Sea surface low-speed small target detection method based on tensor decomposition

Abstract

The invention discloses a sea surface low-speed small target detection method based on tensor decomposition, and the method comprises the steps: converting a target echo signal into a TFR three-dimensional tensor space, enabling sea clutters to be continuously distributed in a distance dimension in the space, and presenting a low-rank characteristic; the target only exists in a specific distance unit, so that the sparse characteristic is presented; on the basis, effective separation of the target and the clutter can be realized by utilizing low-rank and sparsity differences of the clutter and the target and combining tensor robust principal component analysis; considering that clutters of all distance units are difficult to meet strict low-rank performance, in the decomposition process, target energy exists in low-rank components and clutter residues exist in sparse components, so that a method of module value subtraction of the low-rank components and the sparse components and inter-frame joint detection is adopted to improve the signal-clutter-noise ratio of a target, and the resolution of the target is improved. And reliable detection of a low-speed 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 a sea surface based on tensor decomposition. Background Art

[0002] Marine territories are widely used in aquaculture, mining, energy, trade, tourism, national defense and other fields. Radar, as an active microwave target detection device, has the ability to detect and perceive targets all day and all weather, and plays an important role in the cognition and monitoring of the ocean. Unlike ground and air radar detection systems, sea radar echoes contain a large number of sea surface reflection echoes. The formation mechanism of these sea clutter is complex and dynamically variable, which brings severe challenges to sea surface target detection. Sea target detection technology in a complex and variable environment has become a key constraint factor affecting radar performance, which is mainly manifested in the following two points: First, the sea surface environment is complex and changeable, which makes it difficult to recognize clutter characteristics; second, the target has low observable characteristics, which greatly increases the difficulty of radar detection.

[0003] The most widely used detection methods are the incoherent and coherent detection algorithms based on energy accumulation. The core idea of ​​the incoherent detection algorithm is to compare the power of the surrounding reference unit with the unit to be detected. When the power of the reference unit exceeds the power threshold calculated by the unit to be detected, the point is considered to be the target point. Classic incoherent detection methods include the unit average constant false alarm rate (CA-CFAR) detection algorithm, the ordered statistical CFAR detection algorithm, and the large or small CFAR detection algorithm. However, due to the small radar scattering cross-section of the sea surface, the application of slow small targets is severely limited in the background of low signal-to-noise ratio. The coherent detection algorithm is mainly used in coherent radars to suppress clutter and enhance the target signal energy through moving target indicator (MTI) and moving target detection (MTD). However, due to the low speed of the target, it often overlaps with the sea clutter band, resulting in the suppression of target energy while suppressing clutter, making it difficult to effectively detect slow moving targets. Summary of the invention

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

[0007] The original radar echo signal is obtained and preprocessed to obtain a time domain signal; the time domain signal is converted into a TFR three-dimensional tensor space to construct a 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 sparse part containing sea clutter and the sparse part containing the target;

[0009] The difference tensor is obtained by subtracting the low-rank part from the sparse part; 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 peak 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 to construct 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 distance-slow time two-dimensional data, and then short-time Fourier transform is performed along each distance unit to obtain time-frequency slices. The STFT expression is as follows:

[0014]

[0015] Where x(n) represents the time domain signal of the distance unit, h(n) is the window function, n represents the slow time sampling point, m represents the window sampling point position, k represents the frequency sampling point, N represents the total number of frequency sampling points, e is a natural constant, and j is an imaginary unit;

[0016] Rearrange each time-frequency slice STFT(m,k) in the order of distance units to obtain the TFR three-dimensional tensor

[0017] Furthermore, the use of the TRPCA algorithm to perform low-rank sparse decomposition on the tensor to obtain a sparse part containing sea clutter and a sparse part containing the target includes:

[0018] Solve using the augmented Lagrangian function using the alternating direction method of multipliers:

[0019] (2-1) Initialization ρ,μ 0 , μ max and ε; where and are the low-rank tensor, sparse tensor and Lagrange multiplier at the first iteration, ρ is the step size increment, μ 0 is the initial step size, μ max is the maximum step length, ε is the decision threshold; and μ 0 The subscript of is the update iteration count, the initial value is 0, and the subscripts k and k+1 of these parameters represent the corresponding kth and k+1th iteration results;

[0020] (2-2) Update

[0021] and

[0022]

[0023] Among them, ||·|| * and ||·‖ F They refer to the nuclear norm and Frobenius norm of the tensor respectively, n 1 ,n 2 ,n 3 They are the sizes of the three dimensions of time, frequency domain, and distance respectively;

[0024] (2-3) Update

[0025] (2-4) Update μ k+1 =min(ρμ k ,μ max );

[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 difference graph of frequency domain distance to construct a peak point relative peak height graph, including:

[0028] Select a point as the test point, compare the values ​​of the point with the four adjacent points above, below, left and right, if the point has the largest value, it is the peak point, fill in the difference between the point and the mean of the four adjacent points in the peak point relative peak height diagram R; if it is not a peak point, fill in 0 in the corresponding position in the peak point relative peak height diagram R; traverse all points in the two-dimensional frequency domain distance difference diagram D in turn; sum the TFR three-dimensional tensor along the time dimension to obtain the two-dimensional frequency domain distance diagram D', and use the outlier detection method to obtain the abnormal point position diagram containing sea clutter and target positions.

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

[0030] (4-1) Find the peak point of the two-dimensional frequency domain distance difference map D, and calculate the relative peak height to obtain the relative peak height map R:

[0031]

[0032] Where D(f,r) represents the value at the position corresponding to the frequency f and the distance sampling point r in the two-dimensional difference map D of the frequency domain, and (f,r) represents the index coordinates;

[0033] (4-2) For the original tensor The frequency domain distance two-dimensional image D' is obtained by summing along the time dimension, and then outlier detection is performed on each distance unit of D' to obtain the abnormal point location map O, where the outlier value is 1 and the non-outlier value is 0:

[0034]

[0035] Wherein, D'(f,r) represents the value at the position corresponding to the frequency f and the distance sampling point r in the frequency domain distance two-dimensional image D'.

[0036] Further, 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 R' of the difference corresponding to a frame of echo signal as the frame to be detected F t , find F t All non-zero points in P = [p 1 ,p 2 ,…,p N ] is called the point to be detected, where N is the number of points to be detected;

[0038] (5-2) Select F r The relative peak height graph R' of the difference between the preset number of data frames before and after is used as the reference frame F r;

[0039] (5-3) Select a point to be tested in P in For p n 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 the detection range; detect all reference frames F r Whether there is a non-zero point in the detection range, count the number of frames with non-zero points, if the number exceeds F r 4 / 5 of the number of frames, then p n If it is a target, it will be retained. Otherwise, it will be set to zero for sea clutter. Perform this operation on all points in P in turn to complete F. t Inter-frame joint object detection.

[0040] A terminal device comprises 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] The present invention utilizes 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, which overcomes the detection problem caused by low target energy or annihilation by sea clutter in previous detection methods; the difference method is used to further enhance the contrast between the target and sea clutter, making the target more prominent compared with the traditional incoherent detection method; in addition, the method also uses a processing method of multiplying the outlier position map with the relative peak height map to further reduce the influence of noise and weak absolute value of target energy, so that the method has more robust detection performance in a strong clutter environment. The algorithm is verified using a publicly measured sea clutter data set, and the average recognition accuracy of the target reaches 84.33%. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It 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 It is a schematic diagram of the construction process of the TFR three-dimensional tensor space of the present invention;

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

[0048] Figure 5 It is the result of the present invention using TRPCA decomposition on the public data set and the result of subtracting the sparse part from the low-rank part; wherein (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 It is an intermediate process diagram when the present invention performs target detection; wherein (a) is an abnormal point location diagram, (b) is a peak point relative peak height diagram, and (c) is a relative peak height diagram of the difference between the abnormal point location diagram and the relative peak height diagram;

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

[0051] Figure 8 It is the 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 a complex variable environment, the present invention provides a method for detecting slow small targets on the sea surface based on tensor decomposition. The 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 difference in low rank and sparsity between clutter and target, and combines tensor robust principal component analysis (TRPCA) to achieve effective separation of target and clutter. Considering that the clutter of each distance unit is difficult to meet the strict low rank property, during the decomposition process, the target energy will be present in the low-rank component, and the sparse component will have clutter residue. 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 realize 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 This is the singular value distribution diagram of sea clutter in the public data set. The singular value distribution 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, thus proving 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 the distance-slow time two-dimensional data, and then the short time Fourier transform (STFT) is performed along each distance unit to obtain the time-frequency slice. The STFT expression is as follows:

[0056]

[0057] Among them, x(n) represents the time domain signal of the distance unit, h(n) is the window function, n represents the slow time sampling point, m represents the position of the windowed sampling point, k represents the frequency sampling point, N represents the total number of frequency sampling points, e is a natural constant, and j is an imaginary unit.

[0058] Rearrange each time-frequency slice STFT(m,k) in the order of distance units to obtain the TFR three-dimensional tensor

[0059] Step 2: TFR three-dimensional tensor Find the modulus value, and then use the TRPCA algorithm to Perform low-rank sparse decomposition to obtain the sparse 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 ρ,μ 0 , μ max and ε. Among them, and are the low-rank tensor, sparse tensor and Lagrange multiplier at the first iteration, ρ is the step size increment, μ 0 is the initial step size, μ max is the maximum step length, ε is the decision threshold; where, and μ 0 The subscript of is the update iteration count, the initial value is 0, and the subscripts k and k+1 of these parameters represent the corresponding kth and k+1th iteration results;

[0061] (2-2) Update

[0062] and

[0063]

[0064] Among them, ||·|| * and ||·|| F They refer to the nuclear norm and Frobenius norm of the tensor respectively. According to experience, λ can be set to n 1 ,n 2 ,n 3 They are the sizes of the three dimensions of time, frequency domain, and distance respectively;

[0065] (2-3) Update

[0066] (2-4) Update μ k+1 =min(ρμ k ,μ max );

[0067] (2-5) Check whether it converges. If Output current and Otherwise return (2-2); where ||·| | ∞ represents the infinity norm of the 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 The sum is calculated along the time dimension to obtain the two-dimensional frequency domain distance difference map D and the two-dimensional frequency domain distance image D'.

[0069] Step 4: perform peak point detection on the frequency domain distance two-dimensional difference map D, and construct a peak point relative peak height map R; perform outlier detection on the frequency domain distance two-dimensional image D', and construct an abnormal point position map O.

[0070] In the frequency domain distance two-dimensional difference map D, the energy of the target point is often stronger than the surrounding points, showing a "peak" shape. This type of "peak" point is called a peak point. Then, according to this definition, the peak point is found in the frequency domain distance two-dimensional difference map D and the peak point relative peak height map R is drawn.

[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 point value is the largest, it is the peak point, fill the corresponding position in the peak point relative peak height graph R with the difference between the point and the average of the four adjacent points compared; if it is not a peak point, fill the corresponding position in the peak point relative peak height graph R with 0. Traverse all the points in the two-dimensional difference graph D of the frequency domain distance in turn. To reduce the influence of the noise peak point, the original tensor The frequency domain distance two-dimensional graph D' is obtained by summing along the time dimension. The outlier detection method is used to obtain the outlier point location map including sea clutter and target location. This paper uses the generalized extreme Studentized deviation test to detect outliers. The specific process of step 4 is as follows.

[0072] (4-1) Find the peak point of the two-dimensional frequency domain distance difference map D, and calculate the relative peak height to obtain the relative peak height map R:

[0073]

[0074] Wherein, D(f,r) represents the value at the position corresponding to the frequency f and the distance sampling point r in the two-dimensional frequency domain distance difference map D, and (f,r) represents the index coordinate.

[0075] (4-2) For the original tensor The frequency domain distance two-dimensional image D' is obtained by summing along the time dimension, and then outlier detection is performed on each distance unit of D' to obtain the abnormal point location map O, where the outlier value is 1 and the non-outlier value is 0:

[0076]

[0077] Wherein, D'(f,r) represents the value at the position corresponding to the frequency f and the distance sampling point r in the frequency domain distance two-dimensional image D'.

[0078] Step 5, multiply the abnormal point position map O with the relative peak height map R to obtain the difference relative peak height map R'; use the difference relative peak height map R' 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.

[0079] Among them, the unit point where the target is located in the difference relative peak height map R' will be retained, and it has 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, the 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 occurrences of the peak points of the corresponding units in the reference frames before and after the peak point unit of the frame to be detected can be counted as the basis for the final judgment of the target. The specific process is as follows:

[0080] (5-1) Select the relative peak height graph R' of the difference corresponding to a frame of echo signal as the frame to be detected F t , find F t All non-zero points in P = [p 1 ,p 2 ,…,p N] is called the point to be detected, where N is the number of points to be detected;

[0081] (5-2) Select F r The relative peak height graph R' of the difference between a certain number of data frames before and after is used as the reference frame F r ;

[0082] (5-3) Select a point to be tested in P in For p n 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 the detection range; detect all reference frames F r Whether there is a non-zero point in the detection range, count the number of frames with non-zero points, if the number exceeds F r 4 / 5 of the number of frames, then p n If it is a target, it will be retained. Otherwise, it will be set to zero for sea clutter. Perform this operation on all points in P in turn to complete F. t Inter-frame joint object detection.

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

[0084] Example:

[0085] This embodiment uses IPIX public measured sea clutter data, which provides echo data of 14 range units. Each range unit collects 131072 pulse echo signals and two polarization channels H and V.

[0086] For this data, the specific steps of the sea surface low-speed small target detection method based on TRPCA are as follows:

[0087] Step 1: Establishment of TFR three-dimensional tensor space

[0088] The original data is divided into 1024 frames with 128 pulses per frame. Figure 3 As shown, the time-frequency diagram 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 diagrams 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.

[0089] Step 2: Low-rank sparse decomposition

[0090] right Find the modulus value, and then use the TRPCA algorithm to Perform low-rank sparse decomposition to obtain the sparse 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.

[0091] Step 3: Get the difference map

[0092] Use the sparse part to subtract the low-rank part

[0093] Get the difference tensor, then sum it along the time dimension to get the two-dimensional difference graph D of the frequency domain distance. The result is as follows Figure 5 as shown in (d).

[0094] Step 4: Obtain the abnormal point location map and the peak point relative peak height map

[0095] In the frequency domain distance two-dimensional difference map D, 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 map R by formula (2). In addition to the peak points of the target and the sea clutter of the target-like, there are also some noise peak points (lower energy and relatively lighter color) in the relative peak height map R. In order to reduce the influence of the noise peak points, the original tensor The frequency domain distance two-dimensional map D' is obtained by summing along the time dimension. Outlier detection is performed on each distance unit to obtain outliers including sea clutter and target positions, and the outlier position map O is obtained according to formula (3).

[0096] 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 (location map, only showing the peak point location, 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 quasi-target sea clutter, there are also some noise peak points (lower energy), and (c) is the result of multiplying the outlier location map with the relative peak height map, the difference relative peak height map (energy map, color represents energy strength), which filters out the interference of the noise peak.

[0097] Step 5: Inter-frame joint target detection

[0098] By multiplying the abnormal point location map O with the relative peak height map R, the unit point where the target is located will be retained, and it will 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 frame F to be detected with the difference relative peak height map R' is screened out. t All non-zero points, then select F t5 frames before and after, a total of 10 frames, are used as reference frames F r 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 F r Whether there is a non-zero point in the corresponding unit, and count the F with peak value r 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 set to zero for sea clutter. t This operation is performed on all peak points to complete the inter-frame joint target detection of one frame. The above operation is repeated to finally complete the inter-frame joint target detection of all data frames.

[0099] Figure 7 It is a comparison chart of the results before and after multi-frame joint detection. The top is the result of 5 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 is the result of the nth frame after detection. At this time, the discontinuous sea clutter points have been eliminated, leaving only the target points.

[0100] The method proposed in the present invention is compared with two 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 are tested, each group of data is divided into 1024 frames, each frame has 128 pulses, and each pulse has 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%.

[0101] In summary, the detection method of low-rank sparse decomposition can effectively separate the target and sea clutter, and the present invention can effectively improve the detection performance of low-speed small targets under strong clutter background.

[0102] 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 embodiments of the present application, and should all be included in the protection scope 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 sparse part containing sea clutter and the sparse part containing the target; The difference tensor is obtained by subtracting the low-rank part from the sparse part; 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 peak 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 distance-slow time two-dimensional data, and then short-time Fourier transform is performed along each distance unit to obtain time-frequency slices. The STFT expression is as follows: Where x(n) represents the time domain signal of the distance unit, h(n) is the window function, n represents the slow time sampling point, m represents the window sampling point position, k represents the frequency sampling point, N represents the total number of frequency sampling points, e is a natural constant, and j is an imaginary unit; Rearrange each time-frequency slice STFT(m,k) in 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 method of using the TRPCA algorithm to perform low-rank sparse decomposition on the tensor to obtain a sparse part containing sea clutter and a sparse part containing the target includes: Solve using the alternating direction method of multipliers via the augmented Lagrangian function: (2-1) Initialization ρ,μ0,μ max and ε; where and are the low-rank tensor, sparse tensor and Lagrange multiplier at the first iteration, ρ is the step size increment, μ0 is the initial step size, μ max is the maximum step length, ε is the decision threshold; The subscripts of and μ0 are update iteration counts, with an initial value of 0. Subsequent subscripts of these parameters such as k and k+1 represent the corresponding k-th and k+1-th iteration results. (2-2) Update and Among them, ||·|| * and ||·|| F They refer to the nuclear norm and Frobenius norm of the tensor respectively, n1, n2, and n3 are the sizes of the three dimensions of time, frequency domain, and distance respectively; (2-3) Update (2-4) update k+1 =min(ρμ k ,m max ); (2-5) Check whether it converges. If Output current and 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 step of 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 values ​​of the point with the four adjacent points above, below, left and right, if the point has the largest value, it is the peak point, fill in the difference between the point and the mean of the four adjacent points in the peak point relative peak height diagram R; if it is not a peak point, fill in 0 in the corresponding position in the peak point relative peak height diagram R; traverse all points in the two-dimensional frequency domain distance difference diagram D in turn; sum the TFR three-dimensional tensor along the time dimension to obtain the two-dimensional frequency domain distance diagram D', and use the outlier detection method to obtain the abnormal point position diagram containing sea clutter and target positions.

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: (4-1) Find the peak point of the two-dimensional frequency domain distance difference map D, and calculate the relative peak height to obtain the relative peak height map R: Where D(f,r) represents the value at the position corresponding to the frequency f and the distance sampling point r in the two-dimensional difference map D of the frequency domain, and (f,r) represents the index coordinates; (4-2) For the original tensor The frequency domain distance two-dimensional image D' is obtained by summing along the time dimension, and then outlier detection is performed on each distance unit of D' to obtain the abnormal point location map O, where the outlier value is 1 and the non-outlier value is 0: Wherein, D'(f,r) represents the value at the position corresponding to the frequency f and the distance sampling point r in the frequency domain distance two-dimensional image D'.

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 before and after 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: (5-1) Select the relative peak height graph R' of the difference corresponding to a frame of echo signal as the frame to be detected F t , find F t All non-zero points in P=[p1,p2,…,p N ] is called the point to be detected, where N is the number of points to be detected; (5-2) Select F r The relative peak height graph R' of the difference between the preset number of data frames before and after is used as the reference frame F r ; (5-3) Select a point to be tested in P in For p n 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 the detection range; detect all reference frames F r Whether there is a non-zero point in the detection range, count the number of frames with non-zero points, if the number exceeds F r 4 / 5 of the number of frames, then p n If it is a target, it will be retained. Otherwise, it will be set to zero for sea clutter. Perform this operation on all points in P in turn to complete F. t 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, 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.

8. A computer-readable storage medium, wherein a computer program is stored in the medium; characterized in that: 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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