Joint Parameter Estimation Method for Off-grid Targets Based on the LADMM-DNN Network

Abstract

The present invention discloses an off-grid target joint parameter estimation method based on the LADMM-DNN network. The method is as follows: First, a multi-target sparsity model based on the FMCW difference frequency signal is established. Then, the LADMM-DNN network is built. After using the observed signal to construct the training set required by the LADMM-DNN network, the data in the training set is sent into the LADMM-DNN network to learn the features in the FMCW signal. Finally, the data not in the training set is input into the trained network to obtain the estimated values of the distance and angle of the target. Compared with traditional parameter estimation methods, the present invention realizes gridless estimation of target parameters and improves the accuracy of parameter estimation while obtaining better parameters through deep learning training for fast sparse reconstruction.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and particularly relates to an off-grid target joint parameter estimation method based on an LADMM-DNN network. Background Technique

[0002] Compared with traditional pulsed radars, Frequency-Modulated Continuous Wave (FMCW) radars have the advantages of higher range resolution, simpler structure, and stronger anti-interference ability. Therefore, in recent years, FMCW radars have been widely used in military and civilian fields.

[0003] Regarding the problem of target parameter estimation for FMCW radars, in addition to directly processing the difference frequency signal formed by mixing the received echo and the transmitted echo to estimate the target parameters, such as the two-dimensional MUSIC (Multiple Signal Classification, MUSIC) algorithm, the sparsity of the FMCW difference frequency signal in the time domain and spatial domain is also utilized to transform the target parameter estimation problem into the solution of a sparse linear inverse problem. A relatively important and effective algorithm for solving traditional sparse linear inverse problems is ADMM (Alternating Direction Method of Multipliers, ADMM). It mainly adopts the idea of divide and conquer, using two or more low-dimensional sub-problems to replace the original complex high-dimensional problem to reduce the processing cost and time.

[0004] However, the parameters in ADMM include the penalty parameter and the regularization parameter. The selection of these parameters is generally the relatively optimal value determined manually according to experience, but it may not be the optimal value. Improper parameter selection may lead to a decrease in the estimation performance of the method. At the same time, based on the ADMM method, the continuous parameter space is divided into discrete finite grid points, and it is assumed that all signal parameters can fall on the preselected grid points. However, in practical applications, the signal parameters may not be exactly represented by the grid points, which will cause model mismatch and may lead to performance deterioration. Summary of the Invention

[0005] The purpose of the present invention is to provide an off-grid target joint parameter estimation method based on an LADMM-DNN network, which improves the existing technology through deep learning methods to solve the problems of parameter selection in ADMM and model mismatch between the true parameter value and the predicted grid point parameter value, and improves the accuracy of parameter estimation.

[0006] The technical solution for achieving the purpose of the present invention is as follows: An off-grid target joint parameter estimation method based on an LADMM-DNN network, the steps are as follows:

[0007] Step 1: Establish a multi-target sparsity model based on the FMCW difference frequency signal;

[0008] Step 2: Build an LADMM-DNN network;

[0009] Step 3: Use the observation signal to construct the training set required for the LADMM-DNN network;

[0010] Step 4: Feed the data in the training set into the LADMM-DNN network for learning to train the network;

[0011] Step 5: Test the trained neural network with data not in the training set to obtain the distance and angle parameter information of the target to be estimated.

[0012] Furthermore, the establishment of the multi-target sparsity model based on the FMCW difference frequency signal in Step 1 is as follows:

[0013] Step 1.1: Mix the transmitted signal and the received signal of the FMCW radar to obtain the difference frequency signal. The difference frequency signal model y(t) of the simplified FMCW signal is:

[0014]

[0015] where P is the number of targets, p represents the target number; t is time, γ is the frequency modulation slope, c is the propagation speed of the signal in space, λ is the wavelength at the current frequency, l is the l-th receiving antenna, d is the element spacing of the uniform array, R p and θ p are the distance and angle of the p-th target respectively;

[0016] Step 1.2: Sample the time t, and a total of N sets of sampling points of t = t1,...,t N are collected. Based on Step 1.1, the model is vectorized to obtain the vectorized model

[0017]

[0018] where, f c is the carrier frequency of the transmitted signal, the angle matrix is A θ = [a(θ1),...,a(θ P )], a(θ P ) = [1,exp(j2πf c dsinθ p / c),...,exp(j2πf c (L - 1)dsinθ p / c)] T, where \(L\) is the total number of receiving antennas; the distance matrix is \(A^T\) r = [\(a^T(R_1),...,a^T(R\) P )], \(a^T(R\) P ) = [\(\exp(j4\pi\gamma R\) P _{t1} / c),...,\(\exp(j4\pi\gamma R\) P _t N / c))] T , \(p = 1,...,P\), \(\odot\) is the Khatri - Rao product, and the matrix is the noise matrix;

[0019] Step 1.3: Sparsify the model in Step 1.2 to obtain the multi - target sparsity model \(Y\) based on the FMCW difference - frequency signal as follows:

[0020]

[0021] where the matrix \(D\) is an over - complete dictionary matrix constructed according to the matrix , \(i = 1,...,N\) θ , \(j = 1,...,N\) r , \(N\) θ and \(N\) r are the number of discretized grid points in the angle space and the distance space respectively, and \(s\) is a sparse vector, which is the zero - padded extended form of the target in the grid.

[0022] Furthermore, the construction of the LADMM - DNN network described in Step 2 is as follows:

[0023] Step 2.1: Expand ADMM in depth and construct the LADMM network according to the iteration rules of ADMM. The LADMM network consists of a reconstruction layer \(S\) k , a threshold transformation layer \(Z\) k and a multiplier update layer \(M\) k together to form a multi - layer feed - forward network. The output of the reconstruction layer \(S\) k is defined as follows:

[0024] S k : \(s\) k = (\(D\) T ^TD+\rho k I) -1 ^{-1}(D T ^Ty+\rho k z k-1 -\mu k-1 )

[0025] where \(D\) is the dictionary matrix, \((\cdot)^T\) T is the transpose operation, \(z\) k-1 and \(\mu\) k-1are the outputs of the threshold transformation layer and the multiplier update layer of the (k-1)-th layer respectively, and ρ k is the learnable penalty parameter of the k-th layer, y is the observed signal, and I is the identity matrix;

[0026] The output of the threshold transformation layer Z k is defined as follows:

[0027]

[0028] where λ k is the learnable regularization parameter, h θ (·) is the soft thresholding function, θ = λ / ρ, and at the k-th iteration, the function is defined as follows:

[0029] h θ (x k ) = sign(x k )max(|x k | - θ, 0)

[0030] The output of the multiplier update layer M k is defined as follows:

[0031] M k : μ k = μ k-1 + η k ρ k (s k - z k )

[0032] where η k is the learnable update rate parameter;

[0033] Step 2.2: Build a distance offset estimation network and an angle offset estimation network based on DNN, which together form a DNN-based offset estimation network.

[0034] Furthermore, the training set required to construct the LADMM-DNN network using the observed signal in Step 3 is as follows:

[0035] Step 3.1: Use the observed signal y as the input and the original sparse signal s as the training label to construct the training set of the LADMM network;

[0036] Step 3.2: Construct the pseudo-spectrum of the observed signal:

[0037]

[0038] where D H is the conjugate transpose of the dictionary matrix, and y is the observed signal;

[0039] Step 3.3: The sparse recovery signal obtained by passing the observed signal y through the LADMM network and the pseudo-spectrum together constitute the input ξ of the distance offset estimation network. Using the distance deviation value as the training label, a training set for the distance offset estimation network is constructed;

[0040] Step 3.4: Construct a sparse vector with distance coefficients:

[0041]

[0042] where, is the sparse recovery signal, is the distance coefficient corresponding to the distance at the m-th grid point, and diag(·) represents generating a diagonal matrix;

[0043] Step 3.5: Add the sparse vector of distance coefficients to the input ξ of the distance deviation estimation network as the input of the angle deviation estimation network. Using the angle deviation value as the training label, a training set for the angle offset estimation network is constructed.

[0044] An off-grid target joint parameter estimation device based on the LADMM-DNN network, the device includes:

[0045] A multi-target sparsity model construction module for establishing a multi-target sparsity model based on the FMCW difference frequency signal;

[0046] An LADMM-DNN network construction module for building an LADMM-DNN network;

[0047] A training set construction module for constructing a training set required for the LADMM-DNN network using the observed signal;

[0048] A network training module for sending the data in the training set into the LADMM-DNN network to learn and train the network;

[0049] A network testing module for testing the trained neural network with data not in the training set to obtain the distance and angle parameter information of the target to be estimated;

[0050] The device performs off-grid target joint parameter estimation based on the off-grid target joint parameter estimation method described above.

[0051] A mobile terminal, including a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that when the processor executes the program, it implements the off-grid target joint parameter estimation method.

[0052] A computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, the steps in the off-grid target joint parameter estimation method are implemented.

[0053] Compared with the prior art, the present invention has the following remarkable advantages: (1) By deeply expanding ADMM into the LADMM network and building the network with the known ADMM iteration rule, fast sparse reconstruction can be achieved; (2) By estimating the offset through the DNN network, the model mismatch problem between the true parameter value and the predicted grid point parameter value can be solved, and the accuracy of parameter estimation can be improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a schematic flowchart of the off-grid target joint parameter estimation method based on the LADMM-DNN network of the present invention.

[0055] Figure 2 is a schematic structural diagram of the LADMM network of the present invention.

[0056] Figure 3 is a change curve graph of the RMSE of the LADMM-DNN network estimating distance with the change of signal-to-noise ratio in an embodiment of the present invention.

[0057] Figure 4 is a change curve graph of the RMSE of the LADMM-DNN network estimating angle with the change of signal-to-noise ratio in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0058] The present invention will be further described in detail below in conjunction with the drawings and specific embodiments.

[0059] Combined with Figure 1 , an off-grid target joint parameter estimation method based on the LADMM-DNN network of the present invention includes the following steps:

[0060] Step 1, establish a multi-target sparsity model based on the FMCW difference frequency signal;

[0061] Step 2, build the LADMM-DNN network;

[0062] Step 3, use the observation signal to construct the training set required for the LADMM-DNN network;

[0063] Step 4, send the data in the training set into the LADMM-DNN network to learn and train the network;

[0064] Step 5, test the trained neural network with the data not in the training set to obtain the distance and angle parameter information of the target to be estimated.

[0065] As a specific example, the establishment of the multi-target sparsity model based on the FMCW difference frequency signal described in step 1 is as follows:

[0066] Step 1.1: Mix the transmitted signal and the received signal of the FMCW radar to obtain a difference frequency signal. The difference frequency signal model y(t) of the simplified FMCW signal is:

[0067]

[0068] where P is the number of targets, p represents the target number; t is time, γ is the frequency modulation slope, c is the propagation speed of the signal in space, λ is the wavelength at the current frequency, l is the l-th receiving antenna, d is the element spacing of the uniform array, R p and θ p are the distance and angle of the p-th target respectively;

[0069] Step 1.2: Sample the time t, and a total of N sets of sampling points of t = t1,..., t N are collected. Based on step 1.1, the model is vectorized to obtain the vectorized model

[0070]

[0071] where, f c is the carrier frequency of the transmitted signal, the angle matrix is A θ = [a(θ1),..., a(θ P )], a(θ P ) = [1, exp(j2πf c dsinθ p / c),..., exp(j2πf c (L - 1)dsinθ p / c)] T , L is the total number of receiving antennas; the distance matrix is AT r = [aT(R1)..., aT(R P )], aT(R P ) = [exp(j4πγR P t1 / c),..., exp(j4πγR P t N / c))] T , p = 1,..., P, ⊙ is the Khatri-Rao product, and the matrix is the noise matrix;

[0072] Step 1.3. Sparsify the model in Step 1.2 to obtain the multi-target sparsity model Y based on the FMCW difference frequency signal as follows:

[0073]

[0074] Among them, the matrix D is the overcomplete dictionary matrix constructed according to the matrix , i = 1, ..., N θ , j = 1, ..., N r , N θ and N r are the number of discretized grid points in the angular space and the distance space respectively, s is the sparse vector, which is the zero-padded extended form of the target in the grid.

[0075] As a specific example, the construction of the LADMM-DNN network described in Step 2 is as follows:

[0076] Step 2.1. Expand ADMM in depth and construct the LADMM network according to the iteration rules of ADMM. The LADMM network consists of a reconstruction layer S k , a threshold transformation layer Z k and a multiplier update layer M k together constitute a multi-layer feedforward network. The output of the reconstruction layer S k is defined as follows:

[0077] S k :s k =(D T D + ρ k I) -1 (D T y + ρ k z k-1 - μ k-1 )

[0078] Among them, D is the dictionary matrix, (·) T is the transpose operation, z k-1 and μ k-1 are the outputs of the threshold transformation layer and the multiplier update layer of the (k - 1)th layer respectively, ρ k is the learnable penalty parameter of the kth layer, y is the observed signal, and I is the identity matrix;

[0079] The output of the threshold transformation layer Z k is defined as follows:

[0080]

[0081] Among them, λ k is the learnable regularization parameter, h θ(·) is a soft-thresholding shrinkage function, θ = λ / ρ, and at the k-th iteration, the function is defined as follows:

[0082] h θ (x k ) = sign(x k ) max(|x k | - θ, 0)

[0083] The output of the multiplier update layer M k is defined as follows:

[0084] M k : μ k = μ k-1 + η k ρ k (s k - z k )

[0085] where η k is a learnable update rate parameter;

[0086] Step 2.2: Based on the DNN, construct a distance offset estimation network and an angle offset estimation network, which together form a DNN-based offset estimation network.

[0087] As a specific example, the training set required to construct the LADMM-DNN network using the observation signal in Step 3 is as follows:

[0088] Step 3.1: Use the observation signal y as the input and the original sparse signal s as the training label to construct the training set of the LADMM network;

[0089] Step 3.2: Construct the pseudo-spectrum of the observation signal:

[0090]

[0091] where D H is the conjugate transpose of the dictionary matrix, and y is the observation signal;

[0092] Step 3.3: Combine the sparse recovery signal obtained by passing the observation signal y through the LADMM network and the pseudo-spectrum to form the input ξ of the distance offset estimation network, and use the distance deviation value as the training label to construct the training set of the distance offset estimation network;

[0093] Step 3.4: Construct a sparse vector with a distance coefficient:

[0094]

[0095] where, is the sparse recovery signal, is the distance coefficient corresponding to the distance at the m-th grid point, and diag(·) represents generating a diagonal matrix;

[0096] Step 3.5, add the distance coefficient sparse vector based on the distance deviation estimate network input ξ as the input of the angle deviation estimate network, and use the angle deviation value as the training label to construct the training set of the angle offset estimate network.

[0097] The present invention also provides an off-grid target joint parameter estimation device based on the LADMM-DNN network, and the device includes:

[0098] A multi-target sparsity model construction module for establishing a multi-target sparsity model based on the FMCW difference frequency signal;

[0099] An LADMM-DNN network construction module for building an LADMM-DNN network;

[0100] A training set construction module for constructing the training set required by the LADMM-DNN network using the observation signal;

[0101] A network training module for sending the data in the training set into the LADMM-DNN network to learn and train the network;

[0102] A network testing module for testing the trained neural network with data not in the training set to obtain the distance and angle parameter information of the target to be estimated;

[0103] The device performs off-grid target joint parameter estimation based on the off-grid target joint parameter estimation method described above.

[0104] The present invention also provides a mobile terminal, including a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that when the processor executes the program, it implements the off-grid target joint parameter estimation method.

[0105] The present invention also provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, it implements the steps in the off-grid target joint parameter estimation method.

[0106] Embodiment

[0107] The FMCW radar parameters are set as: frequency f cis 77 GHz, the bandwidth is 150 MHz, and the chirp duration is 7.33 microseconds. The receiving array is a uniform linear array, the number of antennas L is 8, and the element spacing d is c / 2f c . Consider that the distances R between two point targets and the radar are {8.6548 m, 4.1514 m} respectively, and the incident angles θ are {-0.5513°, -8.7083°} respectively. The distances and angles of these two targets are also not on the grid points. The comparison algorithms used in this experiment are: ADMM, LADMM network and two-dimensional MUSIC algorithm. The index used for evaluation in the experiment is the Root Mean Square Error (RMSE).

[0108] Figure 3 is the graph of the RMSE of the estimated distance of the LADMM-DNN network varying with the signal-to-noise ratio, Figure 4 is the graph of the RMSE of the estimated angle of the LADMM-DNN network varying with the signal-to-noise ratio. It can be seen from the graph that when the signal-to-noise ratio increases, the performance of the LADMM-DNN network is better than other algorithms. Comparing the two curves of the LADMM network and ADMM, the angle estimation performance of the LADMM network with optimized parameters is slightly better than that of ADMM, and the difference in distance estimation performance is small. Comparing the two curves of LADMM-DNN and LADMM, when the distance and angle offset estimation networks are added to the LADMM network, the problem of mismatch between the actual parameter values and the grid point parameter values is solved, and the estimation performance has been greatly improved. At the same time, the change trends of these two curves are basically the same, indicating that the performance of the LADMM-DNN network will be affected by the prediction performance of the LADMM network. If the LADMM network does not accurately estimate the grid points, the LADMM-DNN network cannot improve the estimation performance.

[0109] The above-described embodiments have further detailed the purpose, technical solution and beneficial effects of the present invention. These embodiments are selected and specifically described in this specification to better explain the principle and practical application of the present invention, so that those skilled in the art can well understand and utilize the present invention. The present invention is only limited by the claims and their full scope and equivalents.

Claims

1. A joint parameter estimation method for off-grid targets based on the LADMM-DNN network, characterized in that The steps are as follows: Step 1: Establish a multi-target sparsity model based on the FMCW beat signal; Step 2: Build the LADMM-DNN network, specifically as follows: Step 2.1: Expand ADMM in depth, build the LADMM network according to the iteration rule of ADMM. The LADMM network consists of a reconstruction layer S k , a threshold transformation layer Z k , and a multiplier update layer M k , jointly constituting a multi-layer feed-forward network. The output of the reconstruction layer S k is defined as follows: S k : s k = (D T D + ρ k I) -1 (D T y + ρ k z k-1 - μ k-1 ) where D is the dictionary matrix, (·) T is the transpose operation, z k-1 and μ k-1 are the outputs of the threshold transformation layer and the multiplier update layer in the (k - 1)-th layer respectively, ρ k is the learnable penalty parameter in the k-th layer, y is the observed signal, and I is the identity matrix; Threshold transformation layer Z k The output is defined as follows: where λ k is a learnable regularization parameter, and h θ (·) is a soft-thresholding function, θ = λ / ρ, and at the k-th iteration, the function is defined as follows: h θ (x k ) = sign(x k ) max(|x k | - θ, 0) Multiplier update layer M k The output is defined as follows: M k : μ k = μ k-1 + η k ρ k (s k - z k ) where η k is a learnable update rate parameter; Step 2.2: Based on the DNN, build a distance offset estimation network and an angle offset estimation network, which together constitute an offset estimation network based on the DNN; Step 3: Use the observed signal to construct the training set required for the LADMM-DNN network, specifically as follows: Step 3.1: Use the observed signal y as the input and the original sparse signal s as the training label to construct the training set of the LADMM network; Step 3.2: Construct the pseudo-spectrum of the observed signal: where D H is the conjugate transpose of the dictionary matrix, and y is the observed signal; Step 3.

3. The sparse recovery signal obtained by passing the observed signal y through the LADMM network and the pseudo-spectrum together constitute the input ξ of the distance offset estimation network. Using the distance deviation value as the training label, a training set for the distance offset estimation network is constructed; Step 3.4: Construct a sparse vector with distance coefficients: Among them, is the sparse recovery signal, is the distance coefficient corresponding to the distance at the m-th grid point, and diag(·) represents generating a diagonal matrix; Step 3.5: Add the distance coefficient sparse vector on the basis of the distance deviation amount estimation network input ξ As the input of the angle deviation amount estimation network, use the angle deviation value as the training label to construct the training set of the angle offset amount estimation network; Step 4: Feed the data in the training set into the LADMM-DNN network for learning to train the network; Step 5: Use the data not in the training set to test the trained network to obtain the distance and angle parameter information of the target to be estimated.

2. The off-grid target joint parameter estimation method based on the LADMM-DNN network according to claim 1, characterized in that The establishment of the multi-target sparsity model based on the FMCW beat signal in Step 1 is specifically as follows: Step 1.1: Mix the transmitted signal and the received signal of the FMCW radar to obtain a beat signal. The simplified beat signal model y(t) is: where P is the number of targets, p represents the target number; t is time, γ is the frequency modulation slope, c is the propagation speed of the signal in space, λ is the wavelength at the current frequency, l is the l-th receiving antenna, d is the element spacing of the uniform array, R p and θ p are the distance and angle of the p-th target respectively; Step 1.2: Sample the time t, and a total of N sets of sampling points of t = t1,..., t are collected. Based on Step 1.1, vectorize the model to obtain the vectorized model N and Among them, f c is the carrier frequency of the transmitted signal, and the angle matrix is A θ =[a(θ1),...,a(θ P )], a(θ P )=[1,exp(j2πf c dsinθ p / c),...,exp(j2πf c (L-1)dsinθ p / c)] T , where L is the total number of receiving antennas; the distance matrix is AT r =[aT(R1)...,aT(R P )], aT(R P )=[exp(j4πγR P t1 / c),...,exp(j4πγR P t N / c))] T , p = 1,..., P, ⊙ is the Khatri-Rao product, and the matrix is the noise matrix; Step 1.3: Perform sparse processing on the model in Step 1.2 to obtain a multi-target sparsity model Y based on the FMCW beat signal: Among them, matrix D is an over-complete dictionary matrix constructed according to matrix , i = 1, ..., N θ , j = 1, ..., N r , N θ and N r are respectively the number of discretized grid points in the angular space and the distance space. s is a sparse vector, which is the zero-padded extended form of the target in the grid.

3. An off-grid target joint parameter estimation device based on the LADMM-DNN network, characterized in that, The device includes: A multi-target sparsity model construction module for establishing a multi-target sparsity model based on the FMCW beat signal; An LADMM-DNN network construction module for building the LADMM-DNN network; A training set construction module for using the observed signal to construct the training set required for the LADMM-DNN network; A network training module for feeding the data in the training set into the LADMM-DNN network for learning to train the network; A network testing module for using the data not in the training set to test the trained network to obtain the distance and angle parameter information of the target to be estimated; The device performs off-grid target joint parameter estimation based on the off-grid target joint parameter estimation method described in any one of claims 1 to 2.

4. A mobile terminal, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the off-grid target joint parameter estimation method described in any one of claims 1 to 2.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the off-grid target joint parameter estimation method described in any one of claims 1 to 2.

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