A radar constant false alarm rate detection method and system based on deep unfolding

Abstract

The application provides a radar constant false alarm detection method and system based on deep unfolding, wherein the method comprises the following steps: constructing a data training set based on multiple preset ranges of radar echo signals; training a deep unfolding network of vector approximate message passing by using the data training set to obtain a trained deep unfolding network; obtaining radar echo signals; inputting the radar echo signals into the trained deep unfolding network to obtain a reconstructed sparse signal and a non-sparse noise estimation of the reconstructed sparse signal; obtaining a recovery error power based on the non-sparse noise estimation; updating the recovery error power by using a preset false alarm rate until the recovery error power converges, so that a constant false alarm detection result is obtained.

Description

Technical Field

[0001] The present invention relates to the field of radar target detection, and in particular to a radar constant false alarm detection method and system based on depth expansion. Background Art

[0002] Traditional high-resolution radar-based target detection requires acquiring and transmitting complete sampled signals, which increases the system's storage space and transmission bandwidth pressure. Sub-Nyquist radar systems utilize signal sparsity to reduce resource consumption in multiple dimensions, including the time and frequency domains.

[0003] In recent years, several sparse recovery algorithms have emerged in the art. Examples include the iterative shrinking threshold algorithm, the fast iterative shrinking threshold algorithm, the complex approximate message passing algorithm, and the vector approximate message passing algorithm. However, these sparse recovery methods typically require manual tuning of algorithm parameters to achieve optimal results, making them unsuitable for real-world applications.

[0004] With the development of deep unfolding technology, each iteration of a traditional sparse recovery algorithm can be unfolded into each layer of a deep network. The parameters of each iteration of the sparse recovery algorithm can be trained using training data. This type of algorithm effectively solves the problem of optimal parameter selection in practical applications, reduces the number of iterative convergence times, and improves recovery accuracy.

[0005] However, the sparse recovery algorithm based on deep expansion breaks the specific parameter constraints of the traditional sparse recovery algorithm, and the recovered error power cannot be directly output from the algorithm, which restricts its application in constant false alarm detection of sub-Nyquist radar. Summary of the Invention

[0006] The present invention aims to solve one of the technical problems in the related art at least to a certain extent.

[0007] To this end, the first object of the present invention is to propose a radar constant false alarm detection method based on deep expansion to solve the problem that the deep expansion algorithm based on vector approximate message passing cannot output the recovered error power.

[0008] The second object of the present invention is to provide a radar constant false alarm detection system based on depth expansion.

[0009] A third object of the present invention is to provide an electronic device.

[0010] A fourth object of the present invention is to provide a computer-readable storage medium.

[0011] To achieve the above-mentioned object, the first aspect of the present invention proposes a radar constant false alarm detection method based on deep expansion, comprising:

[0012] Constructing a data training set based on multiple preset ranges of radar echo signals, and using the data training set to train a deep unfolding network for vector approximate message passing to obtain a trained deep unfolding network;

[0013] Acquire a radar echo signal, and input the radar echo signal into a trained deep unrolling network to obtain a reconstructed sparse signal and a non-sparse noisy estimate of the reconstructed sparse signal;

[0014] Obtaining a recovered error power based on the non-sparse band noise estimation;

[0015] The restored error power is updated using a preset false alarm rate until the restored error power converges, thereby obtaining a constant false alarm detection result.

[0016] In the method of the first aspect of the present invention, the data training set is constructed based on multiple preset ranges of the radar echo signal, including: generating multiple complex test data and corresponding noise based on a preset amplitude range, a preset sparsity range, a preset signal-to-noise ratio range, and a preset phase range of the radar echo signal; and constructing a data training set based on the complex test data, the noise, and a complex observation matrix.

[0017] In the method of the first aspect of the present invention, the data training set is constructed based on the complex test data, the noise and the complex observation matrix, including: splicing the real part and the imaginary part of the complex test data to obtain a complex test data target matrix; splicing the real part and the imaginary part of the noise to obtain a noise target matrix; splicing the real part and the imaginary part of the complex observation matrix to obtain a complex observation target matrix; and constructing a data training set based on the complex test data target matrix, the noise target matrix and the complex observation target matrix.

[0018] In the method of the first aspect of the present invention, the recovery error power is obtained based on the non-sparse noisy estimate, including: establishing a first target vector with the same size as the non-sparse noisy estimate; assigning a value to the first target vector, and obtaining a second target vector based on the assigned first target vector and the non-sparse noisy estimate; and calculating the recovery error power based on the second target vector.

[0019] In the method of the first aspect of the present invention, assigning a value to the first target vector includes: assigning a value to the first target vector using the support set of the reconstructed sparse signal or the detection result under a preset false alarm rate.

[0020] In the method of the first aspect of the present invention, the calculation of the restored error power based on the second target vector includes: calculating the restored error power based on the column vector corresponding to the support set of the second target vector.

[0021] In the method of the first aspect of the present invention, the use of a preset false alarm rate to update the recovered error power until the recovered error power converges includes: judging whether the number of iterations is greater than 1, and if so, judging whether the recovered error power of the current number of iterations converges; if not, calculating the non-sparse band noise estimate complex modulus square sum detection threshold; performing constant false alarm detection based on the non-sparse band noise estimate complex modulus square sum detection threshold to obtain a detection result of the current number of iterations; obtaining a detection result under a preset false alarm rate based on a preset false alarm rate, updating the number of iterations and obtaining a new recovery error power of the current number of iterations based on the detection result under the preset false alarm rate and the non-sparse band noise estimate, until the recovery error power converges.

[0022] To achieve the above-mentioned object, the second aspect of the present invention proposes a radar constant false alarm detection system based on deep expansion, comprising:

[0023] a sparse recovery deep unfolding module, configured to construct a data training set based on multiple preset ranges of the radar echo signal, and to train a deep unfolding network using the data training set to obtain a trained deep unfolding network; and to obtain a radar echo signal, and to input the radar echo signal into the trained deep unfolding network to obtain a reconstructed sparse signal and a non-sparse noisy estimate of the reconstructed sparse signal;

[0024] A power estimation module, configured to obtain a recovered error power based on the non-sparse band noise estimation;

[0025] The iterative judgment and constant false alarm detection module is used to update the restored error power using a preset false alarm rate until the restored error power converges, thereby obtaining a constant false alarm detection result.

[0026] To achieve the above-mentioned purpose, the third aspect of the present invention proposes an electronic device, comprising: a processor, and a memory communicatively connected to the processor; the memory stores computer-executable instructions; the processor executes the computer-executable instructions stored in the memory to implement the method proposed in the first aspect of the present invention.

[0027] To achieve the above-mentioned purpose, the fourth aspect of the present invention proposes a computer-readable storage medium, in which computer-executable instructions are stored. When the computer-executable instructions are executed by a processor, they are used to implement the method proposed in the first aspect of the present invention.

[0028] The present invention provides a radar constant false alarm detection method, system, electronic device, and storage medium based on deep unfolding. A data training set is constructed based on multiple preset ranges of radar echo signals, and a deep unfolding network based on vector approximate message passing is trained using the data training set to obtain a trained deep unfolding network. A radar echo signal is obtained and input into the trained deep unfolding network to obtain a reconstructed sparse signal and a non-sparse noise estimate of the reconstructed sparse signal. A recovered error power is obtained based on the non-sparse noise estimate. The recovered error power is updated using a preset false alarm rate until the recovered error power converges, thereby obtaining a constant false alarm detection result. In this case, the characteristic of the deep unfolding network based on vector approximate message passing that the recovered error is Gaussian is utilized. The deep unfolding network based on vector approximate message passing is trained using the data training set to obtain a trained deep unfolding network. The reconstructed sparse signal and the non-sparse noise estimate of the reconstructed sparse signal are obtained for the radar echo signal to obtain the recovered error power. The trained deep unfolding network is then iterated until convergence, thereby ensuring a relatively accurate estimate of the recovered error power. This solves the problem that existing deep unfolding algorithms based on vector approximate message passing cannot output the recovered error power.

[0029] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0031] Figure 1 A schematic flow chart of a radar constant false alarm detection method based on depth expansion provided by an embodiment of the present invention;

[0032] Figure 2 A schematic diagram of a specific flow chart of a radar constant false alarm detection method based on depth expansion provided by an embodiment of the present invention;

[0033] Figure 3 A schematic diagram of the processing flow of the sparse recovery depth expansion module provided in an embodiment of the present invention;

[0034] Figure 4 A schematic diagram of the processing flow of the iterative judgment and constant false alarm detection module provided in an embodiment of the present invention;

[0035] Figure 5 This is an example diagram of the power estimation effect provided by an embodiment of the present invention;

[0036] Figure 6 This is an example diagram of the detection effect provided by an embodiment of the present invention;

[0037] Figure 7 This is a block diagram of a radar constant false alarm detection system based on depth expansion provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0038] The following describes embodiments of the present invention in detail, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and are not to be construed as limiting the present invention.

[0039] The following describes a radar constant false alarm detection method and system based on depth expansion according to an embodiment of the present invention with reference to the accompanying drawings.

[0040] The embodiment of the present invention provides a radar constant false alarm detection method based on deep expansion to solve the problem that the deep expansion algorithm based on vector approximate message passing cannot output the recovered error power.

[0041] Figure 1 A schematic flow chart of a radar constant false alarm detection method based on depth expansion provided by an embodiment of the present invention. Figure 2 This is a schematic diagram of a specific flow chart of a radar constant false alarm detection method based on depth expansion provided by an embodiment of the present invention.

[0042] like Figure 1 As shown, the radar constant false alarm detection method based on depth expansion includes the following steps:

[0043] Step S101 : constructing a data training set based on multiple preset ranges of radar echo signals, and using the data training set to train a deep unfolding network of vector approximate message passing to obtain a trained deep unfolding network.

[0044] In step S101, a data training set is constructed based on multiple preset ranges of the radar echo signal, including: generating multiple complex test data and corresponding noise based on a preset amplitude range, a preset sparsity range, a preset signal-to-noise ratio range, and a preset phase range of the radar echo signal; and constructing a data training set based on the complex test data, the noise, and the complex observation matrix. Specifically, constructing the data training set based on the complex test data, the noise, and the complex observation matrix includes: concatenating the real and imaginary parts of the complex test data to obtain a complex test data target matrix; concatenating the real and imaginary parts of the noise to obtain a noise target matrix; concatenating the real and imaginary parts of the complex observation matrix to obtain a complex observation target matrix; and constructing the data training set based on the complex test data target matrix, the noise target matrix, and the complex observation target matrix.

[0045] In step S101 , the input and output of the deep unfolding network of vector approximate message passing are both real data.

[0046] Step S102: Acquire a radar echo signal, and input the radar echo signal into a trained deep expansion network to obtain a reconstructed sparse signal and a non-sparse noisy estimate of the reconstructed sparse signal.

[0047] In step S102, the radar echo signal is in complex form, and the acquired radar echo signal is the complex test data y. Inputting the complex test data y into the trained deep expansion network can obtain a reconstructed sparse signal and a non-sparse noisy estimate of the reconstructed sparse signal.

[0048] Specifically, Figure 3 Schematic diagram of the processing flow of the sparse recovery depth expansion module provided by the embodiment of the present invention. The sparse recovery depth expansion module performs step S101 and step S102 (see Figure 2 ) to realize the training and testing process of the deep unfolding network of vector approximate message passing. The training process trains the deep unfolding network of vector approximate message passing through training data sets with different generation parameters to make sparse recovery applicable to a wide range of application scenarios. The testing process inputs the acquired radar echo signal into the trained deep unfolding network of vector approximate message passing to obtain the reconstructed sparse signal and the non-sparse noisy estimation of the reconstructed sparse signal (see Figure 3 ).

[0049] The specific process of the sparse recovery depth expansion module includes the following steps:

[0050] Step 11: Determine the generation parameters of the training data, which may refer to a plurality of preset ranges, for example, the plurality of preset ranges may include a preset amplitude range [a min ,a max ], preset sparsity range [p min ,p max ], preset signal-to-noise ratio range [SNR min ,SNR max ], preset phase range [-π, +π]. Randomly generate different complex test data x based on the generation parameters train , so that its amplitude is within the preset amplitude range [a min ,a max ] is evenly distributed within the preset sparsity range [p min ,p max ] is evenly distributed within the preset phase range [-π, +π], and the phase is evenly distributed within the preset phase range [-π, +π]. train The size is N / 2×K (i.e. x train The number of rows is equal to N / 2 and the number of columns is equal to K). Generate the corresponding noise n train , n train The size is M / 2×K (i.e. n trainThe number of rows is equal to M / 2 and the number of columns is equal to K), so that x train The signal power and n train The noise power signal-to-noise ratio is within the preset signal-to-noise ratio range [SNR min ,SNR max ], where N is the first preset number, M is the second preset number, and K is the batch size of each training data generation.

[0051] Step 12: Place the x train Decompose into the real part of the complex test data x train,R and the imaginary part x of the complex test data train,I , x train,R and x train,I The size of x is N / 2×K. train,R and x train,I Splice into a new data matrix (i.e., retest data target matrix) x train,R,I , x train,R,I The size of is N×K, where x train,R,I =[x train,R ;x train,I ]. train Decomposed into the noise real part n train,R and the imaginary part of the noise n train,I , n train,R and n train,I The size of n is M / 2×K. train,R and n train,I Splice into a new data matrix (ie, noise target matrix) n train,R,I , n train,R,I The size is M×K, where n train,R,I =[n train,R ;n train,I ]. Get the complex observation matrix A, the size of A is M / 2×N / 2, and decompose the complex observation matrix A into the real part of the complex observation matrix A R and the imaginary part of the complex observation matrix A I , A R and A I The size is M / 2×N / 2, and A R and A I Splice into a new matrix (i.e., complex observation target matrix) A R,I , A R,I =[A R ,-A I ; A I ,A R ], A R,I The size of is M × N. Get the complex test data y, the size of y is M / 2 × 1, and decompose the complex test data y into the real part of the complex test data y Rand the imaginary part y of the complex test data I ,y R and y I The size of y is M / 2×1. R and y I Splice into a new test data vector (ie, complex test data target vector) y R,I , size is M×1, where y R,I =[y R ;y I ].

[0052] Step 13: Construct data training set y train,R,I And train: y train,R,I Continuously input vector approximate message passing to the deep unfolding network and train the network parameters. train,R,I =A R,I* x train,R,I+ n train,R,I ,y train,R,I The size of is M×K. The detailed training method and parameters are as follows: Each layer of network is trained 15000 times, and y is randomly generated in each training. train,R,I Input network, the current layer t outputs the sparse reconstruction result of the signal with x train,R,I The mean squared error of is used as the loss function to train the parameters of the current layer t (it should be noted that when training the parameters of the current layer t, the parameter gradients of the remaining layers are frozen and do not participate in the training). This process is repeated until the parameters of each layer are trained. This results in a trained deep unfolding network for vector approximate message passing (referred to as a trained deep unfolding network), also known as a trained sparse recovery deep unfolding network.

[0053] Step 14: After training, the complex test data target vector y R,I Input the trained vector approximate message passing deep unfolding network to obtain the final non-sparse noisy estimate of the reconstructed sparse signal and reconstructing sparse signals The non-sparse noisy estimate and reconstructing sparse signals is a real number with size N×1.

[0054] In an embodiment of the present invention, the calculation steps of the deep unfolding network of vector approximate message passing are as follows:

[0055] Step 21: The complex observation target matrix A R,I Perform truncated singular value decomposition, that is, A R,I =USV T, where the size of U is M×R, the size of S is R×R, and the size of V is N×R, where R is the rank of the complex observation matrix A, where U is a unitary matrix; S is a diagonal matrix; V T is the conjugate transpose of the orthogonal matrix V;

[0056] Step 22: Set the number of layers of the network to T (for example, set T=7);

[0057] Step 23: Definition is the scalar parameter to be trained at the current layer t. Each layer is assigned an initial value of 1.0. The t in the subscript (i.e., the current layer t) is the number of network layers that the network is currently executing. Define α = {α t ,t=1,2,...,T}, where α t is the scalar parameter to be trained at the current layer t. Each layer is initialized to 1.0. Let t = 1 and proceed to step 24 to start the calculation of the first layer of the network.

[0058] Step 24: Calculation in Among them, I R is the unit matrix, size is R×R, U T is the conjugate transpose of U; y is the complex test data, when t = 1, is an all-zero vector. is a scalar. When t=1, The ||·||2 operator is the two-norm of the vector;

[0059] Step 25: Calculation in

[0060] where s i are the diagonal elements of the diagonal matrix S;

[0061] Step 26: Calculation

[0062] Step 27: Calculation

[0063] Step 28: Calculation in Where sgn(·) is the sign function, if the input is greater than or equal to 0, the output is 1, if the input is less than zero, the output is -1, max{·,·} is the maximum value function, the function outputs the maximum value of the two inputs. t,i is the vector r t the elements of

[0064] Step 29: Calculate v t =<η′(r t ; σ t,α)>*(1-Δ)+Δ, where Δ=1e-6, e is a natural constant, ||·||0 is the zero norm of the input vector;

[0065] Step 30: Calculate the next layer t+1 of the current layer t

[0066] Step 31: Calculate the next layer t+1 of the current layer t

[0067] Step 32: Set t = t + 1 to update the current layer, return to step 24, and enter the next layer iteration until t = T. The output of the current layer t: reconstruct the sparse signal Non-sparse noisy estimation r for reconstructing sparse signals t The last layer outputs a non-sparse noisy estimate and reconstructing sparse signals The non-sparse noisy estimate The size of is N×1. Reconstructing sparse signals The size is N×1.

[0068] Step S103: obtaining restored error power based on non-sparse band noise estimation.

[0069] In step S103, the recovered error power is obtained based on the non-sparse noise estimate, including: establishing a first target vector of the same size as the non-sparse noise estimate; assigning a value to the first target vector, obtaining a second target vector based on the assigned first target vector and the non-sparse noise estimate; and calculating the recovered error power based on the second target vector. The assigning a value to the first target vector includes assigning a value to the first target vector using a support set of a reconstructed sparse signal or a detection result at a preset false alarm rate. The calculating the recovered error power based on the second target vector includes calculating the recovered error power based on a column vector corresponding to the support set of the second target vector.

[0070] Specifically, the power estimation module performs step S103 (see Figure 2 ) to realize the recovery error determination process and the recovery error power calculation process. Among them, the recovery error determination process is based on the reconstructed sparse signal Or the detection result of the i-th iteration under the preset false alarm rate Reconstructing sparse signals is the output of the depth expansion module of sparse recovery at the initial iteration (i.e., i=1), and the detection result of the i-th iteration under the preset false alarm rate is The output of the iterative judgment and constant false alarm detection module is obtained when the iteration index i≥2 (described later). Reconstructing the sparse signal And the detection result of the i-th iteration under the preset false alarm rate Can be seen as a signal is a real number. The minimum variance unbiased estimation is used to calculate the recovered error power. The input of the power estimation module includes the non-sparse noise estimation and signal The input of the power estimation module includes the recovery error power (σ 2 ) i .

[0071] The specific process of the power estimation module includes the following steps:

[0072] Step 41: Build a non-sparse noisy estimate of the reconstructed sparse signal The first target vector z of the same size, z has a size of N×1;

[0073] Step 42: Assign the value of each element of the first target vector z established in step 41 to 0 or 1. The assignment rule is: The corresponding position of the support set of (i≥1) is assigned 0, and the remaining positions are assigned 1. The support set is defined as: the set of non-zero position numbers in the vector;

[0074] Step 43: The first target vector z obtained in step 42 after the assignment is combined with the non-sparse noisy estimate of the reconstructed sparse signal Multiply the corresponding elements to get the second target vector Expressed as The size of is N×1, and “.*” indicates the dot multiplication operation;

[0075] Step 44: For the second target vector in step 43 The corresponding elements of its support set form a new column vector, denoted as The size is L×1, where L is the second target vector in step 43 The number of non-zero elements;

[0076] Step 45: Calculate the restored error power as Where mean(·) represents the mean operation. For the corresponding σ under different iteration times 2 It can be written as (σ 2 ) i , where the iteration index i represents the number of times the module is executed for the i-th time.

[0077] Step S104 : updating the restored error power using the preset false alarm rate until the restored error power converges, thereby obtaining a constant false alarm detection result.

[0078] In step S104, the recovery error power is updated using the preset false alarm rate until the recovery error power converges, including: determining whether the number of iterations is greater than 1, and if so, determining whether the recovery error power of the current number of iterations converges; if not, calculating a non-sparse band noise estimated complex modulus sum square detection threshold; performing constant false alarm detection based on the non-sparse band noise estimated complex modulus sum square detection threshold to obtain a detection result of the current number of iterations; obtaining a detection result under the preset false alarm rate based on the preset false alarm rate, updating the number of iterations and obtaining a new recovery error power of the current number of iterations based on the detection result under the preset false alarm rate and the non-sparse band noise estimate, until the recovery error power converges.

[0079] Figure 4 Schematic diagram of the processing flow of the iterative judgment and constant false alarm detection module provided by the embodiment of the present invention. Specifically, the iterative judgment and constant false alarm detection module executes step S104 (see Figure 2 ) to obtain the constant false alarm detection result. The input of the iterative judgment and constant false alarm detection module includes the recovery error power (σ 2 ) i , non-sparse noisy estimation The output of the iterative judgment and constant false alarm detection module includes the detection result of the i-th iteration under the preset false alarm rate The iterative judgment and constant false alarm detection module stores the preset iterative false alarm rate (ie, the preset false alarm rate) Pfa select , the false alarm rate Pfa of all actual detection results to be calculated set (size is 1×K), the recovery error power of the i-1th iteration (σ 2 ) i-1 , convergence judgment threshold tol.

[0080] The specific process of the iterative judgment and constant false alarm detection module includes the following steps:

[0081] Step 50: Consider the i-th iteration as the current iteration, and determine whether the current iteration number is greater than 1. If so, proceed to step 52; otherwise (i.e., i=1), proceed to step 51.

[0082] Step 51: If i ≥ 2, calculate |(σ 2 ) i -(σ 2 ) i-1 | 2 / ((σ 2 ) i-1 ) 2 , if |(σ 2 ) i -(σ 2 ) i-1 |2 / ((σ 2 )i-1 ) 2 <tol, indicating that the power estimation converges, then the previous iteration of the current iteration is selected is the final detection result (i.e., constant false alarm detection result), (σ 2 ) i is the final recovery error power (also called power estimation value), and the output complex signal recovery error power is (σ 2 ) I =2(σ 2 ) i Otherwise, go to step 52 (see Figure 4 );

[0083] Step 52: Reconstruct the non-sparse noisy estimate of the sparse signal The size is N×1, and its real number part For the first N / 2 rows, the imaginary part For the next N / 2 rows, sum the squares of the real and imaginary parts to get the square of the complex modulus of the non-sparse noise estimate of the reconstructed sparse signal Record The size is N / 2×1;

[0084] Step 53: In the i-th iteration, calculate the false alarm rate Pfa of all actual detection results to be calculated set The detection threshold at each false alarm rate is Where Pfa is the false alarm rate Pfa of all actual detection results to be calculated set Elements of

[0085] Step 54: The target is considered to exist at the location The corresponding element value remains unchanged; otherwise, it is considered that the target does not exist. The corresponding position element is set to 0, and the detection result when the false alarm rate is Pfa can be obtained. Record The size is N / 2×1, find(·) is the find function;

[0086] Step 55: Pfa set Repeat step 54 for each element Pfa in step 54. Splice to get the detection result of the current iteration The size is N / 2×K, the test results Each column is the detection result under the corresponding false alarm rate;

[0087] Step 56: Select Pfa=Pfa select When the detection threshold The test results at The location where there is no target, the non-sparse noisy estimation of the reconstructed sparse signal The corresponding real and imaginary elements are set to 0, and the values ​​of the other position elements remain unchanged, and the real form of the detection result under the preset false alarm rate is obtained. Record "!=" means not equal. Update the current number of iterations (i.e. i=i+1) and update the real number form before Sent to the power estimation module to participate in the calculation of the new current iteration number (see Figure 4 ).

[0088] In order to verify the effect of the method of the present invention, verification was performed as follows.

[0089] Figure 5 This is an example diagram of the power estimation effect provided by an embodiment of the present invention. Figure 6 This is an example diagram of the detection effect provided by the embodiment of the present invention. Figure 5 This is an embodiment of the present invention for estimating the recovery error power, wherein the number of network layers is set to T = 7, the training data parameters are uniformly distributed within the preset amplitude range [0.7, 1.3], the sparsity is uniformly distributed within the preset sparsity range [0.01, 0.05], the phase is uniformly distributed within the preset phase range [-π, +π], the preset signal-to-noise ratio range is [8dB, 18dB], and the batch size K = 2000. The signal-to-noise ratio is set to 13dB, the observation matrix is ​​a partial Fourier matrix of size 600×1000, the signal amplitude is 1.0, and the sparsity is 0.03.

[0090] The recovered error power after convergence is (σ 2 ) I , with a standard deviation of σ I ,in The complex estimate of the reconstructed sparse signal is calculated as Where j is the imaginary unit. The real complex sparse signal is x o ,calculate Calculate w VAMP_Est The empirical cumulative distribution function (ECDF) of the real and imaginary parts is F VAMP_Est，R (x) and F VAMP_Est，I (x), further, calculate w VAMP_Est The ECDF of the real part and the imaginary part, the part with the target and the part without the target is Where H1 represents the presence of a target and H0 represents the absence of a target. Define the ECDF of the standard normal distribution as Φ(x). Calculate Where σ is the real signal x o The non-support set corresponds to The standard deviation of the recovery error estimated by the corresponding element in represents the true value of the standard deviation of the recovery error. VAMP_Ideal The ECDF of the real part, the imaginary part, the part with the target, and the part without the target is Figure 5 The corresponding blue lines in (a), (b), (c), and (d) (the legend is the difference between the estimated standard deviation normalized ECDF and the standard normal distribution ECDF) are Figure 5 The orange lines corresponding to (a), (b), (c), and (d) (the legend is the difference between the true standard deviation normalized ECDF and the standard normal distribution ECDF) are

[0091] The orange line is almost always close to zero, indicating that the recovery error obtained by the vector approximate message passing deep expansion network sparse recovery is Gaussian distributed. The blue line is close to the orange line and almost always close to zero, indicating that the estimated value of the recovery error power of the present invention is relatively accurate.

[0092] Figure 6 This is an embodiment of the target detection of the present invention, and the application scenario is similar to Figure 5 The same is true for the recovered error power estimation embodiment. Figure 6 The horizontal axis is the preset false alarm rate, and the vertical axis is the detection rate. The target detection rate of the present invention (VAMP Iter Estimate) is improved compared with the CROD algorithm (CROD) and the two structures of the CAMP algorithm (CAMP Arch.1 and CAMP Arch.2) under the same false alarm rate. The detection rate of the present invention is close to the performance upper bound (VAMP Ideal Up Bound) obtained under the condition of known recovery error power. In this case, the recovery error power value is the value of the real signal x. o The non-support set corresponds to The corresponding elements in are estimated.

[0093] In order to implement the above embodiment, the present invention further proposes a radar constant false alarm detection system based on depth expansion.

[0094] Figure 7 This is a block diagram of a radar constant false alarm detection system based on depth expansion provided by an embodiment of the present invention.

[0095] like Figure 7 As shown, the radar constant false alarm detection system based on depth expansion includes a sparse recovery depth expansion module 11, a power estimation module 12 and an iterative judgment and constant false alarm detection module 13, wherein:

[0096] The sparse recovery deep unfolding module 11 is used to construct a data training set based on multiple preset ranges of the radar echo signal, and use the data training set to train the deep unfolding network of vector approximate message passing to obtain a trained deep unfolding network; it is also used to obtain the radar echo signal, input the radar echo signal into the trained deep unfolding network to obtain a reconstructed sparse signal and a non-sparse noisy estimate of the reconstructed sparse signal;

[0097] A power estimation module 12, configured to obtain a restored error power based on non-sparse band noise estimation;

[0098] The iterative judgment and constant false alarm detection module 13 is used to update the restored error power using a preset false alarm rate until the restored error power converges, thereby obtaining a constant false alarm detection result.

[0099] Furthermore, in a possible implementation of an embodiment of the present invention, in the sparse recovery depth expansion module 11, a data training set is constructed based on multiple preset ranges of the radar echo signal, including: generating multiple complex test data and corresponding noise based on the preset amplitude range, preset sparsity range, preset signal-to-noise ratio range, and preset phase range of the radar echo signal; and constructing a data training set based on the complex test data, noise, and complex observation matrix.

[0100] Furthermore, in a possible implementation of an embodiment of the present invention, in the sparse recovery depth expansion module 11, a data training set is constructed based on complex test data, noise and complex observation matrix, including: splicing the real part and imaginary part of the complex test data to obtain a complex test data target matrix; splicing the real part and imaginary part of the noise to obtain a noise target matrix; splicing the real part and imaginary part of the complex observation matrix to obtain a complex observation target matrix; and constructing a data training set based on the complex test data target matrix, the noise target matrix and the complex observation target matrix.

[0101] Furthermore, in a possible implementation of an embodiment of the present invention, in the power estimation module 12, the recovered error power is obtained based on the non-sparse noise estimation, including: establishing a first target vector of the same size as the non-sparse noise estimation; assigning a value to the first target vector, and obtaining a second target vector based on the assigned first target vector and the non-sparse noise estimation; and calculating the recovered error power based on the second target vector.

[0102] Furthermore, in a possible implementation of the embodiment of the present invention, in the power estimation module 12, assigning a value to the first target vector includes: assigning a value to the first target vector using a support set of a reconstructed sparse signal or a detection result under a preset false alarm rate.

[0103] Furthermore, in a possible implementation of the embodiment of the present invention, in the power estimation module 12, the recovered error power is calculated based on the second target vector, including: the recovered error power is calculated based on the column vector corresponding to the support set of the second target vector.

[0104] Furthermore, in a possible implementation of an embodiment of the present invention, in the sparse recovery depth expansion module 11, the recovery error power is updated using a preset false alarm rate until the recovery error power converges, including: determining whether the number of iterations is greater than 1, and if so, determining whether the recovery error power of the current number of iterations converges; if not, calculating the non-sparse band noise estimation complex modulus square sum detection threshold; performing constant false alarm detection based on the non-sparse band noise estimation complex modulus square sum detection threshold to obtain a detection result of the current number of iterations; obtaining a detection result under a preset false alarm rate based on the preset false alarm rate, updating the number of iterations and obtaining a new recovery error power of the current number of iterations based on the detection result under the preset false alarm rate and the non-sparse band noise estimation, until the recovery error power converges.

[0105] It should be noted that the aforementioned explanation of the embodiment of the radar constant false alarm detection method based on depth expansion is also applicable to the radar constant false alarm detection system based on depth expansion of this embodiment, and will not be repeated here.

[0106] In an embodiment of the present invention, a data training set is constructed based on multiple preset ranges of radar echo signals, and a deep unfolding network based on vector approximate message passing is trained using the data training set to obtain a trained deep unfolding network. A radar echo signal is obtained and input into the trained deep unfolding network to obtain a reconstructed sparse signal and a non-sparse noised estimate of the reconstructed sparse signal. A recovered error power is obtained based on the non-sparse noised estimate. The recovered error power is updated using a preset false alarm rate until the recovered error power converges, thereby obtaining a constant false alarm detection result. In this case, the characteristic of the deep unfolding network based on vector approximate message passing that the recovered error is Gaussian is utilized. The deep unfolding network based on vector approximate message passing is trained using the data training set to obtain a trained deep unfolding network. The reconstructed sparse signal and the non-sparse noised estimate of the reconstructed sparse signal are then obtained for the radar echo signal to obtain the recovered error power. The trained deep unfolding network is then iterated until convergence, thereby ensuring a relatively accurate estimate of the recovered error power. This solves the problem that existing deep unfolding algorithms based on vector approximate message passing cannot output the recovered error power.

[0107] The method and system of the present invention are based on deep expansion of vector approximation message passing, suitable for radar constant false alarm detection of sparse signals. They accurately estimate the recovery error of the deep expansion algorithm of vector approximation message passing, enabling its application in constant false alarm detection of sub-Nyquist radar systems.

[0108] Specifically, in order to overcome the shortcoming that the deep expansion algorithm based on vector approximate message passing cannot output the recovery error power, the method and system of the present invention propose a constant false alarm detection algorithm. First, the deep expansion network of vector approximate message passing is trained by training data with different generation parameters (such as amplitude, signal-to-noise ratio, sparsity, etc.). Data collected by radar is input into the trained deep expansion network as test data to obtain a reconstructed sparse signal and a non-sparse noise estimation of the sparse signal. Secondly, it is assumed that there is no target at the position outside the support set of the reconstructed sparse signal, and the corresponding element in the non-sparse noise estimation of the sparse signal is identified as the recovery error, and the power value of the recovery error is estimated based on the recovered error. Based on the estimated recovery error power and a preset false alarm rate, a detection result is obtained and the portion without the target is determined. The recovery error power is estimated again, and the process is repeated until the estimated value of the recovery error power converges. Target detection is performed based on the recovery error power after final convergence, and a constant false alarm detection result can be obtained.

[0109] The advantages of the present invention are: 1) The vector approximate message passing deep expansion sparse recovery method maps each iteration of the vector approximate message passing algorithm to each layer of a deep network. Training data allows the algorithm's parameters to adapt to the training scenario. However, this violates the parameter constraints of the vector approximate message passing algorithm, making it unable to output a specific value for the recovered error power and unsuitable for sub-Nyquist radar constant false alarm detection tasks. 2) To address this issue, the present invention proposes a constant false alarm detector that uses a sparse signal reconstructed by vector approximate message passing deep expansion to first determine the location of target-free locations and estimate the power of the recovered error. The recovered error power is then continuously updated based on detection results at a preset false alarm rate until the estimated power of the recovered error converges. The converged recovered error power is then selected for target detection, yielding the final constant false alarm detection result. 3) The present invention provides a more accurate estimate of the recovered error power value. This is achieved by utilizing information from the sparse signal reconstructed after sparse recovery and taking advantage of the Gaussian distribution of the recovered error in the vector approximate message passing deep expansion sparse recovery method. In each iteration, the error power is estimated and recovered using the minimum variance unbiased estimator, and the method is continuously iterated until convergence, so that the estimation of the recovered error power is relatively accurate. On the other hand, the present invention is known to the environmental noise. In practical applications, the environmental noise power is usually difficult to obtain, and its estimation error is large. The constant false alarm control effect of the detection method requiring environmental noise power will be reduced in practical applications. Therefore, the present method is more suitable for actual observation scenarios.

[0110] In order to implement the above embodiments, the present invention also proposes an electronic device, comprising: a processor, and a memory communicatively connected to the processor; the memory stores computer-executable instructions; the processor executes the computer-executable instructions stored in the memory to implement the method provided by the above embodiments.

[0111] In order to implement the above embodiments, the present invention further provides a computer-readable storage medium, in which computer-executable instructions are stored. When the computer-executable instructions are executed by a processor, they are used to implement the methods provided in the above embodiments.

[0112] In order to implement the above embodiments, the present invention further provides a computer program product, including a computer program, which implements the methods provided in the above embodiments when executed by a processor.

[0113] In the descriptions of the foregoing embodiments, the reference terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine different embodiments or examples described in this specification and features of different embodiments or examples, unless they are mutually inconsistent.

[0114] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "plurality" means at least two, such as two, three, etc., unless otherwise specifically defined.

[0115] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code comprising one or more executable instructions for implementing the steps of a custom logical function or process, and the scope of the preferred embodiments of the present invention includes alternative implementations in which functions may be performed out of the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present invention pertain.

[0116] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device). For purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection with one or more wires (electronic devices), a portable computer disk cartridge (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and programmable read-only memory (EPROM or flash memory), fiber optic devices, and a portable compact disc read-only memory (CDROM). Furthermore, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium and then editing, interpreting or processing it in another suitable manner if necessary, and then storing it in a computer memory.

[0117] It should be understood that various parts of the present invention can be implemented using hardware, software, firmware, or a combination thereof. In the above-described embodiments, multiple steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0118] Those skilled in the art will understand that all or part of the steps in the method of the above embodiment can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiment.

[0119] In addition, the functional units in the various embodiments of the present invention may be integrated into a single processing module, or each unit may exist physically separately, or two or more units may be integrated into a single module. The aforementioned integrated modules may be implemented in the form of hardware or in the form of software functional modules. If the integrated modules are implemented in the form of software functional modules and sold or used as independent products, they may also be stored in a computer-readable storage medium.

[0120] The storage medium mentioned above may be a read-only memory, a magnetic disk, or an optical disk, etc. Although the embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and are not to be construed as limiting the present invention. Persons skilled in the art may make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

Claims

1. A radar constant false alarm detection method based on depth expansion, characterized in that: include: Constructing a data training set based on multiple preset ranges of radar echo signals, and using the data training set to train a deep unfolding network for vector approximate message passing to obtain a trained deep unfolding network; Acquire a radar echo signal, and input the radar echo signal into a trained deep unrolling network to obtain a reconstructed sparse signal and a non-sparse noisy estimate of the reconstructed sparse signal; Obtaining a restored error power based on the non-sparse band noise estimation, comprising: Create a first target vector z of the same size as the non-sparse noisy vector, with a size of N×1; The support set of the reconstructed sparse signal or the detection result under the preset false alarm rate is used to assign the value of each element of the first target vector z to 0 or 1. The assignment rule is: the corresponding position of the non-sparse noisy support set is assigned to 0, and the remaining positions are assigned to 1. The support set is defined as: the set of non-zero position numbers in the vector; Multiply the assigned first target vector z by the corresponding element of the non-sparse noisy estimate to obtain the second target vector; For the second target vector, the corresponding elements of its support set form a new column vector , the size is L×1, L is the number of non-zero elements in the second target vector; Calculate the restored error power as , where mean(·) represents the mean operation; The restored error power is updated using a preset false alarm rate until the restored error power converges, thereby obtaining a constant false alarm detection result.

2. The radar constant false alarm detection method based on depth expansion according to claim 1, characterized in that: The data training set is constructed based on multiple preset ranges of radar echo signals, including: Generate multiple retest data and corresponding noise based on a preset amplitude range, a preset sparsity range, a preset signal-to-noise ratio range, and a preset phase range of the radar echo signal; A data training set is constructed based on the complex test data, the noise and the complex observation matrix.

3. The radar constant false alarm detection method based on depth expansion according to claim 2, characterized in that: The constructing of a data training set based on the complex test data, the noise and the complex observation matrix comprises: A complex test data target matrix is ​​obtained by splicing the real part and the imaginary part of the complex test data; A noise target matrix is ​​obtained by concatenating the real part and the imaginary part of the noise; A complex observation target matrix is ​​obtained by concatenating the real part and the imaginary part of the complex observation matrix; A data training set is constructed based on the complex test data target matrix, the noise target matrix, and the complex observation target matrix.

4. The radar constant false alarm detection method based on depth expansion according to claim 1, characterized in that: The updating of the recovered error power by using a preset false alarm rate until the recovered error power converges includes: Determine whether the number of iterations is greater than 1, and if so, determine whether the recovered error power of the current number of iterations converges; If there is no convergence, the detection threshold of the square sum of the complex modulus of the non-sparse noise estimate is calculated; Performing constant false alarm detection based on the non-sparse band noise estimation complex modulus square sum detection threshold to obtain a detection result of the current iteration number; A detection result under a preset false alarm rate is obtained based on a preset false alarm rate, the number of iterations is updated, and a new recovery error power of the current number of iterations is obtained based on the detection result under the preset false alarm rate and the non-sparse band noise estimation, until the recovery error power converges.

5. A radar constant false alarm detection system based on depth expansion, characterized in that: include: a sparse recovery deep unfolding module, configured to construct a data training set based on multiple preset ranges of the radar echo signal, and to train a deep unfolding network using the data training set to obtain a trained deep unfolding network; and to obtain a radar echo signal, and to input the radar echo signal into the trained deep unfolding network to obtain a reconstructed sparse signal and a non-sparse noisy estimate of the reconstructed sparse signal; A power estimation module, configured to obtain a recovered error power based on the non-sparse band noise estimation; The power estimation module is specifically used to: Create a first target vector z of the same size as the non-sparse noisy vector, with a size of N×1; The support set of the reconstructed sparse signal or the detection result under the preset false alarm rate is used to assign the value of each element of the first target vector z to 0 or 1. The assignment rule is: the corresponding position of the non-sparse noisy support set is assigned to 0, and the remaining positions are assigned to 1. The support set is defined as: the set of non-zero position numbers in the vector; Multiply the assigned first target vector z by the corresponding element of the non-sparse noisy estimate to obtain the second target vector; For the second target vector, the corresponding elements of its support set form a new column vector , the size is L×1, L is the number of non-zero elements in the second target vector; Calculate the restored error power as , where mean(·) represents the mean operation; The iterative judgment and constant false alarm detection module is used to update the restored error power using a preset false alarm rate until the restored error power converges, thereby obtaining a constant false alarm detection result.

6. An electronic device, characterized in that: include: a processor, and a memory communicatively connected to the processor; The memory stores computer-executable instructions; and the processor executes the computer-executable instructions stored in the memory to implement the method according to any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer-executable instructions, which are used to implement the method according to any one of claims 1 to 4 when executed by a processor.

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