A method for estimating target motion parameters using airborne multi-channel CSSAR ground acceleration

Abstract

The present invention discloses an airborne multi-channel CSSAR ground acceleration target motion parameter estimation method. First, the ATI phase of the target signal in the raw data domain of two adjacent channels of the multi-channel CSSAR system is obtained. Then, the baseband Doppler center of the target is estimated by using the fractional Fourier transform (FrFT) method and the baseband Doppler center is compensated in the azimuth time domain and range frequency domain. The target is imaged by phase multiplication in the two-dimensional frequency domain, thereby obtaining the position information of the target in the SAR image. Next, the slope of the ATI phase history is fitted by the least squares method to obtain the velocity v along the heading direction. ta The estimated value; then estimate the Doppler ambiguity number M and obtain the radial velocity v tr The estimated value of; then obtain the initial velocity v of the target along the x-axis and y-axis x and v y Finally, we get the acceleration a of the target along the x-axis and y-axis. x and a y The present invention achieves accurate estimation of target velocity and acceleration, which helps to overcome the difficult problem of ground acceleration target motion parameter estimation in the SAR-GMTI field.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and in particular relates to a method for estimating motion parameters of a ground acceleration target. Background Art

[0002] Airborne circular stripmap synthetic aperture radar (CSSAR) is a relatively new type of airborne SAR. Its advantages include a short revisit period and a wide observation range, making it suitable for wide-area air-to-ground reconnaissance and ground moving target indication (GMTI). However, the radar's circular motion also leads to coupling between the target's position, velocity, and acceleration during its phase history, making parameter estimation of ground moving targets difficult for airborne CSSAR. Consequently, methods for estimating ground moving target parameters used in conventional airborne linear SAR cannot be directly applied to airborne CSSAR.

[0003] High resolution is a key development trend in SAR, enabling more detailed target information and significantly enhancing SAR's ability to capture the observed scene. However, this increased resolution also results in a longer synthetic aperture time. This longer synthetic aperture time makes it difficult to neglect higher-order terms in the target acceleration and range equations, thus increasing the difficulty of designing parameter estimation methods for ground-moving targets. Therefore, there is an urgent need to develop accurate motion parameter estimation methods for airborne CSSAR. Summary of the Invention

[0004] In order to overcome the shortcomings of the existing technology, the present invention provides an airborne multi-channel CSSAR ground acceleration target motion parameter estimation method. First, the ATI phase of the target signal in the raw data domain of two adjacent channels of the multi-channel CSSAR system is obtained; then, the baseband Doppler center of the target is estimated by using the fractional Fourier transform (FrFT) method and the baseband Doppler center is compensated in the azimuth time domain-range frequency domain. The target is imaged by phase multiplication in the two-dimensional frequency domain, thereby obtaining the position information of the target in the SAR image; then, the slope of the ATI phase history is fitted by the least squares method to obtain the velocity v along the heading direction. ta The estimated value; then estimate the Doppler ambiguity number M and obtain the radial velocity v tr The estimated value of; then obtain the initial velocity v of the target along the x-axis and y-axis x and v y Finally, we get the acceleration a of the target along the x-axis and y-axis. x and a yThe present invention realizes accurate estimation of target velocity and acceleration, which helps to break through the difficult problem of ground acceleration target motion parameter estimation in the SAR-GMTI field.

[0005] The technical solution adopted by the present invention to solve the technical problem includes the following steps:

[0006] Step 1: Obtain the ATI phase of the raw data domain target signal of two adjacent channels of the multi-channel CSSAR system;

[0007] Step 2: Use the fractional Fourier transform (FrFT) method to estimate the baseband Doppler center of the target and perform baseband Doppler center compensation in the azimuth time domain and range frequency domain. Target imaging is achieved through phase multiplication in the two-dimensional frequency domain to obtain the target's position information in the SAR image.

[0008] Step 3: Use the least squares method to fit the slope of the ATI phase history, and use the position information of the target in the SAR image obtained in step 2 to obtain the heading velocity v ta estimated value of;

[0009] Step 4: Estimate the Doppler ambiguity number M and use the baseband Doppler center obtained in step 2 to obtain the radial velocity v tr estimated value of;

[0010] Step 5: According to the v obtained in step 3 and step 4 ta and v tr The estimated value of the target along the x-axis and y-axis is obtained by x and v y estimated value of;

[0011] Step 6: Use the maximum contrast method to perform a two-dimensional search on the quadratic and cubic coefficients of the target distance equation to obtain the acceleration a of the target along the x-axis and y-axis. x and a y estimated value.

[0012] Furthermore, the step 1 is specifically as follows:

[0013] Step 1-1: After carrier frequency demodulation and range compression, the target echo signal received by the i-th, i=1, 2, 3 channels is expressed as:

[0014]

[0015] Where,

[0016]

[0017]

[0018]

[0019] where p r (·) is the range compression impulse response function, ω a,i (·) is the two-way antenna pattern of the i-th channel, t r is the distance time, t a is the azimuthal slow time, c is the speed of light, λ is the wavelength, R i (t a ) is the distance from the equivalent phase center of the i-th channel to the target; δR(t a ) is the distance difference between the equivalent phase center of channel 2 and the equivalent phase center of channel 1, and is also the distance difference between the equivalent phase center of channel 3 and the equivalent phase center of channel 2. Its expression is t b is the moment when the target is located in the positive side view direction of the equivalent phase center of the reference channel, r b For the goal in t a =t b The distance from the coordinate origin at the moment, R b t a =t b The distance from the radar to the target at the moment is further expressed as r a is the radius of the radar platform, h is the height of the radar platform, v ta t a =t b The projection of the target velocity at the moment in the direction of the radar platform velocity is the heading velocity, ω is the angular velocity of the radar platform, and d is the distance between adjacent equivalent phase centers, that is, the baseline length;

[0020] Step 1-2: Taking channel 1 as the reference, after channel equalization and registration, the target echo signal received by channel 2 is expressed as:

[0021]

[0022] Where,

[0023]

[0024] R2(t a +△t a )≈R1(t a )+v tr ·△t a (7)

[0025]

[0026] Where R2(t a+△t a ) is the target distance equation of channel 2 after registration, v tr t a =t b The projection of the target velocity at the moment in the radial direction from the target to the radar is the radial velocity;

[0027] Step 1-3: The target echo signal received by channel 3 after registration is expressed as:

[0028]

[0029] Where,

[0030]

[0031]

[0032] Step 1-4: Get the signal after DPCA of two offset phase center antennas:

[0033]

[0034]

[0035] Then the ATI signal is expressed as:

[0036]

[0037] Substituting equations (12) and (13) into equation (14), the phase history of the ATI signal is obtained as follows:

[0038]

[0039] Furthermore, the step 2 is specifically as follows:

[0040] Step 2-1: The definition of FrFT is as follows:

[0041]

[0042] Where p is the order of fractional Fourier transform, u is the fractional Fourier Doppler frequency, is the fractional Fourier transform operator, kernel function K p (t a ,u) is:

[0043]

[0044] Where α = pπ / 2 represents the rotation angle of the time-frequency plane;

[0045] Step 2-2: Substitute equation (12) into equation (16) to obtain the fractional Fourier transform of the signal after DPCA. When the peak amplitude of the FrFT domain is the largest, it corresponds to the optimal rotation angle α0, and the baseband Doppler center f of the signal is ac,b It is estimated from the peak position of the fractional Fourier spectrum with the optimal rotation angle α0; therefore, a one-dimensional search is performed on α:

[0046]

[0047]

[0048] in is the fractional Fourier Doppler frequency at the peak position of the fractional Fourier spectrum;

[0049] Using the stationary phase principle, the signal of equation (12) is transformed into the range frequency domain, and we get:

[0050]

[0051] Among them, f r is the distance frequency, f c is the carrier frequency, W r (·) is the range-frequency envelope;

[0052] Step 2-3: Assume that the estimated target baseband Doppler center is Then the baseband Doppler center compensation function is constructed as:

[0053]

[0054] Multiplying equation (21) and equation (20) yields the target signal after baseband Doppler center compensation:

[0055]

[0056]

[0057]

[0058]

[0059] Among them, f ac is the target Doppler center frequency, further expressed as f ac =f ac,b +M·PRF, M is the target Doppler ambiguity number, PRF is the pulse repetition frequency of the system transmission signal, l2 and l3 are the quadratic and cubic coefficients of the target distance equation respectively;

[0060] Step 2-4: Perform azimuth Fourier transform on equation (22) to obtain:

[0061] S(f r ,f a )=∫S(f r ,t a )exp{-j2πf a t a}dt a (26)

[0062] where f a is the baseband Doppler frequency, and satisfies -PRF / 2≤f a ≤PRF / 2;

[0063] The stationary phase expression obtained by applying the stationary phase principle is:

[0064]

[0065] Where,

[0066]

[0067] According to the series inversion method, we get

[0068] t a =A1y+A2y 2 (29)

[0069] Where,

[0070]

[0071]

[0072] Substituting equation (29) into equation (26), we obtain the two-dimensional frequency domain expression of the target signal:

[0073]

[0074] Where,

[0075]

[0076] Where W a (·) is the azimuth frequency envelope;

[0077] Step 2-5: Construct the following reference function:

[0078]

[0079] Multiplying Equation (34) and Equation (32) and then performing a two-dimensional inverse Fourier transform, we get the expression of the target signal in the image domain:

[0080]

[0081] where p a (·) is the azimuth compression impulse response function;

[0082] Assume that the azimuth position and range position of the target in the image domain are t r,img and t a,img , then according to formula (35), t a =t b Target azimuth angle θ at time b , the distance R from the target to the radar b and the distance r from the target to the origin of the coordinate system b , estimated by the following formula:

[0083]

[0084]

[0085]

[0086] Furthermore, in step 3, the slope of the ATI phase history fitted by the least squares method is assumed to be According to formula (15), the speed v along the course is obtained ta The estimated value of is:

[0087]

[0088] Furthermore, the step 4 is specifically as follows:

[0089] Step 4-1: The Doppler ambiguity number is estimated using the following formula:

[0090]

[0091]

[0092] Where DFT2(·) represents the two-dimensional Fourier transform, Indicates f r The inverse Fourier transform of represents the summation along the Doppler domain, represents the maximum value along the fast time domain, r ref is the distance from the center of the scene to the origin of the coordinate system, R ref The shortest distance from the radar to the center of the scene;

[0093] Step 4-2: If the estimated target baseband Doppler center is The Doppler ambiguity number of the target is Then the estimate of the Doppler center frequency is:

[0094]

[0095] Therefore, according to formula (23) and formula (42), we can get v tr The estimation formula is:

[0096]

[0097] Furthermore, in step 5, according to the v obtained in steps 3 and 4 ta and v tr The estimated value of the target along the x-axis and y-axis is obtained by x and v y The estimated value of is:

[0098]

[0099]

[0100] Furthermore, the step 6 is specifically as follows:

[0101] Step 6-1: Use the maximum contrast method: estimate l2 and l3, that is:

[0102]

[0103] Where,

[0104]

[0105] s(t r ,t a ; l2, l3) = IDFT2{S(f r ,f a )·H2(f r ,f a )} (48)

[0106] Where IDFT(·) represents the two-dimensional inverse Fourier transform, E(·) represents the spatial averaging operation, and Contrast(·) is the image contrast;

[0107] Step 6-2: Assume that the estimated quadratic and cubic coefficients of the target distance equation are and According to equations (24) and (25), the acceleration a of the target along the x-axis and y-axis is obtained: x and a y The estimated value of is:

[0108]

[0109]

[0110] The beneficial effects of the present invention are as follows:

[0111] This invention utilizes the slope of the target signal's ATI phase history—a key factor—to propose a method for decoupling the target's position, velocity, and acceleration, enabling accurate estimation of both velocity and acceleration. This invention contributes to a breakthrough in the SAR-GMTI field, which is a difficult problem in estimating ground acceleration target motion parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0112] Figure 1 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0113] The present invention will be further described below with reference to the accompanying drawings and examples.

[0114] This paper proposes an accurate parameter estimation method for ground moving targets using airborne multi-channel CSSAR, combining target information from the time, frequency, and image domains. This method decouples the target's position, velocity, and acceleration by utilizing the target's Doppler center frequency, Doppler modulation rate, position in the SAR image, and the slope of the Along-Track Interferometry (ATI) phase.

[0115] Step 1: Obtain the ATI phase of the raw data domain target signal of two adjacent channels of the multi-channel CSSAR system;

[0116] Step 1-1: After carrier frequency demodulation and range compression, the target echo signal received by the i-th, i=1, 2, 3 channels is expressed as:

[0117]

[0118] Where,

[0119]

[0120]

[0121]

[0122] where p r (·) is the range compression impulse response function, ω a,i (·) is the two-way antenna pattern of the i-th channel, t r is the distance time, t a is the azimuthal slow time, c is the speed of light, λ is the wavelength, R i (t a ) is the distance from the equivalent phase center of the i-th channel to the target; δR(t a) is the distance difference between the equivalent phase center of channel 2 and the equivalent phase center of channel 1, and is also the distance difference between the equivalent phase center of channel 3 and the equivalent phase center of channel 2. Its expression is t b is the moment when the target is located in the positive side view direction of the equivalent phase center of the reference channel, r b For the goal in t a =t b The distance from the coordinate origin at the moment, R b t a =t b The distance from the radar to the target at the moment is further expressed as r a is the radius of the radar platform, h is the height of the radar platform, v ta t a =t b The projection of the target velocity at the moment ω on the direction of the radar platform velocity is the heading velocity, ω is the angular velocity of the radar platform, and d is the distance between adjacent equivalent phase centers, i.e., the baseline length. For simplicity, the constant amplitude term in the target signal is ignored.

[0123] Step 1-2: Taking channel 1 as the reference, after channel equalization and registration, the target echo signal received by channel 2 is expressed as:

[0124]

[0125] Where,

[0126]

[0127] R2(t a +△t a )≈R1(t a )+v tr ·△t a (7)

[0128]

[0129] Where R2(t a +△t a ) is the target distance equation of channel 2 after registration, v tr t a =t b The projection of the target velocity at the moment in the radial direction from the target to the radar is the radial velocity;

[0130] Step 1-3: The target echo signal received by channel 3 after registration is expressed as:

[0131]

[0132] Where,

[0133]

[0134]

[0135] Step 1-4: Get the signal after two Displaced Phase Center Antennas (DPCA):

[0136]

[0137]

[0138] Since R2(t a +△t a ) and R1(t a ) tr ·△t a and R3(t a +△t a ) and R2(t a ) tr ·△t a +d·(v ta -r b ω)△t a / R b is much smaller than a distance sampling unit, so the difference between them can be ignored in the distance envelope;

[0139] Then the ATI signal is expressed as:

[0140]

[0141] Substituting equations (12) and (13) into equation (14), the phase history of the ATI signal is obtained as follows:

[0142]

[0143] Step 2: Based on the signal model of the target raw data domain obtained in step 1, the baseband Doppler center of the target is estimated using the fractional Fourier transform (FrFT) method and the baseband Doppler center is compensated in the azimuth time domain and range frequency domain. Target imaging is achieved in the two-dimensional frequency domain through phase multiplication, thereby obtaining the target's position information in the SAR image.

[0144] Step 2-1: The definition of FrFT is as follows:

[0145]

[0146] Where p is the order of fractional Fourier transform, u is the fractional Fourier Doppler frequency, is the fractional Fourier transform operator, kernel function K p (t a ,u) is:

[0147]

[0148] Where α = pπ / 2 represents the rotation angle of the time-frequency plane;

[0149] Step 2-2: Substitute equation (12) into equation (16) to obtain the fractional Fourier transform of the signal after DPCA. When the peak amplitude of the FrFT domain is the largest, it corresponds to the optimal rotation angle α0, and the baseband Doppler center f of the signal is ac,b It is estimated from the peak position of the fractional Fourier spectrum with the optimal rotation angle α0; therefore, to find the optimal rotation angle, a one-dimensional search is performed on α:

[0150]

[0151]

[0152] in is the fractional Fourier Doppler frequency at the peak position of the fractional Fourier spectrum;

[0153] Using the stationary phase principle, the signal of equation (12) is transformed into the range frequency domain, and we get:

[0154]

[0155] Among them, f r is the distance frequency, f c is the carrier frequency, W r (·) is the range-frequency envelope; for simplicity, the constant amplitude term in Equation (20) is ignored;

[0156] Step 2-3: Assume that the estimated target baseband Doppler center is Then the baseband Doppler center compensation function is constructed as:

[0157]

[0158] Multiplying equation (21) and equation (20) yields the target signal after baseband Doppler center compensation:

[0159]

[0160]

[0161]

[0162]

[0163] Among them, f ac is the target Doppler center frequency, further expressed as f ac =f ac,b +M·PRF, M is the target Doppler ambiguity number, PRF is the pulse repetition frequency of the system transmission signal, l2 and l3 are the quadratic and cubic coefficients of the target distance equation respectively;

[0164] Step 2-4: Perform azimuth Fourier transform on equation (22) to obtain:

[0165] S(f r ,f a )=∫S(f r ,t a )exp{-j2πf a t a}dt a (26)

[0166] where f a is the baseband Doppler frequency, and satisfies -PRF / 2≤f a ≤PRF / 2;

[0167] The stationary phase expression obtained by applying the stationary phase principle is:

[0168]

[0169] Where,

[0170]

[0171] According to the series inversion method, we get

[0172] t a =A1y+A2y 2 (29)

[0173] Where,

[0174]

[0175]

[0176] Substituting equation (29) into equation (26), we obtain the two-dimensional frequency domain expression of the target signal:

[0177]

[0178] Where,

[0179]

[0180] Where W a (·) is the azimuth frequency envelope;

[0181] Step 2-5: From equations (32) and (33), we can see that by compensating for the last two exponential terms in equation (33), we can achieve target focusing. Therefore, we construct the following reference function:

[0182]

[0183] Multiplying Equation (34) and Equation (32) and then performing a two-dimensional inverse Fourier transform, we get the expression of the target signal in the image domain:

[0184]

[0185] where p a (·) is the azimuth compression impulse response function;

[0186] Since the target does not have an azimuth offset in the image domain, its position at t can be easily obtained. a =t b The position parameters at time t, assuming that the azimuth position and range position of the target in the image domain are t r,img and t a,img (with time as the dimension), then according to formula (35), t a =t b Target azimuth angle θ at time b , the distance R from the target to the radar b and the distance r from the target to the origin of the coordinate system b , estimated by the following formula:

[0187]

[0188]

[0189]

[0190] Step 3: Fit the slope of the ATI phase history using the least squares method And using the position information of the target in the SAR image obtained in step 2, the speed v along the heading is obtained ta The estimated value of is:

[0191]

[0192] Step 4: Estimate the Doppler ambiguity number M and use the baseband Doppler center obtained in step 2 to obtain the radial velocity v tr estimated value of;

[0193] Step 4-1: When a target has Doppler ambiguity, it appears offset in the range-Doppler domain. Therefore, for a specific target, the residual range bin migration can be corrected using linear phase multiplication in the range-frequency domain. After the residual range bin migration is fully corrected, the target's trajectory in the range-Doppler plane is parallel to the Doppler axis, and the incoherent sum along the range direction is maximized. Therefore, the Doppler ambiguity number is estimated using the following formula:

[0194]

[0195]

[0196] Where DFT2(·) represents the two-dimensional Fourier transform, Indicates f r The inverse Fourier transform of represents the summation along the Doppler domain, represents the maximum value along the fast time domain, r ref is the distance from the center of the scene to the origin of the coordinate system, R ref The shortest distance from the radar to the center of the scene; no information about the target is used here.

[0197] Step 4-2: If the estimated target baseband Doppler center is The Doppler ambiguity number of the target is Then the estimate of the Doppler center frequency is:

[0198]

[0199] Therefore, according to formula (23) and formula (42), we can get v tr The estimation formula is:

[0200]

[0201] Step 5: According to the v obtained in step 3 and step 4 ta and v tr The estimated value of the target along the x-axis and y-axis is obtained by x and v y The estimated value of is:

[0202]

[0203]

[0204] Step 6: Use the maximum contrast method to perform a two-dimensional search on the quadratic and cubic coefficients of the target distance equation to obtain the acceleration a of the target along the x-axis and y-axis. x and a y estimated value of;

[0205] Step 6-1: Use the maximum contrast method: estimate l2 and l3, that is:

[0206]

[0207] Where,

[0208]

[0209]

[0210] Where IDFT(·) represents the two-dimensional inverse Fourier transform, E(·) represents the spatial averaging operation, and Contrast(·) is the image contrast;

[0211] Step 6-2: Assume that the estimated quadratic and cubic coefficients of the target distance equation are and According to equations (24) and (25), the acceleration a of the target along the x-axis and y-axis is obtained: x and a y The estimated value of is:

[0212]

[0213] Specific embodiment:

[0215] The parameters of the airborne multi-channel CSSAR system are shown in Table 1, and the target parameters are shown in Table 2. The resolution is set to 1m×1m. Tables 3 to 5 show the estimated results of the three target motion parameters. As can be seen from the tables, the absolute error accuracy of the target velocity is accurate to one decimal place and is less than 0.3m / s. The absolute error accuracy of the target acceleration is accurate to three decimal places and is less than 0.004m / s. 2 The target motion parameters are well estimated.

[0216] Table 1 Multi-channel airborne CSSAR-GMTI system parameters

[0217] Radar platform speed 125m / s Sampling frequency 180MHz Flight radius 2.3km Transmitted signal bandwidth 150MHz Radar platform height 8km Synthetic Aperture Time 1.2s carrier frequency 10GHz Pulse repetition frequency 1600Hz Adjacent equivalent phase center 0.2m Scene center distance 10km

[0218] Table 2 Moving target parameters

[0219] T1 T2 T3 <![CDATA[v x (m / s)]]> 28 3 -29 <![CDATA[v y (m / s)]]> 22 -30 -5 <![CDATA[a x (m / s 2 )]]> 0.4 -1 -0.1 <![CDATA[a y (m / s 2 )]]> -0.8 0.5 1 <![CDATA[θ0(rad)]]> -0.0618 -0.0740 -0.0926 <![CDATA[r0(km)]]> 8.3033 8.3083 8.3333

[0220] Table 3 v ta and v tr Estimation results

[0221]

[0222] Table 4 vx and v y Estimation results

[0223]

[0224] Table 5a x and a y Estimation results

[0225]

Claims

1. An airborne multi-channel CSSAR ground acceleration target motion parameter estimation method, characterized in that: The following steps are involved: Step 1: Obtain the ATI phase of the raw data domain target signal of two adjacent channels of the multi-channel CSSAR system; Step 2: Use the fractional Fourier transform (FrFT) method to estimate the baseband Doppler center of the target and perform baseband Doppler center compensation in the azimuth time domain and range frequency domain. Target imaging is achieved through phase multiplication in the two-dimensional frequency domain to obtain the target's position information in the SAR image. Step 3: Use the least squares method to fit the slope of the ATI phase history, and use the position information of the target in the SAR image obtained in step 2 to obtain the heading velocity v ta estimated value of; Step 4: Estimate the Doppler ambiguity number M and use the baseband Doppler center obtained in step 2 to obtain the radial velocity v tr estimated value of; Step 5: According to the v obtained in step 3 and step 4 ta and v tr The estimated value of the target along the x-axis and y-axis is obtained by x and v y estimated value of; Step 6: Use the maximum contrast method to perform a two-dimensional search on the quadratic and cubic coefficients of the target distance equation to obtain the acceleration a of the target along the x-axis and y-axis. x and a y estimated value.

2. The method for estimating target motion parameters using airborne multi-channel CSSAR ground acceleration according to claim 1, characterized in that: The step 1 is specifically as follows: Step 1-1: After carrier frequency demodulation and range compression, the target echo signal received by the i-th, i=1, 2, 3 channels is expressed as: Where, where p r (·) is the range compression impulse response function, ω a,i (·) is the two-way antenna pattern of the i-th channel, t r is the distance time, t a is the azimuthal slow time, c is the speed of light, λ is the wavelength, R i (t a ) is the distance from the equivalent phase center of the i-th channel to the target; δR(t a ) is the distance difference between the equivalent phase center of channel 2 and the equivalent phase center of channel 1, and is also the distance difference between the equivalent phase center of channel 3 and the equivalent phase center of channel 2. Its expression is t b is the moment when the target is located in the positive side view direction of the equivalent phase center of the reference channel, r b For the goal in t a =t b The distance from the coordinate origin at the moment, R b t a =t b The distance from the radar to the target at the moment is further expressed as r a is the radius of the radar platform, h is the height of the radar platform, v ta t a =t b The projection of the target velocity at the moment in the direction of the radar platform velocity is the heading velocity, ω is the angular velocity of the radar platform, and d is the distance between adjacent equivalent phase centers, that is, the baseline length; Step 1-2: Taking channel 1 as the reference, after channel equalization and registration, the target echo signal received by channel 2 is expressed as: Where, R2(t a +Δt a )≈R1(t a )+v tr ·Δt a (7) Where R2(t a +Δt a ) is the target distance equation of channel 2 after registration, v tr t a =t b The projection of the target velocity at the moment in the radial direction from the target to the radar is the radial velocity; Step 1-3: The target echo signal received by channel 3 after registration is expressed as: Where, Step 1-4: Get the signal after DPCA of two offset phase center antennas: Then the ATI signal is expressed as: Substituting equations (12) and (13) into equation (14), the phase history of the ATI signal is obtained as follows:

3. The method for estimating target motion parameters using airborne multi-channel CSSAR ground acceleration according to claim 2, characterized in that: The step 2 is specifically as follows: Step 2-1: The definition of FrFT is as follows: Where p is the order of the fractional Fourier transform, u is the fractional Fourier Doppler frequency, F p [·] is the fractional Fourier transform operator, kernel function K p (t a ,u) is: Where α = pπ / 2 represents the rotation angle of the time-frequency plane; Step 2-2: Substitute equation (12) into equation (16) to obtain the fractional Fourier transform of the signal after DPCA; when the peak amplitude of the FrFT domain is the largest, it corresponds to the optimal rotation angle α0, and the baseband Doppler center f of the signal is ac,b It is estimated from the peak position of the fractional Fourier spectrum with the optimal rotation angle α0; therefore, a one-dimensional search is performed on α: in is the fractional Fourier Doppler frequency at the peak position of the fractional Fourier spectrum; Using the stationary phase principle, the signal of equation (12) is transformed into the range frequency domain, and we get: Among them, f r is the distance frequency, f c is the carrier frequency, W r (·) is the range-frequency envelope; Step 2-3: Assume that the estimated target baseband Doppler center is Then the baseband Doppler center compensation function is constructed as: Multiplying equation (21) and equation (20) yields the target signal after baseband Doppler center compensation: Among them, f ac is the target Doppler center frequency, further expressed as f ac =f ac,b +M·PRF, M is the target Doppler ambiguity number, PRF is the pulse repetition frequency of the system transmission signal, l2 and l3 are the quadratic and cubic coefficients of the target distance equation respectively; Step 2-4: Perform azimuth Fourier transform on equation (22) to obtain: S(f r ,f a )=∫S(f r ,t a )exp{-j2πf a t a }dt a (26) where f a is the baseband Doppler frequency, and satisfies -PRF / 2≤f a ≤PRF / 2; The stationary phase expression obtained by applying the stationary phase principle is: Where, According to the series inversion method, we get t a =A1y+A2y 2 (29) Where, Substituting equation (29) into equation (26), we obtain the two-dimensional frequency domain expression of the target signal: S(f r ,f a )=W r (f r )W a (f a )×exp{jΘ(f r ,f a )} (32) Where, Where W a (·) is the azimuth frequency envelope; Step 2-5: Construct the following reference function: Multiplying Equation (34) and Equation (32) and then performing a two-dimensional inverse Fourier transform, we get the expression of the target signal in the image domain: where p a (·) is the azimuth compression impulse response function; Assume that the azimuth position and range position of the target in the image domain are t r,img and t a,img , then according to formula (35), t a =t b Target azimuth angle θ at time b , the distance R from the target to the radar b and the distance r from the target to the origin of the coordinate system b , estimated by the following formula:

4. The method for estimating target motion parameters using airborne multi-channel CSSAR ground acceleration according to claim 3, wherein: In step 3, the slope of the ATI phase history fitted by the least squares method is assumed to be According to formula (15), the speed v along the course is obtained ta The estimated value of is:

5. The method for estimating target motion parameters using airborne multi-channel CSSAR ground acceleration according to claim 4, characterized in that: The step 4 is specifically as follows: Step 4-1: The Doppler ambiguity number is estimated using the following formula: Where DFT2(·) represents the two-dimensional Fourier transform, Indicates f r The inverse Fourier transform of represents the summation along the Doppler domain, represents the maximum value along the fast time domain, r ref is the distance from the center of the scene to the origin of the coordinate system, R ref The shortest distance from the radar to the center of the scene; Step 4-2: If the estimated target baseband Doppler center is The Doppler ambiguity number of the target is Then the estimate of the Doppler center frequency is: Therefore, according to formula (23) and formula (42), we can get v tr The estimation formula is:

6. The method for estimating target motion parameters using airborne multi-channel CSSAR ground acceleration according to claim 5, characterized in that: In step 5, according to the v obtained in steps 3 and 4, ta and v tr The estimated value of the target along the x-axis and y-axis is obtained by x and v y The estimated value of is:

7. The method for estimating target motion parameters using airborne multi-channel CSSAR ground acceleration according to claim 6, characterized in that: The step 6 is specifically as follows: Step 6-1: Use the maximum contrast method: estimate l2 and l3, that is: Where, s(t r ,t a ;l2,l3)=IDFT2{S(f r ,f a )·H2(f r ,f a )} (48) Where IDFT(·) represents the two-dimensional inverse Fourier transform, E(·) represents the spatial averaging operation, and Contrast(·) is the image contrast; Step 6-2: Assume that the estimated quadratic and cubic coefficients of the target distance equation are and According to equations (24) and (25), the acceleration a of the target along the x-axis and y-axis is obtained: x and a y The estimated value of is:

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