Improved high-orbit synthetic aperture radar CS imaging method

Abstract

The invention discloses an improved CS imaging method for a high-orbit synthetic aperture radar. According to the method, firstly, a high-orbit SAR polynomial approximation equivalent slope distance model is established; 2, performing six-order Taylor series expansion on the slant range process; step 3, carrying out two-dimensional Fourier transform on the high-orbit SAR signal echo model; 4, solving an azimuth stationary phase point by using a series inversion method; 5, the two-dimensional frequency spectrum is organized through power series expansion; 6, improving a CS algorithm, and carrying out three-time phase compensation; step 7, carrying out a distance-Doppler domain Chirp Scaling operation; 8, distance compression is carried out; ninthly, consistent distance migration correction is carried out; tenth, carrying out azimuth compression; and eleventhly, carrying out azimuth phase compensation. Compared with a traditional high-orbit SAR fourth-order slope distance model, the method can meet the higher slope distance error precision requirement.

Description

Technical Field

[0001] The invention relates to an improved high-orbit synthetic aperture radar CS imaging method, belonging to the technical field of synthetic aperture radar. Background Art

[0002] SAR data is acquired in the two-dimensional time domain, but due to processing efficiency reasons, the data is often transformed into the range Doppler domain and the two-dimensional frequency domain for imaging processing. In order to accurately design the matched filter of the imaging processing algorithm, it is crucial to establish a high-precision equivalent range model that is compatible with the actual slant range history, and on this basis derive the correct two-dimensional spectrum analytical expression of the signal. The two-dimensional spectrum of traditional airborne and low-orbit SAR signals is derived based on the hyperbolic slant range model, but this slant range model is based on the assumption that the platform is in uniform linear motion, which cannot meet the accuracy requirements of geosynchronous orbit SAR. Therefore, the traditional frequency domain algorithm is no longer applicable to high-orbit SAR satellites.

[0003] Bao Min from Xidian University and Huang Lijia from the Institute of Electronics of the Chinese Academy of Sciences proposed to expand the double root slant range history into a fourth-order Taylor series at the zero slow time, and then use the series inversion method to obtain the high-order approximate expression of the stationary phase point, and then obtain the high-order approximate expression of the signal's two-dimensional spectrum. On this basis, an improved Chirp Scaling (CS) imaging algorithm suitable for the high-orbit SAR curve trajectory model was proposed. This method does not require the selection of roots, is flexible, has strong scalability, and is easy to implement. It is the mainstream slant range model for high-orbit SAR.

[0004] Because the high-orbit 20m SAR satellite is in the L-band, they only need to expand the slant range model to the fourth order to meet the double-pass slant range error tolerance of λ / 8. However, for the next generation of high-orbit SAR satellites with higher frequency bands and higher resolutions, the fourth-order slant range model cannot meet the accuracy requirements of the imaging algorithm, and the slant range model needs to be upgraded to a higher-order high-orbit SAR imaging algorithm. In view of the above problems and status quo, the present invention proposes an improved high-orbit SAR CS imaging algorithm. Summary of the invention

[0005] The technical problem solved by the present invention is that the fourth-order slant range model of the traditional high-orbit SAR is only applicable to low-frequency band and low-resolution scenes such as the high-orbit 20m SAR satellite L. The next generation of high-orbit SAR satellites with higher frequency bands and higher resolutions need to be upgraded to a higher-order slant range model to meet the accuracy requirements of the imaging algorithm. In view of the above problems existing in the prior art, the present invention proposes an improved high-orbit synthetic aperture radar CS imaging method, which derives the slant range model and the two-dimensional spectrum expression to the sixth order, and solves the above problems well.

[0006] The technical solution of the present invention is:

[0007] An improved high-orbit synthetic aperture radar CS imaging method, the steps are as follows:

[0008] Step 1: Establish a high-orbit SAR polynomial approximation equivalent slant range model and perform a sixth-order Taylor series expansion on the slant range history of the point target;

[0009] Step 2: Perform two-dimensional Fourier transform on the high-orbit SAR point target echo signal model;

[0010] Step 3: Use the series inversion method to solve the azimuth stationary phase point;

[0011] Step 4: Use power series expansion to organize the two-dimensional spectrum;

[0012] Step 5: Perform three-time phase compensation;

[0013] Step 6: Perform Chirp Scaling operation in the range-Doppler domain;

[0014] Step 7: Perform distance compression;

[0015] Step 8: Perform consistent distance migration correction;

[0016] Step 9: Perform azimuth compression;

[0017] Step 10: Perform azimuth phase compensation.

[0018] Furthermore, the establishment of a high-orbit SAR polynomial approximation equivalent slant range model is specifically as follows:

[0019] Assume that the position vectors of the satellite and point target in the earth fixed coordinate system are R S (t) and R T (t), the equivalent slant range model of high-orbit SAR polynomial approximation is the instantaneous slant range R(t) from the point target to the satellite:

[0020] R(t)=R S (t)-R T (t)

[0021] Its Taylor series expansion is as follows:

[0022]

[0023] Among them, R ST =R S -R T , V ST =V S -V T , A ST =A S -A T , B ST =B S-B T , C ST =C S -C T , D ST =D S -D T , E ST =E S -E T , R ST 、V ST , A ST , B ST , C ST , D ST 、E ST are the vectors of various orders from satellite to point target, R S , A S , B S , C S , D S 、E S Characterize the satellite vector, R T 、V T , A T , B T , C T , D T 、E T Characterize the point target vector;

[0024] The sixth-order Taylor series expansion of the point target slant range history R(t) is as follows:

[0025] Establish the point target slope range history expression R(t) = |R(t)|, first establish the identity

[0026]

[0027] R ST is the slant range scalar value from the satellite to the point target at the beam center moment;

[0028] Taylor expansion of x

[0029] x=x 1 t+x 2 t 2 +x 3 t 3 +x 4 t 4 ++x 5 t 5 +x 6 t 6 …

[0030] in

[0031]

[0032] right Taylor expansion

[0033]

[0034] At this point, the expression of the point target slant range history R(t) is obtained as follows:

[0035]

[0036] Among them, R C is the beam center slant distance, V C , A C , B C , C C , D C 、E C They represent the first, second, third, fourth, fifth and sixth derivatives of the distance history at the beam center, respectively, and have the meanings of velocity, acceleration, quadratic acceleration, cubic acceleration, quartic acceleration and quintic acceleration;

[0037] R C =R ST

[0038] V C =(x 1 / 2)R ST

[0039] A C =(x 2 -x 1 2 / 4)R ST

[0040] B C =(3x 3 -3x 1 x 2 / 2-3x 1 2 / 8)R ST

[0041]

[0042] D C =(60x 5 -30x 2 x 3 -30x 1 x 4 +45x 1 x 2 2 / 2+45x 1 2 x 3 / 2-75x 13 x 2 / 4+105x 1 5 / 32)R ST

[0043]

[0044] Furthermore, the two-dimensional Fourier transform of the high-orbit SAR point target echo signal model is specifically:

[0045] High-orbit SAR point target echo signal model 0 (τ,η) is:

[0046]

[0047] Among them, A 0 is an arbitrary complex constant, τ is the distance time, η is the azimuth time, η a is the beam center deviation time, w r (τ) is the distance envelope, w a (η) is the azimuth envelope, f 0 is the radar center frequency, K r is the chirp modulation frequency, R(η) is the instantaneous slant distance, and c is the speed of light;

[0048] After performing Fourier transform on the distance of the point target echo signal model, the Fourier transform is then performed on the azimuth. The phase Φ(f τ ,η) is expressed as

[0049]

[0050] And the phase Φ(f τ ,η) Take the derivative with respect to η and we get

[0051]

[0052] Among them, f τ is the distance frequency, f η is the azimuth frequency.

[0053] Furthermore, using the series inversion method, the expression of the stationary phase point η in the azimuth direction is solved as follows:

[0054]

[0055] Substitute the stationary phase expression into Φ′(f τ ,η) to obtain the analytical two-dimensional frequency domain signal Θ(f τ ,f η )expression

[0056] Furthermore, the two-dimensional spectrum Θ(f τ ,f η ), specifically:

[0057] For Θ(f τ ,f η ) to organize:

[0058]

[0059] Among them, f dc is the Doppler center frequency;

[0060] right and conduct The power series expansion of the two-dimensional spectrum is organized into the following expression form

[0061]

[0062] in, and distance frequency domain f r Irrelevant, it is the azimuth modulation signal term;

[0063]

[0064] and distance frequency domain f r The first-order term is related to the target distance migration term;

[0065]

[0066] and distance frequency domain f r The quadratic term is related to the frequency modulation of the range signal taking into account the quadratic range compression term;

[0067]

[0068] and distance frequency domain f r The third term is related to the second modulation frequency of the distance signal, that is, the slope of the modulation frequency.

[0069]

[0070] Furthermore, the sorted two-dimensional spectrum is used to improve the CS algorithm and perform cubic phase compensation to degenerate the distance signal into a linear frequency modulation signal. The cubic phase compensation function can be expressed as follows:

[0071]

[0072] Furthermore, the sorted two-dimensional spectrum is used to improve the CS algorithm and perform ChirpScaling operation in the range-Doppler domain, specifically:

[0073] In the range Doppler domain, the distance R 0 The point target at the reference distance R c The difference in distance migration ΔR(f η ,R 0 ) is expressed as follows

[0074] ΔR(f η ,R 0 )=R CM (f η ,R 0 )-R CM (f η ,R c )

[0075] Assume the distance is R 0 The distance migration amount R of the point target at CM (f η ,R 0 ) After Chirp Scaling processing, the reference distance R c The distance migration R CM (f η ,R c ) has the same trajectory, denoted as R CM_ref (f η ,R 0 ), and intersect at the Doppler center frequency f dc If f dc ΔR(f dc ,R 0 )for

[0076] ΔR(f dc ,R 0 )=R CM (f dc ,R 0 )-R CM (f dc ,R c )

[0077] R CM (f dc ,R 0 ) is the distance R 0 The distance migration of the point target at CM (f dc ,R c ) is the reference distance R c The distance migration amount at

[0078] After processing, R CM_ref (f η ,R 0 ) is expressed as

[0079] R CM_ref (f η ,R 0 )=R CM (f η ,R c )+ΔR(f dc ,R 0 )=R CM (f η ,R c )+ΔR(f η ,R 0 ) / α(f η )

[0080] Among them, α(f η ) is the correction coefficient required for Chirp Scaling operation, and its calculation formula is as follows

[0081]

[0082] The chirp scaling equation is expressed as

[0083]

[0084] Among them, K m (τ,f η ) is the range modulation frequency including the secondary range modulation, expressed as

[0085]

[0086] After phase multiplication in the range Doppler domain, the complementary RCMC is completed, that is, the signal range migration trajectory on each range gate is the same as the migration trajectory on the reference range gate; the signal after Chirp Scaling is expressed as

[0087]

[0088] The second exponential term is the additional azimuth phase introduced by the Chirp Scaling operation, which is compensated during azimuth compression.

[0089] Furthermore, distance compression is performed, specifically:

[0090] After the Chirp Scaling operation, the range modulation rate becomes α(f η )K m (τ,f η ), the distance compression function is expressed as

[0091]

[0092] Furthermore, a consistent distance migration correction is performed, specifically:

[0093] After the RCMC, the phase is multiplied by the range migration amount on the reference range gate to compensate for the range migration correction function H. rcmc (f τ ,f η ) is written as follows

[0094]

[0095] Furthermore, azimuth compression is performed, specifically:

[0096] Azimuth compression function H a (τ,f η )as follows

[0097]

[0098] Furthermore, azimuth phase compensation is performed, specifically:

[0099] Azimuth phase compensation function H 1 (τ,f η ) is expressed as

[0100]

[0101] The advantages of the present invention compared with the prior art are:

[0102] The present invention proposes an improved high-orbit SAR CS imaging algorithm. Compared with the traditional high-orbit SAR fourth-order slant range model, this method can meet higher slant range error accuracy requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 This is a flow chart of an improved high-orbit SAR CS imaging algorithm;

[0104] Figure 2 This is a schematic diagram of the imaging results of the improved CS algorithm for high-orbit SAR of the present invention. DETAILED DESCRIPTION

[0105] The present invention provides an improved high-orbit synthetic aperture radar CS imaging method, such as Figure 1 As shown, the steps include:

[0106] Step 1: Establish a high-orbit SAR polynomial approximation equivalent slant range model.

[0107] Assume that the position vectors of the satellite and point target in the earth fixed coordinate system are RS (t) and R T (t), then the instantaneous slant range from the point target to the satellite is R(t):

[0108] R(t)=R S (t)-R T (t)

[0109] Its Taylor series expansion is as follows:

[0110]

[0111] Among them, R ST =R S -R T , V ST =V S -V T , A ST =A S -A T , B ST =B S -B T , C ST =C S -C T , D ST =D S -D T , E ST =E S -E T , R ST 、V ST , A ST , B ST , C ST , D ST 、E ST are the vectors of various orders from satellite to point target, R S , A S , B S , C S , D S 、E S Characterize the satellite vector, R T 、V T , A T , B T , C T , D T 、E T A vector representing a point target.

[0112] Step 2: Perform a sixth-order Taylor series expansion on the point target slant range history R(t).

[0113] Starting from the slope range history, the slope range history expression of the point target can be established R(t) = |R(t)|. First, the identity is established

[0114]

[0115] Among them, R ST It is the scalar value of the slant range from the satellite to the point target at the beam center.

[0116] Taylor expansion of x

[0117] x=x 1 t+x 2 t 2 +x 3 t 3 +x 4 t 4 ++x 5 t 5 +x 6 t 6 …

[0118] in

[0119]

[0120] right Taylor expansion

[0121]

[0122] At this point, the expression of the point target slope range history R(t) can be obtained:

[0123]

[0124] Among them, R C is the beam center slant distance, V C , A C , B C , C C , D C 、E C They respectively represent the first, second, third, fourth, fifth and sixth derivatives of the distance history at the beam center, and have the meanings of velocity, acceleration, quadratic acceleration, cubic acceleration, quartic acceleration and quintic acceleration.

[0125] R C =R ST

[0126] V C =(x 1 / 2)R ST

[0127] A C =(x 2 -x 1 2 / 4)R ST

[0128] B C =(3x 3 -3x 1 x 2 / 2-3x 1 2 / 8)R ST

[0129]

[0130] D C =(60x 5 -30x 2 x 3 -30x 1 x 4 +45x 1 x 2 2 / 2+45x 1 2 x 3 / 2-75x 1 3 x 2 / 4+105x 1 5 / 32)R ST

[0131]

[0132] Step 3: Perform two-dimensional Fourier transform on the high-orbit SAR point target echo signal model.

[0133] The raw data received by the radar system is first demodulated to baseband in order to set the center of the range frequency domain to zero. The demodulated high-orbit SAR point target echo signal model s 0 (τ,η) can be expressed as

[0134]

[0135] Among them, A 0 is an arbitrary complex constant, τ is the distance time, η is the azimuth time, η a is the beam center deviation time, w r (τ) is the distance envelope, w a (η) is the azimuth envelope, f 0 is the radar center frequency, K r is the chirp frequency, R(η) is the instantaneous slant distance, c is the speed of light, first, the distance Fourier transform of the above equation can be written as

[0136] s 1 (f τ ,η)=∫s 0(τ,η)exp(-j2πf τ τ)dτ

[0137] Among them, f τ is the range frequency. According to the stationary phase principle (POSP), the range time at which the derivative is zero is found

[0138]

[0139] Using the expression for τ, the integral can be written as

[0140]

[0141] Among them, A 1 is a constant, is the envelope of the distance spectrum. Perform azimuth Fourier transform on the above equation

[0142] s 2 (f τ ,f η )=∫s 1 (f τ ,η)exp(-j2πf η η)dη

[0143] Among them, f η is the distance frequency.

[0144] Next, we solve the stationary phase point. The phase Φ(f τ ,η) can be expressed as

[0145]

[0146] And the phase Φ(f τ ,η) Take the derivative with respect to η and we get

[0147]

[0148] Among them, f τ is the distance frequency, f η is the azimuth frequency.

[0149] Step 4: Use the series inversion method to solve the azimuth stationary phase point.

[0150] In the hyperbolic slant range model used in traditional airborne SAR and low-orbit SAR, the highest term of Φ'(η) with respect to η is a first-order term. We only need to set Φ'(η) = 0 and solve the first-order equation to obtain the stationary phase point. However, the highest term of η in high-orbit SAR is a fifth-order term, which makes it difficult to solve. Here, the series inversion method can be used for solution. The idea is as follows:

[0151] If any function can be expressed as a sum of polynomials, and the constant is zero

[0152] y=a 1 x+a 2 x 2 +a 3 x 3 +a 4 x 4 +a 5 x 5 +…

[0153] The inverse function x(y) can be solved by the series inversion method. x(y) also has the form of a sum of polynomials, and the constant is equal to zero.

[0154] x=A 1 y+A 2 y 2 +A 3 y 3 +A 4 y 4 +A 5 y 5 +…

[0155] Arranged according to the polynomial order, we get the following identity

[0156] y=a 1 A 1 y+(a 1 A 2 +a 2 A 1 2 )y 2 +(a 1 A 3 +2a 2 A 1 A 2 +a 3 A 1 3 )y 3 +(a 1 A 4 +a 2 (A 2 2 +2A 1 A 3 )+3a 3 A 1 2 A 2 )y 4

[0157] +(a 1 A 5 +a 3 (2A 1A 2 2 +A 1 2 A 3 +A 1 (A 2 2 +2A 1 A 3 ))+a 5 A 1 5 +a 2 (2A 1 A 4 +2A 2 A 3 ))y 5

[0158] According to the principle that the coefficients on both sides of the identity are equal, the functions of each order of the inverse function can be found:

[0159]

[0160] According to the above principles, we can get

[0161]

[0162] According to the series inversion method, the expression of the stationary phase point η can be obtained as

[0163]

[0164] Regarding the stationary phase point η, when the azimuth time η is equal to the following formula,

[0165]

[0166] The azimuth Fourier transform expression can be obtained. The azimuth time η is called the azimuth stationary phase point, which is a well-known definition in the industry.

[0167] Substitute the stationary phase expression into Φ'(f τ ,η) can be used to obtain the analytical two-dimensional frequency domain signal expression

[0168]

[0169] Step 5: Use power series expansion to organize the two-dimensional spectrum.

[0170] In order to facilitate the derivation and implementation of the imaging algorithm, the two-dimensional spectrum phase of the above equation needs to be rearranged so that its phase composition is similar to that of traditional airborne SAR and low-orbit SAR. First, the above equation is rearranged

[0171]

[0172] Among them, fdc is the Doppler center frequency.

[0173] Since geosynchronous orbit SAR generally meets Therefore, it can be and conduct The power series expansion of

[0174]

[0175]

[0176] According to the above expansion, the two-dimensional spectrum can be organized into the following expression form

[0177]

[0178] in, and distance frequency domain f r Irrelevant, is the azimuth modulation signal term

[0179]

[0180] and distance frequency domain f r The first-order term is related to the target distance migration term.

[0181]

[0182] and distance frequency domain f r The quadratic term is related to the frequency modulation of the range signal considering the quadratic range compression term (SRC).

[0183]

[0184] and distance frequency domain f r The third term is related to the second modulation frequency of the distance signal, that is, the slope of the modulation frequency.

[0185]

[0186] The CS algorithm achieves signal scale change and translation by frequency modulating the Chirp signal, so that the processing process does not require interpolation, and the echo signal can be processed by complex multiplication and fast Fourier transform. Since the frequency scaling or translation cannot be too large, otherwise it will cause changes in the signal center frequency and bandwidth. Therefore, the CS algorithm corrects the range migration in two steps: first, perform complementary RCMC, that is, compensate for the space-varying characteristics of the range migration in the range Doppler domain, and correct the range migration curves of the targets at different distances to the same form; second, perform consistent RCMC, that is, quickly complete the accurate correction of the residual range migration in the two-dimensional frequency domain through phase multiplication. Since the CS algorithm takes into account the dependence of SRC on the azimuth frequency, its secondary compression effect is equivalent to that of the second SRC method in the RD algorithm, but it is much better than the RD algorithm in processing efficiency. Combined with the two-dimensional spectrum expression of the echo signal derived in step 5, the improved CS algorithm process is given below:

[0187] Step 6: Cubic phase compensation.

[0188] Since the CS algorithm is to scale the linear frequency modulation signal, firstly, a third phase compensation is performed to degenerate the distance signal into a linear frequency modulation signal. The third phase compensation function can be expressed as follows:

[0189]

[0190] Step 7: Range-Doppler domain Chirp Scaling operation.

[0191] In the range Doppler domain, the distance R 0 The point target at the reference distance R c The difference in distance migration ΔR(f η ,R 0 ) can be expressed as follows

[0192] ΔR(f η ,R 0 )=R CM (f η ,R 0 )-R CM (f η ,R c )

[0193] Assume the distance is R 0 The point target distance migration R CM (f η ,R 0 ) After Chirp Scaling processing, the reference distance R c The distance R CM (f η ,Rc ) has the same trajectory and can be expressed as R CM_ref (f η ,R 0 ), and intersect at the Doppler center frequency f dc Then f dc ΔR(f dc ,R 0 )for

[0194] ΔR(f dc ,R 0 )=R CM (f dc ,R 0 )-R CM (f dc ,R c )

[0195] After processing, R CM_ref (f η ,R 0 ) can be expressed as

[0196] R CM_ref (f η ,R 0 )=R CM (f η ,R c )+ΔR(f dc ,R 0 )=R CM (f η ,R c )+ΔR(f η ,R 0 ) / α(f η )

[0197] Among them, α(f η ) is the correction coefficient required for Chirp Scaling operation, and its calculation formula is as follows

[0198]

[0199] Since α(f η ) expression is complex and difficult to derive by analytical methods. Therefore, a numerical fitting method can be used to solve it: First, the reference distance R c As the center, N point targets are set at equal intervals along the distance direction, and the corresponding slant range is R ci (i=1,2,...N), according to R ci and f dc The one-dimensional matrix of dc As the center, N azimuth frequencies are set at equal intervals along the azimuth direction, and the corresponding frequency is f ηi(i=1,2,...N), the above matrix can be fitted to get α(f η ). The Chirp Scaling variable equation can be expressed as

[0200]

[0201] Among them, K m (τ,f η ) is the range modulation frequency including the secondary range modulation, which can be expressed as

[0202]

[0203] After phase multiplication in the range Doppler domain, the complementary RCMC is completed, that is, the signal range migration trajectory on each range gate is the same as the migration trajectory on the reference range gate. The signal after Chirp Scaling can be expressed as

[0204]

[0205] The second exponential term is the additional azimuth phase introduced by the Chirp Scaling operation, which can be compensated during azimuth compression.

[0206] Step 8: Perform distance compression.

[0207] After the Chirp Scaling operation, the range modulation rate becomes α(f η )K m (τ,f η ), so the distance compression function can be expressed as

[0208]

[0209] Step 9: Perform consistent distance migration correction.

[0210] After the RCMC, the phase can be multiplied according to the range migration amount on the reference range gate to compensate for it, and the range migration correction function H rcmc (f τ ,f η ) can be written as follows

[0211]

[0212] Step 10: Perform azimuth compression.

[0213] Improved CS algorithm azimuth compression function H a (τ,f η )as follows

[0214]

[0215] Step 11: Perform azimuth phase compensation.

[0216] Azimuth phase compensation function H 1 (τ,f η ) can be expressed as

[0217]

[0218] To sum up, the final SAR image is obtained.

[0219] Example:

[0220] The effect of the present invention is further illustrated by simulation experiments below.

[0221] In order to verify the effectiveness of the proposed method, the parameters in Table 1 are selected for simulation verification. Figure 2 At the perigee time 0, the point target simulation results are obtained by using the improved CS imaging algorithm of the high-orbit SAR proposed in the present invention. Table 2 shows the corresponding pulse pressure results.

[0222] Table 1 Computer simulation parameters

[0223] Track height 35786km Center frequency 5.4GHz Orbital inclination 12° bandwidth 120MHz Eccentricity 0.5 Pulse Width 1us Argument of perigee 88° Bottom View 4° Ascending node right ascension 106° Synthetic Aperture Time 100s

[0224] Table 2 Point target compression results based on CS algorithm

[0225]

[0226] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

Claims

1. An improved high-orbit synthetic aperture radar CS imaging method, characterized in that: include: Step 1: Establish a high-orbit SAR polynomial approximation equivalent slant range model and perform a sixth-order Taylor series expansion on the slant range history of the point target; Step 2: Perform two-dimensional Fourier transform on the high-orbit SAR point target echo signal model; Step 3: Use the series inversion method to solve the azimuth stationary phase point; Step 4: Use power series expansion to organize the two-dimensional spectrum; Step 5: Perform three-time phase compensation; Step 6: Perform Chirp Scaling operation in the range-Doppler domain; Step 7: Perform distance compression; Step 8: Perform consistent distance migration correction; Step 9: Perform azimuth compression; Step 10: Perform azimuth phase compensation.

2. The improved high-orbit synthetic aperture radar CS imaging method according to claim 1, characterized in that: The establishment of the high-orbit SAR polynomial approximation equivalent slant range model is specifically as follows: Assume that the position vectors of the satellite and point target in the earth fixed coordinate system are R S (t) and R T (t), the equivalent slant range model of high-orbit SAR polynomial approximation is the instantaneous slant range R(t) from the point target to the satellite: R(t)=R S (t)-R T (t) Its Taylor series expansion is as follows: Among them, R ST =R S -R T , V ST =V S -V T , A ST =A S -A T , B ST =B S -B T , C ST =C S -C T , D ST =D S -D T , E ST =E S -E T , R ST 、V ST , A ST , B ST , C ST , D ST 、E ST are the vectors of various orders from satellite to point target, R S , A S , B S , C S , D S 、E S Characterize the satellite vector, R T 、V T , A T , B T , C T , D T 、E T Characterize the point target vector; The sixth-order Taylor series expansion of the point target slant range history R(t) is as follows: Establish the point target slope range history expression R(t) = |R(t)|, first establish the identity R ST is the slant range scalar value from the satellite to the point target at the beam center moment; Taylor expansion of x x=x1t+x2t 2 +x3t 3 +x4t 4 ++x5t 5 +x6t 6 … in right Taylor expansion of 1+x At this point, the expression of the point target slope range history R(t)R(t) is obtained as follows: Among them, R C is the beam center slant distance, V C , A C , B C , C C , D C 、E C They represent the first, second, third, fourth, fifth and sixth derivatives of the distance history at the beam center, respectively, and have the meanings of velocity, acceleration, quadratic acceleration, cubic acceleration, quartic acceleration and quintic acceleration; R C =R ST V C =(x1 / 2)R ST A C =(x2-x1 2 / 4)R ST B C =(3x3-3x1x2 / 2-3x1 2 / 8)R ST <h2 style=";text-align:left;direction:ltr">D<h2 style=";text-align:left;direction:ltr"> C <h2 style=";text-align:left;direction:ltr"> (60x5-30x2x3-30x1x4+45x1x2<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> / 2+45x1<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> x3 / 2-75x1<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> x2 / 4+105x1<h2 style=";text-align:left;direction:ltr"> 5 <h2 style=";text-align:left;direction:ltr"> / 32)R<h2 style=";text-align:left;direction:ltr"> ST 3. The improved high-orbit synthetic aperture radar CS imaging method according to claim 2, characterized in that: The two-dimensional Fourier transform of the high-orbit SAR point target echo signal model is specifically: The high-orbit SAR point target echo signal model s0(τ,η) is: Where A0 is an arbitrary complex constant, τ is the distance time, η is the azimuth time, and η a is the beam center deviation time, w r (τ) is the distance envelope, w a (η) is the azimuth envelope, f0 is the radar center frequency, K r is the chirp modulation frequency, R(η) is the instantaneous slant distance, and c is the speed of light; After performing Fourier transform on the distance of the point target echo signal model, the Fourier transform is then performed on the azimuth. The phase Φ(f τ ,η) is expressed as And the phase Φ(f τ ,η) Take the derivative with respect to η and we get Among them, f τ is the distance frequency, f η is the azimuth frequency.

4. The improved high-orbit synthetic aperture radar CS imaging method according to claim 3, characterized in that: Using the series inversion method, the expression of the stationary phase point η in azimuth is solved as follows: Substitute the stationary phase expression into Φ′(f τ ,η) to obtain the analytical two-dimensional frequency domain signal Θ(f τ ,f η )expression 5. The improved high-orbit synthetic aperture radar CS imaging method according to claim 4, characterized in that: The two-dimensional spectrum Θ(f τ ,f η ), specifically: For Θ(f τ ,f η ) to organize: Among them, f dc is the Doppler center frequency; right and conduct The power series expansion of the two-dimensional spectrum is organized into the following expression form in, and distance frequency domain f r Irrelevant, it is the azimuth modulation signal term; and distance frequency domain f r The first-order term is related to the target distance migration term; and distance frequency domain f r The quadratic term is related to the frequency modulation of the range signal taking into account the quadratic range compression term; and distance frequency domain f r The third term is related to the second modulation frequency of the distance signal, that is, the slope of the modulation frequency.

6. The improved high-orbit synthetic aperture radar CS imaging method according to claim 5, characterized in that: The sorted two-dimensional spectrum is used to improve the CS algorithm and perform cubic phase compensation to degenerate the distance signal into a linear frequency modulation signal. The cubic phase compensation function can be expressed as follows 7. The improved high-orbit synthetic aperture radar (CS) imaging method according to claim 5, characterized in that: The sorted two-dimensional spectrum is used to improve the CS algorithm and perform the Chirp Scaling operation in the range-Doppler domain, specifically: In the range Doppler domain, the point target at distance R0 is relative to the reference range R c The difference in distance migration ΔR(f η , R0) is expressed as follows ΔR(f η ,R0)=R CM (f η ,R0)-R CM (f η ,R c ) Assume that the distance migration amount R of the point target at the distance R0 is CM (f η ,R0) after Chirp Scaling processing, and the reference distance R c The distance migration R CM (f η ,R c ) has the same trajectory, denoted as R CM_ref (f η ,R0), and intersect at the Doppler center frequency f dc If f dc ΔR(f dc ,R0) is ΔR(f dc ,R0)=R CM (f dc ,R0)-R CM (f dc ,R c ) R CM (f dc , R0) is the distance migration of the point target at the distance R0, R CM (f dc ,R c ) is the reference distance R c The distance migration amount at After processing, R CM_ref (f η , R0) is expressed as R CM_ref (f η ,R0)=R CM (f η ,R c )+ΔR(f dc ,R0)=R CM (f η ,R c )+ΔR(f η ,R0) / α(f η ) Among them, α(f η ) is the correction coefficient required for Chirp Scaling operation, and its calculation formula is as follows The chirp scaling equation is expressed as Among them, K m (τ,f η ) is the range modulation frequency including the secondary range modulation, expressed as After phase multiplication in the range Doppler domain, the complementary RCMC is completed, that is, the signal range migration trajectory on each range gate is the same as the migration trajectory on the reference range gate; the signal after Chirp Scaling is expressed as The second exponential term is the additional azimuth phase introduced by the Chirp Scaling operation, which is compensated during azimuth compression.

8. The improved high-orbit synthetic aperture radar (CS) imaging method according to claim 7, characterized in that: Perform distance compression, specifically: After the Chirp Scaling operation, the range modulation rate becomes α(f η )K m (τ,f η ), the distance compression function is expressed as 9. The improved high-orbit synthetic aperture radar (CS) imaging method according to claim 7, characterized in that: Perform consistent distance migration correction, specifically: After the RCMC, the phase is multiplied by the range migration amount on the reference range gate to compensate for the range migration correction function H. rcmc (f τ ,f η ) is written as follows 10. The improved high-orbit synthetic aperture radar (CS) imaging method according to claim 7, characterized in that: Perform azimuth compression, specifically: Azimuth compression function H a (τ,f η )as follows 11. The improved high-orbit synthetic aperture radar (CS) imaging method according to claim 7, characterized in that: Perform azimuth phase compensation, specifically: Azimuth phase compensation function H1(τ,f η ) is expressed as

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