A sea surface slow-moving small target detection method based on tensor decomposition

Abstract

The application discloses a sea surface slow small target detection method based on tensor decomposition, which converts target echo signals into a TFR three-dimensional tensor space, in which sea clutter is continuously distributed in the distance dimension and presents a low-rank characteristic; the target only exists in a specific distance unit, thus presenting a sparse characteristic; based on this, the application utilizes the low-rank characteristic and sparse characteristic difference of the clutter and the target, and combines tensor robust principal component analysis to realize effective separation of the target and the clutter; considering that the clutter in each distance unit is difficult to meet strict low-rank characteristic, in the decomposition process, target energy exists in the low-rank component, and the sparse component exists again in the clutter residue, thus a method of subtracting the low-rank component from the sparse component and inter-frame joint detection is adopted to improve the signal-to-clutter-and-noise ratio of the target, and reliable detection of the slow target is realized.

Description

Technical Field

[0001] The present invention relates to the field of radar technology, and in particular to a method for detecting slow small targets on the sea surface based on tensor decomposition. Background Art

[0002] Maritime territories are widely used in aquaculture, mining, energy, trade, tourism, and national defense. Radar, as an active microwave target detection device, possesses all-day, all-weather target detection and perception capabilities, playing a vital role in understanding and monitoring the ocean. Unlike ground-based and air-based radar detection systems, sea radar echoes contain a large number of sea surface reflections. The formation mechanism of this sea clutter is complex and dynamically changing, posing a severe challenge to sea surface target detection. Sea target detection technology in complex and changing environments has become a key constraint on radar performance, primarily due to the following two factors: First, the complex and changing sea surface environment makes it difficult to understand clutter characteristics; second, the low observability of targets greatly increases the difficulty of radar detection.

[0003] Currently, the most widely used detection methods are incoherent and coherent detection algorithms based on energy accumulation. The core concept of incoherent detection algorithms is to compare the power of surrounding reference cells with the cell to be detected. When the power of the reference cell exceeds the power threshold calculated for the cell to be detected, the target is identified. Classic incoherent detection methods include the cell-averaged constant false alarm rate (CA-CFAR) detection algorithm, the ordered statistical CFAR detection algorithm, and the large or small selection CFAR detection algorithm. However, due to the small radar cross-section of small, slow-moving targets on the sea surface, their application is severely limited in low signal-to-noise ratio environments. Coherent detection algorithms are primarily used in coherent radar systems, using moving target indicator (MTI) and moving target detection (MTD) to suppress clutter and enhance target signal energy. However, due to the low speed of the target, it often overlaps with the sea clutter band. This results in both target energy suppression and clutter suppression, making effective detection of slow-moving targets difficult. Summary of the Invention

[0004] Aiming at the bottleneck problem of radar detection of slow small targets, this paper proposes a method for detecting slow small targets on the sea surface based on tensor decomposition from the perspective of expanding dimensions, based on time-frequency two-dimensional analysis. The distance dimension information is introduced to construct a three-dimensional time-frequency-range (TFR) tensor space. The low rank and sparsity of clutter and targets in the three-dimensional space are utilized, combined with mainstream tensor decomposition methods, to achieve effective detection of slow sea surface targets.

[0005] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0006] A method for detecting slow small targets on the sea surface based on tensor decomposition, comprising:

[0007] The original radar echo signal is obtained and preprocessed to obtain the time domain signal; the time domain signal is converted into the TFR three-dimensional tensor space to construct the TFR three-dimensional tensor of the time domain signal;

[0008] The modulus of the TFR three-dimensional tensor is calculated, and then the TRPCA algorithm is used to perform low-rank sparse decomposition on the tensor to obtain the low-rank part containing sea clutter and the sparse part containing the target;

[0009] The low-rank part is subtracted from the sparse part to obtain a difference tensor; the difference tensor and the TFR three-dimensional tensor are summed along the time dimension to obtain a two-dimensional frequency domain distance difference map and a two-dimensional frequency domain distance image;

[0010] Perform peak point detection on the two-dimensional difference image of frequency domain distance and construct a peak point relative height map; perform outlier detection on the two-dimensional image of frequency domain distance and construct an abnormal point location map;

[0011] Multiply the abnormal point position map with the relative peak height map to obtain the difference relative peak height map; use the difference relative peak height map of the current frame as the frame to be detected, determine the point to be detected from the frame to be detected, and select a preset number of difference relative peak height maps adjacent to the current frame before and after as reference frames, and use the reference frames to determine whether the point to be detected is the target.

[0012] Furthermore, the step of converting the time domain signal into a TFR three-dimensional tensor space and constructing a TFR three-dimensional tensor of the time domain signal includes:

[0013] After acquiring the original radar echo signal, the time domain signal is obtained through AD sampling, down-conversion, and pulse compression processing. The time domain signal is rearranged in frames to obtain range-slow time two-dimensional data. Then, a short-time Fourier transform is performed along each range unit to obtain time-frequency slices. The STFT expression is as follows:

[0014] (1)

[0015] in, represents the time domain signal of the range unit, is the window function, represents the slow time sampling point, Indicates the window sampling point position, represents the frequency sampling point, Indicates the total number of frequency sampling points, e is a natural constant,j is an imaginary unit;

[0016] Slice each time-frequency Rearrange the order of distance units to obtain the TFR three-dimensional tensor .

[0017] Furthermore, the tensor is subjected to low-rank sparse decomposition using the TRPCA algorithm to obtain a low-rank part containing sea clutter and a sparse part containing the target, including:

[0018] Solve using the alternating direction multiplier method via the augmented Lagrangian function:

[0019] (2-1) Initialization , , , and ;in, 、 and are the low-rank tensor, sparse tensor, and Lagrange multiplier at the first iteration, respectively. is the step size increment, is the initial step size, is the maximum step length, is the judgment threshold; 、 、 and The subscript of is the update iteration count, the initial value is 0, and the subscripts of these parameters are and etc. represent the corresponding and Iteration results;

[0020] (2-2) Update

[0021] and

[0022] ;

[0023] in, and They refer to the nuclear norm and Frobenius norm of the tensor respectively, , They are the sizes of the three dimensions of time, frequency domain and distance respectively;

[0024] (2-3) Update ;

[0025] (2-4) Update ;

[0026] (2-5) Check whether it converges. If Output current and , otherwise return (2-2); where, Represents the infinity norm of a tensor.

[0027] Furthermore, the peak point detection is performed on the two-dimensional frequency domain distance difference map to construct a peak point relative peak height map, including:

[0028] Select a point as the test point, compare the value of the point with the four adjacent points above, below, left and right, if the value of the point is the largest, it is the peak point, and the peak point relative peak height graph is Fill in the corresponding position in the table with the difference between the point and the mean of the four adjacent points being compared; if it is not a peak point, then the peak point relative peak height graph Fill in 0 in the corresponding position; traverse the two-dimensional difference map of frequency domain distance in sequence All points in the frequency domain; sum the TFR three-dimensional tensor along the time dimension to obtain a two-dimensional frequency domain distance graph ,The outlier detection method is used to obtain the outlier location map containing sea clutter and target locations.

[0029] Furthermore, the specific method of constructing the peak point relative peak height map and the abnormal point location map is:

[0030] (4-1) Finding the two-dimensional difference graph of frequency domain distance The peak point of the peak is obtained by calculating the relative peak height. :

[0031] (2)

[0032] in, Represents a two-dimensional difference map of frequency domain distance mid-frequency , distance sampling point The value at the corresponding position, Represents index coordinates;

[0033] (4-2) TFR three-dimensional tensor Summing along the time dimension to obtain a two-dimensional image of frequency domain distance , then Each distance unit performs outlier detection to obtain an outlier location map , its outlier value is 1 and its non-outlier value is 0:

[0034] (3)

[0035] in, Represents a two-dimensional image of frequency domain distance mid-frequency , distance sampling point The value at the corresponding position.

[0036] Furthermore, the difference relative peak height map of the current frame is used as the frame to be detected, the point to be detected is determined from the frame to be detected, and a preset number of difference relative peak height maps adjacent to the current frame are selected as reference frames, and the reference frames are used to determine whether the point to be detected is a target, including:

[0037] (5-1) Select the relative peak height graph of the difference corresponding to a frame of echo signal As the frame to be detected , looking for All non-zero points in is called the point to be detected, where is the number of points to be tested;

[0038] (5-2)Select Relative peak height graph of the difference between the preset number of data frames before and after As a reference frame ;

[0039] (5-3)Select A point to be tested ,in for The index values ​​of the coordinates correspond to the frequency sampling points and the distance sampling points respectively; it will include and 、 The set of 5 index values ​​including is called detection range; detect all reference frames Is there a non-zero point in the detection range? Count the number of frames with non-zero points. If the number exceeds 4 / 5 of the number of frames, then it is considered If it is a target, it will be retained, otherwise it will be set to zero as sea clutter; All points in the execution of this operation are completed Inter-frame joint object detection.

[0040] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, the method for detecting slow small targets on the sea surface based on tensor decomposition is implemented.

[0041] A computer-readable storage medium stores a computer program; when the computer program is executed by a processor, the method for detecting slow small targets on the sea surface based on tensor decomposition is implemented.

[0042] Compared with the prior art, the present invention has the following technical features:

[0043] This method leverages the low rank and sparsity of sea clutter and target signals in three-dimensional tensor space to establish a sea clutter and target separation method based on low-rank sparse decomposition. This overcomes the detection issues of previous detection methods caused by low target energy or annihilation by sea clutter. A subtraction method is used to further enhance the contrast between the target and sea clutter, making the target more prominent compared to traditional incoherent detection methods. Furthermore, the method multiplies the outlier location map with the relative peak height map to further reduce the impact of noise and weak target energy absolute values, resulting in more robust detection performance in strong clutter environments. The algorithm was validated using a publicly available measured sea clutter dataset, achieving an average target recognition accuracy of 84.33%. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is the distribution map of singular values ​​of sea clutter in the public dataset;

[0045] Figure 2 is a flow chart of the present invention;

[0046] Figure 3 Schematic diagram of the TFR three-dimensional tensor space construction process of the present invention;

[0047] Figure 4 Schematic diagram of low-rank sparse decomposition of the TFR three-dimensional tensor space under ideal conditions of the present invention;

[0048] Figure 5 The results of the present invention using TRPCA decomposition on the public data set and the difference between the sparse part and the low-rank part; (a) is the original frequency domain distance two-dimensional graph, (b) is the low-rank part decomposed by TRPCA, (c) is the sparse part decomposed by TRPCA, and (d) is the difference graph obtained by subtracting the sparse part from the low-rank part;

[0049] Figure 6 : is an intermediate process diagram of target detection performed by the present invention; wherein (a) is an outlier location diagram, (b) is a peak point relative height diagram, and (c) is a relative peak height diagram of the difference between the outlier location diagram and the relative peak height diagram;

[0050] Figure 7 This is a comparison chart of the results before and after multi-frame joint detection;

[0051] Figure 8 This is a comparison result of the detection effect between the method of the present invention and two existing different target detection methods. DETAILED DESCRIPTION

[0052] In order to further improve the target detection performance in complex and variable environments, the present invention provides a method for detecting slow small targets on the sea surface based on tensor decomposition. This method converts the target echo signal into the TFR three-dimensional tensor space, in which the sea clutter is continuously distributed in the distance dimension, showing a low-rank characteristic; the target only exists in a specific distance unit, so it shows a sparse characteristic. Based on this, the present invention utilizes the low-rank and sparsity differences between clutter and target, and combines tensor robust principal component analysis (TRPCA) to achieve effective separation of target and clutter. Considering that the clutter in each distance unit is difficult to meet the strict low-rank property, the decomposition process will result in the presence of target energy in the low-rank component and the presence of clutter residue in the sparse component. Therefore, the method of subtracting the modulus of the low-rank component and the sparse component and inter-frame joint detection is adopted to improve the signal-to-noise ratio of the target and achieve reliable detection of slow targets.

[0053] The low rank of sea clutter can be proved by the pipeline rank and singular value distribution of the tensor. Figure 1 The singular value distribution diagram of sea clutter in the public dataset shows a cliff-like drop, with the maximum and minimum values ​​differing by 380 times. The information carried by smaller singular values ​​can be ignored, which proves that sea clutter has the characteristics of low rank.

[0054] Step 1: Obtain the original radar echo signal and preprocess it to obtain the time domain signal; convert the time domain signal into the TFR three-dimensional tensor space and construct the TFR three-dimensional tensor of the time domain signal .

[0055] After acquiring the original radar echo signal, the time domain signal is obtained through AD sampling, down-conversion, pulse compression, and other processing. The time domain signal is rearranged in frames to obtain two-dimensional range-slow time data. Then, a short-time Fourier transform (STFT) is performed along each range unit to obtain time-frequency slices. The STFT expression is as follows:

[0056] (1)

[0057] in, represents the time domain signal of the range unit, is the window function, represents the slow time sampling point, Indicates the window sampling point position, represents the frequency sampling point, Indicates the total number of frequency sampling points, e is a natural constant, j Is an imaginary unit.

[0058] Slice each time-frequency Rearrange the order of distance units to obtain the TFR three-dimensional tensor .

[0059] Step 2: TFR three-dimensional tensor Calculate the modulus value and then use the TRPCA algorithm to analyze the tensor Perform low-rank sparse decomposition to obtain the low-rank part containing sea clutter and the sparse part containing the target Here we can use the Alternating Direction Method of Multiplier (ADMM) to solve it through the augmented Lagrangian function, as follows:

[0060] (2-1) Initialization , , , and .in, 、 and are the low-rank tensor, sparse tensor, and Lagrange multiplier at the first iteration, respectively. is the step size increment, is the initial step size, is the maximum step length, is the decision threshold; 、 、 and The subscript of is the update iteration count, the initial value is 0, and the subscripts of these parameters are and etc. represent the corresponding and Iteration results;

[0061] (2-2) Update

[0062] and

[0063] ;

[0064] in, and They refer to the nuclear norm and Frobenius norm of the tensor respectively, According to experience, it can be set , They are the sizes of the three dimensions of time, frequency domain and distance respectively;

[0065] (2-3) Update ;

[0066] (2-4) Update ;

[0067] (2-5) Check whether it converges. If Output current and , otherwise return (2-2); where, Represents the infinity norm of a tensor.

[0068] Step 3: Use the sparse part to subtract the low-rank part Get the difference tensor; for the difference tensor and the TFR three-dimensional tensor , sum along the time dimension to obtain the two-dimensional difference map of frequency domain distance And the frequency domain distance 2D image .

[0069] Step 4: Calculate the two-dimensional difference graph of the frequency domain distance Perform peak point detection and construct a peak point relative height graph ; For frequency domain distance two-dimensional image Perform outlier detection and build an outlier location map .

[0070] Two-dimensional difference map of distance in frequency domain The energy of the target point is often stronger than that of the surrounding points, showing a "peak" shape. Such "peak" points are called peak points. Then, according to this definition, the two-dimensional difference map of the frequency domain distance is Find the peak point and draw the peak point relative height graph .

[0071] Select a point as the test point, compare the value of the point with the four adjacent points above, below, left and right, if the value of the point is the largest, it is the peak point, and the peak point relative peak height graph is Fill in the corresponding position in the table with the difference between the point and the mean of the four adjacent points being compared; if it is not a peak point, then the peak point relative peak height graph Fill in 0 in the corresponding position. Traverse the two-dimensional difference graph of frequency domain distance in sequence To reduce the influence of noise peak points, the TFR three-dimensional tensor Summing along the time dimension yields a two-dimensional frequency domain distance graph , an outlier detection method is used to obtain an outlier location map containing sea clutter and target locations. This paper uses the generalized extreme Studentized deviance test to detect outliers. The specific process of step 4 is shown below.

[0072] (4-1) Finding the two-dimensional difference graph of frequency domain distance The peak point of the peak is obtained by calculating the relative peak height. :

[0073] (2)

[0074] in, Represents a two-dimensional difference map of frequency domain distance mid-frequency , distance sampling point The value at the corresponding position, Represents index coordinates.

[0075] (4-2) TFR three-dimensional tensor Summing along the time dimension to obtain a two-dimensional image of frequency domain distance , then Each distance unit performs outlier detection to obtain an outlier location map , its outlier value is 1 and its non-outlier value is 0:

[0076] (3)

[0077] in, Represents a two-dimensional image of frequency domain distance mid-frequency , distance sampling point The value at the corresponding position.

[0078] Step 5: Map the outlier locations Relative peak height graph Multiply to get the difference relative peak height graph ; The difference of the current frame relative to the peak height map As the frame to be detected, determine the point to be detected from the frame to be detected, and select a preset number of difference relative peak height images adjacent to the current frame as reference frames, and use the reference frames to determine whether the point to be detected is a target.

[0079] Among them, the difference relative peak height graph The unit point where the internal target is located will be retained, and it will have a higher relative peak height; at the same time, individual sea clutter units similar to the target will also be retained; in order to further extract the target and eliminate the sea clutter, an inter-frame joint target detection method is used here. In multi-frame data, the unit where the target is located remains unchanged or changes in a small range, showing continuity; the sea clutter unit does not have temporal continuity and is not continuous between frames; based on this, the number of peak points of the corresponding units in the reference frames before and after the peak point unit retained in the frame to be detected is counted, which can be used as the basis for the final target judgment. The specific process is as follows:

[0080] (5-1) Select the relative peak height graph of the difference corresponding to a frame of echo signal As the frame to be detected , looking for All non-zero points in is called the point to be detected, where is the number of points to be tested;

[0081] (5-2)Select Relative peak height graph of the difference between a certain number of data frames before and after As a reference frame ;

[0082] (5-3)Select A point to be tested ,in for The index values ​​of the coordinates correspond to the frequency sampling points and the distance sampling points respectively; it will include and 、 The set of 5 index values ​​including is called detection range; detect all reference frames Is there a non-zero point in the detection range? Count the number of frames with non-zero points. If the number exceeds 4 / 5 of the number of frames, then it is considered If it is a target, it will be retained, otherwise it will be set to zero as sea clutter; All points in the execution of this operation are completed Inter-frame joint object detection.

[0083] (5-4) Repeat steps (5-1) to (5-3) until inter-frame joint target detection is completed for all data frames.

[0084] Example:

[0085] This example uses IPIX publicly available measured sea clutter data, which provides echo data for 14 range bins. Each range bin collects 131,072 pulse echo signals, using two polarization channels, H and V. For this data, the TRPCA-based method for detecting small, low-speed targets on the sea surface follows these steps:

[0086] Step 1: Establish TFR three-dimensional tensor space

[0087] The original data is divided into 1024 frames with 128 pulses as one frame. Figure 3 As shown, the time-frequency map of each distance unit in each frame is calculated using formula (1), with a window length of 64 pulses and a step length of 2 pulses. Then the time-frequency maps of 14 distance units are combined to obtain the TFR three-dimensional tensor space , the three dimensions are time dimension, frequency dimension and distance dimension in order.

[0088] Step 2: Low-rank sparse decomposition

[0089] right Calculate the modulus value and then use the TRPCA algorithm to Perform low-rank sparse decomposition to obtain the low-rank part containing sea clutter and the sparse part containing the target The results before and after decomposition are as follows Figure 5 As shown in (a), (b), and (c); for the convenience of presentation, the TFR three-dimensional tensor is summed along the time dimension.

[0090] Step 3: Get the difference map

[0091] Use the sparse part to subtract the low-rank part Get the difference tensor, then sum it along the time dimension to get the two-dimensional difference map of frequency domain distance , the results are as follows Figure 5 As shown in (d).

[0092] Step 4: Obtain the abnormal point location map and the peak point relative peak height map

[0093] Two-dimensional difference map of distance in frequency domain Compare the values ​​of a certain point with the four points above, below, left and right to find the peak point, and calculate the relative peak height using formula (2) Relative peak height graph In addition to the peak points of the target and the sea clutter of the target-like object, there are also some noise peak points (low energy and relatively light color). In order to reduce the influence of the noise peak points, the TFR three-dimensional tensor is Summing along the time dimension yields a two-dimensional frequency domain distance graph , perform outlier detection on each distance unit to obtain outliers including sea clutter and target positions, and obtain the outlier position map according to formula (3) .

[0094] See also Figure 6 , where (a) is the outlier location map, marking the sea clutter and target units, (b) is the peak point relative peak height map (position map, only showing the peak point position, not the energy), and all the peak units and relative peak height values ​​in the difference map are found. In addition to the peak points of the target and target-like sea clutter, there are also some noise peak points (lower energy), and (c) is the result of multiplying the outlier location map and the relative peak height map, the difference relative peak height map (energy map, color represents energy strength), which filters out the interference of noise peaks.

[0095] Step 5: Inter-frame joint target detection

[0096] Map the location of the outliers Relative peak height graph Multiplying by , the unit point where the target is located will be retained and have a higher relative peak height. However, the sea clutter unit points of some types of targets will also be retained, increasing the false alarm rate of detection. In order to further screen out the target and eliminate false alarms, the inter-frame joint target detection method is adopted here. First, the difference relative peak height map is screened Frames to be detected All non-zero points, then select 5 frames before and after, a total of 10 frames, are used as reference frames Select a point to be detected and detect the small range unit (the peak point and the two units above and below the Doppler dimension) in the reference frame. Is there a non-zero point in the corresponding unit? Count the peaks. Frame number, if there are non-zero points in at least 8 frames within this range, the point is considered to be a target and retained, otherwise it is sea clutter and is set to zero. This operation is performed on all peak points to complete the inter-frame joint target detection for one frame. Repeat the above operation to finally complete the inter-frame joint target detection for all data frames.

[0097] Figure 7 This is a comparison of the results before and after multi-frame joint detection. The top shows the results of five consecutive frames before detection. In addition to the target, there are also some types of sea clutter. The target appears continuously in multiple frames and the position is relatively fixed, while the position of sea clutter is not fixed. The bottom shows the result of the nth frame after detection. At this time, the discontinuous sea clutter points have been eliminated, leaving only the target points.

[0098] The method proposed in this invention is compared with two other methods. The two detection methods are as follows. Method 1 is the CFAR detection method, and Method 2 is the CFAR detection method after MTI filtering (filter parameters are [1, -1]). A total of 10 groups of data were tested, each group of data was divided into 1024 frames, each frame had 128 pulses, and each pulse had 14 distance units. The comparison results are as follows: Figure 8 As shown, the present invention has an extremely high detection rate in all groups of data, stable detection performance, and an average detection rate of up to 84.33%.

[0099] In summary, the detection method of low-rank sparse decomposition can effectively separate the target and sea clutter. The present invention can effectively improve the detection performance of low-speed small targets in a strong clutter background.

[0100] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A method for detecting slow small targets on the sea surface based on tensor decomposition, characterized in that: include: Obtain the original radar echo signal and preprocess it to obtain the time domain signal; Convert the time domain signal into the TFR three-dimensional tensor space and construct the TFR three-dimensional tensor of the time domain signal; The modulus of the TFR three-dimensional tensor is calculated, and then the TRPCA algorithm is used to perform low-rank sparse decomposition on the tensor to obtain the low-rank part containing sea clutter and the sparse part containing the target; The low-rank part is subtracted from the sparse part to obtain a difference tensor; the difference tensor and the TFR three-dimensional tensor are summed along the time dimension to obtain a two-dimensional frequency domain distance difference map and a two-dimensional frequency domain distance image; Perform peak point detection on the two-dimensional difference image of frequency domain distance and construct a peak point relative height map; perform outlier detection on the two-dimensional image of frequency domain distance and construct an abnormal point location map; Multiply the abnormal point position map with the relative peak height map to obtain the difference relative peak height map; use the difference relative peak height map of the current frame as the frame to be detected, determine the point to be detected from the frame to be detected, and select a preset number of difference relative peak height maps adjacent to the current frame before and after as reference frames, and use the reference frames to determine whether the point to be detected is the target.

2. The method for detecting slow small targets on the sea surface based on tensor decomposition according to claim 1, characterized in that: The step of converting the time domain signal into the TFR three-dimensional tensor space and constructing the TFR three-dimensional tensor of the time domain signal includes: After acquiring the original radar echo signal, the time domain signal is obtained through AD sampling, down-conversion, and pulse compression processing. The time domain signal is rearranged in frames to obtain range-slow time two-dimensional data. Then, a short-time Fourier transform is performed along each range unit to obtain time-frequency slices. The STFT expression is as follows: (1) in, represents the time domain signal of the range unit, is the window function, represents the slow time sampling point, Indicates the window sampling point position, represents the frequency sampling point, Indicates the total number of frequency sampling points, e is a natural constant, j is an imaginary unit; Slice each time-frequency Rearrange the order of distance units to obtain the TFR three-dimensional tensor .

3. The method for detecting slow small targets on the sea surface based on tensor decomposition according to claim 1, characterized in that: The TRPCA algorithm is used to perform low-rank sparse decomposition on the tensor to obtain a low-rank part containing sea clutter and a sparse part containing the target, including: Solve using the alternating direction multiplier method via the augmented Lagrangian function: (2-1) Initialization , , , and ;in, 、 and are the low-rank tensor, sparse tensor, and Lagrange multiplier at the first iteration, respectively. is the step size increment, is the initial step size, is the maximum step length, is the judgment threshold; 、 、 and The subscript of is the update iteration count, the initial value is 0, and the subscripts of these parameters are and Represents the corresponding and Iteration results; (2-2) Update and ； in, and They refer to the nuclear norm and Frobenius norm of the tensor respectively, , They are the sizes of the three dimensions of time, frequency domain and distance respectively; (2-3) Update ,in represents the TFR three-dimensional tensor; (2-4) Update ; (2-5) Check whether it converges. If Then output the current low-rank tensor and sparse tensor, otherwise return (2-2); where, Represents the infinity norm of a tensor.

4. The method for detecting slow small targets on the sea surface based on tensor decomposition according to claim 1, characterized in that: The performing peak point detection on the two-dimensional frequency domain distance difference map and constructing a peak point relative peak height map includes: Select a point as the test point, compare the value of the point with the four adjacent points above, below, left and right, if the value of the point is the largest, it is the peak point, and the peak point relative peak height graph is Fill in the corresponding position in the table with the difference between the point and the mean of the four adjacent points being compared; if it is not a peak point, then the peak point relative peak height graph Fill in 0 in the corresponding position; traverse the two-dimensional difference map of frequency domain distance in sequence All points in the frequency domain; sum the TFR three-dimensional tensor along the time dimension to obtain a two-dimensional frequency domain distance graph ,The outlier detection method is used to obtain the outlier location map containing sea clutter and target locations.

5. The method for detecting slow small targets on the sea surface based on tensor decomposition according to claim 1, characterized in that: The specific method of constructing the peak point relative peak height map and the abnormal point location map is as follows: (4-1) Finding the two-dimensional difference graph of frequency domain distance The peak point of the peak is obtained by calculating the relative peak height. : (2) in, Represents a two-dimensional difference map of frequency domain distance mid-frequency , distance sampling point The value at the corresponding position, Represents index coordinates; (4-2) TFR three-dimensional tensor Summing along the time dimension to obtain a two-dimensional image of frequency domain distance , then Each distance unit performs outlier detection to obtain an outlier location map , its outlier value is 1 and its non-outlier value is 0: (3) in, Represents a two-dimensional image of frequency domain distance mid-frequency , distance sampling point The value at the corresponding position.

6. The method for detecting slow small targets on the sea surface based on tensor decomposition according to claim 1, characterized in that: The difference relative peak height map of the current frame is used as the frame to be detected, the point to be detected is determined from the frame to be detected, and a preset number of difference relative peak height maps adjacent to the current frame are selected as reference frames. The reference frames are used to determine whether the point to be detected is a target, including: (5-1) Select the relative peak height graph of the difference corresponding to a frame of echo signal As the frame to be detected , looking for All non-zero points in is called the point to be detected, where is the number of points to be tested; (5-2)Select Relative peak height graph of the difference between the preset number of data frames before and after As a reference frame ; (5-3)Select A point to be tested ,in for The index values ​​of the coordinates correspond to the frequency sampling points and the distance sampling points respectively; it will include and 、 The set of 5 index values ​​including is called detection range; detect all reference frames Is there a non-zero point in the detection range? Count the number of frames with non-zero points. If the number exceeds 4 / 5 of the number of frames, then it is considered If it is a target, it will be retained, otherwise it will be set to zero as sea clutter; All points in the execution of this operation are completed Inter-frame joint object detection.

7. A terminal device comprising a processor, a memory, and a computer program stored in the memory; characterized in that: When the processor executes the computer program, it implements the method for detecting slow small targets on the sea surface based on tensor decomposition according to any one of claims 1 to 6.

8. A computer-readable storage medium storing a computer program; wherein: When the computer program is executed by a processor, the method for detecting slow small targets on the sea surface based on tensor decomposition according to any one of claims 1 to 6 is implemented.

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