Super-resolution arrival time estimation method based on sub-Nyquist sampling signal

Abstract

The invention provides a super-resolution arrival time estimation method based on a sub-Nyquist sampling signal. The method comprises the following steps: describing signal propagation and a problem model; establishing a sub-Nyquist sampling signal reconstruction framework; establishing a super-resolution TOA estimation framework; and establishing a loss function. According to the SRKSE model provided by the invention, the sub-Nyquist sampling signal can be effectively utilized to carry out TOA estimation, the requirement on an ADC (Analog to Digital Converter) is reduced, the TOA estimation precision is remarkably improved, the processing cost and the storage space are reduced, and the SRKSE model is particularly suitable for the high-precision positioning requirement in a low-power-consumption scene; the dual-cross attention mechanism Dual-CA effectively promotes information flow and feature association in the signal reconstruction process, and improves the quality of signal reconstruction; the kernel sparse coding scheme effectively reduces quantization errors, and the new sparse sinc kernel function coding scheme can reduce off-network errors and avoid over-fitting risks, so that the accuracy and reliability of TOA estimation are improved.

Description

Technical Field

[0001] The present invention relates to wireless communication and signal processing technology, and also covers the fields of artificial intelligence, navigation and positioning, and in particular to a super-resolution arrival time estimation method based on sub-Nyquist sampling signals. Background Art

[0002] The value of location information is increasingly prominent in many application areas today, such as various robots, healthcare, autonomous driving, and industrial asset tracking. The Global Navigation Satellite System (GNSS) is the mainstream solution for positioning services. However, in actual applications, GNSS is significantly affected by various objective factors such as occlusion and intentional interference, making it difficult to provide accurate positioning services continuously and stably under all time and space conditions.

[0003] In order to overcome the limitations of GNSS, the use of opportunity signals (SOP) for navigation and positioning came into being. Opportunity signals come from a wide range of sources, including cellular communication systems, low earth orbit (LEO) satellites, wireless local area networks (WLAN), Bluetooth, frequency modulation (FM) and ultra-wideband (UWB). There are many ways to obtain positioning information using opportunity signals, including methods based on time, angle, Doppler frequency and fingerprint recognition.

[0004] Among these methods, time-based positioning methods are widely used due to their high accuracy and simple implementation. The key to this method is to estimate the time of arrival (TOA) of the received signal, and then infer the distance between the transmitter and the receiver by calculating the signal flight time (TOF) in combination with the speed of light. Among them, TOF is determined by the difference between the signal transmission time (TOT) and TOA. This method only requires single antenna observation and is very suitable for low-cost and low-energy consumption scenarios.

[0005] Traditional TOA estimation methods mostly use matched filters based on generalized cross-correlation (GCC) and perform TOA estimation based on threshold or maximum likelihood (ML) criteria. However, when such methods are implemented digitally, the sampling rate needs to exceed the Nyquist rate, which requires the analog-to-digital converter (ADC) to have a higher sampling rate, which will undoubtedly significantly increase the cost of the transceiver. As wireless signals develop towards higher frequency bands and wider bandwidths, time-based positioning methods face major challenges in data exchange and processing efficiency.

[0006] In order to improve the accuracy of TOA estimation and reduce ADC requirements, researchers have proposed subspace decomposition and compressed sensing methods, such as Multiple Signal Classification (MUSIC) and Orthogonal Matching Pursuit (OMP). However, these methods require a grid containing all the true TOA values ​​to be estimated to be set in advance. In practical applications, the true values ​​often do not match the grid, resulting in discrete grid errors. In addition, the MUSIC algorithm must perform real-time Fast Fourier Transform (FFT) and Channel Frequency Response (CFR) estimation before subspace operations, while the navigation and positioning system needs to perform TOA estimation continuously, which will face very large computational overhead, making these methods inapplicable in low-power scenarios, especially at sub-Nyquist rates.

[0007] Compressed sensing technology relies on the sparse characteristics of wireless channels and received signals in the time and frequency domains. Through random sampling methods, it can reconstruct signals at a sampling rate far below the Nyquist rate, which can reduce the demand for a large number of ADC resources. Compressed sensing (CS) technologies such as Orthogonal Matching Pursuit (OMP) take advantage of this sparsity and perform well in improving TOA estimation accuracy, improving data processing efficiency, and reducing energy consumption. In addition, Bayesian Compressed Sensing (BCS) uses a flexible probabilistic model framework and is effective in reducing off-grid errors. However, in some cases, the BCS method derived from the Gaussian noise assumption has uncertainty in the prior information of the parameter probability distribution. In complex applications, these off-grid estimation methods are difficult to meet accuracy requirements.

[0008] In recent years, with the powerful ability of deep networks to handle uncertain models, some deep learning methods have been proposed for TOA estimation. Among them, end-to-end convolutional neural networks (CNNs) are used to directly explore the nonlinear mapping between sampled received signals and estimated parameters. However, there are some problems with this type of method: on the one hand, the architecture adopted by most methods is a black box design with poor interpretability, which reduces its reliability in positioning problems in certain security fields. On the other hand, due to the risk of overfitting in the off-grid parameter estimation problem, the estimation accuracy of end-to-end deep learning methods is limited. Summary of the invention

[0009] In view of the problems existing in the prior art, the present invention provides a super-resolution arrival time estimation method based on sub-Nyquist sampling signal, which is characterized by comprising the following steps:

[0010] Step 1: Describe signal propagation and problem model;

[0011] Assume that there is a stationary or quasi-stationary transmitter and multiple receivers. The receiver intercepts the transmitted signal in a short time interval T, 0≤t≤T. At this time, the channel is assumed to be a semi-static frequency selective channel, and the channel is time-invariant during the observation period. For GPS, UWB and OFDM systems, the multipath fading far-field model is as follows:

[0012]

[0013] r(t)=h(t)s(t-τ p )+w(t) (2)

[0014] Among them, h(t) is the channel model, s(t) is the transmitted signal, r(t) is the received signal, w(t) represents zero mean and variance σ 2 Additive Gaussian white noise, P is the number of multipath signals, α p is the attenuation coefficient of the unknown path, δ(·) is the Dirac function, τ p represents the pth TOA estimation parameter associated with the propagation delay and fading path;

[0015] Therefore, the signal received by the receiver is:

[0016]

[0017] Define the following vector consisting of the above signal and noise sampling sequence, where the Nyquist sampling frequency is f s , the number of sampling points is N, nT s =n / f s,n=1,2,...,N is the time grid corresponding to the sampling point, T s is the time interval of the sampling grid:

[0018]

[0019] Where r, w, s, and A represent the Nyquist sampling array of the received signal, the noise sampling array, the transmitted signal sampling array, and the discrete channel diagonal matrix, respectively. The upper right subscript T of the array represents the matrix transpose.

[0020] Written in matrix form, that is:

[0021] r=As+w (5)

[0022] There is a non-zero value in r corresponding to P multipaths, and other noise is considered zero; the original or fully sampled signal is first sparsely sampled by the measurement matrix, that is, the compressed signal y is transformed by the following equation:

[0023] y=Φr (6)

[0024] Where Φ is an M×N measurement matrix, and M<<N; only M samples need to be processed in the TOA estimation in each time interval;

[0025] The signal reconstruction problem is formulated as a convex optimization problem:

[0026]

[0027] in, is the deviation term between the compressed signal y and the original signal r, reflecting the data fidelity. represents the sparse regularization term Where λ is the regularization parameter, is a sparsity constraint function; the receiver performs discrete sampling on r, and the signal r(t) obtained by sampling at the receiving end is written as:

[0028]

[0029] In the formula, represents the signal amplitude to be estimated, represents the propagation time to be estimated;

[0030] Overcomplete dictionary L represents the predefined delay grid number in the overcomplete dictionary, represents the predefined delay estimation value in the overcomplete dictionary, i.e., contains L>>P potential predefined TOA values; the manifold matrix of TOA parameters can be expanded to an overcomplete form; is a sparse vector, Respectively represent The corresponding received signal amplitude values, the two correspond to each other, and there are only P non-zero amplitude values ​​corresponding to the P real delay value positions;

[0031] Formula (8) is reformulated as a sparse representation model:

[0032]

[0033] Where R(n) represents the sparse representation function spectrum only related to n;

[0034] For the deep network estimation algorithm, a one-hot representation model is used to encode the unknown TOA parameters; the TOA parameter τ p The most similar value in the overcomplete dictionary D As an estimate, Taken from the overcomplete dictionary D, it means that in D p The closest value; in addition, The position in D is based on exist The location is determined, Indicated in Medium and α p The closest The true value of the TOA parameter can be represented by a sparse vector Encoding, involving only P non-zero values Others are zero; the one-hot encoding scheme uses a sparse vector E = [e 1 ,e 2 ,…,e l ,…,e L ] for the parameter τ p Encode, e 1 ,e 2 ,…,e l ,…,e L They represent the encoding values ​​of the lth sparse vector respectively, written as:

[0035]

[0036] If all true TOA values ​​are contained in the predefined overcomplete dictionary, that is, for any value τ p , there is always a grid point is exactly equal to τ p , then E can accurately represent the TOA parameter; but the true TOA value may not be completely on the overcomplete set, that is, there exists Then τ p Its nearest grid point The quantization error caused by the difference between will reduce the generalization performance of the network model;

[0037] Step 2: Establish a sub-Nyquist sampling signal reconstruction framework;

[0038] (1) Traditional signal reconstruction iterative process;

[0039] Step 1: For k iterations, first calculate the intermediate value g of the kth crossover (k) :g (k) =r (k-1) -ρ (k) Φ T (Φr (k-1) -y)+γ (k) (r (k-1) -r (k-2) ), where r (k) represents the output signal at the kth iteration, y represents the downsampled signal, and ρ (k) and γ (k) are the first and second learnable step size parameters, which are adjusted continuously during the iteration process to optimize the signal reconstruction effect, Φ T represents the transpose of the measurement matrix, where r (k-1) -ρ (k) Φ T (Φr (k-1) -y) constitutes the gradient descent term; γ (k) (r (k-1) -r (k-2) ) is the inertia term;

[0040] Step 2: Calculate the value r of the signal reconstructed by the kth cross iteration (k) : in, Represents r and g (k) The difference measure between them is used to update r by minimizing this difference to make it closer to the original signal;

[0041] (2) Introducing the Dual-CA submodule;

[0042] Step 1: Reconstruct the signal value R at the k-1th iteration in the DUN network (k-1) Perform channel segmentation; input Divided into two parts, represents the real number domain, C represents the number of feature channels, including the first two channel features of the segmentation and the remaining channel features B (k-1) is the input of the gradient descent term, Z (k-1) is the input of the inertia term;

[0043] Step 2: Calculate the inertial cross attention ISCA module; output Z of the (k-2)th iteration (k-2)As the "value" value in the ISCA module and the "key" value The (k-1)th iteration outputs Z (k-1) As the Query value right and Normalize Z using the normalization layer LN function (k -1) and Z (k-2) Normalize and get the first normalized value LN(Z (k-2) ) and the second normalized value LN(Z (k-1) ); LN(Z (k-2) ) and LN(Z (k-1) ) Input the cross attention CA module for calculation;

[0044] Step 3: Calculate the CA module output. The CA module operation in step 6 is expressed as Embed the input using 1×1 convolution Conv V (·), Conv K (·), Conv Q (·)right Perform convolution operation, in step 7, Perform convolution operation to obtain (C-2)×N feature representation; for simplicity, V, K, and Q are used in formula (11) to represent They also represent the Use a depthwise convolution Dconv with a kernel of 3 V (·), Dconv k (·) and Dconv Q (·) Encode channel space context; convert V, K, Q into new labeled intermediate input values and They are the depth convolution output values ​​respectively. Depthwise convolution output value And the depth convolution output value Converting it to a specific feature size yields:

[0045]

[0046] Step 4: Calculate the attention matrix By and Perform matrix multiplication and apply the softmax function to reweight the result to obtain the attention matrix in for The transpose of

[0047] step5: According to the attention matrix A Perform weighted summation to obtain Through the convolution layer Conv with an output kernel of 1 O (·) Enhance the feature extraction process to obtain the output of the ISCA module It is the output mapping of the CA module in step 3, and the calculation method is the same as step 3;

[0048] Step 6: Calculate the projection cross attention PGCA module; for the input B of the gradient descent term (k-1) , calculate the iterative process value of the gradient descent term

[0049] Step 7: Output of ISCA and Through LN function normalization, we get The normalized layer output and The normalized layer output Input it to the CA module and get O (k) Represents the output value of the PGCA module at the kth iteration;

[0050] step8: Place O (k) and Perform a concatenation operation to obtain a new feature representation, reshape it into a shape that matches the original input channel dimension, and pass it through convolution Conv O (·) Perform a mixing operation to obtain the output value of the Dual-CA module Concat(.,.) means O (k) and splicing in the channel dimension;

[0051] (3) The overall operation process of the signal reconstruction module;

[0052] step1: Indicates that the Dual-CA module is connected to the input R (k-1) and Z (k-2) Perform the operation of step (2) of the second step above; in this step, the output signal R of the k-1th iteration is (k-1) and the partial output Z of the k-2th iteration (k-2)The input is given to the Dual-CA submodule, and the ISCA and PGCA modules inside the Dual-CA submodule work together to achieve feature-level information fusion and processing of the input signal, and obtain an optimized feature domain output;

[0053] step2: Represents the feedforward network module, which represents the (k) Perform FFN operation; G (k) Input to the feed-forward network FFN submodule; the FFN submodule consists of multiple fully connected layers, which processes the input feature G (k) Further nonlinear transformation and mapping are performed to extract higher-level feature representations, and the reconstructed multi-channel pseudo original signal R is obtained by adjusting the weights and bias parameters of the fully connected layer. (k) At this time, the final iteration k takes the maximum value of the iteration setting; for R (k) Extract the first two channels as the reconstructed original signal The two channels represent the real and imaginary parts of the IQ samples;

[0054] Step 3: Establish a super-resolution TOA estimation framework;

[0055] (1) Using kernel sparse coding to estimate TOA;

[0056] Step 1: Reconstruct the signal The analysis is performed and the true value of TOA parameters is characterized by the kernel sparse coding scheme; in order to reconstruct the signal The TOA parameter τ is encoded in p , it is necessary to determine the maximum value of the output spectrum That is, use sinc interpolation to estimate the TOA value:

[0057]

[0058] in, represents the normalized weight of the lth optimal filter;

[0059] Step 2: Calculate the improved kernel sparse coding model; when all true TOA values ​​τ p When both are contained in D, the estimated value Equal to all true TOA values ​​τ p When , there will be a minimum error, so that the TOA estimation vector can be accurately determined For deep learning-based methods, during the training process, the overcomplete dictionary The output spectrum of the sinc function of the value is considered as the training label, representing the true TOA value; this relationship is expressed as:

[0060]

[0061] M=[m 1 ,m 2 ,...,m l ,...,m L ] (14)

[0062] in, Represents the convolution symbol; the TOA value is represented by the peak value of the spectrum M, m 1 ,m 2 ,…,m l ,…,m L The output spectra of the parameters in the 1st, 2nd, …, 1st, …, Lth overcomplete dictionaries and the TOA parameters to be estimated are represented respectively. However, the accuracy of the parameter representation depends on the overcomplete dictionary, especially whether the τ of the training TOA is included. p To further reduce the estimation error, an offset hyperparameter β is introduced into the amplitude of the sinc kernel function. p , the real TOA value τ p The offset from the nearest grid Calculated as Where c is a predefined coefficient; Formula (13) is improved as follows:

[0063]

[0064] (2) Constructing the TOA estimation module;

[0065] The core of the TOA estimation module is composed of the time estimation TE module, the input of which is The output is the kernel sparse coding estimated spectrum The TE module consists of three main components: a residual block and two spatial attention SA blocks; residual block: the reconstructed signal is first processed by the residual block; spatial attention SA block: within the residual block process, the signal passes through two SA blocks in sequence; each SA block weights the spatial dimension of the input feature map through the spatial attention mechanism; the first SA block processes the feature map output by the residual block, and the second SA block further processes the feature map adjusted by the first SA block; the residual block and the SA block are connected in series; the residual block first extracts features, and then the SA block pays attention to the spatial dimension weighted;

[0066] SA obtains the global receptive field of the feature map through global average pooling and maximum pooling operations, and then uses two fully connected layers and ReLU activation functions to learn the nonlinear relationship between feature channels;

[0067] The residual block builds a direct connection from the previous layer TOA features to the current layer; its output is a combination of the previous layer features and the current layer extracted features; the network adopts a lightweight structure, changing the traditional summation residual to the product residual, that is, multiplying the current layer output with the previous layer output;

[0068] Step 4: Establish loss function;

[0069] For the signal reconstruction part, the reconstructed signal is used The mean square error MSE with the original signal r is used as the error metric, that is, Represents the loss function of the signal reconstruction part; for the TOA estimation part, the TE network output is used The MSE with M is used as the error metric, that is represents the loss function of the TOA estimated spectrum; loss function Defined as:

[0070]

[0071] By minimizing this loss function, the neural network can be trained to optimize the signal reconstruction and TOA estimation process.

[0072] The present invention aims to reduce the sampling cost of analog-to-digital converters (ADCs) and solve the problem of super-resolution multipath delay time of arrival (TOA) estimation under low sampling conditions. The advantages of the present invention are as follows:

[0073] 1. High-precision TOA estimation

[0074] The SRKSE model can effectively utilize sub-Nyquist sampling signals for TOA estimation. While reducing the requirements for ADC, it significantly improves the accuracy of TOA estimation, reduces processing costs and storage space, and is particularly suitable for high-precision positioning requirements in low-power scenarios.

[0075] 2. Efficient signal reconstruction

[0076] The dual cross attention mechanism (Dual-CA) effectively promotes the information flow and feature association in the signal reconstruction process, improves the quality of signal reconstruction, and lays a solid foundation for subsequent accurate TOA estimation.

[0077] 3. Reduced Errors and Improved Reliability

[0078] The kernel sparse coding scheme effectively reduces the quantization error, and the new sparse sinc-kernel function coding scheme reduces the off-grid error and avoids the risk of overfitting, thereby improving the accuracy and reliability of TOA estimation and enhancing the performance of the entire positioning system. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 A flow chart showing a super-resolution arrival time estimation method based on sub-Nyquist sampling signals of the present invention is shown;

[0080] Figure 2 Showing the network flow structure diagram of the present invention;

[0081] Figure 3 The accuracy of multipath delay TOA estimation is compared with that of various methods at different SNRs using LTE signal data;

[0082] Figure 4 The accuracy of the delay TOA estimation of the invented method at different sampling rates is shown using LTE signal data and UWB measured signal data in factories, rooms, offices and other environments with obstacles such as cabinets and glass. DETAILED DESCRIPTION

[0083] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0084] The present invention proposes a super-resolution TOA estimation method based on a compressed sensing deep unfolding network. The method is based on a signal reconstruction and kernel sparse encoding (SRKSE) model. The model first uses a deep unfolding network (DUN) to reconstruct a signal below the Nyquist limit sampling rate and reconstruct the original signal information. Then, kernel sparse encoding is performed on the reconstructed signal. Through these two steps, the quantization error can be reduced, thereby effectively training the neural network and realizing super-resolution TOA estimation. Specifically, the following steps are included:

[0085] Step 1: Describe signal propagation and problem model;

[0086] Assume that there is a stationary or quasi-stationary transmitter and multiple receivers. The receiver intercepts the transmitted signal in a short time interval T (0≤t≤T). At this time, the channel is assumed to be a semi-static frequency selective channel, and the channel is time-invariant during the observation period. For GPS, UWB and OFDM systems, the widely used multipath fading far-field model is as follows:

[0087]

[0088] r(t)=h(t)s(t-τ p )+w(t) (2)

[0089] Among them, h(t) is the channel model, s(t) is the transmitted signal, r(t) is the received signal, w(t) represents zero mean and variance σ 2 Additive Gaussian white noise, P is the number of multipath signals, α p is the attenuation coefficient of the unknown path, δ(·) is the Dirac function, τ p represents the pth TOA estimation parameter associated with the propagation delay and fading path.

[0090] Therefore, the signal received by the receiver is:

[0091]

[0092] Define the following vector consisting of the above signal and noise sampling sequence, where the Nyquist sampling frequency is f s , the number of sampling points is N, nT s =n / f s ,n=1,2,...,N is the time grid corresponding to the sampling point, T s is the time interval of the sampling grid:

[0093]

[0094] Among them, r, w, s, and A represent the Nyquist sampling array of the received signal, the noise sampling array, the transmitted signal sampling array, and the discrete channel diagonal matrix, respectively. The upper right subscript T of the array represents the matrix transpose.

[0095] Written in matrix form, that is:

[0096] r=As+w (2)

[0097] There is a non-zero value in r corresponding to P multipaths, and other noise is considered zero. The sampling rate of different signals is different, but it is usually above several thousand hertz. The resolution of the sampling grid is high, and the number of multipaths is around 10, so the sampling length grid is much larger than the number of multipaths, that is, N>>P, which reflects the sparsity of r(t). Therefore, CS technology can reconstruct the signal at a rate lower than the Nyquist theorem requirement, while significantly reducing the ADC processing cost and storage space in the TOA estimation network. Specifically, the original or fully sampled signal is first sparsified by the measurement matrix, that is, the compressed signal y is transformed by the following equation:

[0098] y=Φr (5)

[0099] Where Φ is an M×N measurement matrix, and M<<N. In this way, only M samples need to be processed in the TOA estimation in each time interval.

[0100] Therefore, the signal reconstruction problem can be formulated as a convex optimization problem:

[0101]

[0102] in is the deviation term between the compressed signal y and the original signal r, reflecting the data fidelity. represents the sparse regularization term Where λ is a regularization parameter used to control the degree of sparsity. is a sparsity constraint function, which is used to maintain the sparse characteristics of the signal, which is crucial for accurately reconstructing the signal under subsampling conditions. Because in practical applications, the signal is often sparse in the time domain or frequency domain, and this feature can be used to reduce the number of samples required for reconstruction and improve reconstruction efficiency and accuracy. The receiver performs discrete sampling on r, so the signal r(t) obtained by sampling at the receiving end can be written as:

[0103]

[0104] In the formula, represents the signal amplitude to be estimated, Represents the propagation time to be estimated.

[0105] In addition to the complex full signal reconstruction and the numerical errors introduced into the signal reconstruction, there are also off-grid errors (or ), because the true value to be estimated may not be on the grid to be estimated, these errors will lead to inaccurate results and overfitting risks of deep learning networks. To solve these problems, the invention proposes an overcomplete dictionary L represents the predefined delay grid number in the overcomplete dictionary, Representing the predefined delay estimation values ​​in the overcomplete dictionary, ie, containing L>>P potential predefined TOA values, then the manifold matrix of TOA parameters can be expanded to an overcomplete form.

[0106] is a sparse vector, Respectively represent The corresponding received signal amplitude values ​​correspond to each other, and there are P non-zero amplitude values ​​only at the P real delay value positions.

[0107] Formula (8) can be restated as a sparse representation model:

[0108]

[0109] Where R(n) represents the sparse representation function spectrum that is only related to n.

[0110] For general deep network estimation algorithms, a one-hot representation model (L.Wu, Z.-M.Liu, Z.-T.Huang, Deep convolution network for direction of arrival estimation with sparse prior, IEEE Signal Processing Letters 26(11)(2019)) is used to encode the unknown TOA parameters. In the one-hot representation scheme, the TOA parameter τ p The most similar value in the overcomplete dictionary D As τ p The estimated value of Taken from the overcomplete dictionary D, where Indicates that in D p The closest In addition, The position in D is based on exist The location is determined, Indicated in Medium and α p The closest This is because the channel impulse response τ in formula (3) p and α p Therefore, the true value of the TOA parameter can be encoded by a sparse vector α, involving only P non-zero values The others are zero. Therefore, the one-hot encoding scheme uses a sparse vector E = [e 1 ,e 2 ,...,e l ,...,e L ] for the parameter τ p Encode, e 1 ,e 2 ,…,e l ,…,e L They represent the encoding values ​​of the lth sparse vector respectively, which can be written as:

[0111]

[0112] If all true TOA values ​​are contained in the predefined overcomplete dictionary, that is, for any value τ p , there is always a grid point is exactly equal to τ p, then E can accurately represent the TOA parameter. However, the true TOA value may not be completely on the overcomplete set, that is, there exists (This formula represents τ p does not exist in the set D), then τ p Its nearest grid point The quantization error caused by the difference between them will reduce the generalization performance of the network model.

[0113] In summary, signal reconstruction error reduces the resolution of TOA estimation, thereby affecting the accuracy of sparse coding; while quantization error may reduce the generalization performance of the network model and lead to inaccurate TOA estimation. Therefore, it is necessary to solve the problems caused by signal reconstruction and quantization errors.

[0114] Step 2: Establish a sub-Nyquist sampling signal reconstruction framework;

[0115] In terms of signal reconstruction, in order to solve the defects of insufficient flexibility and easy loss of information transmission in traditional methods when dealing with signal reconstruction problems, the present invention proposes an innovative signal reconstruction method, the core of which is to combine the deep unfolding network compressed sensing method (Deep Unfolding Network, DUN) with the dual cross attention (Dual-CA) sub-module (JIE CHONG SONG, CHONG MOU, SHIQI WANG. Optimization-inspired cross-attention transformer for compressive sensing [C] / / 2023 IEEE / CVFConference on Computer Vision and Pattern Recognition (CVPR). Vancouver, BC, Canada: IEEE, 2023: 6174-6184.) to achieve effective reconstruction of sub-sampling rate signals.

[0116] (1) Traditional signal reconstruction iterative process;

[0117] The traditional method is based on the non-convex optimization method of gradient descent and inertial force to perform iterative calculation of signal reconstruction. This method has been proven to be effective in the field of large-scale linear inverse problem processing by many studies. The specific iterative process is as follows:

[0118] Step 1: For k iterations, first calculate the intermediate value g of the kth crossover (k) The calculation formula is g (k) =r (k-1) -ρ (k) Φ T (Φr(k-1) -y)+γ (k) (r (k-1) -r (k-2) ). In this formula, r (k) represents the output signal at the kth iteration, y represents the downsampled signal, and ρ (k) and γ (k) are the first and second learnable step size parameters, which are adjusted continuously during the iteration process to optimize the signal reconstruction effect, Φ T represents the transpose of the measurement matrix, where r (k-1) -ρ (k) Φ T (Φr (k-1) -y) constitutes the gradient descent term, which is used to update the signal in the direction of minimizing the reconstruction error; γ (k) (r (k-1) -r (k-2) ) is the inertia term, which introduces the difference between the first two iteration signals and multiplies it by the inertia coefficient γ (k) , which helps to accelerate convergence and stabilize the iterative process.

[0119] Step 2: Calculate the value r of the signal reconstructed by the kth cross iteration (k) , and its calculation formula is In this formula, Represents r and g (k) By minimizing this difference, r is updated to make it closer to the true signal.

[0120] (2) Dual-CA submodule;

[0121] The above traditional methods have large computational complexity and slow convergence. The first part of the above method is implemented by using the deep unfolding network compressed sensing technology (Peter Ochs, Yunjin Chen, Thomas Brox, and Thomas Pock. iPiano: Inertial proximal algorithm for nonconvex optimization. SIAM Journal on Imaging Sciences, 7 (2): 1388–1419, 2014. 3). The present invention introduces a dual cross attention (Dual-CA) submodule, the core goal of which is to achieve efficient information transmission at the feature level and enhance the information interaction capability of the network during signal reconstruction.

[0122] Step 1: Reconstruct the signal value R at the k-1th iteration in the DUN network (k-1) Perform channel splitting. Input Divided into two parts, represents the real number domain, C represents the number of feature channels, including the first two channel features of the segmentation and the remaining channel features The purpose of this segmentation is to process different types of information separately. (k-1) It will be used as the input of the gradient descent term, mainly carrying key information directly related to signal reconstruction, and the signal estimation is optimized through the gradient descent algorithm; Z (k-1) As the input of the inertia term, it focuses on introducing the historical information of the signal, accelerating the convergence and stabilizing the reconstruction process through inertia force.

[0123] Step 2: Calculate the Inertia-Supplied Cross Attention (ISCA) module. In the ISCA module, the (k-2)th iteration output Z (k-2) As the Value in the ISCA module and Key value The (k-1)th iteration outputs Z (k-1) As a Query value First of all, and These inputs are normalized using the Layer Normalization (LN) function. (k-1) and Z (k-2) Normalize and get the first normalized value LN(Z (k-2) ) and the second normalized value LN(Z (k-1) Then, LN(Z (k-2) ) and LN(Z (k-1) ) is input into the Cross Attention (CA) module for calculation.

[0124] Step 3: Calculate the output of the CA module. The CA module is used in step 2 above and step 5 and step 7 below. The CA module operation is expressed as The specific operation of the CA module is as follows: embed the input and use 1×1 convolution Conv V (·), Conv K (·), Conv Q (·)right (In step 7, ) is convolved to obtain a (C-2)×N feature representation. For simplicity, V, K, and Q are used in formula (11) to represent (also respectively represents the ). Then use the depth convolution Dconv with a kernel of 3V (·), Dconv k (·) and Dconv Q (·) Encode the channel space context, and finally, convert V, K, Q into new labeled intermediate input values and (Deep convolution output value Depth convolution output value And the depth convolution output value ), convert it into a specific feature size, and get

[0125]

[0126] Step 4: Calculate the attention matrix By ( The transpose of Perform matrix multiplication and apply the softmax function to reweight the result to obtain the attention matrix

[0127] step5: According to the attention matrix A Perform weighted summation to obtain Then pass the convolution layer Conv with an output kernel of 1 O (·)(o represents output) Enhance the feature extraction process to obtain the final output of the ISCA module is the output mapping of the CA module in step 3, and the calculation method is the same as step 3. In this way, the ISCA module can adaptively learn more useful multi-channel inertial forces, enhance the memory effect of the network in the signal reconstruction process, and enable the network to better use historical information to optimize the current signal estimation.

[0128] Step 6: Calculate the Projection-Guided Cross Attention (PGCA) module. For the input B of the gradient descent term (k-1) , first calculate the gradient descent iterative process value This calculation process is similar to the calculation of the gradient descent term above, but for B (k-1) The purpose of the operation is to consider the measurement matrix Φ and the sub-sampled signal y to obtain B (k-1) Update it to make it closer to the real signal.

[0129] Step 7: Output ISCA and After normalization by LN function, we get The normalized layer output and The normalized layer output And pass it as input to the CA module for calculation, we get in O (k) Indicates the output value of the PGCA module.

[0130] step8: Place O (k) and The concatenation operation is performed to obtain a new feature representation, which is then reshaped into a shape that matches the original input channel dimension and passed through the convolution Conv O (·) Perform a mixing operation to obtain the output value of the Dual-CA module Concat(.,.) means O (k) and The PGCA module not only inherits the advantages of the above-mentioned iterative process based on gradient descent and inertial force, but also realizes the effective fusion of multi-channel information between gradient descent terms and inertial terms through clever design, thereby improving the accuracy and stability of signal reconstruction.

[0131] (3) The overall operation process of the signal reconstruction module;

[0132] The overall operation process of the signal reconstruction module is as follows:

[0133] step1: First, Indicates that the Dual-CA module is connected to the input R (k-1) and Z (k-2) Perform the operation of step (2) of the second step above (i.e., the "Dual-CA" submodule) as described above. In this step, the output signal R of the k-1th iteration is (k-1) and the partial output Z of the k-2th iteration (k-2) It is passed as input to the Dual-CA submodule, and through the collaborative work of the ISCA and PGCA modules inside the Dual-CA submodule, the feature-level information fusion and processing of the input signal is realized to obtain an optimized feature domain output.

[0134] step2: Represents the feedforward network module, which represents the (k) Perform the FFN operation as described below. (k) Input to the Feed-Forward Network (FFN) submodule. The FFN submodule consists of multiple fully connected layers, which (k)Further nonlinear transformation and mapping are performed to extract higher-level feature representations, and by adjusting the weights and bias parameters of the fully connected layer, the multi-channel pseudo original signal R is finally obtained. (k) (At this point, the final iteration k takes the maximum value of the iteration setting). (k) Extract the first two channels as the reconstructed original signal These two channels represent the real and imaginary parts of the IQ samples, respectively, providing more accurate and rich signal information for subsequent TOA estimation.

[0135] In summary, through the signal reconstruction process designed above, the present invention can make full use of the sparse characteristics and historical information of the signal under sub-sampling rate conditions, and reconstruct the original signal information to the greatest extent through the synergy of the DUN-CS perception method and the dual cross-attention sub-module, effectively reduce the signal reconstruction error, improve the signal quality, and provide a solid data foundation for subsequent TOA estimation. At the same time, it significantly improves the interpretability and reliability of the entire network in the signal processing process, so that it performs well in the TOA estimation task in low-power consumption scenarios.

[0136] Step 3: Establish a super-resolution TOA estimation framework;

[0137] After completing signal reconstruction, the present invention uses a kernel sparse coding scheme to process the reconstructed signal to achieve super-resolution TOA estimation.

[0138] (1) Using kernel sparse coding to estimate TOA;

[0139] Step 1: Reconstruct the signal The analysis is performed and the kernel sparse coding scheme is used to characterize the true value of the TOA parameter. The TOA parameter τ is encoded in p , first we need to determine the maximum value of the output spectrum That is, the TOA value is estimated by using sinc interpolation (the sinc function is an interpolation method used to update the kernel function, such as ),Right now

[0140]

[0141] in represents the normalized weight of the lth optimal filter, which is obtained from the GCC cross-correlation function and FIR filter technology (CHAN Y, RILEY J, PLANT J. Modeling of time delay and its application to estimation'of nonstationary delay[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1981, 29(3): 577-581.).

[0142] Step 2: Calculate the improved kernel sparse coding model. Ideally, only when Equal to the true TOAτ p When , the L amplitude values ​​in the corresponding sinc kernel function dictionary D are non-zero. At this time, the amplitude values ​​of other points in D are zero. Therefore, when all true TOA values ​​τ p When both are contained in D, the estimated value Equal to all true TOA values ​​τ p When , there will be a minimum error, so that the TOA estimation vector can be accurately determined For deep learning-based methods, during the training process, the overcomplete dictionary The output spectrum of the sinc function of the value is considered as the training label, representing the true TOA value. This relationship is expressed as:

[0143]

[0144] M=[m 1 ,m 2 ,...,m l ,...,m L ] (14)

[0145] in, Represents the convolution symbol. The TOA value is represented by the peak of the spectrum M, m 1 ,m 2 ,…,m l ,…,m L The output spectra of the parameters in the 1st, 2nd, …, 1st, …, Lth overcomplete dictionaries and the TOA parameters to be estimated are represented respectively. However, the accuracy of the parameter representation depends on the overcomplete dictionary, especially whether the τ of the training TOA is included. p To further reduce the estimation error, an offset hyperparameter β is introduced into the amplitude of the sinc kernel function. p , the real TOA value τ p The offset from the nearest grid Calculated as Where c is a predefined coefficient. Formula (13) is improved as follows:

[0146]

[0147] This improvement provides additional information near the true TOA value, enhances the visibility of off-grid features, and helps improve the efficiency of feature extraction during deep learning. At the same time, the sinc-kernel function has a higher concentration than the Gaussian kernel function with equivalent kernel width, which can reduce the probability of misjudging the TOA value near the peak.

[0148] (2) Constructing the TOA estimation module;

[0149] The core of the TOA estimation module is composed of the time estimation (TE) module, the input of which is The output is the kernel sparse coding estimated spectrum The TE module consists of three main components: a residual block and two spatial attention (SA) blocks. Specifically, the connection and control relationship between these components is as follows: Residual block: The reconstructed signal is first processed by the residual block. The residual structure helps to extract important features in the input data and effectively avoid the problem of gradient disappearance or explosion, thereby improving the learning effect and stability of the network; Spatial Attention (SA) block: In the residual block process, the signal will pass through two SA blocks in sequence. Each SA block weights the spatial dimensions of the input feature map through the spatial attention mechanism so that the model can focus on more significant spatial areas and suppress the interference of unimportant areas. The first SA block processes the feature map output by the residual block, and the second SA block further processes the feature map adjusted by the first SA block to improve the expression of spatial information. Connection and control relationship: The residual block and the SA block are connected in series. The residual block first extracts features, and then the SA block pays attention to the spatial dimension to further optimize the expression of spatial features. The weighting mechanism in each SA block is independently controlled, and the key information is strengthened through spatial attention to improve the accuracy of TOA estimation.

[0150] SA obtains the global receptive field of the feature map through global average pooling and maximum pooling operations, and then uses two fully connected layers and ReLU activation functions (both fully connected layers and ReLU activation functions belong to SA blocks) to learn the nonlinear relationship between feature channels. This process enables the model to effectively capture and emphasize important spatial features, thereby improving the ability to focus on key areas.

[0151] The residual block avoids the disappearance of TOA features by building a direct connection from the previous layer of TOA features to the current layer. Its output is a combination of the previous layer features and the current layer extracted features, which effectively improves the network's ability to distinguish key features and alleviates the gradient vanishing problem during deep network training. The invented network adopts a lightweight structure and improves on the traditional residual network. The traditional summation residual is changed to the product residual, that is, the current layer output is multiplied by the previous layer output, which can provide richer nonlinear characteristics than the summation method and help the model better fit complex data patterns.

[0152] Step 4: Establish loss function;

[0153] The present invention proposes a new loss function to optimize the network training process.

[0154] For the signal reconstruction part, the reconstructed signal is used The mean square error (MSE) with the original signal r is used as the error metric, that is, It represents the loss function of the signal reconstruction part, which is used to measure the quality of signal reconstruction. For the TOA estimation part, the TE network output The MSE with M is used as the error metric, that is Represents the loss function of the TOA estimation spectrum, which is used to evaluate the accuracy of TOA estimation. The final loss function Defined as:

[0155]

[0156] By minimizing the loss function, the neural network can be trained to optimize the signal reconstruction and TOA estimation process, so that in the case of sub-sampled signals, the signal reconstruction quality is higher, thereby providing more effective information for TOA estimation, thereby improving the accuracy of TOA estimation. Specific embodiments

[0158] like Figure 3 As shown in the figure, in order to verify the robustness of the present invention in different noise environments, the algorithm performance is evaluated using LTE transmission signals with different signal-to-noise ratios (SNR) (the "Proposed" in the figure represents the method proposed in the present invention). Under different SNR conditions, the performance of the network under different signal-to-noise ratios and compressed sensing rates is shown in the graph. We compared the proposed method with the classic algorithms (MUSIC, OMP and SBL), and the results showed that the proposed algorithm outperformed the traditional algorithms in all aspects, and even achieved the estimation accuracy of full sampling under high SNR signal conditions.

[0159] At the same time, a comparison was made with deep learning-based methods (traditional convolutional neural networks (CNNs) and off-grid super-resolution delay estimation methods). The results showed that the method of the present invention, as a lightweight network, has a simpler structure, requires fewer training parameters, is more efficient, and has lower estimation errors. This is because traditional methods rely on fully sampled signals for accurate delay estimation, which makes them ineffective in downsampling scenarios. Although CNN-based deep learning methods can extract delay features in downsampling scenarios, the inherent information loss of downsampled signals limits their estimation accuracy, resulting in inaccurate features extracted by CNN. The method of the present invention benefits from the integration of traditional iterative optimization techniques in the network, which reduces network parameters and greatly improves the accuracy and interpretability of the model.

[0160] like Figure 4 As shown, the proposed algorithm is validated on three datasets with different sampling rates ( Figure 4 .a is the LTE dataset, Figure 4 .b and Figure 4 .c is a UWB measured data set of real scenes). The results show that with the increase of sampling rate (corresponding to more signal sampling points), the feature extraction accuracy of the deep learning network is improved, the signal reconstruction efficiency is improved, and the evaluation error of the data set is reduced accordingly. In addition, given the sparsity of the signal, some key features are sufficient for delay estimation. Excessive increase in the compressed sensing rate will introduce more noise features and will not substantially improve network training. When the compressed sensing sampling rate is 1% of the Nyquist sampling rate, the model can still be effectively trained with high accuracy and achieve an ideal root mean square error (RMSE), which proves the efficiency of the proposed algorithm in reducing costs.

[0161] In summary, the relevant conclusions of the present invention verify the ability of the proposed method to accurately estimate multipath time delay (TOA) in different signal noise environments. Although the proposed method adopts a lightweight network structure with a network parameter of only 0.5M, the interpretability and reliability of the algorithm are further improved by combining the traditional iterative optimization algorithm with the deep unfolding network (DUN). The present invention can improve the super-resolution estimation performance of multipath time delay TOA for multiple signals in multiple environments, providing a solid foundation for location information services in various fields.

Claims

1. A super-resolution arrival time estimation method based on sub-Nyquist sampling signal, characterized in that: The following steps are involved: Step 1: Describe signal propagation and problem model; Assume that there is a stationary or quasi-stationary transmitter and multiple receivers. The receiver intercepts the transmitted signal in a short time interval T, 0≤t≤T. At this time, the channel is assumed to be a semi-static frequency selective channel, and the channel is time-invariant during the observation period. For GPS, UWB and OFDM systems, the multipath fading far-field model is as follows: r(t)=h(t)s(t-τ p )+w(t) (2) Among them, h(t) is the channel model, s(t) is the transmitted signal, r(t) is the received signal, w(t) represents zero mean and variance σ 2 Additive Gaussian white noise, P is the number of multipath signals, α p is the attenuation coefficient of the unknown path, δ(·) is the Dirac function, τ p represents the pth TOA estimation parameter associated with the propagation delay and fading path; Therefore, the signal received by the receiver is: Define the following vector consisting of the above signal and noise sampling sequence, where the Nyquist sampling frequency is f s , the number of sampling points is N, nT s =n / f s ,n=1,2,...,N is the time grid corresponding to the sampling point, T s is the time interval of the sampling grid: Where r, w, s, and A represent the Nyquist sampling array of the received signal, the noise sampling array, the transmitted signal sampling array, and the discrete channel diagonal matrix, respectively. The upper right subscript T of the array represents the matrix transpose. Written in matrix form, that is: r=As+w (5) There is a non-zero value in r corresponding to P multipaths, and other noise is considered zero; the original or fully sampled signal is first sparsely sampled by the measurement matrix, that is, the compressed signal y is transformed by the following equation: y=Φr (6) Where Φ is an M×N measurement matrix, and M<<N; only M samples need to be processed in the TOA estimation in each time interval; The signal reconstruction problem is formulated as a convex optimization problem: in, is the deviation term between the compressed signal y and the original signal r, reflecting the data fidelity. represents the sparse regularization term Where λ is the regularization parameter, is a sparsity constraint function; the receiver performs discrete sampling on r, and the signal r(t) obtained by sampling at the receiving end is written as: In the formula, represents the signal amplitude to be estimated, represents the propagation time to be estimated; Overcomplete dictionary L represents the predefined delay grid number in the overcomplete dictionary, represents the predefined delay estimation value in the overcomplete dictionary, i.e., contains L>>P potential predefined TOA values; the manifold matrix of TOA parameters can be expanded to an overcomplete form; is a sparse vector, Respectively represent The corresponding received signal amplitude values, the two correspond to each other, and there are only P non-zero amplitude values ​​corresponding to the P real delay value positions; Formula (8) is reformulated as a sparse representation model: Where R(n) represents the sparse representation function spectrum only related to n; For the deep network estimation algorithm, a one-hot representation model is used to encode the unknown TOA parameters; the TOA parameter τ p The most similar value in the overcomplete dictionary D As an estimate, Taken from the overcomplete dictionary D, it means that in D p The closest value; in addition, The position in D is based on exist The location is determined, Indicated in Medium and α p The closest The true value of the TOA parameter can be represented by a sparse vector Encoding, involving only P non-zero values Others are zero; the one-hot encoding scheme uses a sparse vector E = [e1, e2, ..., e l ,...,e L ] for the parameter τ p Encode, e1,e2,…,e l ,…,e L They represent the encoding values ​​of the lth sparse vector respectively, written as: If all true TOA values ​​are contained in the predefined overcomplete dictionary, that is, for any value τ p , there is always a grid point is exactly equal to τ p , then E can accurately represent the TOA parameter; but the true TOA value may not be completely on the overcomplete set, that is, there exists Then τ p Its nearest grid point The quantization error caused by the difference between will reduce the generalization performance of the network model; Step 2: Establish a sub-Nyquist sampling signal reconstruction framework; (1) Traditional signal reconstruction iterative process; Step 1: For k iterations, first calculate the intermediate value g of the kth crossover (k) :g (k) =r (k-1) -ρ (k) Φ T (Φr (k-1) -y)+γ (k) (r (k-1) -r (k-2) ), where r (k) represents the output signal at the kth iteration, y represents the downsampled signal, and ρ (k) and γ (k) are the first and second learnable step size parameters, which are adjusted continuously during the iteration process to optimize the signal reconstruction effect, Φ T represents the transpose of the measurement matrix, where r (k-1) -ρ (k) Φ T (Φr (k-1) -y) constitutes the gradient descent term; γ (k) (r (k-1) -r (k-2) ) is the inertia term; Step 2: Calculate the value r of the signal reconstructed by the kth cross iteration (k) : in, Represents r and g (k) The difference measure between them is used to update r by minimizing this difference to make it closer to the original signal; (2) Introducing the Dual-CA submodule; Step 1: Reconstruct the signal value R at the k-1th iteration in the DUN network (k-1) Perform channel segmentation; input Divided into two parts, represents the real number domain, C represents the number of feature channels, including the first two channel features of the segmentation and the remaining channel features B (k-1) is the input of the gradient descent term, Z (k-1) is the input of the inertia term; Step 2: Calculate the inertial cross attention ISCA module; output Z of the (k-2)th iteration (k-2) As the "value" value in the ISCA module and the "key" value The (k-1)th iteration outputs Z (k-1) As a "query" value right and Normalize Z using the normalization layer LN function (k-1) and Z (k-2) Normalize and get the first normalized value LN(Z (k-2) ) and the second normalized value LN(Z (k-1) ); LN(Z (k-2) ) and LN(Z (k-1) ) Input the cross attention CA module for calculation; Step 3: Calculate the CA module output. The CA module operation in step 6 is expressed as Embed the input using 1×1 convolution Conv V (·), Conv K (·), Conv Q (·)right Perform convolution operation, in step 7, Perform convolution operation to obtain (C-2)×N feature representation; for simplicity, V, K, and Q are used in formula (11) to represent They also represent the Use a depthwise convolution Dconv with a kernel of 3 V (·), Dconv k (·) and Dconv Q (·) Encode channel space context; convert V, K, Q into new labeled intermediate input values and They are the depth convolution output values ​​respectively. Depth convolution output value And the depth convolution output value Converting it to a specific feature size yields: Step 4: Calculate the attention matrix By and Perform matrix multiplication and apply the softmax function to reweight the result to obtain the attention matrix in for The transpose of step5: According to the attention matrix A Perform weighted summation to obtain Through the convolution layer Conv with an output kernel of 1 O (·) Enhance the feature extraction process to obtain the output of the ISCA module It is the output mapping of the CA module in step 3, and the calculation method is the same as step 3; Step 6: Calculate the projection cross attention PGCA module; for the input B of the gradient descent term (k-1) , calculate the iterative process value of the gradient descent term Step 7: Output of ISCA and Through LN function normalization, we get The normalized layer output and The normalized layer output Input it to the CA module and get O (k) Represents the output value of the PGCA module at the kth iteration; step8: Place O (k) and Perform a concatenation operation to obtain a new feature representation, reshape it into a shape that matches the original input channel dimension, and pass it through convolution Conv O (·) Perform a mixing operation to obtain the output value of the Dual-CA module Concat(.,.) means O (k) and splicing in the channel dimension; (3) The overall operation process of the signal reconstruction module; step1: Indicates that the Dual-CA module is connected to the input R (k-1) and Z (k -2) Perform the operation of step (2) of the second step above; in this step, the output signal R of the k-1th iteration is (k-1) and the partial output Z of the k-2th iteration (k-2) The input is given to the Dual-CA submodule, and the ISCA and PGCA modules inside the Dual-CA submodule work together to achieve feature-level information fusion and processing of the input signal, and obtain an optimized feature domain output; step2: Represents the feedforward network module, which represents the (k) Perform FFN operation; G (k) Input to the feed-forward network FFN submodule; the FFN submodule consists of multiple fully connected layers, which processes the input feature G (k) Further nonlinear transformation and mapping are performed to extract higher-level feature representations, and the reconstructed multi-channel pseudo original signal R is obtained by adjusting the weights and bias parameters of the fully connected layer. (k) At this time, the final iteration k takes the maximum value of the iteration setting; for R (k) Extract the first two channels as the reconstructed original signal The two channels represent the real and imaginary parts of the IQ samples, respectively; Step 3: Establish a super-resolution TOA estimation framework; (1) Using kernel sparse coding to estimate TOA; Step 1: Reconstruct the signal The analysis is performed and the true value of TOA parameters is characterized by the kernel sparse coding scheme; in order to reconstruct the signal The TOA parameter τ is encoded in p , it is necessary to determine the maximum value of the output spectrum That is, use sinc interpolation to estimate the TOA value: in, represents the normalized weight of the lth optimal filter; Step 2: Calculate the improved kernel sparse coding model; when all true TOA values ​​τ p When both are contained in D, the estimated value Equal to all true TOA values ​​τ p When , there will be a minimum error, so that the TOA estimation vector can be accurately determined For deep learning-based methods, during the training process, the overcomplete dictionary The output spectrum of the sinc function of the value s is considered as the training label, indicating the true TOA value; this relationship is expressed as: M=[m1,m2,...,m l ,...,m L ] (14) in, Represents the convolution symbol; the TOA value is represented by the peak of the spectrum M, m1, m2, …, m l ,…,m L The output spectra of the parameters in the 1st, 2nd, …, 1st, …, Lth overcomplete dictionaries and the TOA parameters to be estimated are represented respectively. However, the accuracy of the parameter representation depends on the overcomplete dictionary, especially whether the τ of the training TOA is included. p To further reduce the estimation error, an offset hyperparameter β is introduced into the amplitude of the sinc kernel function. p , the real TOA value τ p The offset from the nearest grid Calculated as Where c is a predefined coefficient; Formula (13) is improved as follows: (2) Constructing the TOA estimation module; The core of the TOA estimation module is composed of the time estimation TE module, the input of which is The output is the kernel sparse coding estimated spectrum The TE module consists of three main components: a residual block and two spatial attention SA blocks; residual block: the reconstructed signal is first processed by the residual block; spatial attention SA block: within the residual block process, the signal passes through two SA blocks in sequence; each SA block weights the spatial dimension of the input feature map through the spatial attention mechanism; the first SA block processes the feature map output by the residual block, and the second SA block further processes the feature map adjusted by the first SA block; the residual block and the SA block are connected in series; the residual block first extracts features, and then the SA block pays attention to the spatial dimension weighted; SA obtains the global receptive field of the feature map through global average pooling and maximum pooling operations, and then uses two fully connected layers and ReLU activation functions to learn the nonlinear relationship between feature channels; The residual block builds a direct connection from the previous layer TOA features to the current layer; its output is a combination of the previous layer features and the current layer extracted features; the network adopts a lightweight structure, changing the traditional summation residual to the product residual, that is, multiplying the current layer output with the previous layer output; Step 4: Establish loss function; For the signal reconstruction part, the reconstructed signal is used The mean square error MSE with the original signal r is used as the error metric, that is, Represents the loss function of the signal reconstruction part; for the TOA estimation part, the TE network output is used The MSE with M is used as the error metric, that is represents the loss function of the TOA estimated spectrum; loss function Defined as: By minimizing this loss function, the neural network can be trained to optimize the signal reconstruction and TOA estimation process.

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