Millimeter wave radar angle estimation method oriented to strong stray environment

Abstract

The invention provides a millimeter wave radar angle estimation method oriented to a strong spurious environment, and the method comprises the steps: S1, defining array, spurious and noise parameters, and constructing a training data set of array echo signals; s2, respectively defining a stray learning module and an angle estimation module, and constructing an LcMAMPNet model based on the stray learning module and the angle estimation module; s3, based on the training data set, defining a corresponding loss function, and training the LcMAMPNet model until the LcMAMPNet model meets requirements; and S4, constructing a test data set of echo signals, and performing estimation verification by using the LcMAMPNet model. On the basis of the basic framework of the AMPNet, the spurious learning neural network is introduced to carry out spurious removal preprocessing on the echo signal, so that the spurious resistance of the designed network is enhanced, and the problem that the target angle estimation performance of the millimeter wave radar is poor in a complex spurious environment is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of millimeter-wave radars, and in particular to a millimeter-wave radar angle estimation method in a strong stray environment. Background Art

[0002] Countries around the world are actively promoting the development of high-resolution millimeter-wave radar, primarily due to its enormous potential to improve road safety and promote the development of autonomous vehicles. Digital signal processing chips, as the core semiconductor components in automotive millimeter-wave radar, enable high-precision angle estimation and measurement in complex environments. However, in real-world automotive radar applications, the nonlinear characteristics of highly integrated semiconductor chips, due to dynamic environmental fluctuations and strong target signals, can lead to unexpected spurious output. These spurious components, when superimposed on the original signal, form echo signals with spurious interference, which in turn affects parameter estimation in subsequent signal processing.

[0003] In the field of radar signal processing, angle estimation technology has undergone significant development. Initially, methods have evolved from traditional beamforming to a variety of techniques, including subspace decomposition, maximum likelihood, and compressed sensing. Traditional beamforming methods, limited by array aperture, have limited estimation accuracy. However, their relatively simple implementation has led to their widespread adoption in practical applications. Subspace methods leverage second-order signal statistics to achieve super-resolution angle estimation. However, these methods ignore higher-order statistical information, hindering their effectiveness in complex environments. Maximum likelihood methods, while theoretically capable of achieving optimal estimation accuracy, are highly dependent on initial values ​​and prone to local optima. Compressed sensing methods, such as the alternating direction method of multipliers (ADMM) and approximate message passing (AMP), can reconstruct high-precision angle spectra from a small amount of observation data, enabling high-precision angle estimation. However, these methods rely on iterative optimization processes and require manual tuning of hyperparameters. In recent years, compressed sensing methods based on machine learning have adaptively optimized parameter mapping in a data-driven manner, which not only improves computational efficiency but also reduces dependence on prior assumptions.

[0004] However, the non-ideal characteristics of spurious components pose a key challenge to estimation accuracy. As strong target leakage components, their target characteristics deviate significantly from the traditional Gaussian noise assumption, leading to a mismatch in the sparse recovery model based on compressed sensing. This in turn causes false peaks in the angular spectrum and shifts from the main lobe, significantly degrading the performance of existing algorithms. Summary of the Invention

[0005] In response to the problems existing in the prior art, the present invention provides a millimeter-wave radar angle estimation method for strong stray environments to solve the technical problem that the target characteristics of the stray components in the prior art deviate significantly from the traditional Gaussian noise assumption, resulting in a mismatch between the sparse recovery model based on compressed sensing, and further causing false peaks and main lobe offsets in the angle spectrum, resulting in a sharp decline in the performance of the existing algorithm.

[0006] The present invention provides a millimeter wave radar angle estimation method for a strong stray environment, comprising:

[0007] S1. Define array, spurious and noise parameters and construct a training dataset of array echo signals;

[0008] S2. Define a stray learning module and an angle estimation module respectively, and construct an LcMAMPNet model based on the stray learning module and the angle estimation module;

[0009] S3. Based on the training data set, define a corresponding loss function and train the LcMAMPNet model until the requirements are met;

[0010] S4. Construct a test data set of echo signals and use the LcMAMPNet model to perform estimation verification.

[0011] Optionally, defining array, spurious and noise parameters includes:

[0012] The array adopts a half-wavelength uniform array structure, the array elements are set to 20, the field of view angle FOV range is set to [-15°, 15°], with δ = 0.1° as the interval, the signal-to-noise ratio SNR range is set to [-5dB, 5dB], with Δ SNR =1dB interval, the signal-to-interference ratio SIR range is set to [5dB, 15dB], with Δ SIR =1dB is the interval.

[0013] Optionally, the echo signal includes:

[0014] Received signal, noise signal and spurious signal, the received signal of all receiving channels of the array is expressed as vector y:

[0015] y=As+n+s

[0016] Where y=[y1,y2,…,y M ] T is the received signal vector, A=[a(θ1) a(θ2) ... a(θ N )] is the target array manifold matrix, which consists of the steering vectors of n targets Composition; s=[s1,s2,…,s N ]T is the target signal vector; n=[n1,n2,…,n M ] T represents the additive white Gaussian noise of M array elements; s=[s1,s2,…,s M ] T Indicates the spurious component in the echo signal;

[0017] And define the recovery sparse vector for target angle estimation. When the target is located at a grid point in the sparse vector, the corresponding label value is set to 1; and the grid point without the target is set to 0. In the case of multiple targets, the corresponding label will be set to a number of 1-element sparse vectors according to the angle index of its FOV. The label is expressed as:

[0018]

[0019] Optionally, the spurious learning module includes:

[0020] S2011, decompose the echo signal into real part and imaginary part, thereby obtaining a dual-channel input signal X real and X imag ;

[0021] S2012, the dual-channel input signal X real or X imag Input the first layer of convolutional neural network and output the first feature map;

[0022] S2013. Input the first feature map into the 2nd to H-1th layers of the convolutional neural network, and output a second feature map, where H is the total number of layers of the convolutional neural network in the spurious learning module;

[0023] S2014, inputting the second feature map into the H-th layer of convolutional neural network to obtain a reconstructed noisy output;

[0024] S2015 , reconstructing the real part and the imaginary part of the noise output into complex signals respectively, removing them from the original echo signal, and outputting the target echo signal.

[0025] Optionally, the angle estimation module includes:

[0026] AMP algorithm and MPNN graph neural network, where the AMP algorithm includes:

[0027] S2021. Define the linear estimation model, expressed as:

[0028] y=Ax+w

[0029] in, It is to output the target echo signal; is the measurement matrix; is the sparse signal to be estimated; is complex Gaussian white noise, that is

[0030] S2022. Express the global probability density distribution as p(y,x). When the elements of y and x are independent and identically distributed, decompose the global probability density distribution p(y,x) into:

[0031]

[0032] Among them, f m (x) is the factor p(y m All variables connected to ∣x), represents the signal to be estimated, x n Represents a variable node, f m (x) represents a factor node;

[0033] S2023. Express the message passing of the variable node and the factor node as follows:

[0034]

[0035] Among them, they represent the variables from the node x n Passed to factor node f m (x) message and factor node f m (x) is passed to the variable node x n Message, x \n Indicates that x does not contain x n , t is the t-th iteration;

[0036] S2024, the marginal distribution p(x n |y) is expressed as:

[0037]

[0038] The MPNN graph neural network includes:

[0039] S2031, define node attributes and edge attributes respectively, and set node attributes and edge attribute f j,n Expressed as:

[0040]

[0041] in, and are the mean and variance of the marginal distribution output, σ 2 is the noise level, and a j Represent the nth and jth columns of the manifold matrix respectively;

[0042] S2032. Define each node x n The initial hidden feature vector of is expressed as:

[0043]

[0044] in, is a learnable weight matrix, is a learnable bias vector, N h is the hidden layer size;

[0045] S2033, respectively define the message transmission phase and the readout phase of the MPNN graph neural network, wherein the message transmission phase includes a message generation and propagation module, a message aggregation module and a message update module, and the message generation and propagation module is used to convert any pair of variable nodes x in the MPNN graph neural network into n and x j The corresponding edge e n,j The hidden feature vector of and With its own edge attribute f j,n Connect as cascade feature Expressed as:

[0046]

[0047] And the cascade feature As the input of the multilayer perceptron, the output of the multilayer perceptron is expressed as:

[0048]

[0049] The function D represents a multilayer perceptron, and each edge corresponds to a multilayer perceptron, each of which includes N h1 and N h2 The hidden layer and a size N h The output layer of the hidden layer adopts a rectifier linear unit activation function;

[0050] The message aggregation module is used to aggregate all input messages of the nth variable node from its connected edges Add, where j = 1, 2, .. N, j ≠ n, and and t layer node attributes and cascaded as messages

[0051] Message update module: used to use the message To update the node hidden feature vector Expressed as:

[0052]

[0053] Here, the function U is specified by a gated recurrent unit network, whose current and previous hidden states are and

[0054] S2034, the readout stage uses the readout function R to output the estimation result, and the discrete distribution of its output Expressed as:

[0055]

[0056] The nth variable node feature is transformed from φ(x n ), and the feature of the (n, j)th edge is represented by ψ(x n ,x j ) characterization, expressed as:

[0057]

[0058] Among them, a n Represents the nth column of matrix A, and uses Markov random field to convert the posterior probability p MPNN (x|y) is written as:

[0059]

[0060] Where Z is the normalization constant, and defines the sparse vector when it is extracted from the discrete set B = [0,1], the refinement Using prior information p(x n =B i )=1 / 2,(i=0,1), calculate the posterior mean and variance of the next layer, expressed as:

[0061]

[0062] Posterior mean and variance It is used for the next LcMAMPNet model iteration until it terminates at a fixed number of T iterations.

[0063] Optionally, the loss function includes:

[0064]

[0065] Among them, Num represents the total number of samples, and Υ(y) represents the output sparse vector of the LcMAMPNet model.

[0066] Optionally, the LcMAMPNet model performs estimation verification, including:

[0067] The array signal mean square error, single target angle measurement success rate, resolution success rate and angle estimation root mean square error are used to evaluate the verification results. The array signal mean square error is expressed as:

[0068]

[0069] Where M represents the array signal length; A represents the reconstructed signal of the i-th array element; i～ x is the noise-free echo signal of the i-th array element;

[0070] The single target angle measurement success rate is expressed as:

[0071]

[0072] Among them, Num represents the total number of samples, Δθ res is the array angular resolution, It represents the absolute value of the angle estimation error;

[0073] The resolution success rate is expressed as:

[0074]

[0075] in, and are the absolute values ​​of the differences between the estimated angles of the two targets and the true angles;

[0076] The angle estimation root mean square error is expressed as:

[0077]

[0078] Among them, M is the number of source targets, θ i is the target angle estimate, θ i is the true target angle, and M is the number of source targets.

[0079] Compared with the prior art, the present invention:

[0080] Based on the basic framework of AMPNet, a spurious learning neural network is introduced to perform spurious removal preprocessing on the echo signal, thereby enhancing the anti-spurious performance of the designed network and solving the problem of poor target angle estimation performance in complex spurious environments of millimeter-wave radar. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0082] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0083] Figure 1 Schematic diagram of the system method of the present invention;

[0084] Figure 2 Schematic diagram of the structure of the stray learning-based approximate message passing network (LcMAMPNet);

[0085] Figure 3 Schematic diagram of the network structure of the stray learning module (LcM);

[0086] Figure 4 Schematic diagram of factor graph model;

[0087] Figure 5 This is a schematic diagram of the message passing graph neural network module (MPNN);

[0088] Figure 6(a) shows how different signal indicators change with the target signal-to-noise ratio in a single-target scenario, including the angle measurement success rate (SR):

[0089] Figure 6(b) shows how different signal indicators vary with the target signal-to-noise ratio in a single-target scenario. The angle estimation accuracy (RMSE) is:

[0090] Figure 7(a) shows the variation of different signal indicators with the target signal-to-interference ratio in a single target scenario, angle measurement success rate (SR);

[0091] Figure 7(b) shows how different signal indicators vary with the target signal-to-interference ratio in a single-target scenario. The angle estimation accuracy (RMSE) is:

[0092] Figure 8(a) shows the change of signal MSE in a multi-target scenario, (a) changes with target angle interval;

[0093] Figure 8(b) shows the change of signal MSE in a multi-target scenario, (b) with the change of target signal-to-interference ratio;

[0094] Figure 9 Schematic diagram of the change of signal to interference and noise ratio SINRout in a multi-target scenario;

[0095] Figure 10(a) is a schematic diagram showing the change in target resolution success probability or angle estimation accuracy in a multi-target scenario, showing the change in target resolution success probability with target angle interval;

[0096] Figure 10(b) is a schematic diagram showing the changes in target resolution success probability or angle estimation accuracy in a multi-target scenario, and the changes in target angle estimation accuracy with target angle interval;

[0097] Figure 10(c) is a schematic diagram showing the change in target resolution success probability or angle estimation accuracy in a multi-target scenario, showing the change in target resolution success probability with target signal-to-interference ratio;

[0098] Figure 10(d) is a schematic diagram showing the change in target resolution success probability or angle estimation accuracy in a multi-target scenario, and the change in target angle estimation accuracy with the target signal-to-interference ratio. DETAILED DESCRIPTION

[0099] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other implementation cases obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application. The functional units with the same labels in the examples of the present invention have the same and similar structures and functions.

[0100] See also Figure 1 The present invention provides a millimeter wave radar angle estimation method in a strong stray environment, comprising:

[0101] S1. Define array, spurious and noise parameters and construct a training dataset of array echo signals;

[0102] S2. Define a stray learning module and an angle estimation module respectively, and construct an LcMAMPNet model based on the stray learning module and the angle estimation module;

[0103] S3. Based on the training data set, define a corresponding loss function and train the LcMAMPNet model until the requirements are met;

[0104] S4. Construct a test data set of echo signals and use the LcMAMPNet model to perform estimation verification.

[0105] See also Figure 2 ,In this embodiment, S1, define array, spurious and noise parameters, and construct a training data set of array echo signals.

[0106] The echo signal consists of array received signal, noise signal and spurious components. The received signal of all receiving channels can be expressed as:

[0107]

[0108] That is: y=As+n+s.

[0109] Among them, A=[a(θ1)a(θ2)...a(θ N )] represents the array manifold matrix of the target; a(θ n ) represents the guidance vector of the nth target n represents the additive white Gaussian noise of M array elements; s represents the spurious in the radar echo.

[0110] Generally speaking, radar spurious components are considered to come from the non-ideal linear response of key components in the radar, such as frequency synthesizers, power amplifiers, and mixers. When a strong target is present in the scene as a large signal stimulus, it exceeds the linear range of the chip device, causing the strong target to leak to adjacent frequencies, interfering with the target angle estimation at adjacent frequencies. Therefore, the spurious component s(t) is assumed to be a target characteristic from θ s The interference signal in the direction is used to describe the spurious characteristics.

[0111] s(t)=a(θ s )·σ s (4)

[0112] in It represents the steering vector of the stray interference from θc in the channel dimension, and its power is given by the amplitude σ s express.

[0113] For LcMAMPNet, a single target echo signal training dataset was constructed. In terms of array parameters and spurious and noise settings, the arrays all adopted a half-wavelength uniform array structure with 20 elements. The observation FOV was set to [-15°, 15°], with δ = 0.1° as the interval, and 301 discrete angles were uniformly sampled within the FOV; the SNR range was [-5dB, 5dB], with Δ SNR =1dB interval, uniform sampling in the SNR range to obtain 16 discrete signal-to-noise ratios; SIR range is [5dB, 15dB] with Δ SIR =1dB interval, and uniformly sampled in the SIR range to obtain 16 discrete signal-to-interference ratios. The dataset parameters are shown in Table 1.

[0114] Table 1 Dataset parameter settings

[0115]

[0116] The LcMAMPNet designed in this paper achieves target angle estimation by recovering sparse vectors. Therefore, when a target is located at a grid point in the sparse vector, the corresponding label value is set to 1; grid points without targets are set to 0. For multiple targets, the corresponding labels are set to a number of 1-element sparse vectors based on the angle index of their FOV. Considering that the network involves complex-valued operations, the labels are defined as follows:

[0117]

[0118] S2. Define a stray learning module and an angle estimation module respectively, and construct an LcMAMPNet model based on the stray learning module and the angle estimation module.

[0119] The overall structure of the designed LcMAMPNet is as follows Figure 2 As shown in Figure 2, the network consists of T layers, corresponding to T rounds of iterations of the AMP algorithm. Each layer has the same structure, including the LcM module, the MPNN module, and the AMP angle estimation algorithm. The input of LcMAMPNet is the received signal and The output is the final estimate of the signal x For the tth layer of LcMAMPNet, the input is the estimated signal from the t-1th layer and and the received signal y. Finally, LcMAMPNet iterates until it terminates at a fixed number of layers.

[0120] First, a spurious learning module (LcM) is constructed. The array signal spurious learning aims to restore high-quality signals from array echoes containing spurious and noise while retaining the target angle information to the greatest extent. In recent years, denoising convolutional neural networks (DnCNN) have been frequently used in the field of image signal processing. They were originally proposed for image denoising. It uses an end-to-end convolutional neural network to accurately predict image noise, especially for color noise images. It has an outstanding denoising effect and is more robust to non-Gaussian signals, making it suitable for learning and removing spurious signals. Considering that DnCNN is a real-valued neural network, however, millimeter-wave signals are complex signals and are difficult to directly apply to millimeter-wave radar signal processing. To address this problem, in this step, we designed a spurious learning module (LcM) based on a complex-valued neural network of DnCNN to realize spurious learning in array signals. The network structure of the spurious learning module is shown in the attached figure. Figure 3 shown.

[0121] The designed LCM input is an echo signal containing spurious signals. After being processed by a convolutional neural network, the spurious signals can be obtained, and then the spurious signals can be removed from the original echo signals, and finally the output is a clean target signal.

[0122] The entire LcM module processing process includes the following parts:

[0123] (1) Assuming that the radar array contains M array elements, the echo signal is first decomposed into real and imaginary parts to obtain the dual-channel input signal X real and X imag ;

[0124] (2) The first layer of the convolutional neural network consists of a normal convolution (Conv) and an activation function (ReLu). This layer performs a convolution operation through p 1×3×2 convolution kernels, outputs p 1×M feature maps, and then performs nonlinear activation through the ReLu function to obtain the activated feature map.

[0125] (3) The convolutional neural network layer 2 to layer H-1 are composed of standard convolution (Conv), batch normalization (BN) and activation function (ReLu). This layer undergoes p 1×3×p convolution kernels to output p 1×M feature maps (1×M×p), which are then further batch normalized and nonlinearly activated by the ReLu function to obtain the final feature map output;

[0126] (4) The Hth layer of the convolutional neural network consists only of standard convolution (Conv). This layer undergoes two convolution operations with 1×3×p kernels to obtain the reconstructed noisy output (1×M×p);

[0127] (5) Finally, the real and imaginary parts of the noisy output are reconstructed into complex signals and removed from the original echo signal to obtain a clean target echo signal.

[0128] The spurious learning module is pre-trained separately, and evaluation indicators are designed, using array signal mean square error (MSE), output signal to interference and noise ratio (SINR out ) and the root mean square error (RMSE) of angle measurement were used to evaluate and analyze the performance of the spurious learning module. Experiments show that the proposed LCM module can stably remove strong noise and strong spurious signals from echoes by learning the characteristics of spurious signals.

[0129] Step 2-2, AMP angle estimation module (AMPNet). The AMP angle estimation module consists of two parts: the AMP algorithm and the MPNN graph neural network.

[0130] The AMP algorithm is based on factor graphs and message passing algorithms. It approximates the posterior mean through iterative calculation to obtain the target angle estimation result. It mainly performs message passing calculations around variable nodes and factor nodes in the factor graph. Assuming a linear estimation model:

[0131] y=Ax+w (6)

[0132] in, is the known observation data; is the measurement matrix; is the sparse signal to be estimated; is complex Gaussian white noise, that is

[0133] There exists a global probability density distribution p(y,x|A). For simplicity, A will be omitted in the following text and written as p(y,x). We assume that the elements of y and x are independent and identically distributed. p(y,x) can be decomposed into:

[0134]

[0135] f m (x) is the factor p(y m All variables connected to ∣x) are not the signal to be estimated

[0136] The factor graph consists of two types of nodes, where hollow circles represent variable nodes and solid squares represent factor nodes, as shown in the attached figure. Figure 4 As shown in Figure 2. Based on factor graphs, efficient message passing algorithms for reasoning problems can be obtained by implementing different rules. One of the well-known iterative reasoning algorithms is Belief Propagation (BP), which is expressed by the following equation:

[0137]

[0138] The above formulas represent the variable nodes x n Passed to factor node f m (x) message and factor node f m (x) is passed to the variable node x n Message, where x \n Indicates that x does not contain x n The reason for j≠n and i≠m is to avoid passing messages about oneself, that is, passing external information, so that one does not constantly trust oneself.

[0139] From this we can get the marginal distribution p(x n |y):

[0140]

[0141] Therefore, the mean of the approximated posterior can be used as the result of Bayesian inference. This concludes our brief discussion of statistical inference.

[0142] Table 2 shows the iterative processing flow of the AMP algorithm:

[0143] Table 2 Processing flow of the DOA estimation method based on AMP

[0144]

[0145]

[0146] We construct a message-passing graph neural network (MPNN) module. This is a GNN paradigm abstracted from the popular graph-structured data model. MPNN integrates the graph layout of antenna arrays and source and target locations into the neural network design, enabling complex angle estimation in a data-driven manner. Because its propagation and aggregation modules are very similar to message passing operations on factor graphs, we employ MPNNs in our proposed LcMAMPNet algorithm to solve statistical inference problems.

[0147] As attached Figure 5 As shown, MPNN consists of L cascade layers. For each node x n (n=1, 2, ...N) Use the function D composed of a multilayer perceptron (MLP) to obtain the message m jn (j≠n); update the node hidden feature vector using an aggregation module consisting of a gated recurrent unit (GRU) function U and a linear network Among them, each pair of m jn share the same weight and each node x n Share the same weights of the GRU module U and the linear network. Explain the concepts of GNN and introduce the meaning of nodes and edges and their associated attributes:

[0148] Node: In MPNN, each node x n (n=1, 2, ... N) represents an angular direction in the angle-discrete FOV grid; node attributes, each node has an assigned node attribute, which is invariant when exchanging information between different nodes. In the proposed LcMAMPNet, the MPNN in its tth layer takes the C and D process outputs from the AMP DOA estimation method processing flow as node attributes

[0149] Side: e n,j is the connecting node x n and node x j The existence of an edge depends on the graph structure of the target problem; edge attributes, each edge e n,j There is a specified edge attribute f j,n , which is constant when computing messages. In the proposed LcMAMPNet, MPNN uses the inner product of the guidance vectors in the array manifold matrix A of the target and the noise level σ 2as an edge attribute.

[0150] Hidden feature vector: each node x n There is a hidden feature vector It will be updated in different rounds of MPNN and will be used to calculate the output of MPNN.

[0151] Message: Input message from its connected edge Used to update node x n The hidden feature vector of

[0152] When designing MPNN, the first step is to define the node attributes and edge attributes. Since the MPNN in the t layer of LcMAMPNet takes the output of the linear module from the AMP algorithm as input, it is natural to combine the mean and variance obtained by the C and D processes of the AMP DOA estimation method into a cascade. and variance And merge into variable node x n Attributes In the middle; by inner product of the guide vector from the manifold matrix A (a n and a j represent the nth and jth columns of the popularity matrix A, respectively) to extract the potential information and compare it with the noise level σ 2 Merge to get edge attribute f j,n , used for message passing in MPNN.

[0153]

[0154] The second step is to define each node x n Initialized hidden feature vector By considering the information of the received signal y and the noise level σ 2 The encoding process is implemented by a single-layer neural network given by the following formula:

[0155]

[0156] in is a learnable weight matrix, is a learnable bias vector, N h is the hidden layer size. Based on these definitions and operations, we introduce the details of each stage in MPNN below, including the message generation and propagation module, message aggregation module and message update module in the message passing stage, as well as the readout stage.

[0157] The MPNN used in LcMAMPNet can be divided into two main phases: the message passing phase and the readout phase. The message passing phase includes the message generation and propagation module, the message aggregation module, and the message update module. The first phase runs in all layers, while the readout phase runs only after the last layer.

[0158] (1) Message passing phase

[0159] Message generation and propagation module: For any pair of variable nodes x in MPNN n and x j , in the lth round, the corresponding edge e n,j First, the hidden feature vector and With its own edge attribute f j,n Connect as cascade feature It is expressed by the following formula,

[0160]

[0161] Then, it uses As the input of the multilayer perceptron. Therefore, the output of the multilayer perceptron MLP is given by the following formula, that is

[0162]

[0163] The function D represents MLP. In the message generation and propagation module, each edge has an MLP, and each MLP has two sizes of N h1 and N h2 The hidden layer and a size N h In addition, the rectifier linear unit (ReLU) activation function is used after the output of each hidden layer. Finally, the output Feedback Figure 5 The node x shown n ,in, can be interpreted as the message transmitted from node j to node n in iteration l.

[0164] Message aggregation module: The nth variable node aggregates all input messages from its connected edges (where j=1,2,..N,j≠n) and add and t layer node attributes The cascade is

[0165]

[0166] Message update module: using messages To update the node hidden feature vector Right now

[0167]

[0168] Here, the function U is specified by a gated recurrent unit (GRU) network, whose current and previous hidden states are and As an intermediate variable to update the hidden feature vector In formula 16, and Similar to W1, b1, as the second learnable weight matrix and bias vector. Then, the updated feature vector Sent to the message generation and propagation module for the next iteration.

[0169] (2) Readout stage

[0170] After L rounds of messages are passed in the message passing phase, the readout function R is used to output the estimated result. Therefore, we need to specially design the final result of MPNN to facilitate the input of the next iteration. Here, MPNN is used for classification problems, so the readout function used for each node of the t layer of LcMAMPNet is used to output the final estimated discrete distribution. Right now

[0171]

[0172] The readout function R consists of two functions of size N h1 and N h2 The hidden layer of the MLP is composed of , and ReLU activation is used after the output of each hidden layer, and the distribution It is passed to the amplifier to further refine the estimation results.

[0173] In the field of machine learning, paired Markov random fields (MRF) G = {V, E} can be used to model random variables x = {x1, x2, ... x N}. Where V is the set of nodes in the graph, representing random variables, and E is the set of edges, representing the dependencies between variables. Especially in graph neural networks (GNNs), it can help model the correlation between nodes. Specifically, the nth variable node feature is represented by φ(x n ), and the feature of the (n, j)th edge is represented by ψ(x n ,x j ) Characterization:

[0174]

[0175] where a n Represents the nth column of matrix A. The posterior probability pMPNN (x|y) corresponds to the pairwise MRF of the statistical inference problem, which can be obtained by MPNN and written as

[0176]

[0177] where Z is the normalization constant. In particular, φ(x n ) and ψ(x n ,x j ) can be represented by the information of nodes and edges in MPNN respectively. This shows that the trained MPNN can describe the posterior probability p MPNN (x|y), which is the key to the collaboration between the MPNN module and the AMP algorithm.

[0178] To better understand the output of MPNN, we take radar target angle estimation as an example. When the sparse FOV vector is extracted from the discrete set B = [0, 1], we further refine Using prior information p(x n =B i )=1 / 2,(i=0,1), and calculate the posterior mean and variance of the next layer, which are given by:

[0179]

[0180] Posterior mean and It is used for the next LcMAMPNet iteration until it terminates at a fixed number of iterations T. Compared with the AMP algorithm, the output of LcMAMPNet is is the distribution p obtained by learning from a large amount of data MPNN Calculate in (x|y).

[0181] S3. Based on the training data set, define the corresponding loss function and train the LcMAMPNet model until the requirements are met.

[0182] During training, the network uses the LCM module to remove noise based on the input echo signal. The MPNN module collaborates with the AMP algorithm to estimate angles, calculating the mean squared error between the output sparse vector and the label vector. The optimizer continuously adjusts network parameters over multiple training cycles, each containing multiple batches of samples. Ultimately, network training is completed, resulting in a model that can be used for angle estimation.

[0183] During training, LcMAMPNet estimates target angles by recovering sparse vectors. The labels of grid points where the target is located in the sparse vector are set to 1, while those without the target are set to 0. Taking complex-valued operations into account, the labels are defined in terms of real and imaginary parts. The proposed algorithm uses the L2 loss, which measures the mean squared error (MSE) between the output sparse vector and the label vector, to ensure the accuracy of the network's overall output.

[0184]

[0185] Among them, Num represents the total number of samples, and Υ(y) represents the output sparse vector of LcMAMPNet.

[0186] S4. Construct a test data set of echo signals and use the LcMAMPNet model to perform estimation verification.

[0187] Construct two sets of test sample sets. 1. Single-target test sample set, divided into two types of single-target test data sets. The angles of the targets in both data sets are sampled within [-15°, 15°]. The first type of data increases uniformly at 1dB intervals, with 1000 test samples at each signal-to-noise ratio, and the SIR of each test sample is 10dB, totaling 16,000 test samples; the second type of data increases uniformly at 1dB intervals within SIR = [0dB, 15dB], with 1000 test samples at each signal-to-interference ratio, and the SNR of each test sample is 0dB, totaling 16,000 test samples; 2. Multi-target test sample set, divided into two types of multi-target test data sets. In the first data set, the signal-to-interference ratio (SIR) and signal-to-noise ratio (SNR) of both targets were fixed at 5dB. The angle of target 1 was randomly sampled from [-15°, 9°], while the angle of target 2 was fixed at an angle interval incremented by one from target 1. The target intervals were uniformly increased by 0.3° from [0.9°, 6°]. 1000 test samples were generated for each angle interval, for a total of 18,000 test samples. The second data set consisted of randomly sampled from [-15°, 9°] with a fixed target angle interval of 4°, meaning that the angle of target 2 was 4° incremented from target 1. Both targets were simultaneously sampled from [0dB, 15dB] with a uniform SIR increment of 1dB. 1000 test samples were generated for each SIR, with a fixed SNR of 5dB for each test sample, for a total of 16,000 test samples. These two data sets were used to validate the angle estimation performance in strong spurious and strong noise environments, respectively.

[0188] Next, an implementation example is given with specific parameters.

[0189] In order to verify the target angle estimation method based on stray learning proposed in this paper, performance simulation tests of the method in single-target and multi-target scenarios were carried out, and a comparative analysis was performed with OMP, ADMM, AMP and AMPNet.

[0190] The arrays all use a half-wavelength uniform array structure with 20 elements and an angular resolution of Δθ. res ≈5.73°; ​​FOV = [-15°, 15°], with random sampling at a granularity of δ = 0.3°. LcMAMPNet was trained and tested on the PyTorch platform using stochastic gradient descent and the Adam optimizer, with a learning rate and first-order moment exponential decay sparsity of 0.001 and 0.91, respectively. Other relevant parameter configurations are shown in Table 3.

[0191] Table 3 Basic parameter configuration of LcMAMPNet

[0192]

[0193]

[0194] In order to objectively evaluate the performance of the proposed network, the experiment used four evaluation indicators: array signal mean square error (MSE), single target angle measurement success rate (SR), resolution success rate (PoR) and angle estimation root mean square error (RMSE).

[0195] First, we use the array signal MSE to evaluate the performance of LcMAMPNet in spurious learning. MSE is the deviation between the reconstructed array signal obtained using the LcM module and the noise-free echo signal, that is,

[0196]

[0197] Where M represents the array signal length; A represents the reconstructed signal of the i-th array element; i～ x is the noise-free echo signal of the i-th array element.

[0198] Considering that the experiments are all conducted under strong spurious and high noise backgrounds, SR is defined for evaluating the performance of single target angle estimation, namely:

[0199]

[0200] Among them, Num represents the total number of samples, Δθ resis the array angular resolution, and represents the absolute value of the angle estimation error.

[0201] The output signal-to-interference-noise ratio is similar to the definition of the integrated sidelobe ratio, which is defined as the ratio of the energy within the corresponding resolution unit in the signal angle domain to the energy outside the resolution unit, where S 2 is the average energy within the resolution unit, (IN) 2 is the average energy outside the resolution cell, and the length of the resolution cell is the width of the main lobe.

[0202]

[0203] In order to evaluate the super-resolution angle estimation performance of the proposed algorithm, that is, the resolution performance of two targets within the Rayleigh limit angle interval in a multi-target scene, PoR is used for evaluation, that is,

[0204]

[0205] in, and are the absolute values ​​of the differences between the estimated angles of the two targets and the true angles.

[0206] Finally, the angle estimation RMSE is used to evaluate the estimation accuracy of the target angle, that is,

[0207]

[0208] Where M is the number of sources and targets. i is the target angle estimate, θ i is the true target angle, and M is the number of source targets.

[0209] In another embodiment, two groups of test sample sets are constructed.

[0210] 1. Single target test sample set, divided into two types of single target test data sets. The target angles in both data sets are sampled within [-15°, 15°]. The first type of data increases uniformly at 1dB intervals, with 1000 test samples at each signal-to-noise ratio, and SIR of each test sample = 10dB, for a total of 16,000 test samples; the second type of data increases uniformly at 1dB intervals within SIR = [0dB, 15dB], with 1000 test samples at each signal-to-interference ratio, and SNR of each test sample = 0dB, for a total of 16,000 test samples;

[0211] Second, the multi-target test sample sets are divided into two types of multi-target test data sets. In the first type, the signal-to-interference ratio (SIR) and signal-to-noise ratio (SNR) of the two targets are fixed at 10dB and 0dB, respectively. The angle of target 1 is randomly sampled from [-15°, 9°], while the angle of target 2 is fixed at an angle interval incremented by one from target 1. The target intervals are uniformly increased by 0.3° from [0.9°, 6°]. 1000 test samples are generated for each angle interval, for a total of 18,000 test samples. The second type of data consists of the angle of target 1 being randomly sampled from [-15°, 9°], with a fixed target angle interval of 4°. That is, the angle of target 2 is increased by 4° from target 1. For both targets, the SIR is uniformly increased by 1dB from [0dB, 15dB]. For each SIR, 1000 test samples are generated, with a fixed SNR of 5dB for each test sample, for a total of 16,000 test samples. These two data sets are used to verify the angle estimation performance in strong spurious and strong noise environments, respectively.

[0212] Model validation is performed. For the first type of data set, the angle measurement success rate (SR) and angle estimation accuracy (RMSE) are used to compare the angle estimation results of various angle estimation algorithms under different signal-to-noise ratios.

[0213] As shown in Figure 6(a), the angle measurement success probability of all methods significantly improves with increasing target signal-to-noise ratio (SNR). The proposed LcMAMPNet significantly outperforms non-machine learning angle estimation algorithms such as AMP, OMP, and ADMM, achieving improvements of approximately 5%, 14%, and 26%, respectively, at low SNRs, and slightly exceeding AMPNet. This demonstrates that the approximate message passing algorithm based on spurious learning significantly outperforms traditional algorithms. Furthermore, the introduction of the LcM module makes the proposed algorithm more robust to noise than similar machine learning algorithms, further improving target angle accuracy.

[0214] As shown in Figure 6(b), the target angle estimation accuracy of all methods improves with increasing target signal-to-noise ratio (SNR), with the proposed method significantly outperforming the other methods. Specifically, the proposed LcMAMPNet algorithm improves the angle estimation accuracy by approximately 0.35°, 0.40°, and 0.50°, respectively, compared to OMP, AMP, and ADMM, and slightly improves by 0.05° compared to AMPNet.

[0215] For the second type of data set, the angle measurement success rate (SR) and angle estimation accuracy (RMSE) are also used to compare the angle estimation results of various angle estimation algorithms under different signal-to-interference ratios.

[0216] As shown in Figure 7(a), the target angle measurement success rate gradually increases with increasing target signal-to-interference ratio (SIR). The proposed LcMAMPNet algorithm improves the angle measurement success rate by approximately 13%, 22%, 23%, and 28% compared to AMPNet, OMP, AMP, and ADMM, respectively, at low SIR. Although AMPNet lacks spurious learning capabilities, it still achieves a higher angle measurement success rate than the other three algorithms at low SIR conditions.

[0217] By comparing the results of single target SER changing with target SNR in Figure 6(a) and Figure 7(a), it can be seen that the angle estimation performance of the proposed LcMAMPNet algorithm under low SIR is significantly better than that under low SNR, which shows the important role of the LcM spurious learning module.

[0218] As shown in Figure 7(b), the target angle estimation accuracy of all methods improves with increasing target signal-to-interference ratio (SIR), with the proposed method significantly outperforming the other methods. Specifically, the proposed LcMAMPNet algorithm achieves average accuracy improvements of approximately 0.11°, 0.40°, 0.50°, and 0.50° relative to AMPNet, OMP, AMP, and ADMM, respectively.

[0219] Secondly, the effect of the present invention when multiple targets are displayed:

[0220] First, the spurious learning performance of the proposed method is evaluated.

[0221] For two types of multi-target test datasets, the array signal mean square error (MSE) was used to evaluate the spurious learning effect of LcMAMPNet in the multi-target scenario. As shown in Figure 8(a), the array signal MSE after spurious learning can stably converge to around 0.15 for different angular intervals. As shown in Figure 8(b), due to the presence of spurious components, for echo signals with different target signal-to-interference ratios, the array signal MSE gradually converges with increasing SIR, and after LcM spurious learning, the MSE can be stabilized below 1.

[0222] Attachment Figure 9 The input SINR of the second test dataset is shown. out As a result, it can be seen that as the SIR increases, the output SINR out Gradually approaching a clean signal without noise, the proposed algorithm has limited learning ability for noise and thus cannot completely approach the ideal state.

[0223] In summary, the proposed algorithm has a strong ability to filter out echo signals containing noise. That is, the signal output by the LCM module can approach the ideal signal without noise in the time domain and has strong robustness.

[0224] Next, the angle estimation performance of the proposed method is evaluated.

[0225] For the above two types of test data sets, the resolution success rate (PoR) and angle estimation root mean square error (RMSE) are used to compare various angle estimation algorithms with the proposed algorithm to evaluate their performance under different angle intervals and different target signal-to-interference ratios.

[0226] The first dataset was used to evaluate the variation of the multi-template target resolution success rate and multi-template angle estimation accuracy with target angular spacing. The results, shown in Figure 10(a), show that the three non-machine learning algorithms, OMP, AMP, and ADMM, have extremely low or even no resolution success rates at smaller angular spacings, only gradually improving after 3.6°. AMPNet, on the other hand, uses machine learning to improve the accuracy of the equivalent AWGN model, resulting in a gradual increase in its resolution success rate at around 2° angular spacing. However, it is still limited by the influence of target spurious components, significantly reducing its resolution capability and remaining suboptimal. In this comparison, the LcMAMPNet algorithm's PoR gradually approaches 100% at an angular spacing of 2°, demonstrating high target super-resolution capabilities.

[0227] Figure 10(b) further illustrates the performance of the proposed algorithm by comparing the angle estimation accuracy at different angle intervals. Specifically, the RMSE is higher at smaller angle intervals. As the angle interval increases, the RMSE fluctuates, initially increasing, then decreasing, and finally stabilizing. The proposed method achieves an average RMSE improvement of 0.05°, 0.35°, 0.60°, and 0.80° over AMPNet, ADMM, OMP, and AMP, respectively, achieving an average accuracy of 0.4°.

[0228] Using the second dataset, with a fixed 3.9° angle interval, we evaluated the multi-template target resolution success rate and multi-template angle estimation accuracy as a function of the target signal-to-interference ratio (SIR). The results, shown in Figure 10(c), demonstrate that the proposed algorithm significantly outperforms other super-resolution algorithms and exhibits stronger spurious immunity. Specifically, compared to AMP, ADMM, OMP, and AMPNet, at low SIRs (i.e., SIR ≤ 5dB), LcMAMPNet's target resolution success rate improves by approximately 22%, 40%, 45%, and 60%, respectively. When SIR ≥ 10dB, the PoR approaches 100%. As for angle estimation accuracy, as shown in Figure 10(d), for all compared algorithms, angle estimation accuracy improves with increasing target SIR, with the proposed algorithm achieving the highest accuracy. Specifically, compared to AMP, ADMM, OMP, and AMPNet, LcMAMPNet's angle estimation accuracy improves by approximately 0.05°, 0.21°, 0.33°, and 0.57°, respectively, achieving an average accuracy of 0.7°.

[0229] This paper demonstrates that the proposed method employs a graph neural network (GNN) architecture to deeply integrate the learning of the statistical characteristics of stray components with the AMP iterative process. On the one hand, a convolutional neural network (CNN) is used to extract nonlinear features from stray components, suppressing their impact on the sparse recovery process. On the other hand, an approximate message passing iterative process based on a graph neural network is constructed, mapping node and edge features to node and edge information in the GNN to approximate the true posterior mean. Therefore, while maintaining physical interpretability, LcMAMPNet significantly improves the algorithm's adaptability in complex stray environments.

[0230] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or device comprising the element.

[0231] The foregoing description is intended only to provide specific embodiments of the present invention, which will enable those skilled in the art to understand and implement the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not intended to be limited to the embodiments shown herein, but is intended to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A millimeter wave radar angle estimation method for a strong stray environment, characterized in that: include: S1. Define array, spurious and noise parameters and construct a training dataset of array echo signals; S2. Define a stray learning module and an angle estimation module respectively, and construct an LcMAMPNet model based on the stray learning module and the angle estimation module; S3. Based on the training data set, define a corresponding loss function and train the LcMAMPNet model until the requirements are met; S4. Construct a test data set of echo signals and use the LcMAMPNet model to perform estimation verification.

2. The millimeter wave radar angle estimation method for a strong stray environment according to claim 1, wherein: The definition of array, spurious and noise parameters includes: The array adopts a half-wavelength uniform array structure, the array elements are set to 20, the field of view angle FOV range is set to [-15°, 15°], with δ = 0.1° as the interval, the signal-to-noise ratio SNR range is set to [-5dB, 5dB], with Δ SNR =1dB interval, the signal-to-interference ratio SIR range is set to [5dB, 15dB], with Δ SIR =1dB is the interval.

3. The millimeter wave radar angle estimation method in a strong stray environment according to claim 2, wherein: The echo signal includes: Received signal, noise signal and spurious signal, the received signal of all receiving channels of the array is expressed as vector y: y=As+n+s Where y=[y1,y2,…,y M ] T is the received signal vector, A=[a(θ1)a(θ2)...a(θ N )] is the target array manifold matrix, which consists of the steering vectors of n targets Composition; s=[s1,s2,…,s N ] T is the target signal vector; n=[n1,n2,…,n M ] T represents the additive white Gaussian noise of M array elements; s=[s1,s2,…,s M ] T Indicates the spurious component in the echo signal; And define the recovery sparse vector for target angle estimation. When the target is located at a grid point in the sparse vector, the corresponding label value is set to 1; and the grid point without the target is set to 0. In the case of multiple targets, the corresponding label will be set to a number of 1-element sparse vectors according to the angle index of its FOV. The label is expressed as:

4. The millimeter wave radar angle estimation method in a strong stray environment according to claim 3, wherein: The stray learning module includes: S2011, decompose the echo signal into real part and imaginary part, thereby obtaining a dual-channel input signal X real and X imag ; S2012, the dual-channel input signal X real or X imag Input the first layer of convolutional neural network and output the first feature map; S2013. Input the first feature map into the 2nd to H-1th layers of the convolutional neural network, and output a second feature map, where H is the total number of layers of the convolutional neural network in the spurious learning module; S2014, inputting the second feature map into the H-th layer of convolutional neural network to obtain a reconstructed noisy output; S2015 , reconstructing the real part and the imaginary part of the noise output into complex signals respectively, removing them from the original echo signal, and outputting the target echo signal.

5. The millimeter wave radar angle estimation method in a strong stray environment according to claim 4, wherein: The angle estimation module comprises: AMP algorithm and MPNN graph neural network, where the AMP algorithm includes: S2021. Define the linear estimation model, expressed as: y=Ax+w in, It is to output the target echo signal; is the measurement matrix; is the sparse signal to be estimated; is complex Gaussian white noise, that is S2022. Express the global probability density distribution as p(y,x). When the elements of y and x are independent and identically distributed, decompose the global probability density distribution p(y,x) into: Among them, f m (x) is the factor p(y m All variables connected to ∣x), represents the signal to be estimated, x n represents a variable node, f m (x) represents a factor node; S2023. Express the message passing of the variable node and the factor node as follows: Among them, they represent the variables from the node x n Passed to factor node f m (x) message and factor node f m (x) is passed to the variable node x n Message, x \n Indicates that x does not contain x n , t is the t-th iteration; S2024, the marginal distribution p(x n |y) is expressed as: The MPNN graph neural network includes: S2031, define node attributes and edge attributes respectively, and set node attributes and edge attribute f j,n Expressed as: in, and are the mean and variance of the marginal distribution output, σ 2 is the noise level, and a j Represent the nth and jth columns of the manifold matrix respectively; S2032. Define each node x n The initial hidden feature vector of is expressed as: in, is a learnable weight matrix, is a learnable bias vector, N h is the hidden layer size; S2033, respectively define the message transmission phase and the readout phase of the MPNN graph neural network, wherein the message transmission phase includes a message generation and propagation module, a message aggregation module and a message update module, and the message generation and propagation module is used to convert any pair of variable nodes x in the MPNN graph neural network into n and x j The corresponding edge e n,j The hidden feature vector of and With its own edge attribute f j,n Connect as cascade feature Expressed as: And the cascade feature As the input of the multilayer perceptron, the output of the multilayer perceptron is expressed as: The function D represents a multilayer perceptron, and each edge corresponds to a multilayer perceptron, each of which includes N h1 and N h2 The hidden layer and a size N h The output layer of the hidden layer adopts a rectifier linear unit activation function; The message aggregation module is used to aggregate all input messages of the nth variable node from its connected edges Add, where j = 1, 2, .. N, j ≠ n, and and t layer node attributes and cascaded as messages Message update module: used to use the message To update the node hidden feature vector Expressed as: Here, the function U is specified by a gated recurrent unit network, whose current and previous hidden states are and S2034, the readout stage uses the readout function R to output the estimation result, and the discrete distribution of its output Expressed as: The nth variable node feature is transformed from φ(x n ), and the feature of the (n, j)th edge is represented by ψ(x n ,x j ) characterization, expressed as: Among them, a n Represents the nth column of matrix A, and uses Markov random field to convert the posterior probability p MPNN (x|y) is written as: Where Z is the normalization constant, and defines the sparse vector when it is extracted from the discrete set B = [0,1], the refinement Using prior information p(x n =B i )=1 / 2,(i=0,1), calculate the posterior mean and variance of the next layer, expressed as: Posterior mean and variance It is used for the next LcMAMPNet model iteration until it terminates at a fixed number of T iterations.

6. The millimeter wave radar angle estimation method in a strong stray environment according to claim 5, wherein: The loss function includes: Among them, Num represents the total number of samples, and Υ(y) represents the output sparse vector of the LcMAMPNet model.

7. The millimeter wave radar angle estimation method in a strong stray environment according to claim 6, wherein: The LcMAMPNet model is estimated and validated, including: The array signal mean square error, single target angle measurement success rate, resolution success rate and angle estimation root mean square error are used to evaluate the verification results. The array signal mean square error is expressed as: Where M represents the array signal length; A represents the reconstructed signal of the i-th array element; i～ x is the noise-free echo signal of the i-th array element; The single target angle measurement success rate is expressed as: Among them, Num represents the total number of samples, Δθ res is the array angular resolution, It represents the absolute value of the angle estimation error; The resolution success rate is expressed as: in, and are the absolute values ​​of the differences between the estimated angles of the two targets and the true angles; The angle estimation root mean square error is expressed as: Among them, M is the number of source targets, θ i is the target angle estimate, θ i is the true target angle, and M is the number of source targets.

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