CN116363477A - SAR image ship trail parameter estimation method based on improved residual light-weight network - Google Patents

SAR image ship trail parameter estimation method based on improved residual light-weight network Download PDF

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CN116363477A
CN116363477A CN202310233958.4A CN202310233958A CN116363477A CN 116363477 A CN116363477 A CN 116363477A CN 202310233958 A CN202310233958 A CN 202310233958A CN 116363477 A CN116363477 A CN 116363477A
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丁大志
宗嘉霄
谷继红
丛洲
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Nanjing University of Science and Technology
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Abstract

The invention discloses an SAR image ship trail parameter estimation method based on an improved residual error light-weight network, which comprises the steps of firstly constructing a ship trail SAR image data set, then constructing an improved residual error light-weight network, introducing non-local operation at the bottom layer of an original ResNet-18 network to calculate the association degree of different positions of features, and enhancing global feature perception; reducing the model parameters by updating the 3x3 convolution process to a 3x3 channel-by-channel convolution process and a1 x 1 point-by-point convolution process; finally, the convolution block attention module is added before the full connection layer to enhance the network top-level related feature extraction capability. The network is used for estimating the ship trail parameters of the SAR image, and has the advantages of certain precision and model parameter quantity.

Description

SAR image ship trail parameter estimation method based on improved residual light-weight network
Technical Field
The invention relates to the technical field of deep learning, in particular to an SAR image ship trail parameter estimation method based on an improved residual light-weight network.
Background
The ship wake SAR image is an image obtained by detecting and imaging weak signals generated by sea surface ship motion through SAR. The method can display the trace of the ship left on the sea surface, and can obtain the information of the track, speed, heading and the like of the ship by analyzing the trace.
Aiming at the extraction problem of ship parameters contained in SAR image wake: dong Kaixuan et al extract the wake length by using the wake characteristics of the sea surface ship of the optical remote sensing image and related parameters through two different wake length detection methods of a gray level accumulation method and a Radon transformation method, and simply estimate the ship speed and the ship course by using the wake length characteristics; gu Hui realizes the detection of linear wake based on local Radon transformation, and then, starting from the generation mechanism of Kelvin wake, a two-dimensional estimation method of ship parameters is provided, and under the condition of filtering out the sea background noise of the wake SAR image based on the Markov process, the estimation problem of the ship parameters is emphasized by combining the method; the navigation speed estimation method based on the Kelvin trail wavelength is developed comfortably, the wavelength is extracted based on Kelvin trail fitting, and the navigation speed information is estimated further; fan Wenna et al develop simulations aiming at the full polarization SAR image characteristics of ship wake, explore the differences of ship wake characteristics in SAR images under different polarizations, further combine a ship speed inversion method based on the wake, utilize the ship wake SAR images under different polarizations to develop ship speed inversion, and analyze the influence of sea state, ship movement speed and polarization on inversion results.
The current estimation of parameters such as ship speed, direction, ship size and the like from the wake is mostly carried out based on the shape and the length of the wake, and the wake estimation method has high requirements on the extraction accuracy of the length of the wake and has large application limitation. The estimation is performed by adopting a Convolutional Neural Network (CNN) method, so that the method has stronger self-adaptive capacity for different trails, and manual extraction and fitting of the trails are not needed.
The residual network (ResNet) is a series of deep residual neural networks, wherein the ResNet network comprises ResNet-18, resNet-50, resNet-101, resNet-152 and other models based on different layers, and is composed of a plurality of basic blocks, each basic block comprises two convolution layers and one jump connection, the jump connection directly adds the input into the output of the block to form a residual connection, and the connection can enable gradients to directly reversely propagate into a shallower network, so that the problem of gradient disappearance is avoided. Because the ResNet-18 model has shallower depth, the ResNet-18 model has better balance between calculation efficiency and accuracy, and is a classical model in the field of deep learning.
However, long trails of ships require larger feature sizes for network attention, while ResNet networks are relatively smaller in receptive field. The basic module of the ResNet network consists of two 3x3 convolution layers, the design causes the receptive field of each basic module to be only 3x3, and the stride of each layer of the ResNet network is 1, and operations such as a pooling layer or a convolution layer with larger stride are not adopted to increase the receptive field. Although new network models such as ResNeXt, denseNet, efficientNet have been proposed on this basis, they still have problems such as: the number of parameters is large, the interpretability is poor, the training is difficult and the like.
Disclosure of Invention
The invention aims to provide an SAR image ship wake parameter estimation method based on an improved residual light-weight network.
The technical solution for realizing the purpose of the invention is as follows: in a first aspect, the invention provides an improved residual light-weight network-based SAR image ship wake parameter estimation method, which comprises the following steps:
the first step: modeling a sea surface ship wake model, decomposing the sea surface ship wake into a turbulence wake, a Kelvin wake and a sea surface model, and then respectively modeling the three parts and then carrying out linear superposition to obtain a total sea surface ship wake model.
And a second step of: setting simulation radar parameters, realizing SAR image rapid imaging by utilizing a bouncing ray method (SBR), constructing a data set by simulating different ship parameters, dividing the data set into a training set and a test set with a certain proportion, taking SAR images as input of training samples, taking simulation parameters of ship wake as training labels, and labeling each SAR image with a corresponding label.
And a third step of: an improved residual light-weight network is built, a training sample and a training label are simultaneously sent into the network for training, then the trained network is used for detecting ship parameters of unknown SAR samples, and meanwhile, estimation results are evaluated in precision and parameter quantity.
In a second aspect, the present invention provides a computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the steps of the method of the first aspect when the program is executed.
In a third aspect, the present invention provides a computer readable storage medium having stored thereon a computer program which when executed by a processor performs the steps of the method of the first aspect.
Compared with the prior art, the invention has the beneficial effects that:
(1) The invention provides an improved residual light-weight network, which uses non-local operation to enhance global feature perception, increases receptive field of the network, introduces CBAM to enhance top-level feature learning capability of a network architecture, and decomposes convolution kernel to reduce network parameter quantity, which represents that the network has certain precision and network parameter quantity advantage compared with a main stream network under the condition of not depending on stacking depth;
(2) According to the invention, the improved residual light-weight network is trained by taking the ship trail SAR image as a training sample, and the trained network model can well estimate ship parameters contained in the unknown ship trail SAR image.
Drawings
FIG. 1 is a schematic view of a ship's turbulent wake.
Fig. 2 is a schematic diagram of a ship's kelvin trail.
FIG. 3 is a schematic diagram of a sea surface wake with a ship turbulence wake, a Kelvin wake, and a sea surface linearly superimposed.
Fig. 4 is a schematic diagram of a sea surface wake SAR image simulated by SBR fast imaging.
Fig. 5 is a schematic diagram of a modified residual light weight network.
Detailed Description
An SAR image ship wake parameter estimation method based on an improved residual light-weight network comprises the following steps:
step 1: modeling a sea surface ship wake model, decomposing the sea surface ship wake into a turbulence wake, a Kelvin wake and a sea surface model, modeling the three respectively, and then linearly superposing to obtain a total sea surface ship wake model;
step 2: setting simulation radar parameters, realizing SAR image rapid imaging by using a bouncing ray method, constructing a data set by simulating different ship parameters, dividing the data set into a training set and a test set with a certain proportion, taking SAR images as input of training samples, taking simulation parameters of ship wake as training labels, and labeling corresponding labels for each SAR image;
step 3: an improved residual light-weight network is built, a training sample and a training label are simultaneously sent into the network for training, then the trained network is used for detecting ship parameters of unknown SAR samples, and meanwhile, estimation results are evaluated in precision and parameter quantity.
Further, in step 2, the built data sets are set up at different ship speeds V S And taking ship parameters such as ship length L, ship width B, ship draft D and the like as random variables to generate a ship trail SAR image.
In step 3, an improved residual light-weight network is built, and the steps are as follows:
for an input wake SAR image, firstly, selecting a large convolution kernel of 7×7 to extract features of a bottom layer, wherein the features comprise important information such as contours, details, textures and the like of the image; after 7×7 convolution operation, introducing Non-local operation (Non-local) to calculate the association degree of different positions of the features in the image, and enhancing global feature perception; then through the maximum pooling of 3×3, the non-maximum value is eliminated, and the calculation complexity of the bottom layer is reduced; after that, 4 Conv_x layers are passed, each layer comprises four layers of 3×3 common convolution layers, the number of output channels is 64, 128, 256 and 512, the four layers of common 3×3 convolution processes are updated to be 3×3 channel-by-channel convolution processes and 1×1 point-by-point convolution processes, so that the number of network parameters is reduced; the extraction capability of the related features of the top layer of the network is enhanced by a Convolution Block Attention Module (CBAM), and 1 multiplied by 1 size features of 512 channels are output after being averaged and pooled; and finally, directly outputting the ship parameters through a full connection layer FC.
Details of the non-local operation process are as follows:
assuming that index sequence number at any position of input SAR image feature is i, processing the feature, redefining the feature at i according to the following relation
Figure BDA0004121405870000041
Wherein x is i Is the input feature at i, x j Representing the input features at j, y i Is the output feature at i, and takes the unitary function g (·) as a linear transformation, then there is
g(x j )=W g x j
Wherein W is g The weight matrix to be learned can be realized through 1 multiplied by 1 convolution of a spatial domain, the function f (·,) is a similarity function for measuring the positions i and j, and the expression form is as follows
Figure BDA0004121405870000042
Accordingly, normalization factor
Figure BDA0004121405870000046
Can be expressed as
Figure BDA0004121405870000043
The detailed steps are described below with reference to the drawings and examples.
Examples
Firstly, building a ship turbulence wake model, wherein the width W (x) of the turbulence wake is the distance x from the wake after a ship driving path
Figure BDA0004121405870000044
Wherein L is the length of the ship, B is the width of the ship, and a is approximately equal to 5.
The turbulence height S (k) attenuation model is
Figure BDA0004121405870000045
Wherein k is the wave number corresponding to the energy spectrum, V S For ship speed, L' is the speed integral length, E (k) =ζ 2/3 k -5/3 ,ξ=9.0×10 -6 Y is the position perpendicular to the hull direction.
The turbulent wake modeling results are shown with reference to fig. 1.
Then, establishing a Kelvin wake model of the ship, wherein the width W (x) of the turbulence wake is the distance x from the wake after the ship runs
Figure BDA0004121405870000051
Wherein,,
Figure BDA00041214058700000512
for wake wave height, re represents the real part, θ is the angle of the wave propagation direction relative to the x-axis,
Figure BDA0004121405870000052
Figure BDA0004121405870000053
for the phase coefficient +.>
Figure BDA0004121405870000054
Is wave number of wave component in propagation direction, A (theta) is ship free spectrum, A (theta) satisfies
Figure BDA0004121405870000055
Figure BDA0004121405870000056
Wherein H (K, θ) is a Kochn function, S H For a ship surface, z is the draft, and the current strength σ (x, y, z) can be expressed as
Figure BDA0004121405870000057
Wherein f is the characteristic equation of the ship
Figure BDA0004121405870000058
Where d is sidewall draft.
The Kelvin trail modeling results are shown with reference to FIG. 2.
Then modeling the sea surface, wherein the PM sea spectrum model is a simple and widely applied simulated sea surface model, and the main wave direction sea wave power spectrum model formula is as follows
Figure BDA0004121405870000059
Wherein a=8.10×10 -3 ,b=0.74,k x 、k y Is the spatial wave number of the sea wave,
Figure BDA00041214058700000513
U 19.5 g is the wind speed at 19.5m above the sea surface 0 Gravitational acceleration.
Let the lengths in the x and y directions of the PM sea surface represented by two-dimensional discrete points be L x And L y The discrete points are M and N respectively, and the distance between two adjacent points is delta x and deltay, wherein the above parameter satisfies L x =MΔx,L y By =nΔy, the sea level at any point (m, N) of the PM sea level is
Figure BDA00041214058700000510
Figure BDA00041214058700000511
m k ,n k For a matrix unit sequence, then
Figure BDA0004121405870000061
Figure BDA0004121405870000062
Wherein N is 1 ,N 2 Is a random number matrix compliant with normal distribution N (0, 1). In order to make sea level f (x m ,y n ) Is a real number, and is a real number,
Figure BDA0004121405870000063
should satisfy
Figure BDA0004121405870000064
FIG. 3 presents a schematic view of the results of a model of the combination of turbulent wake, kelvin wake and sea surface.
Then, SAR image simulation is carried out on the combined model by adopting an SBR rapid imaging algorithm, wherein an imaging formula is as follows
Figure BDA0004121405870000065
Where k is the wave number, k x And k is equal to z Wave number components in x and z directions, E 0 For the amplitude of the incident wave, j is imaginaryThe number unit, r, is the observation point distance,
Figure BDA0004121405870000066
is theta or +.>
Figure BDA0004121405870000067
Polarized far field echo.
Fig. 4 is a schematic diagram of a sea surface ship wake SAR image.
The SAR data set is constructed by simulating different ship parameters, and the data set is divided into a training set and a testing set in a certain proportion.
And taking the SAR images as the input of training samples, taking simulation parameters of ship wake as training labels, labeling corresponding labels on each SAR image, and simultaneously sending the training samples and the training labels into a network for training.
Constructing an improved residual light-weight network, taking ResNet-18 as a basis, and for an input trail SAR image, firstly selecting a large convolution kernel of 7 multiplied by 7 to extract the characteristics of the bottom layer, wherein the characteristics comprise important information such as the outline, the detail, the texture and the like of the image;
after the 7 x 7 convolution operation, non-local operations (Non-local) are introduced to calculate the relevance of different locations of features in the image, enhancing the global feature perception. The detailed process is as follows, assuming index number i at any position of the input SAR image feature, processing the feature, redefining the feature at i according to the following relation
Figure BDA0004121405870000068
Wherein x is i Is the input feature at i, x j Representing the input features at j, y i Is the output feature at i, and takes the unitary function g (·) as a linear transformation, then there is
g(x j )=W g x j
Wherein W is g Is a weight matrix to be learned, can be realized by 1×1 convolution of a spatial domain, and the function f (·,) isThe similarity function at i and j is measured, and the expression form is
Figure BDA0004121405870000071
Accordingly, the normalization factor c (x) can be expressed as
Figure BDA0004121405870000072
After non-local operation, through maximum pooling of 3×3, non-maximum values are eliminated, and the calculation complexity of the bottom layer is reduced;
after that, 4 Conv_x layers are passed, each layer comprises four layers of 3×3 common convolution layers, the number of output channels is 64, 128, 256 and 512 respectively, depth Separable Convolution (DSC) is introduced, and the four layers of common 3×3 convolution processes are updated into a 3×3 channel-by-channel convolution process and a1×1 point-by-point convolution process, so that the number of network parameters is reduced;
the network top-level relevant feature extraction capability is then enhanced by a Convolution Block Attention Module (CBAM). The detailed process is as follows: for a given intermediate feature F ε R C×H×W As input, max Pool and Avg Pool are firstly carried out on the characteristic diagram according to channels, two one-dimensional vectors are sent into a shared multi-layer perceptron (MLP), and 1X 1 convolution kernel is used for replacing a full-connection layer to generate one-dimensional channel attention M C ∈R C×1×1 Multiplying the channel attention with F by elements to obtain a characteristic diagram F' after channel attention adjustment; then performing Max Pool and Avg Pool on F' according to the space, splicing the two-dimensional vectors generated, and then performing convolution to finally generate the two-dimensional space attention M S ∈R 1×H×W The spatial attention is then multiplied by F' per element. The CBAM overall generate attention process can be described as
Figure BDA0004121405870000073
Wherein the method comprises the steps of
Figure BDA0004121405870000074
The representations are multiplied by elements, and a broadcasting mechanism is adopted in the middle to perform dimensional transformation and matching of the features.
After CBAM, the 1 x 1 size characteristic of 512 channels is output through averaging pooling, and finally, the parameters of the ship are directly output through a full connection layer FC.
The improved residual network structure is shown in fig. 5.
In the network training process, adam is used as a gradient optimizer, and the average absolute error L of the estimation result is used 1 As a loss function, the following is defined
Figure BDA0004121405870000075
Wherein f (x) i ) Parameter estimation value, y, representing network input image i Representing the true label value, n represents the number of samples per training input.
The evaluation index selects the Relative Root Mean Square Error (RRMSE) and can be estimated with each parameter f (x i ) And true value y i The differences between to represent
Figure BDA0004121405870000081
The beneficial effects of the invention can be illustrated by the following experiments.
(1) Experimental environment:
hardware configuration: intel Core i5 10400F 2.9GHz,40G RAM,Windows 10,Nvidia 3090 40G;
software configuration: operating system Windows10, pycharm development software based on deep learning architecture Python3.9+Pytorch1.12+CUDA11.7 environment.
(2) Training results and analysis:
according to a ship trail modeling formula, the shape of the ship trail, the ship length L, the ship width B, the draft D and the ship movement speed V S Four ship parameters are relevant.
Firstly, a ship wake SAR image dataset is established, four ship parameters are used as variables in the simulation process of the dataset, and wake models under different parameters are calculated by utilizing the wake differences in SAR images caused by different parameters. Then utilizing SBR rapid imaging algorithm, at radar center frequency 10GHz, azimuth angle
Figure BDA0004121405870000083
Under the simulation conditions that the pitch angle theta is 0 degrees, the pitch angle theta is 80 degrees, the VV is polarized, and 300 points are sampled in the azimuth direction and the distance direction respectively, two-dimensional SAR image simulation is carried out according to the parameter sampling range of the table 1. And taking random numbers from four parameters of the ship according to simulation ranges given in the table, and calculating 4800 Zhang Suiji SAR wake images in total.
Table 1 four ship parameter simulation range tables
Figure BDA0004121405870000082
In the experiment, 4800 pictures are firstly randomly divided into a training set and a verification set according to the proportion interval of 9:1, cut into 224 multiplied by 224, and the Adam is used as a gradient optimizer, the Batch size is set to 16, the initial learning rate is set to 0.0001, the training is carried out for 200 rounds, then the learning rate is attenuated to be one tenth of the original, the training is carried out for 100 rounds, the total training is carried out for 300 rounds, and the random discarding rate Drop out of the FC is set to 0.25.
The RRMSE error result of the experiment refers to that after each training round in 300 training rounds is finished, the network model after each training round is used for estimating four parameters of the randomly divided 480 verification set wake SAR images, and the RRMSE average value of the four parameters estimated in each training round is counted, so that the optimal result with the minimum RRMSE is selected in the 300 training rounds, and the optimal training result of the network is represented.
And carrying out an ablation experiment on each part of the network, and taking the network parameter and RRMSE of the network on four ship parameters to be estimated as evaluation indexes. Summarizing, the results of the comparisons in Table 2 were obtained, wherein RRMSE VS 、RRMSE L 、RRMSE B 、RRMSE D Respectively represent V S RRMSE for four parameters, L, B, D, smaller represents higher estimation accuracy and our represents the final improved residual light weight network.
Table 2 training results distribution table under different networks
Figure BDA0004121405870000091
The RRMSE of the network training results of the present invention is compared to the original ResNet-18, where the network is compared to V for a reduction of the network parameters to 1/7 of the original S RRMSE of four parameters L, B, D is reduced by 3.91%, 0.55%, 0.51% and 0.31%, respectively, and a better ship parameter estimation effect is achieved with a smaller network parameter number.
Under the same network training condition, comparing the network our proposed in this section with the mainstream CNN network in recent years, and recording the RRMSE average optimal result of 300 rounds of training to obtain Table 3.
TABLE 3 CNN model vs. results distribution table for each main stream
Figure BDA0004121405870000092
Figure BDA0004121405870000101
The comparison proves that the improved residual light-weight network has the advantages of higher precision and fewer network parameters in terms of estimation of wake SAR ship parameters.
The foregoing is merely a preferred embodiment of the present invention, and it should be noted that it will be apparent to those skilled in the art that variations and modifications can be made without departing from the inventive concept of the present invention.

Claims (10)

1. The SAR image ship wake parameter estimation method based on the improved residual light-weight network is characterized by comprising the following steps of:
the first step: modeling a sea surface ship wake model, decomposing the sea surface ship wake into a turbulence wake, a Kelvin wake and a sea surface model, modeling the three respectively, and then linearly superposing to obtain a total sea surface ship wake model;
and a second step of: setting simulation radar parameters, realizing SAR image rapid imaging by using a bouncing ray method, constructing a data set by simulating different ship parameters, dividing the data set into a training set and a test set with a certain proportion, taking SAR images as input of training samples, taking simulation parameters of ship wake as training labels, and labeling corresponding labels for each SAR image;
and a third step of: an improved residual light-weight network is built, a training sample and a training label are simultaneously sent into the network for training, then the trained network is used for detecting ship parameters of unknown SAR samples, and meanwhile, estimation results are evaluated in precision and parameter quantity.
2. Method according to claim 1, characterized in that in the second step the built data sets are built at different ship speeds V S And taking the ship length L, the ship width B and the ship draft D as random variables to generate a ship trail SAR image.
3. The method according to claim 1, characterized in that in a third step an improved residual light weight network is built, the steps being as follows:
for an input wake SAR image, firstly, selecting a large convolution kernel of 7×7 to extract features of the bottom layer, wherein the features comprise contours, details and textures of the image; after 7×7 convolution operation, introducing non-local operation to calculate the association degree of different positions of the features in the image, and enhancing global feature perception; then through maximum pooling of 3×3, eliminating non-maximum values; after that, 4 Conv_x layers are passed, each layer comprises four layers of 3×3 common convolution layers, the number of output channels is 64, 128, 256 and 512 respectively, and the four layers of common 3×3 convolution processes are updated into a 3×3 channel-by-channel convolution process and a1×1 point-by-point convolution process; then enhancing the extraction capacity of the related features of the top layer of the network through a convolution block attention module, and outputting 1 multiplied by 1 size features of 512 channels through average pooling; and finally, directly outputting the ship parameters through a full connection layer FC.
4. A method according to claim 3, wherein the non-local operation is performed by the following method:
assuming that index sequence number at any position of input SAR image feature is i, processing the feature, redefining the feature at i according to the following relation
Figure FDA0004121405860000011
Wherein x is i Is the input feature at i, x j Representing the input features at j, y i Is the output feature at i, and takes the unitary function g (·) as a linear transformation, then there is
g(x j )=W g x j
Wherein W is g The weight matrix to be learned can be realized through 1 multiplied by 1 convolution of a spatial domain, the function f (·,) is a similarity function for measuring the positions i and j, and the expression form is as follows
Figure FDA0004121405860000021
The normalization factor is expressed as
Figure FDA0004121405860000022
5. The method according to claim 1, wherein in a first step, a ship turbulence wake model is created, the width W (x) of the turbulence wake being at a distance x from the wake after the ship has travelled the path
Figure FDA0004121405860000023
Wherein L is the ship length, B is the ship width, a=5;
the turbulence height S (k) attenuation model is
Figure FDA0004121405860000024
Wherein k is the wave number corresponding to the energy spectrum, V S For ship speed, L' is the speed integral length, E (k) =ζ 2/3 k -5/3 ,ξ=9.0×10 -6 Y is the position perpendicular to the hull direction.
6. The method according to claim 5, wherein in a first step, a ship Kelvin wake model is built, the width W (x) of the turbulent wake being at a distance x from the wake after the ship has travelled the path
Figure FDA0004121405860000025
Wherein,,
Figure FDA0004121405860000026
for wake wave height, re represents the real part, θ is the angle of the wave propagation direction relative to the x-axis,
Figure FDA0004121405860000027
for the phase coefficient +.>
Figure FDA0004121405860000028
Is wave number of wave component in propagation direction, A (theta) is ship free spectrum, A (theta) satisfies
Figure FDA0004121405860000029
Figure FDA00041214058600000210
Wherein H (K, θ) is a Kochn function, S H For a ship surface, z is the draft, and the current strength σ (x, y, z) can be expressed as
Figure FDA0004121405860000031
Wherein f is the characteristic equation of the ship
Figure FDA0004121405860000032
Where d is sidewall draft.
7. The method of claim 6, wherein in the first step, the sea surface is modeled, and the PM sea spectrum model is a simple and widely used simulated sea surface model, wherein the main wave direction sea wave power spectrum model is formulated as follows
Figure FDA0004121405860000033
Wherein a=8.10×10 -3 ,b=0.74,k x 、k y Is the spatial wave number of the sea wave,
Figure FDA0004121405860000034
U 19.5 g is the wind speed at 19.5m above the sea surface 0 Gravitational acceleration;
assuming that it is represented by two-dimensional discrete pointsLengths in x and y directions of PM sea surface are L respectively x And L y The discrete points are M and N respectively, the distance between two adjacent points is delta x and delta y, wherein the parameters meet L x =MΔx,L y By =nΔy, the sea level at any point (m, N) of the PM sea level is
Figure FDA0004121405860000035
Figure FDA0004121405860000036
m k ,n k For a matrix unit sequence, then
Figure FDA0004121405860000037
Wherein N is 1 ,N 2 A random number matrix compliant with normal distribution N (0, 1); in order to make sea level f (x m ,y n ) Is a real number, and is a real number,
Figure FDA0004121405860000038
should satisfy
Figure FDA0004121405860000041
8. The method of claim 7, wherein the combined model is simulated by using an SBR fast imaging algorithm, the imaging formula being
Figure FDA0004121405860000042
Where k is the wave number, k x And k is equal to z Wave number components in x and z directions, E 0 As incident wavesThe amplitude, j, is the imaginary unit, r is the viewpoint distance,
Figure FDA0004121405860000043
is theta or +.>
Figure FDA0004121405860000044
Polarized far field echo.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the steps of the method according to any of claims 1-8 when the program is executed.
10. A computer readable storage medium, on which a computer program is stored, characterized in that the program, when being executed by a processor, implements the steps of the method according to any of claims 1-8.
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