on the first to fourth order term coefficients.

5. The method for analyzing the impact of time synchronization error imaging on Bi-GEO SAR according to claim 4, characterized in that, The calculation of the phase error of the frequency domain imaging algorithm based on the first to fourth order term coefficients includes: The phase error of the frequency domain imaging algorithm is calculated using the following formula: Among them, QPE RD CPE represents the quadratic phase error of the frequency domain imaging algorithm. RD Let k represent the third phase error of the frequency domain imaging algorithm, k1 represent the first-order coefficient of the higher-order slant range history model, k2 represent the second-order coefficient of the higher-order slant range history model, k3 represent the third-order coefficient of the higher-order slant range history model, k4 represent the fourth-order coefficient of the higher-order slant range history model, c represent the speed of light, β represent the coefficient of the preset linear time synchronization error term, f0 represent the signal carrier frequency, and T represent the third-order phase error of the higher-order slant range history model. s Indicates the time for synthesizing the aperture.

6. The method for analyzing the impact of time synchronization error imaging on Bi-GEO SAR according to claim 1, characterized in that, The integral sidelobe ratio of the imaging result calculated based on the preset random phase error standard deviation and the position parameters includes: The integral sidelobe ratio of the imaging results is calculated using the following formula: Where ISLR represents the integrated sidelobe ratio of the imaging result after introducing random time synchronization error, ISLR0 represents the ideal integrated sidelobe ratio of the imaging result, and N s N represents the number of side lobes selected. a σ represents the number of sampling points in the azimuth direction, c represents the speed of light, and σ represents the standard deviation of the random phase error.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that: When the processor executes the computer program, it implements the method as described in any one of claims 1-6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it implements the method as described in any one of claims 1-6.

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