A sea surface moving target heading angle estimation method based on energy trajectory extraction

Abstract

The application discloses a sea surface moving target heading angle estimation method based on energy trajectory extraction. Firstly, echo signals are preprocessed according to prior knowledge auxiliary information, and two schemes are adopted to estimate and extract strong scattering point energy trajectories according to signal signal-to-noise ratios. Then, a multi-parameter optimization model is constructed according to the extracted energy trajectories and by comprehensively considering the influence of radar platform motion errors. Finally, the estimated heading angle of the sea surface moving target is accurately obtained through a differential evolution genetic algorithm. The method can accurately extract and estimate the energy trajectory of the target under the condition of a low signal-to-noise ratio. The multi-parameter model considers the platform motion errors in addition to the key to-be-solved information such as target speed and position, effectively solves the problems of serious interference, inaccuracy and multiple solutions of the existing method for estimating target motion parameters based on solving distance equation sets under a low signal-to-noise ratio.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, specifically relating to a method for estimating the heading angle of a moving target on the sea surface based on energy trajectory extraction. Background Technology

[0002] SAR can acquire important information such as radar images of moving targets on the sea surface, thereby increasing the effectiveness and richness of the information obtained in the process of studying and judging the maritime security situation, and playing an important role in maintaining the security and stability of the maritime area.

[0003] However, since the course of non-cooperative moving targets on the sea surface is often unknown, it is difficult to locate and accurately indicate their position. If the course information of moving targets could be obtained, they could be tracked and located, greatly improving the accuracy of moving target indication.

[0004] Existing methods for estimating the heading of moving targets based on Doppler estimation typically require an imaging step, leading to high computational complexity. Furthermore, these methods struggle to address the issues of low echo signal-to-noise ratios and decreased estimation accuracy when the radar platform exhibits motion errors.

[0005] Therefore, it is necessary to design a moving target heading estimation scheme that is exempt from the imaging step. In addition to the motion parameters of the moving target on the sea surface, the motion error of the radar platform also needs to be estimated. If the latter is not considered, the estimation result will have a large error. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a method for estimating the heading angle of a moving sea surface target based on energy trajectory extraction. This method accurately estimates and extracts the energy trajectory of the strong scattering points of the moving sea surface target, incorporates the motion error of the radar platform into a multi-parameter optimization model, and finally uses a genetic algorithm to estimate the heading angle of the moving sea surface target. This effectively solves the problem of inaccurate target velocity estimation caused by the presence of platform motion error under low signal-to-noise ratio conditions.

[0007] The technical solution adopted in this invention is: a method for estimating the heading angle of a moving target on the sea surface based on energy trajectory extraction, the specific steps of which are as follows:

[0008] Step 1: Establish the spatial geometry of monostatic SAR, then establish the echo model of moving targets on the sea surface using monostatic SAR, and complete the initialization of system parameters;

[0009] First, establish the spatial geometry of a single-base SAR, and set r. T =[X T ,Y T Z T ] and r p =[X p ,Y p Z p] represent the coordinate vectors of the scattering point in the radar platform and the target in the global coordinate system, respectively. T =[v Tx ,v Ty ,v Tz ] and v p =[v px ,v py ,v pz ] represent the velocity vectors of the radar and the scattering point, respectively.

[0010] The two-way range history R(η;r) of the ship target scattering point can be obtained from the SAR spatial geometry configuration. p The expression is as follows:

[0011] R(η;r p )=2||r T +v T η-r p -v p η||

[0012] Where η represents slow time.

[0013] Then, a monostatic SAR sea surface moving target echo model is established, and the system parameters are initialized.

[0014] Assuming the radar transmitted signal is a linear frequency modulated signal, the expressions for the down-converted and demodulated echo signal in the two-dimensional time domain are as follows:

[0015]

[0016] Where τ, η and T a These represent the fast time, slow time, and synthesis aperture time, respectively. σ η This represents the scene scattering coefficient, with the electromagnetic wave velocity c being 3 × 10⁻⁶. 8 m / s, λ represents the wavelength of the transmitted signal, K represents the modulation frequency of the linear frequency modulated signal, and rect(·) represents the rectangular window function.

[0017] The initial system parameters include: pulse repetition frequency, range sampling rate, number of receiving array elements, number of coherent processing pulses, and spatial position and velocity of the receiving and transmitting stations.

[0018] Step 2: Based on step S1, pulse compression is performed on the demodulated two-dimensional time-domain echo signal s(t,η);

[0019] The expression for the range-compressed echo of a moving target on the sea surface is as follows:

[0020]

[0021] Where, σ p Represents the RCS of a moving target, Br This indicates the bandwidth of the transmitted signal.

[0022] Step 3: Migration factor phase compensation to remove distance migration introduced by platform motion;

[0023] The range-to-fast Fourier transform of the echo signal is expressed as follows:

[0024]

[0025] Among them, f τ Represents the range frequency domain variable, phase Φ(f) τ The expression for η is as follows:

[0026]

[0027] Where R0 represents the slant range between the ship target and the radar platform at the imaging center moment, f dc f dr and f d3 f represents the Doppler centroid, Doppler modulation frequency, and third-order Doppler parameter of the ship target, respectively. c =c / λ represents the carrier frequency.

[0028] For s2(f τ ,η;r p Migration factor phase compensation is performed to remove distance migration caused by platform motion, and the compensated migration factor phase H ref The expression is as follows:

[0029]

[0030] The expression for the echo signal after phase compensation is as follows:

[0031]

[0032] For s3(f τ ,η;r p The inverse Fourier transform of the distance is expressed as follows:

[0033]

[0034] Step 4: Multi-target echo separation in the scene;

[0035] For s4(τ,η;r) p The fast Fourier transform of the azimuth direction is expressed as follows:

[0036]

[0037] In s5(τ,f) η ;r pIn the range Doppler domain where the signal is located, the echo signals of targets at different locations in the scene can be directly separated.

[0038] Based on the two-dimensional position of a single moving target in the range-Doppler, construct the corresponding two-dimensional window function H. win Through multi-target echo signals and two-dimensional window function H win Multiplication achieves echo separation of moving targets. Different window functions H are applied to the azimuth direction in the range-Doppler domain. win The target region is segmented and separated, and then the azimuth of the separated single target signal is transformed into an inverse Fourier transform to obtain the signal s6(f). τ ,η;r p The expression is as follows:

[0039] s6(τ,η;r p =IFFT[s5(τ,f η ;r p )·H win ]

[0040] Step 5: Extract and estimate the energy trajectory of strong scattering points;

[0041] The signal-to-noise ratio of the echo is calculated by comparing the peak energy of the pulse-compressed echo with the average energy of the noise region.

[0042] Determine the signal-to-noise ratio (SNR). If it is ≥15dB, it is considered a high SNR. In the case of high SNR, iterate through all range gates under each PFI and extract the energy trajectory range gate positions of the strong scattering points under that PFI according to the maximum SNR criterion. The expression is as follows:

[0043]

[0044] Where G(m,k) represents s6(f τ ,η;r p In the context of the k-th PFI, all distance gates are represented, where m represents the distance gate position. This refers to the distance gate position of the energy trajectory of the strong scattering point at the kth PFI.

[0045] To determine the signal-to-noise ratio (SNR), if it is <15dB, it is considered a low SNR. In the case of a low SNR, a multi-frame joint detection method based on dynamic programming is used to extract the energy trajectory, as shown in the following expression:

[0046]

[0047] in, and Let z represent the energy trajectory neighborhood before and after the update, respectively. xy (m) represents the maximum value in the associated region, and the extracted scattering point energy trajectory is... Na represents the number of echo azimuth sampling points, [·] T This represents the matrix transpose operation.

[0048] Step Six: Multi-parameter optimization modeling and objective function design;

[0049] The parameters to be optimized include: the two-dimensional velocity of the moving target on the sea surface and the position of each scattering point. When constructing the optimization model, the velocity error of the radar platform is also modeled as a parameter. The expression for the parameters to be optimized is as follows:

[0050] Λ=[v px ,v py ,X p1 ,Y p1 ,…,X pi ,Y pi ,…,X pN ,Y pN ,e1,…,e m ]

[0051] Among them, v px and v py X represents the two-dimensional velocity of a moving target on the sea surface. pi and Y pi Let N represent the two-dimensional position coordinates of the i-th scattering intensity point of a moving target on the sea surface, and let N represent the number of ship scattering points in the simultaneous modeling, e1,…,e m This indicates the speed error of the radar platform.

[0052] The corresponding optimization model expression is as follows:

[0053]

[0054] in, This indicates that R represents the energy trajectory of the strong scattering point extracted in step five. t_n (Λ,η) represents the theoretical value of the energy trajectory calculated from Λ.

[0055] Considering the velocity error e of the radar platform, the expression for the platform velocity with error is as follows:

[0056] v Terr =v T +e

[0057] Then the platform's motion trajectory T path The expression is as follows:

[0058]

[0059] Strong scattering point r p =[X p ,Y p Zp ]Movement trajectory Target path The expression is as follows:

[0060]

[0061] If the moving target on the sea surface is always positioned on the two-dimensional sea level, then the height term will always be 0.

[0062] Theoretical value of energy trajectory R t_n (Λ,η) is also the distance history of the strong scattering point of the moving target on the sea surface, which can be calculated from the L2 norm of the platform's trajectory and the moving target's trajectory, as shown in the following expression:

[0063] R t_n (Λ,η)=||T path -Target path ||2

[0064] Step 7: Use the DE algorithm to solve for the target heading angle;

[0065] Based on the nonconvexity of the optimization model established in step six, a genetic algorithm—differential evolution algorithm—is used for optimization, as follows:

[0066] (1) Determine the population size N in the differential evolution algorithm p Maximum number of iterations G m The hybridization parameter CR is determined, and an initial population in the solution space is generated randomly.

[0067] (2) Calculate Λ for each individual in the initial population i objective function value

[0068] (3) Determine whether the termination condition has been met or the number of generations has reached its maximum. If so, terminate the evolution and obtain a set of optimal parameters Λ for the moving target. opt If not, then continue;

[0069] (4) Perform mutation and crossover operations to obtain an intermediate population;

[0070] (5) Select individuals from the original population and the intermediate population to obtain a new generation of population;

[0071] (6) Let the evolutionary generation g = g + 1, and go to step (3);

[0072] Finally, the optimal parameter Λ of the moving target is estimated using the differential evolution algorithm. opt Then, the heading angle estimate of the moving target on the sea surface can be obtained from the optimal two-dimensional motion velocity of the moving target on the sea surface.

[0073] The beneficial effects of this invention are as follows: First, the method of this invention preprocesses the echo signal based on prior knowledge and auxiliary information. Then, based on the signal-to-noise ratio (SNR), two schemes are adopted to estimate and extract the energy trajectory of strong scattering points. Next, based on the extracted energy trajectory, the influence of radar platform motion error is comprehensively considered to construct a multi-parameter optimization model. Finally, a differential evolutionary genetic algorithm is used to accurately obtain the estimated heading angle of the moving target on the sea surface. This invention's method can accurately extract and estimate the target's energy trajectory from the target echo under low SNR conditions. By employing a multi-parameter model, in addition to key information to be solved such as target velocity and position, it also considers platform motion error, effectively solving the problems of severe interference, inaccuracy, and multiple solutions in existing methods for estimating target motion parameters based on solving range equations under low SNR conditions. Attached Figure Description

[0074] Figure 1 This is a flowchart of a method for estimating the heading angle of a sea surface moving target based on energy trajectory extraction, according to the present invention.

[0075] Figure 2 This is a diagram of the single-base SAR spatial geometry configuration used in the embodiments of the present invention.

[0076] Figure 3 This is a schematic diagram of energy trajectory separation and extraction in step five of this embodiment of the invention.

[0077] Figure 4 This is an iterative curve of the target velocity estimated in step seven of this embodiment of the invention.

[0078] Figure 5 The figure shows the accuracy results of heading angle estimation under different signal-to-noise ratios in the embodiments of the present invention. Detailed Implementation

[0079] The method of this invention is mainly verified through simulation experiments, using MATLAB 2022b as the simulation platform. The method of this invention will be further described below with reference to the accompanying drawings and embodiments.

[0080] like Figure 1 As shown in the diagram, the specific steps of the method for estimating the heading angle of a moving target on the sea surface based on energy trajectory extraction according to the present invention are as follows:

[0081] Step 1: Establish the spatial geometry of monostatic SAR, then establish the echo model of moving targets on the sea surface using monostatic SAR, and complete the initialization of system parameters;

[0082] like Figure 2 As shown, firstly, the single-base SAR spatial geometry configuration is established, and r is set. T =[X T ,Y T Z T ] and rp =[X p ,Y p Z p ] represent the coordinate vectors of the scattering point in the radar platform and the target in the global coordinate system, respectively. T =[v Tx ,v Ty ,v Tz ] and v p =[v px ,v py ,v pz ] represent the velocity vectors of the radar and the scattering point, respectively.

[0083] The two-way range history R(η;r) of the ship target scattering point can be obtained from the SAR spatial geometry configuration. p The expression is as follows:

[0084] R(η;r p )=2||r T +v T η-r p -v p η||

[0085] Where η represents slow time.

[0086] Then, a monostatic SAR sea surface moving target echo model is established, and the system parameters are initialized.

[0087] Assuming the radar transmitted signal is a linear frequency modulated signal, the expressions for the down-converted and demodulated echo signal in the two-dimensional time domain are as follows:

[0088]

[0089] Where τ, η and T a These represent the fast time, slow time, and synthesis aperture time, respectively. σ η This represents the scene scattering coefficient, with the electromagnetic wave velocity c being 3 × 10⁻⁶. 8 m / s, λ represents the wavelength of the transmitted signal, K represents the modulation frequency of the linear frequency modulated signal, and rect(·) represents the rectangular window function.

[0090] The initial system parameters include: pulse repetition frequency, range sampling rate, number of receiving array elements, number of coherent processing pulses, and spatial position and velocity of the receiving and transmitting stations.

[0091] The parameters of the single-base SAR system in this embodiment are shown in Table 1.

[0092] Table 1

[0093] parameter numerical values signal frequency 17GHz signal bandwidth 100MHz Pulse repetition frequency 2000Hz Radar platform location (-7869,-40108,28800)m Radar platform speed (0, 1290, -166) m / s

[0094] Step 2: Based on step S1, pulse compression is performed on the demodulated two-dimensional time-domain echo signal s(t,η);

[0095] The expression for the range-compressed echo of a moving target on the sea surface is as follows:

[0096]

[0097] Where, σ p Represents the RCS of a moving target, B r This indicates the bandwidth of the transmitted signal.

[0098] Step 3: Migration factor phase compensation to remove distance migration introduced by platform motion;

[0099] The range-to-fast Fourier transform of the echo signal is expressed as follows:

[0100]

[0101] Among them, f τ Represents the range frequency domain variable, phase Φ(f) τ The expression for η is as follows:

[0102]

[0103] Where R0 represents the slant range between the ship target and the radar platform at the imaging center moment, f dc f dr and f d3 f represents the Doppler centroid, Doppler modulation frequency, and third-order Doppler parameter of the ship target, respectively. c =c / λ represents the carrier frequency.

[0104] For s2(f τ ,η;r p Migration factor phase compensation is performed to remove distance migration caused by platform motion, and the compensated migration factor phase H ref The expression is as follows:

[0105]

[0106] The expression for the echo signal after phase compensation is as follows:

[0107]

[0108] For s3(f τ ,η;r p The inverse Fourier transform of the distance is expressed as follows:

[0109]

[0110] Step 4: Multi-target echo separation in the scene;

[0111] For s4(τ,η;r) p The fast Fourier transform of the azimuth direction is expressed as follows:

[0112]

[0113] In s5(τ,f) η ;r p In the range Doppler domain where the signal is located, the echo signals of targets at different locations in the scene can be directly separated.

[0114] Based on the two-dimensional position of a single moving target in the range-Doppler, construct the corresponding two-dimensional window function H. win Through multi-target echo signals and two-dimensional window function H win Multiplication is performed to achieve echo separation of moving targets. Different window functions H are applied to the azimuth direction in the range-Doppler domain. win The target region is segmented and separated, and then the azimuth of the separated single target signal is transformed into an inverse Fourier transform to obtain the signal s6(f). τ ,η;r p The expression is as follows:

[0115] s6(τ,η;r p =IFFT[s5(τ,f η ;r p )·H win ]

[0116] Step 5: Extract and estimate the energy trajectory of strong scattering points;

[0117] The signal-to-noise ratio of the pulse-compressed echo can be calculated from the energy of the peak value in the echo and the average energy of the noise region. Figure 3 A schematic diagram of energy trajectory extraction and estimation of strong scattering points in the echo after pulse compression under arbitrary signal-to-noise ratio is shown (Schematic diagram of energy trajectory separation and extraction), where ΔR represents the distance-oriented neighborhood of the energy trajectory; due to the influence of noise, the specific energy trajectory extraction methods of scattering points under high / low signal-to-noise ratio are significantly different.

[0118] Determine the signal-to-noise ratio (SNR). If it is ≥15dB, it is considered a high SNR. In the case of a high SNR, iterate through all range gates under each Pulse Repetition Interval (PFI) and extract the strong scattering point energy trajectory range gate positions under that PFI according to the maximum SNR criterion. The expression is as follows:

[0119]

[0120] Where G(m,k) represents s6(f τ ,η;r p In the context of the k-th PFI, all distance gates are represented, where m represents the distance gate position. This refers to the distance gate position of the energy trajectory of the strong scattering point at the kth PFI.

[0121] The signal-to-noise ratio (SNR) is assessed; if it is less than 15 dB, it is considered low. At low SNR, the energy trajectory extraction method based on the maximum SNR criterion will produce significant errors due to noise. A multi-frame joint detection method based on dynamic programming is used to extract the energy trajectory, as shown in the following expression:

[0122]

[0123] in, and Let z represent the energy trajectory neighborhood before and after the update, respectively. xy (m) represents the maximum value in the associated region, and the extracted scattering point energy trajectory is... Na represents the number of echo azimuth sampling points, [·] T This represents the matrix transpose operation.

[0124] Step Six: Multi-parameter optimization modeling and objective function design;

[0125] The parameters to be optimized include: the two-dimensional velocity of the moving target on the sea surface and the positions of each scattering point. In reality, the radar platform itself also has velocity errors, which have a certain impact on the final estimated velocity of the moving target on the sea surface. Therefore, in constructing the optimization model, this embodiment also models the velocity error of the radar platform as a parameter. The expressions for the parameters to be optimized are as follows:

[0126] Λ=[v px ,v py ,X p1 ,Y p1 ,…,X pi ,Y pi ,…,X pN ,Y pN ,e1,…,e m ]

[0127] Among them, v px and v py X represents the two-dimensional velocity of a moving target on the sea surface. pi and Y pi Let N represent the two-dimensional position coordinates of the i-th scattering intensity point of a moving target on the sea surface, and let N represent the number of ship scattering points in the simultaneous modeling, e1,…,e m This indicates the speed error of the radar platform.

[0128] The corresponding optimization model expression is as follows:

[0129]

[0130] in, This indicates that R represents the energy trajectory of the strong scattering point extracted in step five. t_n (Λ,η) represents the theoretical value of the energy trajectory calculated from Λ.

[0131] Considering the velocity error e of the radar platform, the expression for the platform velocity with error is as follows:

[0132] v Terr =v T +e

[0133] Then the platform's motion trajectory T path The expression is as follows:

[0134]

[0135] Strong scattering point r p =[X p ,Y p Z p ]Movement trajectory Target path The expression is as follows:

[0136]

[0137] If the moving target on the sea surface is always positioned on the two-dimensional sea level, then the height term will always be 0.

[0138] Theoretical value of energy trajectory R t_n (Λ,η) is also the distance history of the strong scattering point of the moving target on the sea surface, which can be calculated from the L2 norm of the platform's trajectory and the moving target's trajectory, as shown in the following expression:

[0139] R t-n (Λ,η)=||T path -Target path ||2

[0140] Step 7: Solve for the target heading angle using the Differential Evolution (DE) algorithm;

[0141] Because the optimization model established in step six is ​​a non-convex optimization problem, it cannot be solved using traditional gradient-based methods. This embodiment employs a genetic algorithm—differential evolution algorithm—for optimization, as detailed below:

[0142] (1) Determine the population size N in the differential evolution algorithm p Maximum number of iterations Gm The hybridization parameter CR is determined, and an initial population in the solution space is generated randomly.

[0143] (2) Calculate Λ for each individual in the initial population i objective function value

[0144] (3) Determine whether the termination condition has been met or the number of generations has reached its maximum. If so, terminate the evolution and obtain a set of optimal parameters Λ for the moving target. opt If not, then continue;

[0145] (4) Perform mutation and crossover operations to obtain an intermediate population;

[0146] (5) Select individuals from the original population and the intermediate population to obtain a new generation of population;

[0147] (6) Let the evolutionary generation g = g + 1, and go to step (3);

[0148] Finally, the optimal parameter Λ of the moving target is estimated using the differential evolution algorithm. opt Then, the heading angle of the moving target can be estimated from the optimal two-dimensional velocity of the moving target on the sea surface. Figure 4 The two-dimensional velocity iteration curve of a moving target on the sea surface is shown, demonstrating that the method of this invention can obtain a two-dimensional velocity estimate that converges to near the true value. Figure 5 The results show the heading angle estimation error of moving targets on the sea surface under several different heading angles within a signal-to-noise ratio of 2 to 25 dB. It can be seen that the method of the present invention can accurately estimate the heading angle of moving targets on the sea surface, and its estimation accuracy is within 10°.

[0149] In summary, the method of this invention can accurately estimate and extract the energy trajectory of the strong scattering points of moving targets on the sea surface, and takes the motion error of the radar platform into the multi-parameter optimization model. Finally, the genetic algorithm is used to estimate the velocity of moving targets on the sea surface, which effectively solves the problem of inaccurate target velocity estimation caused by the existence of platform motion error under different signal-to-noise ratios.

[0150] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A sea surface moving target heading angle estimation method based on energy trajectory extraction, the specific steps being as follows: Step one, establishing a single base SAR space geometry, then establishing a single base SAR sea surface moving target echo model and completing system parameter initialization; Firstly, the single base SAR spatial geometry is established, and r T = [X T , Y T , Z T ] and r p = [X p , Y p , Z p ] represent the coordinate vectors of the radar platform and the target scattering point in the global coordinate system, respectively, and v T = [v Tx , v Ty , v Tz ] and v p = [v px , v py , v pz ] represent the velocity vectors of the radar and the scattering point, respectively. The two-way range history R(η; r) of the ship target scattering point can be obtained from the SAR spatial geometry, and is expressed as follows: p ), expressed as follows: R(η; r p ) = 2||r T + v T η-r p -v p η|| wherein η represents the slow time; Then the single base SAR sea surface moving target echo model is established, and the system parameter initialization is completed; Suppose that the radar transmitted signal is a linear frequency modulation signal, then the expression of the echo signal after down conversion and demodulation in two-dimensional time domain is as follows: where τ, η and T a respectively represent fast time, slow time and synthetic aperture time, σ η represents a scene scattering coefficient, an electromagnetic wave velocity c is 3 x 10 8 m / s, λ represents a wavelength of a transmitted signal, K represents a frequency modulation of a linear frequency modulation signal, and rect(·) represents a rectangular window function; The initialization of system parameters includes: pulse repetition frequency, range sampling rate, number of receiving elements, number of coherent processing pulses, spatial positions and velocities of receiving station and transmitting station; Step two, based on step S1, pulse compression is performed on the demodulated two-dimensional time domain echo signal s(t,η); The expression of the sea surface moving target reflected echo after range compression is as follows: where σ p represents the RCS of the moving target, B r represents the bandwidth of the transmitted signal; Step three, phase compensation of the migration factor, removing the range migration introduced by platform motion; The expression of the echo signal after range fast Fourier transform is as follows: where f τ represents the distance from the frequency domain variable, and the phase Φ(f τ ,η) is expressed as follows: where R0represents the slant range between the imaging center time instance of the ship target and the radar platform, f dc , f dr , and f d3 represent the Doppler centroid, Doppler rate, and third-order Doppler parameter of the ship target, respectively, and f c = c / λ represents the carrier frequency; s2(f τ , η; r p ) is subjected to a phase compensation of the migration factor, which removes the distance migration introduced by the platform motion. The compensated migration factor H ref is expressed as follows: The expression of the echo signal after phase compensation is as follows: For s3(f τ ,η;r p The inverse Fourier transform of the distance is expressed as follows: Step four, scene multi-target echo separation; The azimuthal direction of s4(τ,η; r p ) is given by the fast Fourier transform as follows: In the range-Doppler domain where the s5(τ, f η ; r p ) signals reside, the echo signals of targets at different locations in the scene can be directly separated; Based on the two-dimensional position of a single moving target in the range-Doppler, construct the corresponding two-dimensional window function H. win Through multi-target echo signals and two-dimensional window function H win Multiplication is used to separate the echoes of moving targets; different window functions H are applied to the azimuth direction in the range-Doppler domain. win The target region is segmented and separated, and then the azimuth of the separated single target signal is transformed into an inverse Fourier transform to obtain the signal s6(f). τ ,η;r p The expression is as follows: s6(τ,η; r p ) = IFFT[s5(τ, f η ; r p ) · H win ] Step five, energy trajectory extraction and estimation of strong scattering points; The signal-to-noise ratio of the echo is calculated by the energy of the peak value in the pulse compressed echo and the average energy of the noise region; Judging the signal-to-noise ratio condition, if ≥ 15 dB, it is high signal-to-noise ratio, in the high signal-to-noise ratio, traversing all distance gates under each pulse repetition interval PFI, according to the maximum signal-to-noise ratio criterion, extracting the strong scattering point energy track distance gate position under the PFI The expression is as follows: where G(m, k) represents all the range gates of the kth PFI in s6(f τ , η; r p ), m represents the range gate position, i.e. the energy trajectory of the strong scattering point at the range gate position of the kth PFI. The signal-to-noise ratio is judged, if < 15 dB, it is low signal-to-noise ratio, in the low signal-to-noise ratio, a multi-frame joint detection method based on dynamic programming is used to extract the energy trajectory, the expression is as follows: wherein, and respectively represent the energy trajectory neighborhood before and after updating, z xy (m) represents the correlation region maximum value, the extracted scattering point energy trajectory is Na represents the number of echo azimuth sampling points, [·] T represents the transpose operation of the matrix; Step six, multi-parameter optimization modeling and target function design; The parameters to be optimized include: two-dimensional velocity of the sea surface moving target, position of each scattering point, when constructing the optimization model, the velocity error of the radar platform is also modeled as a parameter, then the expression of the parameters to be optimized is as follows: Λ = [v px ,v py ,X p1 ,Y p1 ,…,X pi ,Y pi ,…,X pN ,Y pN ,e1,…,e m ] where v px and v py denote the two-dimensional velocity of the moving target on the sea surface, X pi and Y pi denote the two-dimensional position coordinates of the i-th scattering point of the ship, N denotes the number of scattering points of the ship in the model, e1,…,e m denote the velocity error of the radar platform; The corresponding optimization model expression is as follows: wherein, represents the energy trajectory of the strong scatterer extracted according to step five, R t_n (Λ, η) represents the theoretical value of the energy trajectory calculated from Λ; Considering that the radar platform has a velocity error e, then the expression of the platform velocity with error is as follows: v Terr = v T + e The platform motion trajectory T path The expression is as follows: Strong scattering point r p = [X p , Y p , Z p ] of the motion trajectory Target path The expression is as follows: Wherein, it is assumed that the sea surface moving target is always on the two-dimensional sea level, then the height term is always 0; Energy trajectory theory value R t_n (Λ,η) is also the range history of the strong scattering point of the sea surface moving target, which can be calculated by the two-norm of the platform motion trajectory and the moving target motion trajectory, and the expression is as follows: R t-n (Λ,η)=||T path -Target path ||2 Step seven, solving the target heading angle by using DE algorithm; Based on the non-convexity of the optimization model established in step six, a genetic algorithm, differential evolution algorithm, is used for optimization and solution, which is as follows: (1) determining a population size N in a differential evolution algorithm p , a maximum iteration number G m and a crossover parameter CR, and randomly generating an initial population in a solution space; (2) Calculate the objective function value of each individual Λ i in the initial population (3) judge whether the termination condition is reached or the evolution number reaches the maximum, if yes, terminate the evolution, and get a set of optimal parameters Λ of the moving target opt ; if not, continue (4) mutation and crossover operation is performed to obtain an intermediate population; (5) individuals are selected from the original population and the intermediate population to obtain a new generation population; (6) let the evolution generation g=g+1, go to step (3); Finally, the optimal parameter of the moving target is estimated by the differential evolution algorithm opt The heading angle estimation of the moving target on the sea surface can be obtained from the optimal two-dimensional motion velocity of the moving target on the sea surface.

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